Weight-Transducerless Starting Torque Compensation ... - IEEE Xplore
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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 61, NO. 9, SEPTEMBER 2014
Weight-Transducerless Starting Torque Compensation of Gearless Permanent-Magnet Traction Machine for Direct-Drive Elevators Gaolin Wang, Member, IEEE, Jin Xu, Tielian Li, Guoqiang Zhang, Hanlin Zhan, Li Ding, and Dianguo Xu, Senior Member, IEEE
Abstract—To improve the starting performance of a permanentmagnet traction machine without a weight transducer in a gearless elevator, an adaptive starting torque compensation strategy is proposed in this paper. The dynamic model of the direct-drive elevator traction system considering the rope elasticity, the brake releasing, and the friction torque is established. Based on the dynamic model, the characteristics of the synthetic load torque exerted on the traction machine during elevator start-up are obtained. In order to balance the unknown load torque for the gearless elevator, a fuzzy self-tuning strategy is adopted to generate a suitable starting torque for compensation by tuning the change rate of electromagnetic torque according to the encoder signal. The torque compensator is designed with the aim of getting a minimized sliding distance and avoiding traction sheave reversal. Both simulation and experimental results are provided to verify that the proposed weight-transducerless adaptive starting torque compensation strategy can achieve superior riding comfort of shorter sliding distance, faster dynamic response, and smaller sliding speed. Index Terms—Adaptive starting torque compensation, directdrive system, friction torque, gearless elevator, permanentmagnet synchronous machine (PMSM), riding comfort, weight transducerless.
I. I NTRODUCTION
R
ECENTLY, permanent-magnet synchronous machines (PMSMs) have been widely used in industrial applications [1], [2]. The gearless elevator with a low-speed and high-torque permanent-magnet traction machine has become the development trend of modern elevators. The direct-drive elevator traction system has many advantages such as good riding comfort, high efficiency, attenuated mechanical noise, and elimination of machine room [3], [4]. Recently, some key techniques on novel machine design, advanced control strategy,
Manuscript received July 10, 2013; revised September 21, 2013; accepted October 16, 2013. Date of publication November 7, 2013; date of current version March 21, 2014. This work was supported in part by the Research Fund for the National Science Foundation of China under Grant 51207030, in part by the National Key Basic Research Program of China under Grant 2013CB035600, and in part by the Postdoctoral Science-Research Developmental Foundation of Heilongjiang Province under Grant LBH-Q12087. The authors are with the School of Electrical Engineering and Automation, Harbin Institute of Technology, Harbin 150001, China (e-mail: WGL818@ hit.edu.cn; [email protected]; [email protected]; [email protected]; [email protected]; [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIE.2013.2289894
and energy saving technique have been proposed to improve the performance of the elevator traction system [5]–[9]. As one of the major concerns, improving riding comfort during elevator start-up from the standby mode to the running mode is very significant. In order to achieve a quick balance of torque during the electromagnetic brake releasing at the elevator starting, the load information from the weight transducer installed under the elevator car is usually required for the drive to provide a matched electromagnetic torque with feedforward control. However, the installation of the weight transducer decreases the robustness when the feedback signal is affected by noise and sometimes may not be able to provide the actual load information. As a result, it might make the wrong torque compensation and cause uncomfortable riding feel. Therefore, eliminating the weight transducer and exploiting adaptive starting torque compensation strategy is an emerging technique to improve the starting reliability of the direct-drive elevator nowadays. Various enhanced control strategies have been proposed to improve the robustness against load disturbance when the machine is running [10]–[15]. However, they are unsuitable for the application of the starting torque compensation of the gearless elevator traction system. During the brake releasing when the elevator operates from the standby mode to the running mode, both the sliding distance and mechanical vibration should be considered in order to ensure the riding comfort of the elevator. The generated torque of the traction machine must track the unknown load torque accurately and quickly. In [16], the starting torque compensation was equivalent to a searching issue based on a friction model. However, the difference of the neighboring torque references was quite large, which can cause mechanical vibration. In [17], the load torque was estimated through the acceleration evaluation by the quadratic error comparison. However, the inertia of the elevator traction system should be known. In [18], two starting torque compensation methods using the dichotomy and the staircase method were proposed for the weight-transducerless elevator. Although the compensation methods can track the load torque effectively, the variation of the neighboring electromagnetic torques was still a step type. In [16]–[18], the assumption that the brake released instantaneously was made in the model, and this led to a big change in the torque generated by the traction machine when estimating the load torque. However, in practical applications, the brake releases gradually, and the synthetic load torque exerted on
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The dynamic equation of the counterweight side can be expressed as follows: Mw x˙ 1 − k1 (θm R − x1 ) − b1 (θ˙m R − x˙ 1 ) = 0
(1)
Mw g − k1 Δx10 = 0.
(2)
Similarly, the motion equation of the car side can be expressed as follows:
Fig. 1.
Simplified model of the direct-drive elevator traction system.
the traction machine changes during the process. It is worth developing new methods to avoid mechanical noise caused by the large electromagnetic torque variation. In order to achieve more comfortable riding, the torque generated by the traction machine should be a continuous type during elevator start-up. In this paper, based on the analysis of the dynamic characteristics of the gearless traction system during elevator startup, a novel adaptive starting torque compensation strategy is proposed to improve the system robustness and the riding comfort. This paper is organized as follows. First, in order to explore the characteristics of the synthetic load torque exerted on the traction sheave, a dynamic model of the gearless elevator traction system is built in Section II. According to the model characteristics, an adaptive weight-transducerless starting torque compensation strategy based on fuzzy selftuning is proposed in Section III. The compensation strategy is accomplished by self-tuning the current loop reference only based on the feedback information of the Sin–Cos encoder. In Section IV, the control strategy is verified by simulation and experimental results.
II. DYNAMIC M ODEL OF E LEVATOR T RACTION S YSTEM A. Modeling of the Direct-Drive Elevator Traction System The gearless elevator has three major mechanical components: the traction machine, the car, and the counterweight. A simplified schematic including the main components of a direct-drive elevator traction system is shown in Fig. 1. The traction sheave and the brake pulley are installed on the rotor of the permanent-magnet traction machine. An electromagnetic brake is mounted around the brake pulley to hold the traction system still when the elevator operates in standby mode. The equivalent elasticity and the damping of the rope are described as the dotted line areas. The mechanical position of the traction sheave, the counterweight displacement, and the car displacement are presented as θm , x1 , and x2 , respectively.
Mc x˙ 2 − k2 (−θm R − x2 ) − b2 (−θ˙m R − x˙ 2 ) = 0
(3)
Mc g − k2 Δx20 = 0
(4)
where rigidity coefficient of the rope on the car side; k2 damping coefficient of the rope on the car side; b2 mass of the car; Mc Δx20 elongation of the rope on the car side in steady state. Considering the friction torque exerted on the pulley by the brake, the kinematic analysis of the traction sheave can be described by (5)–(7). In particular, Tf and Tsum0 are the friction torques between the brake pulley and the brake, the traction sheave, and the rope, respectively. Tμ is the friction torque caused by other factors of the system Te − Tsum = Jm θ¨m
(5)
where Tsum =
0; Tsum0 − (Tf + Tμ );
Tf + Tμ > Tsum0 (6) otherwise
Tsum0 = R(Mc g − Mw g) + Rk2 (−θm R − x2 ) + Rb2 (−θm R˙ − x˙ 2 ) − Rk1 (θm R − x1 ) + Rb1 (θ˙m R − x˙ 1 )
(7)
where Te
electromagnetic torque generated by the traction machine; total inertia of the traction system; Jm Tsum resultant friction torque exerted on the traction sheave; radius of the brake pulley. Rz In order to analyze the friction torque characteristics, the relationship between the friction force f and the mechanical velocity vm can be expressed as follows: ⎧ if vm = 0 and |Fl | < Fs ⎨ Fl , f = Fs sign(Fl ), (8) if vm = 0 and |Fl | ≥ Fs ⎩ Fc sign(vm ) + σv, if vm = 0 where Fl is the external force, Fc is the Coulomb friction, σ is the coefficient of viscosity, and Fs is the maximum static friction force. When the brake releases completely, according to the friction model in (8), the torque criterion that drives the traction machine from standstill to the rotating state is |Te − Tsum0 | > Fs R.
(9)
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Fig. 2. Force analysis of the traction sheave and the brake sheave.
Moreover, the criterion that makes the traction machine operate from the rotating state to standstill is |Te − Tsum0 | < Fc R.
(10)
It can be concluded that the torque generated by the traction machine to keep the car at standstill is not a fixed value but a variable one within the range of [Tsum0 − Fc R, Tsum0 + Fc R]. B. Analysis of the Brake Releasing Process Fig. 2 shows the dynamic analysis of the traction system. An area element on the interface of the brake pulley and the brake shoe which corresponds to an angular element dγ is selected to be studied, and γ is the wrap angle of the brake. Assume that the pressure exerted by the brake shoe on the area element is dNi (t). During the brake releasing, the deformation of the brake shoes gets smaller, resulting in the decrease of dNi (t). The friction torque of each element is given as dTf = μdNi (t)Rz
(11)
where μ is the friction coefficient between the pulley and the brake. Assuming that the deformation of each element is the same during the brake releasing, which means that the change rate of dNi (t) for each element is the same, it can be expressed as dN (t) = dNi (t),
i = 1, 2, 3 . . . .
(12)
The total friction torque exerted on the brake pulley by the brake shoes can be calculated by integration Tf =
γ dTf = μdN (t)
π+γ
Rz dγ + μdN (t) 0
= μ (2γdN (t)) Rz .
Rz dγ π
(13)
Equation (13) can be rewritten as (14) if 2γdN (t) is replaced by equivalent pressure N (t) Tf = μN (t)Rz .
(14)
When the brake is releasing, the pressure N (t) between the brake pulley and the brake shoe is decreasing, and so is the maximum static friction between them.
