Model Identification of Hydrostatic Center Frame Control System ...
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Model Identification of Hydrostatic Center Frame Control System based on MATLAB Zhongwen Wang, Ruizhen Duan and Xiaoqiu Xu Rongcheng College of Harbin University of Science and Technology Rongcheng, Shandong Province, China
Abstract—The composition and principle of an electrohydraulic servo oil film stiffness control system of hydrostatic center frame will be introduced, and the system model identification as well as the verification will be carried out based on semi-physical simulation environment of Real-time Workshop (RTW) and system identification toolbox in MATLAB. A control strategy of fuzzy sliding model variable structure will be presented , and it is applied in the model achieved by identifications, adopting the method of fuzzy control system approximating equivalent control and designing switching controller based on fuzzy control gain dynamic regulation, could inhabit the buffeting existing in sliding model variable structure control. Simulation results show that performance of an electrohydraulic servo oil film stiffness control system is improved significantly for hydrostatic center frame based on fuzzy sliding model variable structure controller, which can’t only effectively inhabit buffeting, reduce steady-state error, but also has strong robustness for uncertainties of structure parameter. Index Terms—hydrostatic center frame; electro-hydraulic servo system; oil film stiffness; model identification; sliding model variable structure; semi-physical simulation
I. INTRODUCTION As the key component for heavy NC horizontal boring lathe, hydrostatic center frame was used for supporting heavy or extra heavy long thin shaft type and rotor type work pieces, whose performance had a direct effect on the machining quality and operation efficiency of heavy NC horizontal boring lathe [1-4]. With the continuous improvement for machining accuracy and efficiency of a heavy NC machine tool, improving the stiffness of hydrostatic center frame was very important and urgent. Oil film thickness was a key influencing factor of oil film stiffness; therefore this thesis adopted reasonable oil supply control system for improving the ability which oil film thickness could adapt it to the changes of external conditions. This method could make hydrostatic center frame be of regulating oil film thickness, and attain the objective of improving stiffness and steady state of hydrostatic center frame. Currently, oil film thickness control system of hydrostatic center frame adopted open-loop control; proportional pump supplied constant flow pressure oil for the oil chamber of a bearing block by oil separators. Oil film thickness changed continuously resulting from
© 2013 ACADEMY PUBLISHER doi:10.4304/jnw.8.6.1322-1328
external load, cutting force, thermal effect, surface roughness, which could make oil film thickness deviate from the optimal value, reduce the stiffness of hydrostatic center frame, and have an impact on the mechanical precision and quality of a machine tool. In recent years, research for active control system in hydrostatic center frame had been new development and research directions, and electro-hydraulic servo control technology was widely used in a variety of CNC machining equipments because of its fast response speed and high control precision, strong anti-jamming capability, etc. However, electro-hydraulic servo system was a typical nonlinear system, there were uncertainties, time variation, outside interference and cross-coupling interference, so anti-interference ability of the system was poor, and the overshoot was large [5-8]. So this paper carries on an active control research for hydrostatic center frame based on oil film bearing mechanism and electro-hydraulic servo control technology, proposes a complex control algorithm of sliding mode variable structure based on fuzzy control ,which combines fuzzy control and sliding mode variable structure to form a composite control for electrohydraulic servo control system of hydrostatic center frame oil film, in which the sliding mode control is used to overcome imprecision and disturbance of the system model, and fuzzy systems is designed taking switching function and its change rate as the input variables, which makes the equivalent controller design not depend on system mathematical model, dynamic adjustment control gain of fuzzy system could weaken the buffeting, and give full play to both advantages . The research results which are of innovation and significance are summarized as follows: Firstly, build the mathematics model of an active control system in hydrostatic center frame; Secondly, carry on model identification for oil film control of two-channel electro-hydraulic servo system; Thirdly, design the fuzzy sliding model variable structure controller for active control system in hydrostatic center frame. Finally, carry on simulation and analysis. Simulation results show that this method coordinates the conflict between chattering reduction and high steadystate precision, maintaining the resisting disturbance of sliding mode control ,and the system is of better dynamic characteristic and steady-state performance compared with conventional sliding mode variable structure control,
