Supervisory Control of a Solar Air Conditioning Plant - Semantic Scholar
European Journal of Control (2008)6:451–463 # 2008 EUCA DOI:10.3166/EJC.14.451–463
Supervisory Control of a Solar Air Conditioning Plant with Hybrid Dynamics Christian Sonntag1,, Hao Ding2,, Sebastian Engell1, 1 Process Dynamics and Operations Group, Department of Biochemical and Chemical Engineering, Technische Universität Dortmund, 44221 Dortmund, Germany 2 Institute of Automatic Control Engineering, Department of Electrical Engineering and Information Technology, Technische Universität München, 80290 München, Germany
The control of solar plants is challenging for several reasons, one of which is that the solar irradiation that represents the main energy source cannot be manipulated and is subject to large fluctuations due to changes of the weather conditions. For the solar air conditioning plant considered in this work, which is located at the University of Seville, Spain, additional difficulties arise from the presence of discretely switched valves and pumps and autonomous switches of the continuous dynamics which make it a hybrid system. The main control goal for this process is to minimize the consumption of auxiliary energy while ensuring a safe and robust operation even in the face of large disturbances. The available hybrid models of the plant that are suitable for algorithmic controller synthesis or model-predictive control do not represent the process dynamics accurately enough to ensure a robust plant operation under all conditions. In this paper, a supervisory control scheme is presented that was designed based on a thorough investigation of the energetic aspects of the solar plant and on several identification experiments at the real plant. The application of the control scheme to the real solar plant and to the simulation model illustrates the robustness and the efficiency of the approach.
Correspondence to: Christian Sonntag, E-mail: [email protected] E-mail: [email protected] E-mail: [email protected]
Keywords: Solar plants, refrigeration systems, hybrid systems, supervisory control, process control
1. Introduction Since the need for air conditioning usually coincides with a high amount of solar irradiation, solar plants are well suited as energy sources for air conditioning systems. The control of solar plants is a challenging task for several reasons: (i) in contrast to many other types of power plants, the main energy source (i.e., the solar irradiation) cannot be manipulated and is subject to large fluctuations that are induced by clouds and changes in the meteorological conditions, (ii) the process is subject to varying time delays due to fluid transportation within the plant, and (iii) the dynamics of the process varies depending on the environmental conditions. The control problem for the plant considered in this work is furthermore complicated by the presence of discretely switched inputs (valves and pumps) and autonomous switching of the continuous dynamics that is introduced by embedded discrete control loops. While the problem of designing continuous controllers for solar plants has been studied extensively in academia in the last decades (see e.g., [2, 5, 8, 9, 11]), control schemes that specifically
Received 12 April 2008; Accepted 17 September 2008 Recommended by E.F. Camacho, D.W. Clarke
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consider the hybrid nature of solar plants have not yet been investigated much. The algorithmic design of controllers for hybrid systems (see e.g., [3, 4, 6, 7, 10, 12, 13, 14]) requires the availability of a sufficiently simple plant model. If the goal is just to stabilize the plant under consideration, a model with relatively simple dynamics that provides a guaranteed but very conservative over-approximation of the plant behavior can often be used. The control goal for the solar air conditioning plant, however, is not only to stabilize the plant, but also minimize the consumption of gas within a gas heater. For such quantifiable control goals, over-approximating simple models are often not usable since a quantitative control goal requires the availability of accurate quantitative predictions of the plant behavior. Thus, a dynamic model must be available that faithfully and accurately represents the dynamics of the process in all relevant regions of the state space. While the model of the solar plant that is presented in the first paper of this special section and in [15, 16] is sufficiently simple for algorithmic controller design, its usability for the design of a robust and efficient control scheme is questionable for several reasons: Several simplifying modeling assumptions lead to inaccuracies of the model predictions of the dynamic and stationary plant behavior. As an example, the dynamic submodel of the solar collectors is based on a mean temperature Tsc;m of the water in the collectors, and the outlet temperature is computed by Tsc;o ¼ 2 Tsc;m Tsc;i , where Tsc;i is the inlet temperature of the collectors. If the plant were purely continuous, this assumption would in most situations lead to an accurate prediction of the temperature of the water in the solar collectors. However, if the inlet temperature changes instantaneously (which happens when the discrete inputs are switched), the outlet temperature changes instantaneously in the model as well. This behavior does not occur at the real plant which exhibits a significantly more complex behavior. Furthermore, a major source of complexity of the real plant lies in the existence of variable energy losses and variable time delays between the process units that are not represented by the available model. In addition, some properties of the process equipment that are not represented by a simple simulation model introduce significant disturbances at the real plant. As an example, most temperature sensors are not located within the process units, but in the pipes connecting the units. Since the energy losses within the pipes are much larger than the losses within the process units, the sensors may give temperature readings that do not correspond to the actual temperature within the process unit.
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Since these problems indicate that a simple model structure cannot accurately represent the plant dynamics, and since the effort required to formulate and to parameterize an accurate plant model was prohibitive, this paper presents a supervisory control scheme that has been developed based on a thorough energetic analysis of the process, on the results of several identification experiments, and on insights gained using the simulation model. In this control scheme, the discrete inputs of the solar plant are switched according to logic conditions defined over the available measurements of the process variables such that in each mode, the continuous inputs are chosen to minimize the consumption of auxiliary energy while ensuring a robust plant operation. The remainder of this paper is organized as follows: in Section 2, the solar air conditioning plant is described briefly. The results of the energetic process analysis are presented in Section 3, followed by a description of the supervisory control scheme in Section 4. Section 5 presents the results of the controller tests with the simulation model and at the real plant and discusses the controller performance. Finally, Section 6 concludes the paper.
2. The Solar Air Conditioning Plant The solar air conditioning plant is located in Seville, Spain, and is used to cool the laboratories of the Department of System Engineering and Automatic Control at the University of Seville. It was proposed as a benchmark problem for the application of hybrid control techniques within the EU-funded Network of Excellence HYCON (see e.g., [1]). In this section, the plant and the most important process variables are briefly introduced. A more detailed description of the case study is given in the first paper of this special section and in [15, 16]. Fig. 1 shows a scheme of the solar plant including important measurable process variables. It consists of four main components: an array of solar collectors that deliver up to 50 kW of thermal energy by heating water using solar irradiation, a gas-powered heater with a nominal power of 60 kW, a storage system that consists of two tanks with a capacity of 2500 l each, and an absorption machine. This system generates chilled water by supplying thermal energy in the form of hot water to the absorption machine which provides a cooling power of 35 kW. The chilled water is fed to an air conditioning system (not shown in Fig. 1). If the air conditioning system is switched on,
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(a) Solar Collectors
Environment (c)
Gas Heater Storage Tanks
Absorption (b) Machine
Pipes Fig. 2. Simplified process scheme depicting energy flows within the system.
Fig. 1. Layout of the solar air conditioning plant (taken from [15]) and important measurable process variables. The thick arrows indicate the directions of the flow of water through the system.
the flow rate m_ e is larger than 5000 hl . Otherwise, it is assumed that the system is switched off (i.e., the generation of chilled water is not necessary). A discrete controller within the gas heater starts the gas heater if the temperature of the outflowing water Tgw;o falls below 86 C, and the gas supply is stopped if Tgw;o > 94 C. The gas supply is also stopped for safety reasons if the flow rate of water through the gas heater falls below 1500 hl . The absorption machine only operates if the temperature Tg;i of the hot water is larger than 78 C1. An embedded controller shuts down the absorption machine if this constraint is violated. To start up the absorption machine, Tg;i must be larger than 85 C. The water flow is driven by two pumps (B1 and B4) that can be switched on or off. The discretely switched two-way and three-way valves vl21 , vl22 , vl23 , vl24 , vl25 , vl26 , vl31 , and vm1, which are modeled as binary variables, are used to influence the path of the water flow through the system and, thus, the energy sources used. The absorption machine can be supplied with water from the solar collectors, from the storage tanks, from the gas heater, or from a combination of these sources. Two continuous inputs are used to regulate the flow rates: the speed vB1 2 ½0%; 100% of the pump B1 and the setting of the three-way valve vm3 2 ½0%; 100%.2 The pump B4 works at a constant speed. The main control goal is to regulate the temperature of the chilled water Te;o to a setpoint of 15 C while minimizing the gas consumption (i.e., the time the gas heater is operating) and, with a lower priority, max75 C for the simulation model. vl ¼ 0 corresponds to fully closed, and vl ¼ 1 means fully open. If vm1 ¼ 0, the water flow leaving the solar collectors is fed back to pump B1, and vm3 ¼ 0% indicates that the water flows solely through the gas heater. 1 2
imizing the temperature of the water in the tanks. The constraint Tg;i > 78 C (Tg;i > 75 C for the model) must be fulfilled at all times.