Fig. 3.
Simulation block diagram of the direct-drive elevator system.
Ideally, if the electromagnetic torque is equal to the total load torque during the brake releasing, the traction machine will keep still. Then, the torque that the rope exerts on the traction wheel is constant. More specifically, in Fig. 2, Tc and Tw equal Mc gR and Mw gR, respectively. Under this condition, (7) can be changed as Tsum0 = R(Mc g − Mw g).
(15)
However, it is difficult for the traction machine to produce electromagnetic torque to balance the unknown and changing equivalent load torque precisely at zero speed. If the starting torque is not well compensated, the traction machine will slide a distance due to torque unbalance during the brake releasing. The variations of the velocity and the acceleration of the system would cause the change of stretching force on the rope of both sides. The torque that the rope exerts on the traction sheave is given by (7). In order to obtain the characteristics of Tsum during the brake releasing, the electromechanical simulation model of the direct-drive elevator is established as Fig. 3. The brake is modeled as a first-order system based on its characteristics. The parameters of the traction machine model and the elevator mechanical model are listed in the Appendix. Additionally, N0 = 6000 N, μ = 0.6, and R(Mc g − Mw g) = −530 N · m. The ideal or realistic situation is selected through the terminal 1 or 2 correspondingly. In the realistic situation, the conventional vector control strategy is used. Both the speed controller and the current controllers are proportional–integral (PI) regulators. Simulation results are illustrated in Fig. 4. From Fig. 4, it can be seen that Tsum in real condition is smaller than that in ideal condition when the sliding speed is increasing, and the contrary is the case when the sliding speed is decreasing. That means that the sliding speed and the range of the speed variation would keep relatively small if Te tracks Tsum well in the ideal situation. Since the brake releasing time would change due to the brake shoe abrasion and the adjustment of the braking force, the time constant of the brake is changing,
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Fig. 6. Description of the starting torque compensation process.
Fig. 4.
Simulation results of the elevator system.
Fig. 7. Flowchart of the adaptive starting torque compensation.
Fig. 5. Scheme of the adaptive torque compensation during the elevator start-up.
and it is difficult to establish a precise mathematical model to describe the change of Tsum in ideal situation. III. P ROPOSED W EIGHT-T RANSDUCERLESS A DAPTIVE S TARTING T ORQUE C OMPENSATION S TRATEGY A. Starting Torque Compensation Control Strategy of the Traction Machine According to the dynamic analysis of the aforementioned traction machine system, the control scheme of the starting torque compensation for the direct-drive elevator machine is shown in Fig. 5. Moreover, the starting torque compensating principle is described in Fig. 6. A surface-mounted PMSM is used in the traction system, and the vector control method is adopted. The speed reference is set to zero during the brake
releasing at the end of the standby mode. The fuzzy selftuning of the electromagnetic torque change rate kt∗ includes two control modes: fuzzy compensation and friction correcting. A switch judger determines which mode is active based on the sliding distance and sliding speed, and the detailed switch logic is shown in Fig. 7. Once the PI control is enabled, the output of the fuzzy self-tuning kt∗ will be set to zero. Moreover, if the fuzzy self-tuning is active, the output of the speed PI control i∗q1 will keep constant. The discrete mathematical representation of i∗q1 can be described as follows: i∗q1 (k) = Upω (k)+Uiω (k) = kpω e(k)+
Ts e(k) +Uiω (k−1) τiω (16)
where Upω , Uiω , kpω , and τiω are the proportional output, integral output, proportional gain, and integral time constant of the speed PI controller, respectively; Ts is the sampling period; e(k) is the error between the speed reference and feedback; and k denotes the value at time kTs .
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In addition, i∗q2 is the integration of the fuzzy self-tuning output kt∗ , and its mathematical representation is i∗q2 (k) = i∗q2 (k − 1) + kt∗ (k).
(17)
In Fig. 5, i∗q is equal to the sum of i∗q1 and i∗q2 . Since the bandwidth of the current loop is wider than the one of the speed loop, the system can reach balance rapidly if i∗q matches the load torque. In Fig. 6, the solid line denotes the torque Tsum exerted on the traction sheave. Te shown by the dotted line should trace the torque Tsum in order to make the sliding distance as short as possible. At time tp , the brake releases completely, and Te should satisfy the range [Tc − Fc R, Tc + Fc R] to make the traction machine keep standstill, where Tc = (Mc g − Mw g)R. The detailed flowchart of the proposed starting torque compensation is described as Fig. 7, in which ε and Δ denote the threshold of the sliding distance and sliding speed, respectively. The starting torque compensation strategy can be divided into four stages as follows. Stage I [0, t1 ]: The load torque Tsum0 is less than the sum of friction torque Tf and Tμ , and the traction sheave keeps standstill. The machine-generated torque is zero in this stage. Stage II [t1 , t2 ]: Tsum0 is larger than the maximum static friction torque, and the car begins to slide. Since the sliding distance is less than the threshold of the switch judger, the PI controller is active, and the output of the fuzzy self-tuning is zero. As the bandwidth of the speed loop is limited and the output of the PI controller could not track the load torque timely, the sliding speed would increase in this stage. Stage III [t2 , t3 ]: At time t2 , the sliding distance is larger than the threshold ε, and the sliding speed is larger than the threshold Δ. The compensation mode changes from the PI control to the fuzzy compensation. The electromagnetic torque can trace the load toque with the suitable output of the fuzzy compensator. The control mode would switch between the PI control mode and the fuzzy compensation mode several times in this stage due to the speed variation. Because the load torque increases much faster than the output of the PI controller, the sliding speed direction is invariable, and the fuzzy compensation mode takes a dominant role. Since the brake releases completely at time tp , the variation of torque Tsum is very small after time tp . Stage IV [t3 , t4 ]: At time t3 , the sliding speed is less than the threshold Δ, and the PI control mode is active. The sliding speed will decrease to zero at time t4 with the speed PI regulator. If Te satisfies [Tc − Fc R, Tc + Fc R] at time t4 , the sliding friction force would change into static friction force, and Tsum would be equal to Te rapidly. If Te is larger than Tc + Fc R at time t4 , the friction correcting mode would be active, and Te would minus Fc R in case of a reversed sliding distance.
Fig. 8. Simplified block diagram of the fuzzy self-tuning torque compensator.
Fig. 9.
Membership function of e˜, c˜e˜, and u ˜.
B. Design of the Fuzzy Self-Tuning Torque Compensator The fuzzy self-tuning torque compensator is adopted to track the change of the synthetic load torque. Once it is active, a corresponding electromagnetic torque is generated by the traction machine to keep the elevator car slide at a small speed. The structure of the fuzzy self-tuning torque compensator is illustrated in Fig. 8. The fuzzy compensator has two inputs, namely, the sliding speed error ωr and the change of the sliding speed error α. The output of the fuzzy compensator is kt , and the output of the friction correcting mode is Δif . The sum of kt and Δif is kt∗ which represents the change rate of q-axis current reference i∗q . For convenience, the input variables ωr and α are changed into e˜ and c˜e˜ using the scaling factors Ke and Kce , respectively, and the output of the fuzzy controller u ˜ is also processed by the quantification factor Ku to get the crisp value kt . The universes of discourse of the input fuzzy variables, e˜ and c˜e˜, are [−6, −1]U[1, 6] and [−3,3], respectively. The universe of discourse of the output variable u ˜ is [−6, −1]U[1, 6]. The ˜ and U ˜ are divided into six fuzzy universes of discourse of E ˜ is sets, respectively, and the universe of discourse of C˜ E divided into three fuzzy sets. Considering the sensitivity and stability of the fuzzy compensator, the membership functions of the input and output variables are shown in Fig. 9. The change characteristics of Tsum modeled in Section II are considered to design the fuzzy control rules. The control target is to obtain a minimized sliding distance and to avoid the change of sliding direction. Therefore, the increasing rate of Te should become larger to reduce the sliding distance when the sliding speed becomes larger. On the other hand, the increasing
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TABLE I F UZZY C ONTROL RULES
rate of Te should decrease moderately to avoid rotor reversal when the sliding speed becomes smaller. In addition, using the sliding acceleration as an auxiliary judgment to regulate Te can ensure that it can track the load disturbance timely. The fuzzy control rules are shown in Table I. There are 18 rules for the starting torque compensator. The control rule Ri is designed ˜k , then u ˜m , where ˜j and c˜e˜ is C˜ E ˜ is U as follows: If e˜ is E i = 1, 2, · · · , 18, j, m = 1, 2, · · · , 6, and k = 1, 2, 3. The minimum operation is used to get the fuzzy set of the output ˜i ) = min μ(E ˜i ), μ(C˜ E ˜i ) . μ(U (18)
Fig. 10. Relationship of the fuzzy self-tuning torque compensation rules.
For example, if e˜ = 2.5 and c˜e˜ = 0.5, the control rules R11 and R14 are active to calculate the output fuzzy set. According to the control rule R11 , the weighting coefficient of output fuzzy set N S(˜ u) can be obtained μ (N S(˜ u)) = min{μ(P S(˜ e)) , μ (Z(˜ ce˜))} = min{0.5, 1} = 0.5. Based on the control rule R14 , the weighting coefficient of output fuzzy set N M (˜ u) can be obtained μ(N M (˜ u)) = min{μ(P M (˜ e)), μ(Z(˜ ce˜))} = min{0.5,1} = 0.5. The output fuzzy set is the union of N S(˜ u) and N M (˜ u), which can be expressed as 0.5∧ μ (N S(˜ u)) ∨ 0.5∧ μ (N M (˜ u)) . The center average defuzzifier is adopted to transform the output of the fuzzy inference to a crisp value u ˜ in the fuzzy controller ˜ μ(Ui ) · ui u ˜= (19) ˜i ) μ(U where ui is the center of the corresponding fuzzy set, which equals the mean value of the points whose membership is one in the fuzzy set. In this scheme, the centers of N S(˜ u) and N M (˜ u) are −1.5 and −3.5, respectively. The crisp value u ˜ can be calculated as follows: 0.5 × (−1.5) + 0.5 × (−3.5) = −2.5. u ˜= 0.5 + 0.5
Fig. 11. Schematic diagram of the interface board connecting the encoder and the microprocessor.