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which is fit for effective control of active control system of hydrostatic center frame. II. PROPOSED SCHEME There were two electro-hydraulic position servo synchronous control subsystems in oil film control system of hydrostatic center frame ,and each subsystem separately had electro-hydraulic servo valve, hydraulic cylinder with two rods, displacement sensor, variable, servo amplifier as well as other accessories, etc. Hydraulic pump station and data collection as well as computer control system were shared by two subsystems. Shaft type machining work pieces installed on spindle and bearing block was connected by hydrostatic oil film of oil chamber, separate hydraulic pump supply oil for a controllable oil chamber and the flow of each oil chamber were equal. Hydrostatic oil film gap was formed between a work piece and a bearing block, which was of higher stiffness; the oil film played the role including bearing and rotation lubrication. when a work piece produced deformation or vibration because of external load and bearing block produced displacement, and because of force deformation or thermal wedge disturbance, eddy measures oil film thickness changed, and gave the feedback to computer, completed control algorithm, produced control signal, control current signal of electro-hydraulic servo valve was regulated by power amplifier, driving hydraulic cylinder moved according to requirements to regulate swashplate angle of variable pump, automatic regulation of variable pump flow could meet the flow changes needs of variable control oil chamber in real time, which ensured that oil film gap kept invariant under the best condition, and achieved automatic regulation of oil film thickness, working principal of hydrostatic center frame was shown as Fig. 1. Active control system of hydrostatic center frame was composed by electro-hydraulic position power mechanism with two-way valve controlled cylinder as well as variable pump, etc. The overall system performance largely depended on the characteristic of electro-hydraulic position servo mechanism. According to hydraulic control theory, we could conduct mathematical model of electro-hydraulic position servo system with single channel, simplified transfer function was as: Ka Kv Kq K f (1) G= 2 2ζ k s s 2 2ζ v s( 2 + s + 1)( 2 + s + 1)
ωk ωk ωv ωv where K a was proportional gain of a servo amplifier, K v was flow gain of hydraulic servo value, K q was flow gain
of
hydraulic
servo
cylinder; K f
was
voltage-
displacement proportional component of displacement sensor; ωk was natural frequency of hydraulic cylinder; ζ k was damping ratio of hydraulic cylinder; ωv was natural frequency of electro-hydraulic servo value; ζ v was damping ratio of servo value. © 2013 ACADEMY PUBLISHER
P0
shaft part
h
P1
bearing block
displacement transducer
hydraulic cylinder
U0
P2 variable pump
Uf amplifer
Q2
Q1
Ps
Electro-hydraulic servo valve
Figure 1. Controllable oil chamber diagram of hydrostatic center frame
The relationship of hydraulic cylinder and pump swash plate angle was expressed as: X P ( s )= R ⋅ θ（） s (2) where R was rotation radius of swash plate. Flow equation of variable pump could be expressed as without considering leakage (3) Q( s ) = nK BQθ ( s ) where n
was motor speed; K BQ was discharge
coefficient. Transfer function of variable pump flow and hydraulic cylinder displacement synthesizing (2) and (3). θ ( s ) Q( s ) nK BQ Q( s) (4) Gb ( s ) = = ⋅ = X p ( s) X p (s) θ (s) R III. MODEL VERIFICATION BASED ON MATLAB Mathematical model of electro-hydraulic servo control single-channel system of hydrostatic center frame oil film was of explicit model structure and order, but model parameters was time-variant and uncertain, model identification was based on servo system test and achieved the measured input and output data, the necessary data processing and computing were added, this was a process eliminating the mathematical model equal to measured system [9-10]. We could introduce the collected input and output data using system identification toolbox of MATLAB, the collected input and output data set was carried on filter , averaging and removing trend as well as other pretreatments,we could achieve input and output data
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[11-12]. Pretreated input and output data set was divided into generating model segment and verifying the model segment, where one part was used for model identification of working data and the other part was used for validation data, then generating model segment data was input into identification algorithm,mathematical model was achieved after identifications. Identification model was adopted ARX model and state space model, two-channel open-loop transfer function through transformation arrangement was as: 5.07 s + 6054 G1 ( s ) = 3 s + 22.3s 2 + 5650 s (5) 4.57 s + 5725 G ( s ) = 2 s3 + 22.5s 2 + 5453s Correctness of open-loop transfer function achieved by identification need verification [13-15]. In order to verify the accurate degree of the model identification, we designed the PID position closed loop control system in off-line condition, the simulation program was showed as Fig.4. The position-type digital PID algorithm of the controller was as follows: k
u (k= ) K p e(k ) + K i ∑ e( j ) + K d [e(k ) − e(k − 1)]
(b) Figure 3. Validation of identification model sine response
a) was the model identification test comparison of first channel) was the model identification test comparison of second channel, curve 1 stood for the output of identification model, curve 2 stood for the output of identification experiment, output curve of identification model and output curve of identification experiment fit well according to Fig. 3, variable experiments under different conditions all illustrated the credibility of identification model.