3. Process Analysis 3.1. Energetic Analysis Since the main purpose of the solar plant is to supply thermal energy to the absorption machine, it is only natural to investigate the energetic conditions within the process to derive an energetically efficient control strategy. Fig. 2 shows a simplified scheme of the process that divides the solar plant into three subparts: (i) the energy supply part that consists of the solar collectors, the storage tanks, the gas heater, and the pipes connecting the subsystems, (ii) the absorption machine which, in this setting, is reduced to an energy sink, and (iii) the environment. In this context, the control goal can be understood as the maximization of the inner energy of the energy supply part (without using the gas heater), subject to the fulfillment of the constraint Tg;i > 78 C (Tg;i > 75 C). The inner energy QSP of the supply part is given by the energy content of the water in the four components: QSP ¼ QSC þ QGH þ QT þ QP ;
ð1Þ
and it changes with time according to: Q_ SP ¼ Q_ SI þ Q_ G ðQ_ AM þ Q_ L Þ:
ð2Þ
Here, QSP , QSC , QGH , QT , and QP represent the energy content of the water in the supply part, the solar collectors, the gas heater, the tanks, and the pipes, respectively. Q_ SI and Q_ G represent the energy obtained from the solar irradiation and the gas heater, Q_ AM is the energy consumed by the absorption machine, and Q_ L is the energy lost to the environment. Q_ SI only depends on the solar irradiation and cannot
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be manipulated. In experiments, it was found that Q_ AM can be varied slightly with the flow rate of water into the absorption machine. Hence, the control goal of minimizing Q_ G can be achieved by minimizing both, the energy loss Q_ L to the environment and the flow rate of water to the absorption machine. Under the reasonable assumption that the thermodynamic properties of the water remain constant within the operating regime of the process, the energy content of the water directly corresponds to its temperature, and the losses to the environment are directly related to the difference of the temperatures of the water and the ambient air. Thus, Q_ L can be reduced by minimizing the water temperature within the solar collectors, the gas heater, and the pipes. 3.2. Time Delays and Energy Losses The solar plant is subject to varying time delays due to the transportation of water between its components. Furthermore, the energy losses in the pipes between the process components cause temperature drops that must be considered in the control strategy, e.g., for the estimation of temperature changes that will occur when switching to another water flow pattern. To ensure that the control strategy can robustly operate the process under realistic conditions, over-approximations of the time delays and energy losses were determined in an extensive identification study on the real process. The process was operated over several days with differing environmental conditions (such as irradiation and environmental temperature), and the losses and time delays between the process components were measured for several realistic flow patterns. Fig. 3 depicts the results of this study. The largest temperature loss and the largest time delay occur between the solar collectors and the absorption machine. For high values of Tsc;o , the temperature loss can be over-approximated by a linear function for all
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investigated flow patterns. For smaller values of Tsc;o , a constant over-approximation was determined: 0:443 Tsc;o 32:9 C if Tsc;o > 80 C; lSC;AM ¼ 2 C if Tsc;o 80 C: ð3Þ
4. The Supervisory Control Scheme Fig. 4 shows a schematic representation of the supervisory control scheme that was developed based on the analysis presented in the previous section. The process measurements xðtÞ are sampled by an interface in intervals of 10 s yielding xðnÞ, and the controller computes new values of the discrete and continuous inputs uðnÞ and vðnÞ from these measurements which are then applied to the plant. In a first step, it is checked if the system is in a state which lies outside the nominal operating regime (see Fig. 5). If so, a set of emergency procedures is executed to drive the process back into a nominal mode of operation. If no emergency was detected, the main control algorithm is executed that is implemented as a set of discrete supervisory controllers as described in the following sections. The reason for using several discrete supervisors is the lack of sensitivity of the controlled variable Te;o , which must be regulated to a setpoint of 15 C, to changes of the continuous and discrete inputs: in experiments, it was found that this temperature can only be changed by at most 2 C using the discrete and continuous inputs. Hence, Te;o is not controlled directly. Instead, different discrete supervisors are employed depending on the value of Te;o as shown in Fig. 5. If the value of Te;o lies within the nominal operating region, the discrete and continuous inputs are chosen such that the gas consumption is Controller
u(n)
Discrete Supervisors x(n), v(n)
v(n), u(n)
x(n) u(n) Emergency Procedures x(n), v(n)
v(n), u(n)
x(n) Interface
v(t), u(t)
x(t) Plant
Fig. 3. Maximum values of the temperature losses (l ) and time delays (td ) between the process components.
Fig. 4. Scheme of the supervisory control strategy.
Continuous Control
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minimized while allowing for robust process operation. If Te;o enters the upper warning region or even the forbidden region, the controller switches to different supervisors that attempt to drive Te;o into the nominal region by maximizing the water flow to the absorption machine. Accordingly, if Te;o enters the less critical lower warning region, another discrete supervisor minimizes the water flow to the absorption machine. In the remainder of this section, only the discrete supervisor for the nominal process operation will be described since the supervisors for the other regions were derived in a similar fashion. These supervisors differ from the nominal supervisor in two respects: (i) The goal of the supervisors for the upper warning and critical regions is to drive Te;o back into the nominal region as soon as possible. These supervisors avoid operating modes in which the solar collectors are used since these modes are often subject to sudden and drastic disturbances. In more detail, the
Te,o [°C] 18 17
Forbidden region Upper warning region
Setpoint
15 Nominal region 13 Lower warning region t
Fig. 5. Choice of the discrete supervisor depending on Te;o .
discrete supervisor corresponding to the upper warning region does not employ the operating mode m5, and the supervisor for the critical region does not use any modes in which the solar collectors are employed. (ii) To achieve a maximization or minimization of the energy transfer to the absorption machine, all supervisors use different settings for the continuous inputs, as described in Section 4.2.
4.1. The Discrete Supervisor for Nominal Operation Based on the energetic analysis, eight reasonable operating modes (m1 to m8) were identified that represent a subset of all possible combinations of the discrete inputs (see Table 1). The modes can be assigned to two different categories: m1 and m2 are used if the air conditioning system that is connected to the absorption machine is not operating, i.e., during start-up and shut-down of the system. The remaining modes are only considered when the air conditioning system is switched on. The discrete supervisor consists of two separate finite-state automata that are executed depending on the value of m_ e as shown in Fig. 6. The transition conditions are defined over the process measurements and constant switching thresholds which are chosen to avoid an undesirably large frequency of switching between the modes. Furthermore, the thresholds must be chosen such that robust process operation is guaranteed even in the face of large disturbances and the time delays given in Fig. 3, while the
Table 1. Operating modes and the settings of the discrete inputs. In all modes, vl21 ¼ vl22 , vl23 ¼ vl24 , and vl25 ¼ vl26 Mode
Description and settings of the discrete inputs
m1
Circulation of water in the solar collectors, the absorption machine is not active. B1 ¼ 1; vl21 ¼ vl23 ¼ vl25 ¼ vl31 ¼ B4 ¼ vm1 ¼ 0.
m2
Loading the tanks from the solar collectors, the absorption machine is not active. vl21 ¼ B1 ¼ vm1 ¼ 1; vl23 ¼ vl25 ¼ vl31 ¼ B4 ¼ 0.
m3
The solar collectors supply water to the absorption machine. vl23 ¼ B1 ¼ B4 ¼ vm1 ¼ 1; vl21 ¼ vl25 ¼ vl31 ¼ 0.
m4
The solar collectors and the gas heater supply water to the absorption machine. vl23 ¼ vl31 ¼ B1 ¼ B4 ¼ vm1 ¼ 1; vl21 ¼ vl25 ¼ 0.
m5
The solar collectors supply water to the absorption machine and to the tanks. vl21 ¼ vl23 ¼ B1 ¼ B4 ¼ vm1 ¼ 1; vl25 ¼ vl31 ¼ 0.
m6
The tanks and the gas heater supply water to the absorption machine. vl25 ¼ vl31 ¼ B1 ¼ B4 ¼ 1; vl21 ¼ vl23 ¼ vm1 ¼ 0.
m7
The tanks supply water to the absorption machine. vl25 ¼ B1 ¼ B4 ¼ 1; vl21 ¼ vl23 ¼ vl31 ¼ vm1 ¼ 0.
m8
The gas heater supplies water to the absorption machine. vl31 ¼ B1 ¼ B4 ¼ 1; vl21 ¼ vl23 ¼ vl25 ¼ vm1 ¼ 0
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Nominal operation
Start-up / shut-down
δ 57
m5
m1 δ 21
δ12
δ 56
δ 37
δ 73
δ 35 δ 53
δ 36
δ 54
m2
. l m e > 5000 h
δ 67
δ 76
δ 87
δ 47
m6 δ 86
δ 63
δ 83
m3 l . m e ≤ 5000 h
m7
δ 34
m8
δ 48
δ 43
δ 68
m4
x(n)
u(n), v(n)
Fig. 6. The discrete supervisor for start-up/shut-down and nominal process operation. xðnÞ is a sampled measurement of the process variables, and uðnÞ and vðnÞ are the settings of the continuous and discrete inputs that are computed by the controller based on xðnÞ.
temperature of the water in the energy supply part and, thus, the energy losses to the environment must be minimized. If the air conditioning system is not operating (i.e., m_ e 5000 hl ), the thermal energy obtained from the solar collectors is stored in the tanks (m2 ). If, however, Ttsc;i < Ttsc;o (see Fig. 1), energy would be drained from the tanks in mode m2 , and the system is switched to mode m1. As soon as Tsc;o lSC;T > Ttsc;o (see Fig. 3), the system is switched back to mode m2 . The finite-state automaton for nominal process operation was designed to exploit all existing energy sources before switching into a mode in which the gas heater is used. Hence, modes using only the solar collectors as the energy source always have the highest priority. In principle, if Q_ SI Q_ AM þ Q_ L (see Section 3), the excess energy is stored in the tanks. If Q_ SI < Q_ AM þ Q_ L , additional energy is needed to operate the absorption machine. This energy is preferably taken from the tanks, if possible, and otherwise from the gas heater. To implement this strategy, several switching thresholds are defined for the generator inlet temperature Tg;i . Fig. 7 shows these thresholds and a schematic evolution of Tg;i . The thresholds TLB;SC and TUB;SC are lower and upper bounds that should be adhered to if the plant is operating in mode m5. Due to the large and fast disturbances in this energy source, these thresholds are chosen larger than the lower and upper thresholds for modes that do not utilize the solar collectors (TLB;T and TUB;T ). The threshold TLB;T is the smallest value Tg;i should attain during process operation. If this threshold is crossed, the supervisor switches to a mode that ensures that Tg;i will increase again. Before switching to
Tg,i [°C]
m3
m5
m3 m5
m3
m7
m3
m7
m3 m5
TUB,SC TUB,T TLB,SC TLB,T 78 estimated
estimated
t
Fig. 7. Switching thresholds for the temperature Tg;i and an exemplary schematic evolution of Tg;i (time delays are neglected). It is assumed that the temperature of the water in the tanks is large enough to utilize the mode m7 .