U[0.02%IN , 0.1%IN ], where IN denotes the rated current. The values of e˜ and c˜e˜ can be obtained ⎧ ωr ∈ [0.024, 0.032] rad/s ⎨ 6, e˜ = 250ωr , ωr ∈ [−0.024, −0.004]U[0.004, 0.024] rad/s ⎩ −6, ωr ∈ [−0.032, −0.024] rad/s ⎧ ⎨ 3, c˜e˜ = 0.05α, ⎩ 3,
(20) α ∈ [60, 80] rad/s2 α ∈ [−60, 60] rad/s2 α ∈ [−80, −60] rad/s2 .
(21)
As a result, the value of kt (k) can be calculated by the output scaling function ˜(k). kt (k) = 0.00016IN u
(22)
C. Signal Processing of the SIN/COS Encoder
The interface board connecting the encoder (ERN1387) and the digital signal processor (DSP) TMS320F2808 is a SIN/COS Based on the aforementioned defuzzification, the relation- encoder feedback card as shown in Fig. 11. The differential ship between the inputs and the output is shown in Fig. 10. signals ±A, ±B, ±C, and ±D from the encoder are processed In the scheme, the ranges of ωr and α in the fuzzy controller by a differential operational circuit, and then, four sinusoidal are [−0.032, −0.004]U[0.004, 0.032] rad/s and [−80, 80] rad/s2 , outputs A, B, C, and D can be got. The signals C and D appear respectively; the range of the output kt is [−0.1%IN , −0.02%IN ] as one sinusoidal or cosine period, respectively, per revolution,
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Fig. 12. Experimental waveforms of the rotor position calculation by using the Sin–Cos encoder (Sin–Cos signals A and B, incremental count, and position subdivision result).
and they can be used to calculate the absolute position. The sinusoidal incremental signals A and B are phase shifted by 90◦ and appear as 2048 periods per revolution. A and B are then processed by a hysteresis comparison circuit, and this circuit produces two 90◦ phase-shifted square-wave pulses QA and QB. In particular, the edges of QA and QB will make the register (its value denotes the incremental count) in the enhanced quadrature encoder pulse (eQEP) count up or down. The position is updated at each pulsewidth modulation (PWM) period (i.e., 100 μs). The rotor position θm can be calculated
2π 2 θm = N + θdiv · (23) M π where N is the incremental count, M is the maximum incremental count value and it equals 8192 for the 2048 P/R Sin–Cos encoder, and θdiv is the subdivision calculated from the quadrature signals by the arc-tangent function. The experimental waveforms of the sinusoidal incremental signals (A and B), the incremental count, and the position subdivision results are shown in Fig. 12. The resolution of the subdivision depends on the precision of the A/D conversion and the signal quality of A and B. IV. S IMULATION AND E XPERIMENTAL R ESULTS A. Simulation Results Simulation and experiment have been executed to compare the proposed starting torque compensation strategy with the traditional PI control. The parameters of the traction machine system used in simulation are given in the Appendix. The whole controller is constructed according to the block diagrams shown in Figs. 5 and 8. The simulation results under 80% rated load are shown in Fig. 13. In Fig. 13(a) and (b), the quadrature signals from the Sin–Cos encoder, the subdivision value, and the incremental count value are shown, respectively. In particular, the unit value of the incremental count denotes a sliding distance of 0.23 mm. Fig. 13(c) shows the comparison of the sliding speed using the proposed method and the conventional PI control. It can be seen that the sliding speed
Fig. 13. Simulation results under 80% rated load. (a) Output of the Sin–Cos encoder with conventional PI control. (b) Output of the Sin–Cos encoder with proposed compensation strategy. (c) Sliding speed comparison. (d) q-axis current response comparison.
with the proposed method is smaller and the system reaches the steady state with a shorter time. Fig. 13(d) shows the q-axis current response with the proposed compensation strategy, the conventional PI control, and the ideal load torque tracking, respectively. From the results, the q-axis current response using the proposed compensation strategy is superior over that of the PI control method. B. Experimental Results The proposed adaptive starting torque compensation method is experimented at an 11.7-kW gearless elevator traction machine without using the weight transducer. The parameters of the permanent-magnet traction machine are listed in the Appendix. A Sin–Cos encoder (ERN1387) with 2048 P/R is installed on the machine. A TMS320F2808 DSP is used to execute all the control algorithms. The PWM frequency of the inverter is 10 kHz. The period of the current loop is 100 μs, and the speed control is activated every 1 ms. The proposed compensation algorithm is executed every 100 μs. In the switch judger, the threshold of the sliding distance ε is 0.06 mm, and the threshold of the sliding speed Δ is 0.004 rad/s. To verify the proposed starting torque compensation strategy, the experimental results of the conventional PI control are shown for comparison. The PI controller parameters are carefully designed as shown in Appendix B to satisfy the zero-speed traction mode. The parameters of current PI controllers are kpi = 37.49 and τii = 1.739 × 10−3 s, and the parameters of the speed controller are kpω = 3.61 and τiω = 0.012. The same PI parameters are used in Fig. 5 to cooperate with the fuzzy self-tuning torque compensation strategy.
WANG et al.: WEIGHT-TRANSDUCERLESS STARTING TORQUE COMPENSATION OF TRACTION MACHINE
Fig. 14. Experimental comparison between (a) conventional PI control and (b) proposed compensation strategy under 20% rated load.
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Fig. 16. Experimental comparison between conventional PI control and proposed compensation strategy under rated load.
Fig. 17. Sliding distance comparison of the two methods under different loads.
Fig. 15. Experimental comparison between (a) conventional PI control and (b) proposed compensation strategy under 60% rated load.
Experimental results using the proposed compensation strategy and the conventional PI control method under different loads are illustrated in Figs. 14–16. In Figs. 14–16, the quadrature signals from the Sin–Cos encoder, the sliding distance, and the q-axis current (expressed by per-unit value) are shown. The sliding distances using the conventional PI control and the proposed method are 1.2 and 0.18 mm in Fig. 14, 4.0 and 0.35 mm in Fig. 15, and 7.2 and 0.65 mm in Fig. 16, respectively. From the results, it can be concluded that the sliding distance becomes much shorter and the sliding speed reaches zero faster when the proposed compensation strategy is adopted. Moreover, the q-axis current response is much faster, particularly at the beginning stage of the sliding process, which means that the machine-generated
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torque tracks the load torque timely, and this causes a relatively small sliding speed. Fig. 17 shows a more visualized sliding distance comparison of the two methods under various loads, which verifies the effectiveness of the proposed method further. V. C ONCLUSION In this paper, an adaptive starting torque compensation method of the gearless traction machine for the direct-drive elevator without using a weight transducer has been proposed. The dynamic analysis of the brake releasing process shows that the synthetic load torque in actual condition is smaller than that in ideal condition when the sliding speed is increasing, and the contrary is the case when the sliding speed is decreasing. The adaptive compensation strategy consists of three modes, including the PI control, the fuzzy compensation, and the friction correcting. The rules of the torque compensator are designed in order to get a shorter sliding distance and avoid sliding direction reversal. The effectiveness of the method is verified both in simulation and experiment. By adopting the compensation strategy, the electromagnetic torque generated by the gearless machine tracks the load torque better during elevator start-up. It performs better at improving the riding comfort of the gearless elevator with a shorter sliding distance. A PPENDIX A TABLE II T RACTION M ACHINE PARAMETERS
Fig. 18.
Block diagram of the traction machine vector control system.
the PWM frequency. The controller’s PI tuning focuses on the zero-speed operation mode, and the sliding speed of the traction machine is very low; ωr can be ignored. 1) PI Tuning of the Current Loop Controller: The transfer function of the controlled plant in the current loop can be expressed as Gobj1 (s) =
kf i k v . (τf i s + 1)(τv s + 1)(Ls s + Rs )
(B1)
The time constant of current filter τf i = 2τv = 0.0002 s. Let km = 1/Rs = 4.3478 and τli = Ls /Rs = 0.0652 s. Since τf i and τv are small enough compared with τli , the two inertia elements can be merged into one, and the equivalent time constant τi = τv + τf i = 0.0003 s. Then, (B1) can be rewritten as Gobj1 (s) =
kf i kv km . (τli s + 1)(τi s + 1)
(B2)
The current loop controller is a PI type Gci (s) =
kpi τii s + 1 . τii s
(B3)
In order to design the current loop as a typical type I system Gik (s) = TABLE III
ka s(τi s + 1)
(B4)
E LEVATOR M ECHANICAL PARAMETERS
the pole with a larger time constant in (B2) should be cancelled by Gci (s), so kpi τii s + 1 = τli s + 1.
(B5)
Then, the condition ka = kf i kv km /τii should be met. In order to obtain the faster response and the minimized overshoot, ka τi = 0.5 is a better choice [19]. The PI parameters of the current controller can be obtained: kpi = 37.49, and τii = 1.739 × 10−3 s. Therefore, the closed-loop transfer function of the current loop is A PPENDIX B The traction machine control system is shown in Fig. 18. Gcω and Gci are the transfer functions of the speed and current loop PI controllers, respectively. The inverter is modeled as an inertia element with time constant τv = 1/fs = 0.0001 s, where fs is
Gli (s) =
kli τli s + 1
(B6)
where kli = 1/kf i = 1 and τli = 1/ka = 2 × 10−4 s.The cutoff frequency of the current loop is 1520 Hz, and the phase margin is 65◦ .