(6)
j =0
IV. CONTROL STRATEGY
The hardware-in-the-loop of the PID controller was carried out under the on-line simulation environment, which was showed in Fig. 2. Given the same sine wave signals, we recorded the identification model and the experimental test response curves respectively. The result was shown in Fig.3. The response curves were almost coincident, showing that the identification model and the identification method were right.
Figure 2. Program graph of hardware-in-the-loop simulation
(a)
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A. Fuzzy Sliding Model Variable Structure Control The article gave a fuzzy sliding model complex control strategy integrating sliding model control theory and fuzzy control theory, which could inhibit the buffeting of sliding model variable structure system effectively, guarantee stability of system and extend the application further. The design of sliding model variable structure controller mainly included two problems. Firstly, we chose the switching function s ( x) , designed the switching surface, and kept the sliding motion under the condition of good stability and dynamic quality. Then, we determined the control law u ± ( x) , which satisfied the reachable condition of the sliding model motions and made sliding model bund on the switching surface. If the design of the switching function s ( x) and the control law u ± ( x) were finished, the sliding model control system would be established completely. The electro-hydraulic servo system of oil film control of hydrostatic center frame used an adjustable gain sliding model control. In order to decrease the effect of the buffeting on the accuracy and the stability of the system control, we used the fuzzy system to adjust sliding model gain system on line adaptively, which ensured the quick response of the system, decreased buffeting effectively, soften the control signal, this could achieve robust stability of variation range of inertial parameters and external disturbance, and assured the accuracy of the tracking performance. The fuzzy sliding model variable structure control of oil film control system of hydrostatic center frame was shown as Fig. 4.
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u
vs
u
electro-hydraulic position servo system
-
product
+
eq
fuzzy sliding model control variable
e
d
u
removing fuzzy
x
fuzzy
switching function
d / dt
s
fuzzy control rule
fuzzy
d / dt d / dt
removing fuzzy
fuzzy control rule
s
x
Figure 4. Structure principle diagram of fuzzy sliding control system
B. Fuzzy Sliding Mode Controller Using the fuzzy system to approach the equivalent control, the fuzzy sliding model controller based on the equivalent control was established. At first, we transferred the control object from tracking error e to sliding model function s .Then, when the controlled system was more than second order ,the control input in ordinary controller should be expressed as e, e, , e( n −1) , which was multi-dimensional expression. But in the fuzzy sliding model controller, it could be expressed as ( s, s) , which was always two-dimensional. That decreased the number of the fuzzy rules and simplified the structure of fuzzy control system. In the fuzzy system of equivalent control, we took s and s as the input, and quantized them though the factor of quantization K s and K s′ .The fuzzy set of s and
{ NB, NM , NS , Z 0, PS , PM , PB} universe of discourse was {−3, −2, −1, 0,1, 2,3} . s
was
,
the
We defined the fuzzy set of the output ueq as { NL, NB, NM , NS , Z 0, PS , PM , PB, PL} , the universe of discourse as {−0.8, −0.6, −0.4, −0.2, 0, 0.2, 0.4, 0.6, 0.8} . The design rule of the fuzzy control law was that: if s and s were large positive values, ss was also large positive value. In order to get the rapid decrease of ss ,it was necessary to control the input in a various large positive range .When ss was negative, the system was under the expected working condition and the control various is 0.If s and s were large negative value, ss was large positive value, it was necessary to control the input in a various large negative to get rapid decrease of ss ,the control rule was shown as Table I. TABLE I. THE FUZZY MODEL OF EQUIVALENT CONTROL
s NB NM NS ZO
s NB NL NL NB NM
NM NL NL NM NS
NS NB NB NM NS
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ZO NM NS NS ZO
PS NS ZO ZO PS
PM NS ZO PS PM
PB ZO ZO PS PM
PS PM PB
NS NS ZO
ZO NS ZO
ZO ZO PS
PS PS PM
PM PM PB
PB PB PB
PB PB PL