a new mode, a conservative approximation of the value of Tg;i resulting from the switching (after the corresponding time delay has elapsed) is estimated by subtracting the maximum losses given in Fig. 3 from the output temperature of the process part that provides the energy for the absorption machine in the new mode. Note that in the very unlikely case that the overapproximations that are shown in Fig. 3 are violated and the absorption machine shuts down, the emergency control system ensures that the machine is restarted as soon as possible. In the exemplary scenario shown in Fig. 7, initially the plant is in mode m3 , and the temperature is increasing. Thus, there is an energy excess from the solar collectors. Once the threshold TUB;SC has been reached, the supervisor switches to mode m5 to store the excess energy in the tanks. If the thermal energy provided by the sun is not sufficient anymore to operate the absorption machine, Tg;i will fall below TLB;SC if the plant is in mode m3 . When the lowest threshold TLB;T is reached, the controller switches to a
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mode that ensures that Tg;i will increase again. Since in the example in Fig. 7, the temperature of the water in the tanks is sufficiently large, the supervisor switches to mode m7 . At this point, the supervisor begins to monitor the estimated temperature Tg;i;est ¼ Tsc;o lSC;AM that would result at the inlet of the absorption machine if the plant was switched to mode m3 . The solar collectors are in the recirculation mode at this point, i.e., no energy is drained from the water in the solar collectors, and Tg;i;est will increase. As soon as Tg;i;est reaches TUB;T , the supervisor switches back to mode m3 . The values of the switching thresholds are important tuning parameters to achieve a good trade-off between energy efficiency and robustness. Based on extensive simulation studies and several identification experiments at the real plant in the fall of 2006 and in the spring of 2007, the thresholds were chosen as small as possible to increase the energetic efficiency, but as large as necessary to ensure robustness. The values that were determined for the discrete supervisor that is used in the nominal region of Te;o are shown in Table 2. Since the lower bound for Tg;i is smaller for the simulation model (75 C) than for the real plant (78 C), the threshold values for the simulation model are lower than those for the real plant. Switching to mode m5 at the real plant causes a temperature drop that is much faster than expected from the simulation studies. Thus, the difference between the thresholds TLB;SC (TUB;SC ) and TLB;T (TUB;T ) was chosen larger at the real plant. In the sequel, the transition conditions of the automaton for nominal process operation are described in more detail. The process variables used here are shown in Fig. 1. For simplicity, the conditions are not shown in a disjunctive form, i.e., several conditions can become true for the same variable values. Instead, the transition conditions are sorted by priority. For example, of all transitions leaving the state m3 which represents the mode m3 , 35 has the highest priority, as is shown below. Note that the system is never switched to mode m8 (using only the gas heater) directly if in the previous mode, the gas heater was not used, because the cold water in the gas heater might decrease Tg;i below the lowest admissible bound and thus shut down the absorption machine. Instead, an intermediate mode is used briefly until the temperature of the water from the gas heater has reached the desired value. If in the previous mode, the tanks were used, the intermediate mode is m6 , and if the solar collectors were used, the intermediate mode is m4 3. 3 Some process variables exhibit considerable measurement noise. If necessary, the corresponding measurements are adjusted by averaging several measurements within a very short time window. For simplicity, this averaging is neglected here.
Table 2. Switching thresholds for the discrete supervisor that operates in the nominal region of Te;o .
TLB;T TLB;SC TUB;T TUB;SC
Simulation
Real plant
78 C 79 C 80 C 82 C
81 C 84 C 83 C 89 C
Transitions leaving m3 If the system is in mode m3 , it can be switched into the modes m5, m7 , m6 , and m4 , where m5 has the highest priority. Here, the term Tsc;o ðn 3Þ Tsc;o ðnÞ > Tg;i ðnÞ TLB;T is used to detect sudden drops in the solar irradiation, i.e., large drops that occur within a time window of 30 seconds. In this case, the supervisor switches into another mode to avoid a shutdown of the absorption machine: 35 : Tg;i ðnÞ > TUB;SC Tg;i ðnÞ < TLB;SC _ Tsc;o ðn 3Þ Tsc;o ðnÞ > Tg;i ðnÞ TLB;T ^ Ttam;o ðnÞ lT;AM > TLB;T 36 : Tg;i ðnÞ < TLB;SC _ Tsc;o ðn 3Þ Tsc;o ðnÞ > Tg;i ðnÞ TLB;T ^ Ttam;o ðnÞ lT;AM > TLB;T _ Ttam;o ðnÞ lT;AM > Tsc;o ðnÞ lSC;AM 34 : Tg;i ðnÞ < TLB;SC _ Tsc;o ðn 3Þ Tsc;o ðnÞ > Tg;i ðnÞ TLB;T 37 :
Transitions leaving m4 Since the gas heater is employed in mode m4 , the mode is left as soon as the energy provided by the solar collectors or the tanks is sufficiently large. As mentioned above, this mode is also used as a transit mode to ensure that the outlet temperature of the gas heater is sufficiently large to support the absorption machine. This is reflected in the condition 48 : 43 : Tsc;o ðnÞ lSC;AM > TUB;T 47 : Ttam;o ðnÞ lT;AM > TLB;T 48 : Tgw;o ðnÞ lGH;AM > TLB;T Transitions leaving m5 The conditions of the transitions leaving the state m5 are defined similarly to those leaving the state m3 . However, the term used to detect sudden drops in the solar radiation (Tsc;o ðn 1Þ Tsc;o ðnÞ > Tg;i ðnÞ TLB;SC ) employs a smaller time window of 10 seconds
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since the energy drain from the solar collectors is considerably larger in this mode. 53 : Tg;i ðnÞ < TLB;SC _ Tsc;o ðn 1Þ Tsc;o ðnÞ > Tg;i ðnÞ TLB;SC 57 : Tg;i ðnÞ < TLB;SC _ Tsc;o ðn 1Þ Tsc;o ðnÞ > Tg;i ðnÞ TLB;SC ^ Ttam;o ðnÞ lT;AM > TLB;T 56 : Tg;i ðnÞ < TLB;SC _ Tsc;o ðn 1Þ Tsc;o ðnÞ > Tg;i ðnÞ TLB;SC ^ Ttam;o ðnÞ lT;AM > Tg;o ðnÞ _ Ttam;o ðnÞ lT;AM > Tsc;o ðnÞ lSC;AM 54 : Tg;i ðnÞ < TLB;SC _ Tsc;o ðn 1Þ Tsc;o ðnÞ > Tg;i ðnÞ TLB;SC Transitions leaving m6 , m7 , and m8 The main goal of the supervisor in the modes m6 , m7 , and m8 is to return to a mode in which the solar collectors (or the tanks in m6 and m8) are employed again. Furthermore, the mode m6 is a transit mode, i.e., if the outlet temperature of the gas heater is sufficiently large, the supervisor switches into mode m8: 63 : Tsc;o ðnÞ lSC;AM > TUB;T 67 : Ttam;o ðnÞ lT;AM > TLB;T 68 : Tgw;o ðnÞ lGH;AM > TLB;T 73 : Tsc;o ðnÞ lSC;AM > TUB;T 76 : Ttam;o ðnÞ lT;AM < TLB;T 83 : Tsc;o ðnÞ lSC;AM > TUB;T 87 : Ttam;o ðnÞ lT;AM > TLB;T 86 : Ttam;o ðnÞ lT;AM > Tg;o ðnÞ The temperature sensors that measure Ttam;o ðnÞ and Ttsc;o ðnÞ are not located within the tanks but in the pipes connecting the tanks to the remaining parts of the process. Hence, if the tanks are not used, the water residing in these pipes cools down and renders the temperature measurements unreliable. In this case, the supervisor switches to the modes m5 and m7 during nominal operation for 10 seconds in every 30 minutes to update these temperature measurements. If the air conditioning system is not operating, the modes m2 and m7 are used instead. This updating procedure is only executed if the previous measurements indicate that the tanks hold an amount of energy that is sufficiently large to be usable as a source for the absorption machine. This means that if Ttam;o ðnÞ or
Ttsc;o ðnÞ are smaller than 70 C, the corresponding measurement will not be updated4. 4.2. Continuous Control In our setting, the need for accurate setpoint tracking of the process variables has been replaced by the introduction of the switching thresholds described above. For example, if the process is in mode m3 , regulating Tg;i to a given setpoint is not necessary since the controller automatically switches to mode m5 if the amount of energy gained from the solar irradiation is sufficiently large. Thus, instead of using continuous controllers to adjust the continuous inputs, the inputs are set to constant values in most operating modes which yield small water flow rates to the absorption machine while ensuring that all flow constraints within the plant are met. Only in mode m6 , the distribution of the water flows from the tanks and the gas heater is regulated by an underlying discrete controller that was designed to adjust the distribution of the flows from the tanks and the gas heater such that Tg;i is minimized while ensuring that Tg;i > TLB;T . Thus, the maximum possible amount of energy is drained from the tanks. The controller increases or decreases the value of vm3 in small steps at every sampling instant depending on the current value and the previous evolution of Tg;i . An additional advantage of this approach is that the discontinuities that are introduced by the mode switching do not have to be considered in the design of the continuous control strategy. The constant continuous input values of the discrete supervisor for nominal operation that were determined in simulation studies and identification experiments are shown in Table 3. The parameters were chosen to ensure a small flow rate of water to the absorption machine in the nominal region to minimize the energy consumption of the absorption machine5. This is reflected in the settings of the continuous inputs in the modes m3 to m8. For example, in mode m5 both the pump speed vB1 and the opening degree of the valve vm3 are set to relatively small values for the simulation model. This choice is a trade-off between goal fulfillment and robustness: the setting of vm3 ensures that the flow rate of water into the absorption machine is small while the flow rate into the tanks is 4 In mode m6 , the tanks can be used even if the temperature is smaller than 70 C. However, the energy that is gained from the tanks in this case is too small to justify repeated switching between the modes for measurement updating. 5 As mentioned above, the constant continuous input values for the supervisors for the upper warning and forbidden regions maximize the flow to the absorption machine to drive Te;o into the nominal region; these values are not shown here for reasons of brevity.
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Table 3. Constant values of the continuous inputs for the discrete supervisor that operates in the nominal region of Te;o . C means Controlled. Simulation
Mode Mode Mode Mode Mode Mode Mode Mode
m1 m2 m3 m4 m5 m6 m7 m8
Real plant
vm3
vB1
vm3
vB1
95 80 30 C 10 84
50 % 100 % 20 % 50 % 20 % 50 % 50 % 50 %
95 80 80 C 10 90
50 % 100 % 20 % 50 % 20 % 50 % 50 % 50 %
% % % % %
relatively large6. This ensures that the excess energy is stored in the tanks as fast as possible. The small value of vB1 , on the other hand, reduces the speed of the temperature drop so that the controller can switch to another mode in time without risking a shutdown of the absorption machine. Mode m5 can also serve as an illustration of the problem that even small differences between the simulation model and the plant can have large effects that must be considered in the controller design process. In contrast to the simulation model, the setting of vm3 cannot be reduced below 80% at the real plant since the valve vl31 , which should be closed in mode m5, cannot be closed at the real plant if the temperature of the water flow through the gas heater is too large (which it usually is) for safety reasons. Setting vm3 to 30% would drastically decrease the temperature of the water entering the absorption machine. Thus, the flow pattern within the plant significantly differs from the pattern predicted by the simulation model. This example illustrates one of the major advantages of the presented control scheme over model-based schemes: the rather large plant-model mismatch can be compensated by tuning the controller parameters (i.e., the values of the continuous inputs in this case). 4.3. Emergency Procedures In the case that the energy transfer to the absorption machine is reduced below the minimum threshold and, in consequence, the absorption machine is shut down, a set of emergency procedures is activated that overrides the control actions by the supervisory scheme to return the process into the nominal opera6 Note that although the controller maximizes the flow rate of water into the tanks in the modes m2 and m5 , the flow rate of water is about 10 times smaller in comparison to the flow rate of water to the absorption machine due to structural properties of the plant.