WANG et al.: WEIGHT-TRANSDUCERLESS STARTING TORQUE COMPENSATION OF TRACTION MACHINE
2) PI Tuning of the Speed Loop Controller: The open-loop transfer function of the speed loop is Gobj2 (s) =
kli kf ω Rs τm kΦ s(τli s + 1)(τf ω s + 1)
(B7)
where the electromagnetic time constant τm = JRs / (9.55kΦ kT ) = 0.00274 s, in which kT = NP ψf = 29.13 and J = 4.02 kg · m2 . The time constant of speed filter τf ω = 0.002 s, and the feedback coefficient kf ω = 1. Combine the two inertia elements into one, and the equivalent time constant τh is τh = τf ω + τli = 0.0022 s. Define koω = kli kf ω Rs /(τm kΦ ), and then, koω = 69.2245. Therefore, (B7) can be expressed as Gobj2 (s) =
69.2245 . s(0.0022s + 1)
(B8)
The speed controller is a PI type Gcω (s) =
kpω (τiω s + 1) . τiω s
(B9)
Design the speed loop as a typical type II system, and the open-loop transfer function of the speed loop is expressed as Gnk (s) =
kω (τiω s + 1) s2 (τh s + 1)
(B10)
where kω = koω kpω /τiω . Let h = τiω /τh , and the cutoff frequency can be expressed as ωcω (h + 1) = 2 τiω 2τiω
1 1 = 0.5 + . τiω τh
kω = ωcω
(B11) (B12)
In order to achieve better tracking performance, h should be set in the range of 5–6 [19]. Here, select h = 5, and then τiω = hτh kpω =
(h + 1)τm kΦ . 2hτh kli kf ω Rs
(B13) (B14)
According to the detailed parameters, the PI parameters of the speed controller are τiω = 0.012 and kpω = 3.61. R EFERENCES [1] A. Consoli, G. Scelba, G. Scarcella, and M. Cacciato, “An effective energy-saving scalar control for industrial IPMSM drives,” IEEE Trans. Ind. Electron., vol. 60, no. 9, pp. 3658–3669, Sep. 2013. [2] K. Kamiev, J. Montonen, M. P. Ragavendra, J. Pyrhönen, J. A. Tapia, and M. Niemelä, “Design principles of permanent magnet synchronous machines for parallel hybrid or traction applications,” IEEE Trans. Ind. Electron., vol. 60, no. 11, pp. 4881–4890, Nov. 2013. [3] S. Cicale, L. Albini, F. Parasiliti, and M. Villani, “Design of a permanent magnet synchronous motor with grain oriented electrical steel for directdrive elevators,” in Proc. ICEM, 2012, pp. 1256–1263. [4] E. Jung, H. Yoo, S. K. Sul, H. S. Choi, and Y. Y. Choi, “A nine-phase permanent-magnet motor drive system for an ultrahigh-speed elevator,” IEEE Trans. Ind. Appl., vol. 48, no. 3, pp. 987–995, May/Jun. 2012. [5] L. W. White, S. M. Lukic, and S. Bhattacharya, “Investigations into the minimization of electrical costs for traction-type elevators,” in Proc. ECCE, 2010, pp. 4285–4292.
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[6] J. He, C. Mao, J. Lu, and J. Yang, “Design and implementation of an energy feedback digital device used in elevator,” IEEE Trans. Ind. Electron., vol. 58, no. 10, pp. 4636–4642, Oct. 2011. [7] R. Appunn, B. Riemer, and K. Hameyer, “Contactless power supply for magnetically levitated elevator systems,” in Proc. ICEM, 2012, pp. 600–605. [8] E. Bilbao, P. Barrade, I. Etxeberria-Otadui, A. Rufer, S. Luri, I. Gil, S. Jung, H. Kobayashi, S. Doki, and S. Okuma, “Optimal energy management of an improved elevator with energy storage capacity based on dynamic programming,” in Proc. ECCE, 2012, pp. 3479–3484. [9] X. Wang, Z. Zhang, X. Xu, and Y. Cui, “Influence of using conditions on the performance of PM linear synchronous motor for ropeless elevator,” in Proc. ICEMS, 2011, pp. 1–5. [10] W. Kim, D. Shin, and C. C. Chung, “Microstepping using a disturbance observer and a variable structure controller for permanent-magnet stepper motors,” IEEE Trans. Ind. Electron., vol. 60, no. 7, pp. 2689–2699, Jul. 2013. [11] H. Wang, H. Kong, Z. Man, D. M. Tuan, Z. Cao, and W. Shen, “Sliding mode control for steer-by-wire systems with ac motors in road vehicles,” IEEE Trans. Ind. Electron., vol. 61, no. 3, pp. 1596–1611, Mar. 2014. [12] H. H. Choi and J. W. Jung, “Discrete-time fuzzy speed regulator design for PM synchronous motor,” IEEE Trans. Ind. Electron., vol. 60, no. 2, pp. 600–607, Feb. 2013. [13] I. A. Smadi, H. Omori, and Y. Fujimoto, “Development, analysis, experimental realization of a direct-drive helical motor,” IEEE Trans. Ind. Electron., vol. 59, no. 5, pp. 2208–2216, May 2012. [14] R. Errouissi, M. Ouhrouche, W. H. Chen, and A. M. Trzynadlowski, “Robust cascaded nonlinear predictive control of a permanent magnet synchronous motor with antiwindup compensator,” IEEE Trans. Ind. Electron., vol. 59, no. 8, pp. 3078–3088, Aug. 2012. [15] N. T. T. Vu, D. Y. Yu, H. H. Choi, and J. W. Jung, “T-S fuzzy-modelbased sliding-mode control for surface-mounted permanent-magnet synchronous motors considering uncertainties,” IEEE Trans. Ind. Electron., vol. 60, no. 10, pp. 4281–4291, Oct. 2013. [16] X. Hong, Z. Deng, S. Wang, L. Huang, W. Li, and Z. Lu, “A novel elevator load torque identification method based on friction model,” in Proc. 25th Annu. IEEE APEC, 2010, pp. 2021–2024. [17] S. Bolognani, A. Faggion, L. Sgarbossa, and L. Peretti, “Modelling and design of a direct-drive lift control with rope elasticity and estimation of starting torque,” in Proc. 33rd Annu. IEEE IECON, 2007, pp. 828–832. [18] G. Wang, G. Zhang, R. Yang, and D. Xu, “Robust low-cost control scheme of direct-drive gearless traction machine for elevators without a weight transducer,” IEEE Trans. Ind. Appl., vol. 48, no. 3, pp. 996–1005, May/Jun. 2012. [19] B. C. Kuo, Automatic Control Systems., 8th ed. Englewood Cliffs, NJ, USA: Prentice-Hall, 2002.
Gaolin Wang (M’13) received the B.S., M.S., and Ph.D. degrees in electrical engineering from Harbin Institute of Technology, Harbin, China, in 2002, 2004, and 2008, respectively. In 2009, he joined the Department of Electrical Engineering, Harbin Institute of Technology, as a Lecturer, where he has been an Associate Professor of Electrical Engineering since 2012. From 2009 to 2012, he was a Postdoctoral Fellow with Shanghai STEP Electric Corporation, Shanghai, China. He has authored more than 30 technical papers published in journals and conference proceedings. He is the holder of seven Chinese patents. His current major research interests include permanent-magnet synchronous motor drives, high-performance direct drives for traction systems, position sensorless control of ac motors, and efficiency optimization control of the interior permanent-magnet synchronous machine.
Jin Xu received the B.S. degree in electrical engineering from Harbin Institute of Technology, Harbin, China, in 2013, where he is currently working toward the M.S. degree in power electronics and electrical drives in the School of Electrical Engineering and Automation. His current research interests are in direct-drive permanent-magnet synchronous motor control and position sensorless control.
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Tielian Li received the B.S. degree in electrical engineering from Harbin Engineering University, Harbin, China, in 2012. He is currently working toward the M.S. degree in power electronics and electrical drives in the School of Electrical Engineering and Automation, Harbin Institute of Technology, Harbin. His current research interests are in highperformance direct drives for permanent-magnet traction systems and position sensorless control.
Guoqiang Zhang received the B.S. degree in electrical engineering from Harbin Engineering University, Harbin, China, in 2011 and the M.S. degree in electrical engineering from Harbin Institute of Technology, Harbin, in 2013, where he is currently wording toward the Ph.D. degree in power electronics and electrical drives in the School of Electrical Engineering and Automation. His current research interests are in permanentmagnet synchronous motor drives and position sensorless control.
Hanlin Zhan received the B.S. degree in electrical engineering from Harbin Institute of Technology, Harbin, China, in 2012, where he is currently working toward the M.S. degree in power electronics and electrical drives in the School of Electrical Engineering and Automation. His current research interests are in permanentmagnet synchronous motor drives and parameter identification techniques.
Li Ding received the B.S. degree in electrical engineering from Shanghai University, Shanghai, China, in 2013. He is currently working toward the M.S. degree in power electronics and electrical drives in the School of Electrical Engineering and Automation, Harbin Institute of Technology, Harbin, China. His current research interests are in permanentmagnet synchronous motor drives and position sensorless control.
Dianguo Xu (M’97–SM’12) received the B.S. degree in control engineering from Harbin Engineering University, Harbin, China, in 1982 and the M.S. and Ph.D. degrees in electrical engineering from Harbin Institute of Technology (HIT), Harbin, in 1984 and 1989, respectively. In 1984, he joined the Department of Electrical Engineering, HIT, as an Assistant Professor. Since 1994, he has been a Professor in the Department of Electrical Engineering, HIT. He was the Dean of the School of Electrical Engineering and Automation, HIT, from 2000 to 2010. He is currently the Assistant President of HIT. His research interests include renewable energy generation technology, power quality mitigation, sensorless vector-controlled motor drives, and high-performance servo systems. He has published over 600 technical papers. Dr. Xu is an Associate Editor for the IEEE T RANSACTIONS ON I NDUS TRIAL E LECTRONICS . He serves as the Chairman of the IEEE Harbin Section.