All the control rules were designed according to ss , so the control system of fuzzy sliding model was stable. At last, the fuzzy output was quantized exactly though Product inference engine, Gaussian fuzzifier and center average defuzzifier. C. Design of switching controller The product between switching function and derivative ss was taken as the input variable and the control gain k as the output variable in the fuzzy system with the control gain adjustment. The input ss was quantized though the factor of quantization K ss , and the output k was quantized by the factor of proportionality K k . We defined the input of fuzzy controller ss and the fuzzy set of language value of k as { NB, NM , NS , ZO, PS , PM , PB} , the universe of discourse as {−3, −2, −1, 0,1, 2,3} . The fuzzy rule should satisfy the existence and the accessibility requirement, it needed not only ensure the rapidity that the moving point approaches the switching surface, but also decreased the effect of buffeting .we took the large gain value when far from the sliding model surface, similarly took the lower value when near the surface. The fuzzy control rule of control gain k was shown as table II. ss k
TABLE II. FUZZY RULE TABLE OF CONTROL GAIN NB NM NS ZO PS PM
PB
NB
PB
NM
NS
ZO
PS
PM
V. SIMULATIONS The simulation was an important method of analyzing and studying the system, we could verify the correctness of theoretical analysis and design, simulate the operation process of an actual system, analyze the variety law between system characteristics and parameters, describe the state and characteristics, explore whether the design
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equivalent fuzzy sliding controller 1
Set value Fuzzy gain switching controller 1
Controlled object of main channel
Display Equivalent fuzzy sliding controller 1
fuzzy gain switching controller 1
Controlled object of synchronous channel
Figure 5. MATLAB/ Simulink simulation model
result could meet a design requirement or not, and study whether the control method would improve and increase the system or not [16-17]. Consequently, the simulation was as important as an experiment, and which could avoid complexities resulting from the actual experiment, and completed the simulations that could not be realized by an experiment, which could visually analyze the dynamic performance and steady state performance quickly. This thesis realized the modeling and simulation of hydrostatic center frame control system based on software MATLAB. A. Simulation Model Oil film control electro-hydraulic servo system of hydrostatic center frame was of nonlinear, and its uncertainty of parameters as well as outside disturbance, etc. A lot of parameters changed with working condition and temperature, that was main parameters of oil film control electro-hydraulic servo system of hydrostatic center frame might be uncertain, so we adopted model identification value to replace these parameters, and designed the system control target. When lots of uncertainties existed in system parameters, system output signal y tracked desired signal r. According to basic principle of oil film control of hydrostatic center frame, we used fuzzy sliding model control based on control gain fuzzy control to build MATLAB/ Simulink simulation model with two-channel under MATLAB7.4, and the simulation model were shown as Fig.5.B Simulation results analysis According to pole assignment and parameters uncertainty ranges of identification model in oil film control system as well as existence and accessibility of sliding model ,we set switching parameter of sliding model as = C1 8000, = C2 900 ,in equivalent fuzzy controller, quantization factors of variable s were K s = 0.0005 , K 's = 0.00001 ,scale factor of output
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control variable ueq was K u = 25 ;gain regulating fuzzy controller, quantization factor of variable ss was K ss = 0.0000005 ,scale factor of control gain k was K k = 1.7 .For oil film control electro-hydraulic position servo system of hydrostatic center frame with twochannel, traditional PID control and fuzzy sliding variable structure control with constant gain control as well as fuzzy sliding variable structure control with fuzzy regulating gain control were implemented, then simulations were carried out, unit was input as instruction signal, at the same time, disturbance signal y = 0.1sin 2π t mm was implemented under latter two conditions .simulation results were shown from Fig 6 to Fig 8. Where, a) was step response diagram of oil film thickness, curve 1 stood for input signal, curve 2 and 3 were respectively path curve of oil film thickness in oil chamber located in the first channel and second channel) was track error diagram, curve 1 and 2 were respectively track error path curve of oil film thickness in oil chamber located in the first channel and second channel.