% % % % %
tion regime as soon as possible. Since a shut-down of the absorption machine reduces the difference between Tg;i and Tg;o due to a lack of energy consumption, the emergency mode is activated if the condition Tg;i Tg;o < 1:5 C
ð4Þ
evaluates to true. Here, Tg;i and Tg;o are averaged temperature values that are computed using a standard moving-average filter that operates with a time window of 40 seconds. Averaging is necessary since due to time delays, the condition Tg;i Tg;o < 1:5 C might evaluate to true although the absorption machine is running. In the emergency mode, the lower bound for Tg;i is set to TLB;E ¼ 87 C to ensure that the absorption machine is started again. The start-up is performed using one of the modes m3 , m7 , or m8. As above, the solar collector mode m3 has the highest priority, followed by m7 and m8.
5. Application Results The supervisory control scheme was implemented in MATLAB and was tested extensively at both, the simulation model presented in the first paper of this special section and at the real plant. This section presents the main results of the application studies. In addition to the fine-tuning of the control scheme, a goal of the simulation studies was to determine if the controller is sufficiently robust to stabilize both, the real plant and the simulation model that represents the process only inaccurately. In the tests, the model was simulated for two days using environmental data sets that were recorded at the real plant on a sunny day (day 1) and on a cloudy day (day 2). Fig. 8 shows the trajectories of the most important process variables that were obtained with the
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(d) Outlet temperature of the solar collectors.
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(e) Outlet temperature on the cold side of the absorption machine. Fig. 8. Results of the controller validation at the simulation model using a reference data set over two complete days. On day 1 (day 2), the air conditioning machine is started at 11 hours (25 hours), and it is stopped at 17.5 hours (31.5 hours).
simulation model using the parameterization ‘‘Simulation’’ shown in the Tables 2 and 3. The controller copes well with the given environmental data and operates the absorption machine continuously throughout both days as long as the air conditioning system is engaged. The presence of clouds on the second day does not have a significant influence on the control performance, as is shown in Table 4. The average power that is generated by the gas heater Pgh and the mean squared error (MSE) of the controlled variable do not vary significantly between both days.
The low value of Pgh indicates that the solar collectors can supply a significant share of the necessary energy since the absorption machine produces 35 kW of cooling power. At the end of both days, the controller stores all remaining thermal energy from the solar irradiation in the tanks which leads to an increase of the temperature in the tanks by approximately 0.3 C per day (see Table 4). The reasons for this only very small temperature increase are the large amount of cold water in the tanks and the fact that the flow rate of the water from the solar collectors into the tanks is
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relatively small. This behavior was also observed at the real plant, as is shown below. To overcome this problem, the storage system should be modified such that the high temperature of the inflowing water is preserved so that it can be used to directly support the absorption machine. A closer look at the simulation results of the first day (Fig. 9) reveals again that the simulation model behaves significantly different from the real plant. When the controller switches into mode m3 in which the solar collectors feed the absorption machine, the temperature of the water flowing into the solar collectors is reduced instantly. This change directly translates to an instant significant increase of the outlet temperature Tsc;o due to the modeling assumptions. This is evident from the lower part of Fig. 9. In response to the large and unrealistic temperature increase, the controller switches into mode Table 4. Control performance measures. MSE is the mean squared error of the controlled variable Te;o with respect to the setpoint of 15 C, Pgh is the average power that is generated by the gas heater, and Tt;end represents the temperature in the tanks at the end of the day.
MSE Pgh ½kW Tt;end
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m5 to store the excess energy in the tanks. The real plant does not exhibit this behavior. However, despite this significant plant-model mismatch, the controller is capable of operating the simulated plant over long time horizons. Fig. 10 shows the results of an experiment that was conducted at the real plant on a sunny day (March 8, 2007) using the parameterization ‘‘Real plant’’ that is given in the Tables 2 and 3. The air conditioning system is started after 1.2 hours. Until this time, the controller switches between the modes m1 and m2 to store the energy in the tanks that is gained from the solar irradiation. After 1.6 hours, the outlet temperature of the solar collectors is large enough to switch to mode m3 . From here on, the controller switches between the modes m3 and m8 (using the intermediate mode m4 ) and manages to keep the absorption machine operational for the major part of the experiment. Between 1 and 1.6 hours, the controller cannot keep the absorption machine operational. This can be explained by another peculiarity of the process equipment that was neglected for modeling purposes and that was not detected in the previous identification experiments: since the temperature in the tanks is sufficiently large to be used as an additional energy source, the controller switches to mode m6 to support the gas heater with water from the tanks. Before the switch, the valve vm3 is set to a constant value of 90%. The initial value for the underlying temperature controller in m6 was chosen to to be vm3 ¼ 10% to ensure that initially, only a small amount of water is drained from the tanks. The request of the controller to change the setting of vm3 from 90% to 10% is not executed (almost) instantaneously as expected, but the closing of vm3 is realized with a considerable time delay of approximately 40 seconds. Since during this time, the valves vl25 and vl26 are already opened, the absorption machine is supplied with a considerable amount of relatively cold water from the tanks and thus shuts down. The controller detects this shut-down and restarts the absorption machine by switching to mode m8. This problem can easily be solved by delaying the opening of the tank valves until vm3 has reached a position in which the cold tank water can be used safely. During the complete experiment, the gas heater had to generate an average power of 29.94 kW.
6. Conclusions and Future Work 14.2
14.4 14.6 time [h]
(b) Outlet temperature of the solar collectors Fig. 9. A closer look at the simulated plant operation during day 1.
In this paper, a supervisory control scheme for a real solar air conditioning plant is presented that was designed based on a thorough energetic analysis of the
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Fig. 10. Results of the controller test at the real solar plant on March 8, 2007 (10:30 - 15:25). At the real plant, the pipes of the tanks are equipped with several temperature sensors (see subfigure (f)). The controller uses the average value of these measurements.
solar plant, on identification experiments, and on simulation studies using a simplified model. The main challenge in the controller design was the considerable mismatch between the available models and the behavior of the real plant. Therefore the ideas of performing an algorithmic synthesis based on simple models as well as of model-based online optimization were abandoned and a robust control scheme was designed based upon process insight. In this scheme, measurement information is used directly to trigger switching of the operation modes. The major goal was to design a control system that achieves the best tradeoff between energy-efficient operation and robustness to a large variety of disturbances and uncertainties such as changes in the meteorological conditions, large and fast changes of the solar irradiation, and variable energy losses and time delays within the plant. In the control scheme presented in this paper, the discrete process inputs are adjusted by a switching logic that chooses between a small set of reasonable
operating modes, and in each operating mode, the continuous inputs are either set to constant values that were determined from identification experiments and the energetic analysis, or are adjusted by an underlying controller that regulates the distribution of the water flows from the tanks and from the gas heater to the absorption machine to maximize the amount of energy that is drained from the tanks. The control scheme was tested extensively at the real plant and with the simulation model that is presented in the first paper of this special section. It was found that the controller is capable of robustly controlling both the real and the simulated plant with minor adaptations of parameters due to known differences between the parameters in the simulation and at the real plant. Future work should aim at several areas: (i) The design scheme presented in this paper can in principle be applied to all those energy conversion processes for which the efficiency of operation is directly related to
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the energetic conditions within the plant. To this end, techniques should be developed that allow for a more automated analysis and design approach, for example based on steady-state models of the process under consideration. (ii) While the current parameterization of the control scheme allows for a very robust process operation under all conditions, it may render the controller conservative during nominal operation. For example, if the controller is operated on a cloud-less day, the switching thresholds can be reduced which leads to smaller losses of energy to the environment. Hence, a control scheme that adapts to the meteorological conditions using forecasts or pattern recognition techniques would be of interest. Such a scheme would estimate the probabilities of fast changes in the environmental conditions and adjust the switching thresholds accordingly.
5.
6. 7. 8.
9. 10.
Acknowledgments The authors gratefully acknowledge the financial support by the European Network of Excellence (NoE) HyCon, supported by the European Commission under contract number FP6-IST-511368.
11.