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 61, NO. 9, SEPTEMBER 2014
Weight-Transducerless Starting Torque Compensation of Gearless Permanent-Magnet Traction Machine for Direct-Drive Elevators Gaolin Wang, Member, IEEE, Jin Xu, Tielian Li, Guoqiang Zhang, Hanlin Zhan, Li Ding, and Dianguo Xu, Senior Member, IEEE
Abstract—To improve the starting performance of a permanentmagnet traction machine without a weight transducer in a gearless elevator, an adaptive starting torque compensation strategy is proposed in this paper. The dynamic model of the direct-drive elevator traction system considering the rope elasticity, the brake releasing, and the friction torque is established. Based on the dynamic model, the characteristics of the synthetic load torque exerted on the traction machine during elevator start-up are obtained. In order to balance the unknown load torque for the gearless elevator, a fuzzy self-tuning strategy is adopted to generate a suitable starting torque for compensation by tuning the change rate of electromagnetic torque according to the encoder signal. The torque compensator is designed with the aim of getting a minimized sliding distance and avoiding traction sheave reversal. Both simulation and experimental results are provided to verify that the proposed weight-transducerless adaptive starting torque compensation strategy can achieve superior riding comfort of shorter sliding distance, faster dynamic response, and smaller sliding speed. Index Terms—Adaptive starting torque compensation, directdrive system, friction torque, gearless elevator, permanentmagnet synchronous machine (PMSM), riding comfort, weight transducerless.
I. I NTRODUCTION
R
ECENTLY, permanent-magnet synchronous machines (PMSMs) have been widely used in industrial applications [1], [2]. The gearless elevator with a low-speed and high-torque permanent-magnet traction machine has become the development trend of modern elevators. The direct-drive elevator traction system has many advantages such as good riding comfort, high efficiency, attenuated mechanical noise, and elimination of machine room [3], [4]. Recently, some key techniques on novel machine design, advanced control strategy,
Manuscript received July 10, 2013; revised September 21, 2013; accepted October 16, 2013. Date of publication November 7, 2013; date of current version March 21, 2014. This work was supported in part by the Research Fund for the National Science Foundation of China under Grant 51207030, in part by the National Key Basic Research Program of China under Grant 2013CB035600, and in part by the Postdoctoral Science-Research Developmental Foundation of Heilongjiang Province under Grant LBH-Q12087. The authors are with the School of Electrical Engineering and Automation, Harbin Institute of Technology, Harbin 150001, China (e-mail: WGL818@ hit.edu.cn; [email protected]; [email protected]; [email protected]; [email protected]; [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIE.2013.2289894
and energy saving technique have been proposed to improve the performance of the elevator traction system [5]–[9]. As one of the major concerns, improving riding comfort during elevator start-up from the standby mode to the running mode is very significant. In order to achieve a quick balance of torque during the electromagnetic brake releasing at the elevator starting, the load information from the weight transducer installed under the elevator car is usually required for the drive to provide a matched electromagnetic torque with feedforward control. However, the installation of the weight transducer decreases the robustness when the feedback signal is affected by noise and sometimes may not be able to provide the actual load information. As a result, it might make the wrong torque compensation and cause uncomfortable riding feel. Therefore, eliminating the weight transducer and exploiting adaptive starting torque compensation strategy is an emerging technique to improve the starting reliability of the direct-drive elevator nowadays. Various enhanced control strategies have been proposed to improve the robustness against load disturbance when the machine is running [10]–[15]. However, they are unsuitable for the application of the starting torque compensation of the gearless elevator traction system. During the brake releasing when the elevator operates from the standby mode to the running mode, both the sliding distance and mechanical vibration should be considered in order to ensure the riding comfort of the elevator. The generated torque of the traction machine must track the unknown load torque accurately and quickly. In [16], the starting torque compensation was equivalent to a searching issue based on a friction model. However, the difference of the neighboring torque references was quite large, which can cause mechanical vibration. In [17], the load torque was estimated through the acceleration evaluation by the quadratic error comparison. However, the inertia of the elevator traction system should be known. In [18], two starting torque compensation methods using the dichotomy and the staircase method were proposed for the weight-transducerless elevator. Although the compensation methods can track the load torque effectively, the variation of the neighboring electromagnetic torques was still a step type. In [16]–[18], the assumption that the brake released instantaneously was made in the model, and this led to a big change in the torque generated by the traction machine when estimating the load torque. However, in practical applications, the brake releases gradually, and the synthetic load torque exerted on
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The dynamic equation of the counterweight side can be expressed as follows: Mw x˙ 1 − k1 (θm R − x1 ) − b1 (θ˙m R − x˙ 1 ) = 0
(1)
Mw g − k1 Δx10 = 0.
(2)
Similarly, the motion equation of the car side can be expressed as follows:
Fig. 1.
Simplified model of the direct-drive elevator traction system.
the traction machine changes during the process. It is worth developing new methods to avoid mechanical noise caused by the large electromagnetic torque variation. In order to achieve more comfortable riding, the torque generated by the traction machine should be a continuous type during elevator start-up. In this paper, based on the analysis of the dynamic characteristics of the gearless traction system during elevator startup, a novel adaptive starting torque compensation strategy is proposed to improve the system robustness and the riding comfort. This paper is organized as follows. First, in order to explore the characteristics of the synthetic load torque exerted on the traction sheave, a dynamic model of the gearless elevator traction system is built in Section II. According to the model characteristics, an adaptive weight-transducerless starting torque compensation strategy based on fuzzy selftuning is proposed in Section III. The compensation strategy is accomplished by self-tuning the current loop reference only based on the feedback information of the Sin–Cos encoder. In Section IV, the control strategy is verified by simulation and experimental results.
II. DYNAMIC M ODEL OF E LEVATOR T RACTION S YSTEM A. Modeling of the Direct-Drive Elevator Traction System The gearless elevator has three major mechanical components: the traction machine, the car, and the counterweight. A simplified schematic including the main components of a direct-drive elevator traction system is shown in Fig. 1. The traction sheave and the brake pulley are installed on the rotor of the permanent-magnet traction machine. An electromagnetic brake is mounted around the brake pulley to hold the traction system still when the elevator operates in standby mode. The equivalent elasticity and the damping of the rope are described as the dotted line areas. The mechanical position of the traction sheave, the counterweight displacement, and the car displacement are presented as θm , x1 , and x2 , respectively.
Mc x˙ 2 − k2 (−θm R − x2 ) − b2 (−θ˙m R − x˙ 2 ) = 0
(3)
Mc g − k2 Δx20 = 0
(4)
where rigidity coefficient of the rope on the car side; k2 damping coefficient of the rope on the car side; b2 mass of the car; Mc Δx20 elongation of the rope on the car side in steady state. Considering the friction torque exerted on the pulley by the brake, the kinematic analysis of the traction sheave can be described by (5)–(7). In particular, Tf and Tsum0 are the friction torques between the brake pulley and the brake, the traction sheave, and the rope, respectively. Tμ is the friction torque caused by other factors of the system Te − Tsum = Jm θ¨m
(5)
where Tsum =
0; Tsum0 − (Tf + Tμ );
Tf + Tμ > Tsum0 (6) otherwise
Tsum0 = R(Mc g − Mw g) + Rk2 (−θm R − x2 ) + Rb2 (−θm R˙ − x˙ 2 ) − Rk1 (θm R − x1 ) + Rb1 (θ˙m R − x˙ 1 )
(7)
where Te
electromagnetic torque generated by the traction machine; total inertia of the traction system; Jm Tsum resultant friction torque exerted on the traction sheave; radius of the brake pulley. Rz In order to analyze the friction torque characteristics, the relationship between the friction force f and the mechanical velocity vm can be expressed as follows: ⎧ if vm = 0 and |Fl | < Fs ⎨ Fl , f = Fs sign(Fl ), (8) if vm = 0 and |Fl | ≥ Fs ⎩ Fc sign(vm ) + σv, if vm = 0 where Fl is the external force, Fc is the Coulomb friction, σ is the coefficient of viscosity, and Fs is the maximum static friction force. When the brake releases completely, according to the friction model in (8), the torque criterion that drives the traction machine from standstill to the rotating state is |Te − Tsum0 | > Fs R.
(9)
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Fig. 2. Force analysis of the traction sheave and the brake sheave.
Moreover, the criterion that makes the traction machine operate from the rotating state to standstill is |Te − Tsum0 | < Fc R.
(10)
It can be concluded that the torque generated by the traction machine to keep the car at standstill is not a fixed value but a variable one within the range of [Tsum0 − Fc R, Tsum0 + Fc R]. B. Analysis of the Brake Releasing Process Fig. 2 shows the dynamic analysis of the traction system. An area element on the interface of the brake pulley and the brake shoe which corresponds to an angular element dγ is selected to be studied, and γ is the wrap angle of the brake. Assume that the pressure exerted by the brake shoe on the area element is dNi (t). During the brake releasing, the deformation of the brake shoes gets smaller, resulting in the decrease of dNi (t). The friction torque of each element is given as dTf = μdNi (t)Rz
(11)
where μ is the friction coefficient between the pulley and the brake. Assuming that the deformation of each element is the same during the brake releasing, which means that the change rate of dNi (t) for each element is the same, it can be expressed as dN (t) = dNi (t),
i = 1, 2, 3 . . . .
(12)
The total friction torque exerted on the brake pulley by the brake shoes can be calculated by integration Tf =
γ dTf = μdN (t)
π+γ
Rz dγ + μdN (t) 0
= μ (2γdN (t)) Rz .
Rz dγ π
(13)
Equation (13) can be rewritten as (14) if 2γdN (t) is replaced by equivalent pressure N (t) Tf = μN (t)Rz .
(14)
When the brake is releasing, the pressure N (t) between the brake pulley and the brake shoe is decreasing, and so is the maximum static friction between them.
Fig. 3.