a)
Step response curve of oil film thickness
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b) Track error curve of oil film thickness
b) Track error curve of oil film thickness
Figure 6. Oil film depth step responses curve of classical PID control
Figure 8. Oil film depth step responses curve of fuzzy-regulating gain FSM control
It was known from Fig. 6, under noninterference, oil film control system of hydrostatic center frame achieved track of oil film thickness for unit-step response within 1.7s, at the same time. Slight oscillation appeared and steady-state performance was not very good, but basically kept better control precision.
a) Step response curve of oil film thickness
a)
Track error curve of oil film thickness
Figure 7. Oil film depth step responses curve of constant gain FSM control
a) Step response curve of oil film thickness
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It was known from Fig.7 and Fig.8,when adopting fuzzy sliding variable structure control with constant gain control, because we chose bigger control gain value(k=50), system response speed was fast, for unitstep response, complete track of oil film thickness was implemented within 0.5s, but accompanying with bigger buffeting ,steady-state performance of system was poor. when adopting fuzzy sliding variable structure control with fuzzy regulating gain control ,fuzzy regulation was chosen to carry on online controlling switching gain, control gain eliminates interference term of control system as far as possible under sliding model reaching, at the same time, response speed of oil film control system was also fast, complete track of oil film thickness was implemented within 0.5s for unit-step response, and buffeting greatly reduced, which was beneficial to improvement of system steady-state accuracy in oil film control electro-hydraulic position servo system of hydrostatic center frame. According to simulation results, fuzzy sliding model variable structure control strategy was of faster response speed, short regulation time and excellent steady-state performance compared with traditional PID control, steady position sliding output was still achieved when system was subject to disturbance and parameter changes, which reduced steady state error. Therefore, this strategy was fit for electro-hydraulic servo control system of oil film in hydrostatic center frame considering dynamic performance, and it could achieve excellent control characteristic, which was of strong application value. VI. CONCLUSION This paper brought a scheme about electro-hydraulic servo active control of hydrostatic center frame, and control flow adopting controllable oil chamber with multi-channel, improved oil film stiffness of hydrostatic center frame. Model identification and verification were carried on for electro-hydraulic position servo system; we designed controller taking transfer function achieved by identification and carried on simulation by Simulink. Simulation results showed that the controller could not only effectively inhabit buffeting and reduce steady-state error, but also had strong robustness for the structure parameter uncertainty.
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ACKNOWLEDGMENTS This work was supported by Science Technology Item of Heilongjiang Provincial Education Department (No. 12521125) and Youth Foundation of Harbin University of Science and Technology (No. P20110067)
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[15]
REFERENCES [1] Jiang Gui Yun. Study on design theory for hybrid Bearings based on hydraulic servo control. Chongqing: Chongqing University, 2009:11-152. [2] Han Gui Hua Research on Hydrostatic Thrust Bearing Oil Film Control of Heavy NC Lathe, harbin: Harbin University of Science and Technology, 2009. [3] Shao Junpeng, Yang Xiaodong, Zhou Limin. Numerical Simulation of Integrated Deformation of Heavy Hydrostatic Thrust Bearing and Experimental Research. 2009 International Conference on Intelligent HumanMachine Systems and Cybernetics, Hangzhou, Zhejiang, China, 2009:45-48. [4] Shao J. P, Li H. M. Study on Flow ability of the Gap Oil Film of the Multi-oil Pad Hydrostatic Bearing with Variable Viscosity. IEEE Computer Society. 