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1. Balluchi A, Benvenuti L, Engell S, Johansson KH, Lamnabhi-Lagarrigue F, Lygeros J, Morari M, Papafotiou G, Sangiovanni-Vincentelli AL, Santucci F, Stursberg O. Hybrid control of networked embedded systems. Eur J Control 2005; 11(4–5): 478–508. 2. Camacho EF, Berenguel M, Rubio FR. Advanced Control of Solar Plants. Advances in Industrial Control. Springer, 1997. 3. Engell S. Feedback control for optimal process operation. J Process Control 2007; 17(3): 203–219. 4. Gromov D, Geist S, Raisch J. Timed discrete event control of a parallel production line with continuous output. In Proceedings of 2nd IFAC Conference on
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Analysis and Design of Hybrid Systems, pp. 205–210, 2006. Igreja JM, Lemos JM, Silva RN. Adaptive receding horizon control of a distributed collector solar field. In Proceedings of 44th IEEE Conference on Decision and Control, European Control Conference (CDC-ECC), pp. 1282–1287, 2005. Koutsoukos XD, Antsaklis PJ, Stiver JA, Lemmon MD. Supervisory control of hybrid systems. Proc IEEE 2000; 88(7): 1026–1049. Nourelfath M, Niel E. Modular supervisory control of an experimental automated manufacturing system. Control Eng Pract 2004; 12: 205–216. Nunez-Reyes A, Bordons C. Predictive control of a solar air conditioning plant with simultaneous identification. In Proceedings of 44th IEEE Conference on Decision and Control, European Control Conference (CDC-ECC), pp. 1355–1360, 2005. Nunez-Reyes A, Normey-Rico JE, Bordons C, Camacho EF. A smith predictive based MPC in a solar air conditioning plant. J Process Control 2005; 15: 1–10. Roussel JM, Guia A. Designing dependable logic controllers using the supervisory control theory. In Proceedings of 16th IFAC World Congress, 2005. Paper code: Mo-A17-TO/4. Silva RN, Lemos JM, Rata LM. Variable sampling adaptive control of a distributed collector solar field. IEEE Trans Control Syst Technol 2003; 11(5): 765–772. Sonntag C, Su W, Stursberg O, Engell S. Optimized start-up control of an industrial-scale evaporation system with hybrid dynamics. Control Eng Pract 2008; 16: 976–990. Stursberg O. Supervisory control of hybrid systems based on model abstraction and guided search. Nonlinear Anal 2006; 65(6): 1168–1187. Stursberg O, Lohmann S. Synthesizing safe supervisory controllers for hybrid nonlinear systems. In Proceedings of IMACS World Congress—Scientific Computation, Applied Mathematics and Simulation, 2005. Code: T5I-76-0654. Zambrano D, Bordons C, Garcia-Gabin W, Camacho EF. A solar cooling plant: a benchmark for hybrid systems control. In Proceedings of 2nd IFAC Conference on Analysis and Design of Hybrid Systems, pp.199–204, 2006. Zambrano D, Bordons C, Garcia-Gabin W, Camacho EF. Model development and validation of a solar cooling plant. Int J Refrig 2008; 31: 315–327.
Supervisory Control of a Solar Air Conditioning Plant with Hybrid Dynamics Christian Sonntag1,, Hao Ding2,, Sebastian Engell1, 1 Process Dynamics and Operations Group, Department of Biochemical and Chemical Engineering, Technische Universität Dortmund, 44221 Dortmund, Germany 2 Institute of Automatic Control Engineering, Department of Electrical Engineering and Information Technology, Technische Universität München, 80290 München, Germany
The control of solar plants is challenging for several reasons, one of which is that the solar irradiation that represents the main energy source cannot be manipulated and is subject to large fluctuations due to changes of the weather conditions. For the solar air conditioning plant considered in this work, which is located at the University of Seville, Spain, additional difficulties arise from the presence of discretely switched valves and pumps and autonomous switches of the continuous dynamics which make it a hybrid system. The main control goal for this process is to minimize the consumption of auxiliary energy while ensuring a safe and robust operation even in the face of large disturbances. The available hybrid models of the plant that are suitable for algorithmic controller synthesis or model-predictive control do not represent the process dynamics accurately enough to ensure a robust plant operation under all conditions. In this paper, a supervisory control scheme is presented that was designed based on a thorough investigation of the energetic aspects of the solar plant and on several identification experiments at the real plant. The application of the control scheme to the real solar plant and to the simulation model illustrates the robustness and the efficiency of the approach.
Correspondence to: Christian Sonntag, E-mail: [email protected] E-mail: [email protected] E-mail: [email protected]
Keywords: Solar plants, refrigeration systems, hybrid systems, supervisory control, process control
1. Introduction Since the need for air conditioning usually coincides with a high amount of solar irradiation, solar plants are well suited as energy sources for air conditioning systems. The control of solar plants is a challenging task for several reasons: (i) in contrast to many other types of power plants, the main energy source (i.e., the solar irradiation) cannot be manipulated and is subject to large fluctuations that are induced by clouds and changes in the meteorological conditions, (ii) the process is subject to varying time delays due to fluid transportation within the plant, and (iii) the dynamics of the process varies depending on the environmental conditions. The control problem for the plant considered in this work is furthermore complicated by the presence of discretely switched inputs (valves and pumps) and autonomous switching of the continuous dynamics that is introduced by embedded discrete control loops. While the problem of designing continuous controllers for solar plants has been studied extensively in academia in the last decades (see e.g., [2, 5, 8, 9, 11]), control schemes that specifically
Received 12 April 2008; Accepted 17 September 2008 Recommended by E.F. Camacho, D.W. Clarke
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consider the hybrid nature of solar plants have not yet been investigated much. The algorithmic design of controllers for hybrid systems (see e.g., [3, 4, 6, 7, 10, 12, 13, 14]) requires the availability of a sufficiently simple plant model. If the goal is just to stabilize the plant under consideration, a model with relatively simple dynamics that provides a guaranteed but very conservative over-approximation of the plant behavior can often be used. The control goal for the solar air conditioning plant, however, is not only to stabilize the plant, but also minimize the consumption of gas within a gas heater. For such quantifiable control goals, over-approximating simple models are often not usable since a quantitative control goal requires the availability of accurate quantitative predictions of the plant behavior. Thus, a dynamic model must be available that faithfully and accurately represents the dynamics of the process in all relevant regions of the state space. While the model of the solar plant that is presented in the first paper of this special section and in [15, 16] is sufficiently simple for algorithmic controller design, its usability for the design of a robust and efficient control scheme is questionable for several reasons: Several simplifying modeling assumptions lead to inaccuracies of the model predictions of the dynamic and stationary plant behavior. As an example, the dynamic submodel of the solar collectors is based on a mean temperature Tsc;m of the water in the collectors, and the outlet temperature is computed by Tsc;o ¼ 2 Tsc;m Tsc;i , where Tsc;i is the inlet temperature of the collectors. If the plant were purely continuous, this assumption would in most situations lead to an accurate prediction of the temperature of the water in the solar collectors. However, if the inlet temperature changes instantaneously (which happens when the discrete inputs are switched), the outlet temperature changes instantaneously in the model as well. This behavior does not occur at the real plant which exhibits a significantly more complex behavior. Furthermore, a major source of complexity of the real plant lies in the existence of variable energy losses and variable time delays between the process units that are not represented by the available model. In addition, some properties of the process equipment that are not represented by a simple simulation model introduce significant disturbances at the real plant. As an example, most temperature sensors are not located within the process units, but in the pipes connecting the units. Since the energy losses within the pipes are much larger than the losses within the process units, the sensors may give temperature readings that do not correspond to the actual temperature within the process unit.
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Since these problems indicate that a simple model structure cannot accurately represent the plant dynamics, and since the effort required to formulate and to parameterize an accurate plant model was prohibitive, this paper presents a supervisory control scheme that has been developed based on a thorough energetic analysis of the process, on the results of several identification experiments, and on insights gained using the simulation model. In this control scheme, the discrete inputs of the solar plant are switched according to logic conditions defined over the available measurements of the process variables such that in each mode, the continuous inputs are chosen to minimize the consumption of auxiliary energy while ensuring a robust plant operation. The remainder of this paper is organized as follows: in Section 2, the solar air conditioning plant is described briefly. The results of the energetic process analysis are presented in Section 3, followed by a description of the supervisory control scheme in Section 4. Section 5 presents the results of the controller tests with the simulation model and at the real plant and discusses the controller performance. Finally, Section 6 concludes the paper.
2. The Solar Air Conditioning Plant The solar air conditioning plant is located in Seville, Spain, and is used to cool the laboratories of the Department of System Engineering and Automatic Control at the University of Seville. It was proposed as a benchmark problem for the application of hybrid control techniques within the EU-funded Network of Excellence HYCON (see e.g., [1]). In this section, the plant and the most important process variables are briefly introduced. A more detailed description of the case study is given in the first paper of this special section and in [15, 16]. Fig. 1 shows a scheme of the solar plant including important measurable process variables. It consists of four main components: an array of solar collectors that deliver up to 50 kW of thermal energy by heating water using solar irradiation, a gas-powered heater with a nominal power of 60 kW, a storage system that consists of two tanks with a capacity of 2500 l each, and an absorption machine. This system generates chilled water by supplying thermal energy in the form of hot water to the absorption machine which provides a cooling power of 35 kW. The chilled water is fed to an air conditioning system (not shown in Fig. 1). If the air conditioning system is switched on,
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(a) Solar Collectors
Environment (c)
Gas Heater Storage Tanks
Absorption (b) Machine
Pipes Fig. 2. Simplified process scheme depicting energy flows within the system.
Fig. 1. Layout of the solar air conditioning plant (taken from [15]) and important measurable process variables. The thick arrows indicate the directions of the flow of water through the system.
the flow rate m_ e is larger than 5000 hl . Otherwise, it is assumed that the system is switched off (i.e., the generation of chilled water is not necessary). A discrete controller within the gas heater starts the gas heater if the temperature of the outflowing water Tgw;o falls below 86 C, and the gas supply is stopped if Tgw;o > 94 C. The gas supply is also stopped for safety reasons if the flow rate of water through the gas heater falls below 1500 hl . The absorption machine only operates if the temperature Tg;i of the hot water is larger than 78 C1. An embedded controller shuts down the absorption machine if this constraint is violated. To start up the absorption machine, Tg;i must be larger than 85 C. The water flow is driven by two pumps (B1 and B4) that can be switched on or off. The discretely switched two-way and three-way valves vl21 , vl22 , vl23 , vl24 , vl25 , vl26 , vl31 , and vm1, which are modeled as binary variables, are used to influence the path of the water flow through the system and, thus, the energy sources used. The absorption machine can be supplied with water from the solar collectors, from the storage tanks, from the gas heater, or from a combination of these sources. Two continuous inputs are used to regulate the flow rates: the speed vB1 2 ½0%; 100% of the pump B1 and the setting of the three-way valve vm3 2 ½0%; 100%.2 The pump B4 works at a constant speed. The main control goal is to regulate the temperature of the chilled water Te;o to a setpoint of 15 C while minimizing the gas consumption (i.e., the time the gas heater is operating) and, with a lower priority, max75 C for the simulation model. vl ¼ 0 corresponds to fully closed, and vl ¼ 1 means fully open. If vm1 ¼ 0, the water flow leaving the solar collectors is fed back to pump B1, and vm3 ¼ 0% indicates that the water flows solely through the gas heater. 1 2
imizing the temperature of the water in the tanks. The constraint Tg;i > 78 C (Tg;i > 75 C for the model) must be fulfilled at all times.