Simulation block diagram of the direct-drive elevator system.
Ideally, if the electromagnetic torque is equal to the total load torque during the brake releasing, the traction machine will keep still. Then, the torque that the rope exerts on the traction wheel is constant. More specifically, in Fig. 2, Tc and Tw equal Mc gR and Mw gR, respectively. Under this condition, (7) can be changed as Tsum0 = R(Mc g − Mw g).
(15)
However, it is difficult for the traction machine to produce electromagnetic torque to balance the unknown and changing equivalent load torque precisely at zero speed. If the starting torque is not well compensated, the traction machine will slide a distance due to torque unbalance during the brake releasing. The variations of the velocity and the acceleration of the system would cause the change of stretching force on the rope of both sides. The torque that the rope exerts on the traction sheave is given by (7). In order to obtain the characteristics of Tsum during the brake releasing, the electromechanical simulation model of the direct-drive elevator is established as Fig. 3. The brake is modeled as a first-order system based on its characteristics. The parameters of the traction machine model and the elevator mechanical model are listed in the Appendix. Additionally, N0 = 6000 N, μ = 0.6, and R(Mc g − Mw g) = −530 N · m. The ideal or realistic situation is selected through the terminal 1 or 2 correspondingly. In the realistic situation, the conventional vector control strategy is used. Both the speed controller and the current controllers are proportional–integral (PI) regulators. Simulation results are illustrated in Fig. 4. From Fig. 4, it can be seen that Tsum in real condition is smaller than that in ideal condition when the sliding speed is increasing, and the contrary is the case when the sliding speed is decreasing. That means that the sliding speed and the range of the speed variation would keep relatively small if Te tracks Tsum well in the ideal situation. Since the brake releasing time would change due to the brake shoe abrasion and the adjustment of the braking force, the time constant of the brake is changing,
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Fig. 6. Description of the starting torque compensation process.
Fig. 4.
Simulation results of the elevator system.
Fig. 7. Flowchart of the adaptive starting torque compensation.
Fig. 5. Scheme of the adaptive torque compensation during the elevator start-up.
and it is difficult to establish a precise mathematical model to describe the change of Tsum in ideal situation. III. P ROPOSED W EIGHT-T RANSDUCERLESS A DAPTIVE S TARTING T ORQUE C OMPENSATION S TRATEGY A. Starting Torque Compensation Control Strategy of the Traction Machine According to the dynamic analysis of the aforementioned traction machine system, the control scheme of the starting torque compensation for the direct-drive elevator machine is shown in Fig. 5. Moreover, the starting torque compensating principle is described in Fig. 6. A surface-mounted PMSM is used in the traction system, and the vector control method is adopted. The speed reference is set to zero during the brake
releasing at the end of the standby mode. The fuzzy selftuning of the electromagnetic torque change rate kt∗ includes two control modes: fuzzy compensation and friction correcting. A switch judger determines which mode is active based on the sliding distance and sliding speed, and the detailed switch logic is shown in Fig. 7. Once the PI control is enabled, the output of the fuzzy self-tuning kt∗ will be set to zero. Moreover, if the fuzzy self-tuning is active, the output of the speed PI control i∗q1 will keep constant. The discrete mathematical representation of i∗q1 can be described as follows: i∗q1 (k) = Upω (k)+Uiω (k) = kpω e(k)+
Ts e(k) +Uiω (k−1) τiω (16)
where Upω , Uiω , kpω , and τiω are the proportional output, integral output, proportional gain, and integral time constant of the speed PI controller, respectively; Ts is the sampling period; e(k) is the error between the speed reference and feedback; and k denotes the value at time kTs .
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In addition, i∗q2 is the integration of the fuzzy self-tuning output kt∗ , and its mathematical representation is i∗q2 (k) = i∗q2 (k − 1) + kt∗ (k).
(17)
In Fig. 5, i∗q is equal to the sum of i∗q1 and i∗q2 . Since the bandwidth of the current loop is wider than the one of the speed loop, the system can reach balance rapidly if i∗q matches the load torque. In Fig. 6, the solid line denotes the torque Tsum exerted on the traction sheave. Te shown by the dotted line should trace the torque Tsum in order to make the sliding distance as short as possible. At time tp , the brake releases completely, and Te should satisfy the range [Tc − Fc R, Tc + Fc R] to make the traction machine keep standstill, where Tc = (Mc g − Mw g)R. The detailed flowchart of the proposed starting torque compensation is described as Fig. 7, in which ε and Δ denote the threshold of the sliding distance and sliding speed, respectively. The starting torque compensation strategy can be divided into four stages as follows. Stage I [0, t1 ]: The load torque Tsum0 is less than the sum of friction torque Tf and Tμ , and the traction sheave keeps standstill. The machine-generated torque is zero in this stage. Stage II [t1 , t2 ]: Tsum0 is larger than the maximum static friction torque, and the car begins to slide. Since the sliding distance is less than the threshold of the switch judger, the PI controller is active, and the output of the fuzzy self-tuning is zero. As the bandwidth of the speed loop is limited and the output of the PI controller could not track the load torque timely, the sliding speed would increase in this stage. Stage III [t2 , t3 ]: At time t2 , the sliding distance is larger than the threshold ε, and the sliding speed is larger than the threshold Δ. The compensation mode changes from the PI control to the fuzzy compensation. The electromagnetic torque can trace the load toque with the suitable output of the fuzzy compensator. The control mode would switch between the PI control mode and the fuzzy compensation mode several times in this stage due to the speed variation. Because the load torque increases much faster than the output of the PI controller, the sliding speed direction is invariable, and the fuzzy compensation mode takes a dominant role. Since the brake releases completely at time tp , the variation of torque Tsum is very small after time tp . Stage IV [t3 , t4 ]: At time t3 , the sliding speed is less than the threshold Δ, and the PI control mode is active. The sliding speed will decrease to zero at time t4 with the speed PI regulator. If Te satisfies [Tc − Fc R, Tc + Fc R] at time t4 , the sliding friction force would change into static friction force, and Tsum would be equal to Te rapidly. If Te is larger than Tc + Fc R at time t4 , the friction correcting mode would be active, and Te would minus Fc R in case of a reversed sliding distance.
Fig. 8. Simplified block diagram of the fuzzy self-tuning torque compensator.
Fig. 9.
Membership function of e˜, c˜e˜, and u ˜.
B. Design of the Fuzzy Self-Tuning Torque Compensator The fuzzy self-tuning torque compensator is adopted to track the change of the synthetic load torque. Once it is active, a corresponding electromagnetic torque is generated by the traction machine to keep the elevator car slide at a small speed. The structure of the fuzzy self-tuning torque compensator is illustrated in Fig. 8. The fuzzy compensator has two inputs, namely, the sliding speed error ωr and the change of the sliding speed error α. The output of the fuzzy compensator is kt , and the output of the friction correcting mode is Δif . The sum of kt and Δif is kt∗ which represents the change rate of q-axis current reference i∗q . For convenience, the input variables ωr and α are changed into e˜ and c˜e˜ using the scaling factors Ke and Kce , respectively, and the output of the fuzzy controller u ˜ is also processed by the quantification factor Ku to get the crisp value kt . The universes of discourse of the input fuzzy variables, e˜ and c˜e˜, are [−6, −1]U[1, 6] and [−3,3], respectively. The universe of discourse of the output variable u ˜ is [−6, −1]U[1, 6]. The ˜ and U ˜ are divided into six fuzzy universes of discourse of E ˜ is sets, respectively, and the universe of discourse of C˜ E divided into three fuzzy sets. Considering the sensitivity and stability of the fuzzy compensator, the membership functions of the input and output variables are shown in Fig. 9. The change characteristics of Tsum modeled in Section II are considered to design the fuzzy control rules. The control target is to obtain a minimized sliding distance and to avoid the change of sliding direction. Therefore, the increasing rate of Te should become larger to reduce the sliding distance when the sliding speed becomes larger. On the other hand, the increasing
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TABLE I F UZZY C ONTROL RULES
rate of Te should decrease moderately to avoid rotor reversal when the sliding speed becomes smaller. In addition, using the sliding acceleration as an auxiliary judgment to regulate Te can ensure that it can track the load disturbance timely. The fuzzy control rules are shown in Table I. There are 18 rules for the starting torque compensator. The control rule Ri is designed ˜k , then u ˜m , where ˜j and c˜e˜ is C˜ E ˜ is U as follows: If e˜ is E i = 1, 2, · · · , 18, j, m = 1, 2, · · · , 6, and k = 1, 2, 3. The minimum operation is used to get the fuzzy set of the output ˜i ) = min μ(E ˜i ), μ(C˜ E ˜i ) . μ(U (18)
Fig. 10. Relationship of the fuzzy self-tuning torque compensation rules.
For example, if e˜ = 2.5 and c˜e˜ = 0.5, the control rules R11 and R14 are active to calculate the output fuzzy set. According to the control rule R11 , the weighting coefficient of output fuzzy set N S(˜ u) can be obtained μ (N S(˜ u)) = min{μ(P S(˜ e)) , μ (Z(˜ ce˜))} = min{0.5, 1} = 0.5. Based on the control rule R14 , the weighting coefficient of output fuzzy set N M (˜ u) can be obtained μ(N M (˜ u)) = min{μ(P M (˜ e)), μ(Z(˜ ce˜))} = min{0.5,1} = 0.5. The output fuzzy set is the union of N S(˜ u) and N M (˜ u), which can be expressed as 0.5∧ μ (N S(˜ u)) ∨ 0.5∧ μ (N M (˜ u)) . The center average defuzzifier is adopted to transform the output of the fuzzy inference to a crisp value u ˜ in the fuzzy controller ˜ μ(Ui ) · ui u ˜= (19) ˜i ) μ(U where ui is the center of the corresponding fuzzy set, which equals the mean value of the points whose membership is one in the fuzzy set. In this scheme, the centers of N S(˜ u) and N M (˜ u) are −1.5 and −3.5, respectively. The crisp value u ˜ can be calculated as follows: 0.5 × (−1.5) + 0.5 × (−3.5) = −2.5. u ˜= 0.5 + 0.5
Fig. 11. Schematic diagram of the interface board connecting the encoder and the microprocessor.
U[0.02%IN , 0.1%IN ], where IN denotes the rated current. The values of e˜ and c˜e˜ can be obtained ⎧ ωr ∈ [0.024, 0.032] rad/s ⎨ 6, e˜ = 250ωr , ωr ∈ [−0.024, −0.004]U[0.004, 0.024] rad/s ⎩ −6, ωr ∈ [−0.032, −0.024] rad/s ⎧ ⎨ 3, c˜e˜ = 0.05α, ⎩ 3,
(20) α ∈ [60, 80] rad/s2 α ∈ [−60, 60] rad/s2 α ∈ [−80, −60] rad/s2 .
(21)
As a result, the value of kt (k) can be calculated by the output scaling function ˜(k). kt (k) = 0.00016IN u
(22)
C. Signal Processing of the SIN/COS Encoder
The interface board connecting the encoder (ERN1387) and the digital signal processor (DSP) TMS320F2808 is a SIN/COS Based on the aforementioned defuzzification, the relation- encoder feedback card as shown in Fig. 11. The differential ship between the inputs and the output is shown in Fig. 10. signals ±A, ±B, ±C, and ±D from the encoder are processed In the scheme, the ranges of ωr and α in the fuzzy controller by a differential operational circuit, and then, four sinusoidal are [−0.032, −0.004]U[0.004, 0.032] rad/s and [−80, 80] rad/s2 , outputs A, B, C, and D can be got. The signals C and D appear respectively; the range of the output kt is [−0.1%IN , −0.02%IN ] as one sinusoidal or cosine period, respectively, per revolution,
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Fig. 12. Experimental waveforms of the rotor position calculation by using the Sin–Cos encoder (Sin–Cos signals A and B, incremental count, and position subdivision result).
and they can be used to calculate the absolute position. The sinusoidal incremental signals A and B are phase shifted by 90◦ and appear as 2048 periods per revolution. A and B are then processed by a hysteresis comparison circuit, and this circuit produces two 90◦ phase-shifted square-wave pulses QA and QB. In particular, the edges of QA and QB will make the register (its value denotes the incremental count) in the enhanced quadrature encoder pulse (eQEP) count up or down. The position is updated at each pulsewidth modulation (PWM) period (i.e., 100 μs). The rotor position θm can be calculated
2π 2 θm = N + θdiv · (23) M π where N is the incremental count, M is the maximum incremental count value and it equals 8192 for the 2048 P/R Sin–Cos encoder, and θdiv is the subdivision calculated from the quadrature signals by the arc-tangent function. The experimental waveforms of the sinusoidal incremental signals (A and B), the incremental count, and the position subdivision results are shown in Fig. 12. The resolution of the subdivision depends on the precision of the A/D conversion and the signal quality of A and B. IV. S IMULATION AND E XPERIMENTAL R ESULTS A. Simulation Results Simulation and experiment have been executed to compare the proposed starting torque compensation strategy with the traditional PI control. The parameters of the traction machine system used in simulation are given in the Appendix. The whole controller is constructed according to the block diagrams shown in Figs. 5 and 8. The simulation results under 80% rated load are shown in Fig. 13. In Fig. 13(a) and (b), the quadrature signals from the Sin–Cos encoder, the subdivision value, and the incremental count value are shown, respectively. In particular, the unit value of the incremental count denotes a sliding distance of 0.23 mm. Fig. 13(c) shows the comparison of the sliding speed using the proposed method and the conventional PI control. It can be seen that the sliding speed
Fig. 13. Simulation results under 80% rated load. (a) Output of the Sin–Cos encoder with conventional PI control. (b) Output of the Sin–Cos encoder with proposed compensation strategy. (c) Sliding speed comparison. (d) q-axis current response comparison.
with the proposed method is smaller and the system reaches the steady state with a shorter time. Fig. 13(d) shows the q-axis current response with the proposed compensation strategy, the conventional PI control, and the ideal load torque tracking, respectively. From the results, the q-axis current response using the proposed compensation strategy is superior over that of the PI control method. B. Experimental Results The proposed adaptive starting torque compensation method is experimented at an 11.7-kW gearless elevator traction machine without using the weight transducer. The parameters of the permanent-magnet traction machine are listed in the Appendix. A Sin–Cos encoder (ERN1387) with 2048 P/R is installed on the machine. A TMS320F2808 DSP is used to execute all the control algorithms. The PWM frequency of the inverter is 10 kHz. The period of the current loop is 100 μs, and the speed control is activated every 1 ms. The proposed compensation algorithm is executed every 100 μs. In the switch judger, the threshold of the sliding distance ε is 0.06 mm, and the threshold of the sliding speed Δ is 0.004 rad/s. To verify the proposed starting torque compensation strategy, the experimental results of the conventional PI control are shown for comparison. The PI controller parameters are carefully designed as shown in Appendix B to satisfy the zero-speed traction mode. The parameters of current PI controllers are kpi = 37.49 and τii = 1.739 × 10−3 s, and the parameters of the speed controller are kpω = 3.61 and τiω = 0.012. The same PI parameters are used in Fig. 5 to cooperate with the fuzzy self-tuning torque compensation strategy.
WANG et al.: WEIGHT-TRANSDUCERLESS STARTING TORQUE COMPENSATION OF TRACTION MACHINE
Fig. 14. Experimental comparison between (a) conventional PI control and (b) proposed compensation strategy under 20% rated load.
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Fig. 16. Experimental comparison between conventional PI control and proposed compensation strategy under rated load.
Fig. 17. Sliding distance comparison of the two methods under different loads.
Fig. 15. Experimental comparison between (a) conventional PI control and (b) proposed compensation strategy under 60% rated load.
Experimental results using the proposed compensation strategy and the conventional PI control method under different loads are illustrated in Figs. 14–16. In Figs. 14–16, the quadrature signals from the Sin–Cos encoder, the sliding distance, and the q-axis current (expressed by per-unit value) are shown. The sliding distances using the conventional PI control and the proposed method are 1.2 and 0.18 mm in Fig. 14, 4.0 and 0.35 mm in Fig. 15, and 7.2 and 0.65 mm in Fig. 16, respectively. From the results, it can be concluded that the sliding distance becomes much shorter and the sliding speed reaches zero faster when the proposed compensation strategy is adopted. Moreover, the q-axis current response is much faster, particularly at the beginning stage of the sliding process, which means that the machine-generated
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torque tracks the load torque timely, and this causes a relatively small sliding speed. Fig. 17 shows a more visualized sliding distance comparison of the two methods under various loads, which verifies the effectiveness of the proposed method further. V. C ONCLUSION In this paper, an adaptive starting torque compensation method of the gearless traction machine for the direct-drive elevator without using a weight transducer has been proposed. The dynamic analysis of the brake releasing process shows that the synthetic load torque in actual condition is smaller than that in ideal condition when the sliding speed is increasing, and the contrary is the case when the sliding speed is decreasing. The adaptive compensation strategy consists of three modes, including the PI control, the fuzzy compensation, and the friction correcting. The rules of the torque compensator are designed in order to get a shorter sliding distance and avoid sliding direction reversal. The effectiveness of the method is verified both in simulation and experiment. By adopting the compensation strategy, the electromagnetic torque generated by the gearless machine tracks the load torque better during elevator start-up. It performs better at improving the riding comfort of the gearless elevator with a shorter sliding distance. A PPENDIX A TABLE II T RACTION M ACHINE PARAMETERS
Fig. 18.
Block diagram of the traction machine vector control system.
the PWM frequency. The controller’s PI tuning focuses on the zero-speed operation mode, and the sliding speed of the traction machine is very low; ωr can be ignored. 1) PI Tuning of the Current Loop Controller: The transfer function of the controlled plant in the current loop can be expressed as Gobj1 (s) =
kf i k v . (τf i s + 1)(τv s + 1)(Ls s + Rs )
(B1)
The time constant of current filter τf i = 2τv = 0.0002 s. Let km = 1/Rs = 4.3478 and τli = Ls /Rs = 0.0652 s. Since τf i and τv are small enough compared with τli , the two inertia elements can be merged into one, and the equivalent time constant τi = τv + τf i = 0.0003 s. Then, (B1) can be rewritten as Gobj1 (s) =
kf i kv km . (τli s + 1)(τi s + 1)
(B2)
The current loop controller is a PI type Gci (s) =
kpi τii s + 1 . τii s
(B3)
In order to design the current loop as a typical type I system Gik (s) = TABLE III
ka s(τi s + 1)
(B4)
E LEVATOR M ECHANICAL PARAMETERS
the pole with a larger time constant in (B2) should be cancelled by Gci (s), so kpi τii s + 1 = τli s + 1.
(B5)
Then, the condition ka = kf i kv km /τii should be met. In order to obtain the faster response and the minimized overshoot, ka τi = 0.5 is a better choice [19]. The PI parameters of the current controller can be obtained: kpi = 37.49, and τii = 1.739 × 10−3 s. Therefore, the closed-loop transfer function of the current loop is A PPENDIX B The traction machine control system is shown in Fig. 18. Gcω and Gci are the transfer functions of the speed and current loop PI controllers, respectively. The inverter is modeled as an inertia element with time constant τv = 1/fs = 0.0001 s, where fs is
Gli (s) =
kli τli s + 1
(B6)
where kli = 1/kf i = 1 and τli = 1/ka = 2 × 10−4 s.The cutoff frequency of the current loop is 1520 Hz, and the phase margin is 65◦ .