3. Process Analysis 3.1. Energetic Analysis Since the main purpose of the solar plant is to supply thermal energy to the absorption machine, it is only natural to investigate the energetic conditions within the process to derive an energetically efficient control strategy. Fig. 2 shows a simplified scheme of the process that divides the solar plant into three subparts: (i) the energy supply part that consists of the solar collectors, the storage tanks, the gas heater, and the pipes connecting the subsystems, (ii) the absorption machine which, in this setting, is reduced to an energy sink, and (iii) the environment. In this context, the control goal can be understood as the maximization of the inner energy of the energy supply part (without using the gas heater), subject to the fulfillment of the constraint Tg;i > 78 C (Tg;i > 75 C). The inner energy QSP of the supply part is given by the energy content of the water in the four components: QSP ¼ QSC þ QGH þ QT þ QP ;
ð1Þ
and it changes with time according to: Q_ SP ¼ Q_ SI þ Q_ G ðQ_ AM þ Q_ L Þ:
ð2Þ
Here, QSP , QSC , QGH , QT , and QP represent the energy content of the water in the supply part, the solar collectors, the gas heater, the tanks, and the pipes, respectively. Q_ SI and Q_ G represent the energy obtained from the solar irradiation and the gas heater, Q_ AM is the energy consumed by the absorption machine, and Q_ L is the energy lost to the environment. Q_ SI only depends on the solar irradiation and cannot
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be manipulated. In experiments, it was found that Q_ AM can be varied slightly with the flow rate of water into the absorption machine. Hence, the control goal of minimizing Q_ G can be achieved by minimizing both, the energy loss Q_ L to the environment and the flow rate of water to the absorption machine. Under the reasonable assumption that the thermodynamic properties of the water remain constant within the operating regime of the process, the energy content of the water directly corresponds to its temperature, and the losses to the environment are directly related to the difference of the temperatures of the water and the ambient air. Thus, Q_ L can be reduced by minimizing the water temperature within the solar collectors, the gas heater, and the pipes. 3.2. Time Delays and Energy Losses The solar plant is subject to varying time delays due to the transportation of water between its components. Furthermore, the energy losses in the pipes between the process components cause temperature drops that must be considered in the control strategy, e.g., for the estimation of temperature changes that will occur when switching to another water flow pattern. To ensure that the control strategy can robustly operate the process under realistic conditions, over-approximations of the time delays and energy losses were determined in an extensive identification study on the real process. The process was operated over several days with differing environmental conditions (such as irradiation and environmental temperature), and the losses and time delays between the process components were measured for several realistic flow patterns. Fig. 3 depicts the results of this study. The largest temperature loss and the largest time delay occur between the solar collectors and the absorption machine. For high values of Tsc;o , the temperature loss can be over-approximated by a linear function for all
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investigated flow patterns. For smaller values of Tsc;o , a constant over-approximation was determined: 0:443 Tsc;o 32:9 C if Tsc;o > 80 C; lSC;AM ¼ 2 C if Tsc;o 80 C: ð3Þ
4. The Supervisory Control Scheme Fig. 4 shows a schematic representation of the supervisory control scheme that was developed based on the analysis presented in the previous section. The process measurements xðtÞ are sampled by an interface in intervals of 10 s yielding xðnÞ, and the controller computes new values of the discrete and continuous inputs uðnÞ and vðnÞ from these measurements which are then applied to the plant. In a first step, it is checked if the system is in a state which lies outside the nominal operating regime (see Fig. 5). If so, a set of emergency procedures is executed to drive the process back into a nominal mode of operation. If no emergency was detected, the main control algorithm is executed that is implemented as a set of discrete supervisory controllers as described in the following sections. The reason for using several discrete supervisors is the lack of sensitivity of the controlled variable Te;o , which must be regulated to a setpoint of 15 C, to changes of the continuous and discrete inputs: in experiments, it was found that this temperature can only be changed by at most 2 C using the discrete and continuous inputs. Hence, Te;o is not controlled directly. Instead, different discrete supervisors are employed depending on the value of Te;o as shown in Fig. 5. If the value of Te;o lies within the nominal operating region, the discrete and continuous inputs are chosen such that the gas consumption is Controller
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Fig. 3. Maximum values of the temperature losses (l ) and time delays (td ) between the process components.
Fig. 4. Scheme of the supervisory control strategy.
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minimized while allowing for robust process operation. If Te;o enters the upper warning region or even the forbidden region, the controller switches to different supervisors that attempt to drive Te;o into the nominal region by maximizing the water flow to the absorption machine. Accordingly, if Te;o enters the less critical lower warning region, another discrete supervisor minimizes the water flow to the absorption machine. In the remainder of this section, only the discrete supervisor for the nominal process operation will be described since the supervisors for the other regions were derived in a similar fashion. These supervisors differ from the nominal supervisor in two respects: (i) The goal of the supervisors for the upper warning and critical regions is to drive Te;o back into the nominal region as soon as possible. These supervisors avoid operating modes in which the solar collectors are used since these modes are often subject to sudden and drastic disturbances. In more detail, the
Te,o [°C] 18 17
Forbidden region Upper warning region
Setpoint
15 Nominal region 13 Lower warning region t
Fig. 5. Choice of the discrete supervisor depending on Te;o .
discrete supervisor corresponding to the upper warning region does not employ the operating mode m5, and the supervisor for the critical region does not use any modes in which the solar collectors are employed. (ii) To achieve a maximization or minimization of the energy transfer to the absorption machine, all supervisors use different settings for the continuous inputs, as described in Section 4.2.
4.1. The Discrete Supervisor for Nominal Operation Based on the energetic analysis, eight reasonable operating modes (m1 to m8) were identified that represent a subset of all possible combinations of the discrete inputs (see Table 1). The modes can be assigned to two different categories: m1 and m2 are used if the air conditioning system that is connected to the absorption machine is not operating, i.e., during start-up and shut-down of the system. The remaining modes are only considered when the air conditioning system is switched on. The discrete supervisor consists of two separate finite-state automata that are executed depending on the value of m_ e as shown in Fig. 6. The transition conditions are defined over the process measurements and constant switching thresholds which are chosen to avoid an undesirably large frequency of switching between the modes. Furthermore, the thresholds must be chosen such that robust process operation is guaranteed even in the face of large disturbances and the time delays given in Fig. 3, while the
Table 1. Operating modes and the settings of the discrete inputs. In all modes, vl21 ¼ vl22 , vl23 ¼ vl24 , and vl25 ¼ vl26 Mode
Description and settings of the discrete inputs
m1
Circulation of water in the solar collectors, the absorption machine is not active. B1 ¼ 1; vl21 ¼ vl23 ¼ vl25 ¼ vl31 ¼ B4 ¼ vm1 ¼ 0.
m2
Loading the tanks from the solar collectors, the absorption machine is not active. vl21 ¼ B1 ¼ vm1 ¼ 1; vl23 ¼ vl25 ¼ vl31 ¼ B4 ¼ 0.
m3
The solar collectors supply water to the absorption machine. vl23 ¼ B1 ¼ B4 ¼ vm1 ¼ 1; vl21 ¼ vl25 ¼ vl31 ¼ 0.
m4
The solar collectors and the gas heater supply water to the absorption machine. vl23 ¼ vl31 ¼ B1 ¼ B4 ¼ vm1 ¼ 1; vl21 ¼ vl25 ¼ 0.
m5
The solar collectors supply water to the absorption machine and to the tanks. vl21 ¼ vl23 ¼ B1 ¼ B4 ¼ vm1 ¼ 1; vl25 ¼ vl31 ¼ 0.
m6
The tanks and the gas heater supply water to the absorption machine. vl25 ¼ vl31 ¼ B1 ¼ B4 ¼ 1; vl21 ¼ vl23 ¼ vm1 ¼ 0.
m7
The tanks supply water to the absorption machine. vl25 ¼ B1 ¼ B4 ¼ 1; vl21 ¼ vl23 ¼ vl31 ¼ vm1 ¼ 0.
m8
The gas heater supplies water to the absorption machine. vl31 ¼ B1 ¼ B4 ¼ 1; vl21 ¼ vl23 ¼ vl25 ¼ vm1 ¼ 0
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δ 57
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Fig. 6. The discrete supervisor for start-up/shut-down and nominal process operation. xðnÞ is a sampled measurement of the process variables, and uðnÞ and vðnÞ are the settings of the continuous and discrete inputs that are computed by the controller based on xðnÞ.
temperature of the water in the energy supply part and, thus, the energy losses to the environment must be minimized. If the air conditioning system is not operating (i.e., m_ e 5000 hl ), the thermal energy obtained from the solar collectors is stored in the tanks (m2 ). If, however, Ttsc;i < Ttsc;o (see Fig. 1), energy would be drained from the tanks in mode m2 , and the system is switched to mode m1. As soon as Tsc;o lSC;T > Ttsc;o (see Fig. 3), the system is switched back to mode m2 . The finite-state automaton for nominal process operation was designed to exploit all existing energy sources before switching into a mode in which the gas heater is used. Hence, modes using only the solar collectors as the energy source always have the highest priority. In principle, if Q_ SI Q_ AM þ Q_ L (see Section 3), the excess energy is stored in the tanks. If Q_ SI < Q_ AM þ Q_ L , additional energy is needed to operate the absorption machine. This energy is preferably taken from the tanks, if possible, and otherwise from the gas heater. To implement this strategy, several switching thresholds are defined for the generator inlet temperature Tg;i . Fig. 7 shows these thresholds and a schematic evolution of Tg;i . The thresholds TLB;SC and TUB;SC are lower and upper bounds that should be adhered to if the plant is operating in mode m5. Due to the large and fast disturbances in this energy source, these thresholds are chosen larger than the lower and upper thresholds for modes that do not utilize the solar collectors (TLB;T and TUB;T ). The threshold TLB;T is the smallest value Tg;i should attain during process operation. If this threshold is crossed, the supervisor switches to a mode that ensures that Tg;i will increase again. Before switching to
Tg,i [°C]
m3
m5
m3 m5
m3
m7
m3
m7
m3 m5
TUB,SC TUB,T TLB,SC TLB,T 78 estimated
estimated
t
Fig. 7. Switching thresholds for the temperature Tg;i and an exemplary schematic evolution of Tg;i (time delays are neglected). It is assumed that the temperature of the water in the tanks is large enough to utilize the mode m7 .
a new mode, a conservative approximation of the value of Tg;i resulting from the switching (after the corresponding time delay has elapsed) is estimated by subtracting the maximum losses given in Fig. 3 from the output temperature of the process part that provides the energy for the absorption machine in the new mode. Note that in the very unlikely case that the overapproximations that are shown in Fig. 3 are violated and the absorption machine shuts down, the emergency control system ensures that the machine is restarted as soon as possible. In the exemplary scenario shown in Fig. 7, initially the plant is in mode m3 , and the temperature is increasing. Thus, there is an energy excess from the solar collectors. Once the threshold TUB;SC has been reached, the supervisor switches to mode m5 to store the excess energy in the tanks. If the thermal energy provided by the sun is not sufficient anymore to operate the absorption machine, Tg;i will fall below TLB;SC if the plant is in mode m3 . When the lowest threshold TLB;T is reached, the controller switches to a
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mode that ensures that Tg;i will increase again. Since in the example in Fig. 7, the temperature of the water in the tanks is sufficiently large, the supervisor switches to mode m7 . At this point, the supervisor begins to monitor the estimated temperature Tg;i;est ¼ Tsc;o lSC;AM that would result at the inlet of the absorption machine if the plant was switched to mode m3 . The solar collectors are in the recirculation mode at this point, i.e., no energy is drained from the water in the solar collectors, and Tg;i;est will increase. As soon as Tg;i;est reaches TUB;T , the supervisor switches back to mode m3 . The values of the switching thresholds are important tuning parameters to achieve a good trade-off between energy efficiency and robustness. Based on extensive simulation studies and several identification experiments at the real plant in the fall of 2006 and in the spring of 2007, the thresholds were chosen as small as possible to increase the energetic efficiency, but as large as necessary to ensure robustness. The values that were determined for the discrete supervisor that is used in the nominal region of Te;o are shown in Table 2. Since the lower bound for Tg;i is smaller for the simulation model (75 C) than for the real plant (78 C), the threshold values for the simulation model are lower than those for the real plant. Switching to mode m5 at the real plant causes a temperature drop that is much faster than expected from the simulation studies. Thus, the difference between the thresholds TLB;SC (TUB;SC ) and TLB;T (TUB;T ) was chosen larger at the real plant. In the sequel, the transition conditions of the automaton for nominal process operation are described in more detail. The process variables used here are shown in Fig. 1. For simplicity, the conditions are not shown in a disjunctive form, i.e., several conditions can become true for the same variable values. Instead, the transition conditions are sorted by priority. For example, of all transitions leaving the state m3 which represents the mode m3 , 35 has the highest priority, as is shown below. Note that the system is never switched to mode m8 (using only the gas heater) directly if in the previous mode, the gas heater was not used, because the cold water in the gas heater might decrease Tg;i below the lowest admissible bound and thus shut down the absorption machine. Instead, an intermediate mode is used briefly until the temperature of the water from the gas heater has reached the desired value. If in the previous mode, the tanks were used, the intermediate mode is m6 , and if the solar collectors were used, the intermediate mode is m4 3. 3 Some process variables exhibit considerable measurement noise. If necessary, the corresponding measurements are adjusted by averaging several measurements within a very short time window. For simplicity, this averaging is neglected here.
Table 2. Switching thresholds for the discrete supervisor that operates in the nominal region of Te;o .
TLB;T TLB;SC TUB;T TUB;SC
Simulation
Real plant
78 C 79 C 80 C 82 C
81 C 84 C 83 C 89 C
Transitions leaving m3 If the system is in mode m3 , it can be switched into the modes m5, m7 , m6 , and m4 , where m5 has the highest priority. Here, the term Tsc;o ðn 3Þ Tsc;o ðnÞ > Tg;i ðnÞ TLB;T is used to detect sudden drops in the solar irradiation, i.e., large drops that occur within a time window of 30 seconds. In this case, the supervisor switches into another mode to avoid a shutdown of the absorption machine: 35 : Tg;i ðnÞ > TUB;SC Tg;i ðnÞ < TLB;SC _ Tsc;o ðn 3Þ Tsc;o ðnÞ > Tg;i ðnÞ TLB;T ^ Ttam;o ðnÞ lT;AM > TLB;T 36 : Tg;i ðnÞ < TLB;SC _ Tsc;o ðn 3Þ Tsc;o ðnÞ > Tg;i ðnÞ TLB;T ^ Ttam;o ðnÞ lT;AM > TLB;T _ Ttam;o ðnÞ lT;AM > Tsc;o ðnÞ lSC;AM 34 : Tg;i ðnÞ < TLB;SC _ Tsc;o ðn 3Þ Tsc;o ðnÞ > Tg;i ðnÞ TLB;T 37 :
Transitions leaving m4 Since the gas heater is employed in mode m4 , the mode is left as soon as the energy provided by the solar collectors or the tanks is sufficiently large. As mentioned above, this mode is also used as a transit mode to ensure that the outlet temperature of the gas heater is sufficiently large to support the absorption machine. This is reflected in the condition 48 : 43 : Tsc;o ðnÞ lSC;AM > TUB;T 47 : Ttam;o ðnÞ lT;AM > TLB;T 48 : Tgw;o ðnÞ lGH;AM > TLB;T Transitions leaving m5 The conditions of the transitions leaving the state m5 are defined similarly to those leaving the state m3 . However, the term used to detect sudden drops in the solar radiation (Tsc;o ðn 1Þ Tsc;o ðnÞ > Tg;i ðnÞ TLB;SC ) employs a smaller time window of 10 seconds
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since the energy drain from the solar collectors is considerably larger in this mode. 53 : Tg;i ðnÞ < TLB;SC _ Tsc;o ðn 1Þ Tsc;o ðnÞ > Tg;i ðnÞ TLB;SC 57 : Tg;i ðnÞ < TLB;SC _ Tsc;o ðn 1Þ Tsc;o ðnÞ > Tg;i ðnÞ TLB;SC ^ Ttam;o ðnÞ lT;AM > TLB;T 56 : Tg;i ðnÞ < TLB;SC _ Tsc;o ðn 1Þ Tsc;o ðnÞ > Tg;i ðnÞ TLB;SC ^ Ttam;o ðnÞ lT;AM > Tg;o ðnÞ _ Ttam;o ðnÞ lT;AM > Tsc;o ðnÞ lSC;AM 54 : Tg;i ðnÞ < TLB;SC _ Tsc;o ðn 1Þ Tsc;o ðnÞ > Tg;i ðnÞ TLB;SC Transitions leaving m6 , m7 , and m8 The main goal of the supervisor in the modes m6 , m7 , and m8 is to return to a mode in which the solar collectors (or the tanks in m6 and m8) are employed again. Furthermore, the mode m6 is a transit mode, i.e., if the outlet temperature of the gas heater is sufficiently large, the supervisor switches into mode m8: 63 : Tsc;o ðnÞ lSC;AM > TUB;T 67 : Ttam;o ðnÞ lT;AM > TLB;T 68 : Tgw;o ðnÞ lGH;AM > TLB;T 73 : Tsc;o ðnÞ lSC;AM > TUB;T 76 : Ttam;o ðnÞ lT;AM < TLB;T 83 : Tsc;o ðnÞ lSC;AM > TUB;T 87 : Ttam;o ðnÞ lT;AM > TLB;T 86 : Ttam;o ðnÞ lT;AM > Tg;o ðnÞ The temperature sensors that measure Ttam;o ðnÞ and Ttsc;o ðnÞ are not located within the tanks but in the pipes connecting the tanks to the remaining parts of the process. Hence, if the tanks are not used, the water residing in these pipes cools down and renders the temperature measurements unreliable. In this case, the supervisor switches to the modes m5 and m7 during nominal operation for 10 seconds in every 30 minutes to update these temperature measurements. If the air conditioning system is not operating, the modes m2 and m7 are used instead. This updating procedure is only executed if the previous measurements indicate that the tanks hold an amount of energy that is sufficiently large to be usable as a source for the absorption machine. This means that if Ttam;o ðnÞ or
Ttsc;o ðnÞ are smaller than 70 C, the corresponding measurement will not be updated4. 4.2. Continuous Control In our setting, the need for accurate setpoint tracking of the process variables has been replaced by the introduction of the switching thresholds described above. For example, if the process is in mode m3 , regulating Tg;i to a given setpoint is not necessary since the controller automatically switches to mode m5 if the amount of energy gained from the solar irradiation is sufficiently large. Thus, instead of using continuous controllers to adjust the continuous inputs, the inputs are set to constant values in most operating modes which yield small water flow rates to the absorption machine while ensuring that all flow constraints within the plant are met. Only in mode m6 , the distribution of the water flows from the tanks and the gas heater is regulated by an underlying discrete controller that was designed to adjust the distribution of the flows from the tanks and the gas heater such that Tg;i is minimized while ensuring that Tg;i > TLB;T . Thus, the maximum possible amount of energy is drained from the tanks. The controller increases or decreases the value of vm3 in small steps at every sampling instant depending on the current value and the previous evolution of Tg;i . An additional advantage of this approach is that the discontinuities that are introduced by the mode switching do not have to be considered in the design of the continuous control strategy. The constant continuous input values of the discrete supervisor for nominal operation that were determined in simulation studies and identification experiments are shown in Table 3. The parameters were chosen to ensure a small flow rate of water to the absorption machine in the nominal region to minimize the energy consumption of the absorption machine5. This is reflected in the settings of the continuous inputs in the modes m3 to m8. For example, in mode m5 both the pump speed vB1 and the opening degree of the valve vm3 are set to relatively small values for the simulation model. This choice is a trade-off between goal fulfillment and robustness: the setting of vm3 ensures that the flow rate of water into the absorption machine is small while the flow rate into the tanks is 4 In mode m6 , the tanks can be used even if the temperature is smaller than 70 C. However, the energy that is gained from the tanks in this case is too small to justify repeated switching between the modes for measurement updating. 5 As mentioned above, the constant continuous input values for the supervisors for the upper warning and forbidden regions maximize the flow to the absorption machine to drive Te;o into the nominal region; these values are not shown here for reasons of brevity.