WANG et al.: WEIGHT-TRANSDUCERLESS STARTING TORQUE COMPENSATION OF TRACTION MACHINE
2) PI Tuning of the Speed Loop Controller: The open-loop transfer function of the speed loop is Gobj2 (s) =
kli kf ω Rs τm kΦ s(τli s + 1)(τf ω s + 1)
(B7)
where the electromagnetic time constant τm = JRs / (9.55kΦ kT ) = 0.00274 s, in which kT = NP ψf = 29.13 and J = 4.02 kg · m2 . The time constant of speed filter τf ω = 0.002 s, and the feedback coefficient kf ω = 1. Combine the two inertia elements into one, and the equivalent time constant τh is τh = τf ω + τli = 0.0022 s. Define koω = kli kf ω Rs /(τm kΦ ), and then, koω = 69.2245. Therefore, (B7) can be expressed as Gobj2 (s) =
69.2245 . s(0.0022s + 1)
(B8)
The speed controller is a PI type Gcω (s) =
kpω (τiω s + 1) . τiω s
(B9)
Design the speed loop as a typical type II system, and the open-loop transfer function of the speed loop is expressed as Gnk (s) =
kω (τiω s + 1) s2 (τh s + 1)
(B10)
where kω = koω kpω /τiω . Let h = τiω /τh , and the cutoff frequency can be expressed as ωcω (h + 1) = 2 τiω 2τiω
1 1 = 0.5 + . τiω τh
kω = ωcω
(B11) (B12)
In order to achieve better tracking performance, h should be set in the range of 5–6 [19]. Here, select h = 5, and then τiω = hτh kpω =
(h + 1)τm kΦ . 2hτh kli kf ω Rs
(B13) (B14)
According to the detailed parameters, the PI parameters of the speed controller are τiω = 0.012 and kpω = 3.61. R EFERENCES [1] A. Consoli, G. Scelba, G. Scarcella, and M. Cacciato, “An effective energy-saving scalar control for industrial IPMSM drives,” IEEE Trans. Ind. Electron., vol. 60, no. 9, pp. 3658–3669, Sep. 2013. [2] K. Kamiev, J. Montonen, M. P. Ragavendra, J. Pyrhönen, J. A. Tapia, and M. Niemelä, “Design principles of permanent magnet synchronous machines for parallel hybrid or traction applications,” IEEE Trans. Ind. Electron., vol. 60, no. 11, pp. 4881–4890, Nov. 2013. [3] S. Cicale, L. Albini, F. Parasiliti, and M. Villani, “Design of a permanent magnet synchronous motor with grain oriented electrical steel for directdrive elevators,” in Proc. ICEM, 2012, pp. 1256–1263. [4] E. Jung, H. Yoo, S. K. Sul, H. S. Choi, and Y. Y. Choi, “A nine-phase permanent-magnet motor drive system for an ultrahigh-speed elevator,” IEEE Trans. Ind. Appl., vol. 48, no. 3, pp. 987–995, May/Jun. 2012. [5] L. W. White, S. M. Lukic, and S. Bhattacharya, “Investigations into the minimization of electrical costs for traction-type elevators,” in Proc. ECCE, 2010, pp. 4285–4292.
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[6] J. He, C. Mao, J. Lu, and J. Yang, “Design and implementation of an energy feedback digital device used in elevator,” IEEE Trans. Ind. Electron., vol. 58, no. 10, pp. 4636–4642, Oct. 2011. [7] R. Appunn, B. Riemer, and K. Hameyer, “Contactless power supply for magnetically levitated elevator systems,” in Proc. ICEM, 2012, pp. 600–605. [8] E. Bilbao, P. Barrade, I. Etxeberria-Otadui, A. Rufer, S. Luri, I. Gil, S. Jung, H. Kobayashi, S. Doki, and S. Okuma, “Optimal energy management of an improved elevator with energy storage capacity based on dynamic programming,” in Proc. ECCE, 2012, pp. 3479–3484. [9] X. Wang, Z. Zhang, X. Xu, and Y. Cui, “Influence of using conditions on the performance of PM linear synchronous motor for ropeless elevator,” in Proc. ICEMS, 2011, pp. 1–5. [10] W. Kim, D. Shin, and C. C. Chung, “Microstepping using a disturbance observer and a variable structure controller for permanent-magnet stepper motors,” IEEE Trans. Ind. Electron., vol. 60, no. 7, pp. 2689–2699, Jul. 2013. [11] H. Wang, H. Kong, Z. Man, D. M. Tuan, Z. Cao, and W. Shen, “Sliding mode control for steer-by-wire systems with ac motors in road vehicles,” IEEE Trans. Ind. Electron., vol. 61, no. 3, pp. 1596–1611, Mar. 2014. [12] H. H. Choi and J. W. Jung, “Discrete-time fuzzy speed regulator design for PM synchronous motor,” IEEE Trans. Ind. Electron., vol. 60, no. 2, pp. 600–607, Feb. 2013. [13] I. A. Smadi, H. Omori, and Y. Fujimoto, “Development, analysis, experimental realization of a direct-drive helical motor,” IEEE Trans. Ind. Electron., vol. 59, no. 5, pp. 2208–2216, May 2012. [14] R. Errouissi, M. Ouhrouche, W. H. Chen, and A. M. Trzynadlowski, “Robust cascaded nonlinear predictive control of a permanent magnet synchronous motor with antiwindup compensator,” IEEE Trans. Ind. Electron., vol. 59, no. 8, pp. 3078–3088, Aug. 2012. [15] N. T. T. Vu, D. Y. Yu, H. H. Choi, and J. W. Jung, “T-S fuzzy-modelbased sliding-mode control for surface-mounted permanent-magnet synchronous motors considering uncertainties,” IEEE Trans. Ind. Electron., vol. 60, no. 10, pp. 4281–4291, Oct. 2013. [16] X. Hong, Z. Deng, S. Wang, L. Huang, W. Li, and Z. Lu, “A novel elevator load torque identification method based on friction model,” in Proc. 25th Annu. IEEE APEC, 2010, pp. 2021–2024. [17] S. Bolognani, A. Faggion, L. Sgarbossa, and L. Peretti, “Modelling and design of a direct-drive lift control with rope elasticity and estimation of starting torque,” in Proc. 33rd Annu. IEEE IECON, 2007, pp. 828–832. [18] G. Wang, G. Zhang, R. Yang, and D. Xu, “Robust low-cost control scheme of direct-drive gearless traction machine for elevators without a weight transducer,” IEEE Trans. Ind. Appl., vol. 48, no. 3, pp. 996–1005, May/Jun. 2012. [19] B. C. Kuo, Automatic Control Systems., 8th ed. Englewood Cliffs, NJ, USA: Prentice-Hall, 2002.
Gaolin Wang (M’13) received the B.S., M.S., and Ph.D. degrees in electrical engineering from Harbin Institute of Technology, Harbin, China, in 2002, 2004, and 2008, respectively. In 2009, he joined the Department of Electrical Engineering, Harbin Institute of Technology, as a Lecturer, where he has been an Associate Professor of Electrical Engineering since 2012. From 2009 to 2012, he was a Postdoctoral Fellow with Shanghai STEP Electric Corporation, Shanghai, China. He has authored more than 30 technical papers published in journals and conference proceedings. He is the holder of seven Chinese patents. His current major research interests include permanent-magnet synchronous motor drives, high-performance direct drives for traction systems, position sensorless control of ac motors, and efficiency optimization control of the interior permanent-magnet synchronous machine.
Jin Xu received the B.S. degree in electrical engineering from Harbin Institute of Technology, Harbin, China, in 2013, where he is currently working toward the M.S. degree in power electronics and electrical drives in the School of Electrical Engineering and Automation. His current research interests are in direct-drive permanent-magnet synchronous motor control and position sensorless control.
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Tielian Li received the B.S. degree in electrical engineering from Harbin Engineering University, Harbin, China, in 2012. He is currently working toward the M.S. degree in power electronics and electrical drives in the School of Electrical Engineering and Automation, Harbin Institute of Technology, Harbin. His current research interests are in highperformance direct drives for permanent-magnet traction systems and position sensorless control.
Guoqiang Zhang received the B.S. degree in electrical engineering from Harbin Engineering University, Harbin, China, in 2011 and the M.S. degree in electrical engineering from Harbin Institute of Technology, Harbin, in 2013, where he is currently wording toward the Ph.D. degree in power electronics and electrical drives in the School of Electrical Engineering and Automation. His current research interests are in permanentmagnet synchronous motor drives and position sensorless control.
Hanlin Zhan received the B.S. degree in electrical engineering from Harbin Institute of Technology, Harbin, China, in 2012, where he is currently working toward the M.S. degree in power electronics and electrical drives in the School of Electrical Engineering and Automation. His current research interests are in permanentmagnet synchronous motor drives and parameter identification techniques.
Li Ding received the B.S. degree in electrical engineering from Shanghai University, Shanghai, China, in 2013. He is currently working toward the M.S. degree in power electronics and electrical drives in the School of Electrical Engineering and Automation, Harbin Institute of Technology, Harbin, China. His current research interests are in permanentmagnet synchronous motor drives and position sensorless control.
Dianguo Xu (M’97–SM’12) received the B.S. degree in control engineering from Harbin Engineering University, Harbin, China, in 1982 and the M.S. and Ph.D. degrees in electrical engineering from Harbin Institute of Technology (HIT), Harbin, in 1984 and 1989, respectively. In 1984, he joined the Department of Electrical Engineering, HIT, as an Assistant Professor. Since 1994, he has been a Professor in the Department of Electrical Engineering, HIT. He was the Dean of the School of Electrical Engineering and Automation, HIT, from 2000 to 2010. He is currently the Assistant President of HIT. His research interests include renewable energy generation technology, power quality mitigation, sensorless vector-controlled motor drives, and high-performance servo systems. He has published over 600 technical papers. Dr. Xu is an Associate Editor for the IEEE T RANSACTIONS ON I NDUS TRIAL E LECTRONICS . He serves as the Chairman of the IEEE Harbin Section.