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Table 3. Constant values of the continuous inputs for the discrete supervisor that operates in the nominal region of Te;o . C means Controlled. Simulation
Mode Mode Mode Mode Mode Mode Mode Mode
m1 m2 m3 m4 m5 m6 m7 m8
Real plant
vm3
vB1
vm3
vB1
95 80 30 C 10 84
50 % 100 % 20 % 50 % 20 % 50 % 50 % 50 %
95 80 80 C 10 90
50 % 100 % 20 % 50 % 20 % 50 % 50 % 50 %
% % % % %
relatively large6. This ensures that the excess energy is stored in the tanks as fast as possible. The small value of vB1 , on the other hand, reduces the speed of the temperature drop so that the controller can switch to another mode in time without risking a shutdown of the absorption machine. Mode m5 can also serve as an illustration of the problem that even small differences between the simulation model and the plant can have large effects that must be considered in the controller design process. In contrast to the simulation model, the setting of vm3 cannot be reduced below 80% at the real plant since the valve vl31 , which should be closed in mode m5, cannot be closed at the real plant if the temperature of the water flow through the gas heater is too large (which it usually is) for safety reasons. Setting vm3 to 30% would drastically decrease the temperature of the water entering the absorption machine. Thus, the flow pattern within the plant significantly differs from the pattern predicted by the simulation model. This example illustrates one of the major advantages of the presented control scheme over model-based schemes: the rather large plant-model mismatch can be compensated by tuning the controller parameters (i.e., the values of the continuous inputs in this case). 4.3. Emergency Procedures In the case that the energy transfer to the absorption machine is reduced below the minimum threshold and, in consequence, the absorption machine is shut down, a set of emergency procedures is activated that overrides the control actions by the supervisory scheme to return the process into the nominal opera6 Note that although the controller maximizes the flow rate of water into the tanks in the modes m2 and m5 , the flow rate of water is about 10 times smaller in comparison to the flow rate of water to the absorption machine due to structural properties of the plant.
% % % % %
tion regime as soon as possible. Since a shut-down of the absorption machine reduces the difference between Tg;i and Tg;o due to a lack of energy consumption, the emergency mode is activated if the condition Tg;i Tg;o < 1:5 C
ð4Þ
evaluates to true. Here, Tg;i and Tg;o are averaged temperature values that are computed using a standard moving-average filter that operates with a time window of 40 seconds. Averaging is necessary since due to time delays, the condition Tg;i Tg;o < 1:5 C might evaluate to true although the absorption machine is running. In the emergency mode, the lower bound for Tg;i is set to TLB;E ¼ 87 C to ensure that the absorption machine is started again. The start-up is performed using one of the modes m3 , m7 , or m8. As above, the solar collector mode m3 has the highest priority, followed by m7 and m8.
5. Application Results The supervisory control scheme was implemented in MATLAB and was tested extensively at both, the simulation model presented in the first paper of this special section and at the real plant. This section presents the main results of the application studies. In addition to the fine-tuning of the control scheme, a goal of the simulation studies was to determine if the controller is sufficiently robust to stabilize both, the real plant and the simulation model that represents the process only inaccurately. In the tests, the model was simulated for two days using environmental data sets that were recorded at the real plant on a sunny day (day 1) and on a cloudy day (day 2). Fig. 8 shows the trajectories of the most important process variables that were obtained with the
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1000
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500 0 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 time [h]
(a) Solar irradiation. 8 day 1 day 2 7 6 5 4 3 2 1 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 time [h]
(b) Operating mode. 100
day 1
day 2
90 80 70 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 time [h]
(c) Inlet temperature on the hot side of the absorption machine. 90
day 1
day 2
80 70 60 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 time [h]
(d) Outlet temperature of the solar collectors.
25
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20 15 10 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 time [h]
(e) Outlet temperature on the cold side of the absorption machine. Fig. 8. Results of the controller validation at the simulation model using a reference data set over two complete days. On day 1 (day 2), the air conditioning machine is started at 11 hours (25 hours), and it is stopped at 17.5 hours (31.5 hours).
simulation model using the parameterization ‘‘Simulation’’ shown in the Tables 2 and 3. The controller copes well with the given environmental data and operates the absorption machine continuously throughout both days as long as the air conditioning system is engaged. The presence of clouds on the second day does not have a significant influence on the control performance, as is shown in Table 4. The average power that is generated by the gas heater Pgh and the mean squared error (MSE) of the controlled variable do not vary significantly between both days.
The low value of Pgh indicates that the solar collectors can supply a significant share of the necessary energy since the absorption machine produces 35 kW of cooling power. At the end of both days, the controller stores all remaining thermal energy from the solar irradiation in the tanks which leads to an increase of the temperature in the tanks by approximately 0.3 C per day (see Table 4). The reasons for this only very small temperature increase are the large amount of cold water in the tanks and the fact that the flow rate of the water from the solar collectors into the tanks is
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relatively small. This behavior was also observed at the real plant, as is shown below. To overcome this problem, the storage system should be modified such that the high temperature of the inflowing water is preserved so that it can be used to directly support the absorption machine. A closer look at the simulation results of the first day (Fig. 9) reveals again that the simulation model behaves significantly different from the real plant. When the controller switches into mode m3 in which the solar collectors feed the absorption machine, the temperature of the water flowing into the solar collectors is reduced instantly. This change directly translates to an instant significant increase of the outlet temperature Tsc;o due to the modeling assumptions. This is evident from the lower part of Fig. 9. In response to the large and unrealistic temperature increase, the controller switches into mode Table 4. Control performance measures. MSE is the mean squared error of the controlled variable Te;o with respect to the setpoint of 15 C, Pgh is the average power that is generated by the gas heater, and Tt;end represents the temperature in the tanks at the end of the day.
MSE Pgh ½kW Tt;end
8 7 6 5 4 3 2 1 14
14.2
Day 1
Day 2
1.546 26.3258 70.2822
1.623 26.4478 70.5958
14.4 14.6 time [h]
14.8
15
14.8
15
(a) Operating mode
80
T
sc,o
[°C ]
90
70
60 14
m5 to store the excess energy in the tanks. The real plant does not exhibit this behavior. However, despite this significant plant-model mismatch, the controller is capable of operating the simulated plant over long time horizons. Fig. 10 shows the results of an experiment that was conducted at the real plant on a sunny day (March 8, 2007) using the parameterization ‘‘Real plant’’ that is given in the Tables 2 and 3. The air conditioning system is started after 1.2 hours. Until this time, the controller switches between the modes m1 and m2 to store the energy in the tanks that is gained from the solar irradiation. After 1.6 hours, the outlet temperature of the solar collectors is large enough to switch to mode m3 . From here on, the controller switches between the modes m3 and m8 (using the intermediate mode m4 ) and manages to keep the absorption machine operational for the major part of the experiment. Between 1 and 1.6 hours, the controller cannot keep the absorption machine operational. This can be explained by another peculiarity of the process equipment that was neglected for modeling purposes and that was not detected in the previous identification experiments: since the temperature in the tanks is sufficiently large to be used as an additional energy source, the controller switches to mode m6 to support the gas heater with water from the tanks. Before the switch, the valve vm3 is set to a constant value of 90%. The initial value for the underlying temperature controller in m6 was chosen to to be vm3 ¼ 10% to ensure that initially, only a small amount of water is drained from the tanks. The request of the controller to change the setting of vm3 from 90% to 10% is not executed (almost) instantaneously as expected, but the closing of vm3 is realized with a considerable time delay of approximately 40 seconds. Since during this time, the valves vl25 and vl26 are already opened, the absorption machine is supplied with a considerable amount of relatively cold water from the tanks and thus shuts down. The controller detects this shut-down and restarts the absorption machine by switching to mode m8. This problem can easily be solved by delaying the opening of the tank valves until vm3 has reached a position in which the cold tank water can be used safely. During the complete experiment, the gas heater had to generate an average power of 29.94 kW.
6. Conclusions and Future Work 14.2
14.4 14.6 time [h]
(b) Outlet temperature of the solar collectors Fig. 9. A closer look at the simulated plant operation during day 1.
In this paper, a supervisory control scheme for a real solar air conditioning plant is presented that was designed based on a thorough energetic analysis of the
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Fig. 10. Results of the controller test at the real solar plant on March 8, 2007 (10:30 - 15:25). At the real plant, the pipes of the tanks are equipped with several temperature sensors (see subfigure (f)). The controller uses the average value of these measurements.
solar plant, on identification experiments, and on simulation studies using a simplified model. The main challenge in the controller design was the considerable mismatch between the available models and the behavior of the real plant. Therefore the ideas of performing an algorithmic synthesis based on simple models as well as of model-based online optimization were abandoned and a robust control scheme was designed based upon process insight. In this scheme, measurement information is used directly to trigger switching of the operation modes. The major goal was to design a control system that achieves the best tradeoff between energy-efficient operation and robustness to a large variety of disturbances and uncertainties such as changes in the meteorological conditions, large and fast changes of the solar irradiation, and variable energy losses and time delays within the plant. In the control scheme presented in this paper, the discrete process inputs are adjusted by a switching logic that chooses between a small set of reasonable
operating modes, and in each operating mode, the continuous inputs are either set to constant values that were determined from identification experiments and the energetic analysis, or are adjusted by an underlying controller that regulates the distribution of the water flows from the tanks and from the gas heater to the absorption machine to maximize the amount of energy that is drained from the tanks. The control scheme was tested extensively at the real plant and with the simulation model that is presented in the first paper of this special section. It was found that the controller is capable of robustly controlling both the real and the simulated plant with minor adaptations of parameters due to known differences between the parameters in the simulation and at the real plant. Future work should aim at several areas: (i) The design scheme presented in this paper can in principle be applied to all those energy conversion processes for which the efficiency of operation is directly related to
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the energetic conditions within the plant. To this end, techniques should be developed that allow for a more automated analysis and design approach, for example based on steady-state models of the process under consideration. (ii) While the current parameterization of the control scheme allows for a very robust process operation under all conditions, it may render the controller conservative during nominal operation. For example, if the controller is operated on a cloud-less day, the switching thresholds can be reduced which leads to smaller losses of energy to the environment. Hence, a control scheme that adapts to the meteorological conditions using forecasts or pattern recognition techniques would be of interest. Such a scheme would estimate the probabilities of fast changes in the environmental conditions and adjust the switching thresholds accordingly.
5.
6. 7. 8.
9. 10.
Acknowledgments The authors gratefully acknowledge the financial support by the European Network of Excellence (NoE) HyCon, supported by the European Commission under contract number FP6-IST-511368.
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