2009International Conference on Intelligent HumanMachine Systems and Cybernetics, HangZhou, 2009:15-18. [5] WANG Zhan-Linn. Modern electricity hydraulic servo control . Beijing: Beijing University of Aeronautics Astronautics Press, 2005. [6] LI Hong-ren. Hydraulic control system .Beijing: National Defense Industry Press, 1981. [7] WU Bo. Research on flight simulator motion platform control system based on quantitative feedback theory .Harbin:Harbin Institute of Industry,2007. [8] Jianying Li,Junpeng Shao, Zhongwen Wang and Guihua Han. Study of the electro-hydraulic load simulator based on double servo valve concurrent control. Proceedings of 9th International Conference on Electronic Measurement and Instruments ICEMI2009, Beijing, China, 2009 36993795. [9] SHAO Jun-peng, WANG Zhong-wen, LI Jian-ying, et al. Rule Self-tuning Fuzzy-PID Controller of Electrohydraulic Position servo system . Journal of Central South University: Science and Technology, 2010, 41(3): 960-965. [10] Zhongwen Wang,Junpeng Shao,Jianying Lin and Guihua Han. Research on Controller Design and Simulation of Electro-hydraulic Servo System. ICMA2009. Changchun, China, 2009 380-385. [11] HAN Gui-hua, CHEN Li-hua, SHAO Jun-peng. Study of fuzzy PID controller for industrial steam turbine governing system//ISCIT 2005—International Symposium on Communications and Information Technologies 2005, Proceedings. Beijing, 2005: 1228-1232. [12] XUE Ding-yu, CHEN Yang-quan. System simulink and application based on MATLAB/Simulink. Beijing: Tsinghua University Press, 2002: 404−416. [13] SHAO Jun-peng, WANG Zhong-wen, LI Jian-ying, et al Model Identification and Nonlinear Control of Electro-
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hydraulic Position Servo System. Mechanical Science and Technology for Aerospace Engineering, 2010,29(4) 488492. Sihai Zheng, Layuan Li, Yong Li,A QoS Routing Protocol for Mobile Ad Hoc Networks Based on Multipath, Journal of Networks, Vol. 7, No. 4, pp.691-698, 2012 Shoujia Wang, Wenhui Li, Ying Wang, Yuanyuan Jiang, Shan Jiang, Ruilin Zhao,An Improved Difference of Gaussian Filter in Face Recognition, Journal of Multimedia, Vol. 7, No. 6, pp.429-433, 2012 Tao Gao, Ping Wang, Chengshan Wang, Zhenjing Yao, Feature Particles Tracking for Moving Objects, Journal of Multimedia, Vol. 7, No. 6, pp. 408-414, 2012 N.El RAchkidy, A.Guitton, M. Misson, ”Pivot Routing Improves Wireless Sensor Networks Performance” Journal of Networks, Vol. 7, pp. 962-71, June 2012.
Zhongwen Wang, was born in Anhui province of China in August 15th, 1979, Doctor of Engineering, graduated from Harbin University of Science and Technology in April 2011 and majored in mechanical, manufacturing and automation ; he mainly researched in hydrostatic bearing, numerical control technology and electro-hydraulic servo control. He worked as an assistant in Harbin University of Science and Technology from July in 2003 to July in 2005,and he has worked as a professional teacher in Rongcheng College of Harbin University of Science and Technology since 2011. Ruizhen Duan, was born in Nei Monggol, China in October 23th, 1981, Master of Engineering, graduated from Harbin University of Science and Technology in April 2008 and majored in control theory and control engineering; she mainly researched in automatic control theory and industrial process control. She worked as an engineer in Huawei Technologies Co., Ltd. from April in 2008 to June in 2010, and she has worked as a professional teacher in Rongcheng College of Harbin University of Science and Technology since 2010. Xiaoqiu Xu, who was born in Heilongjiang province of China in May 29th, 1986, Master of Engineering, graduated from Harbin University of Science and Technology in April 2012 and majored in mechanical and electronic engineering; she mainly researched in hydrostatic bearing and numerical control technology. She has worked as a professional teacher in Rongcheng College of Harbin University of Science and Technology since 2012.
JOURNAL OF NETWORKS, VOL. 8, NO. 6, JUNE 2013
Model Identification of Hydrostatic Center Frame Control System based on MATLAB Zhongwen Wang, Ruizhen Duan and Xiaoqiu Xu Rongcheng College of Harbin University of Science and Technology Rongcheng, Shandong Province, China
Abstract—The composition and principle of an electrohydraulic servo oil film stiffness control system of hydrostatic center frame will be introduced, and the system model identification as well as the verification will be carried out based on semi-physical simulation environment of Real-time Workshop (RTW) and system identification toolbox in MATLAB. A control strategy of fuzzy sliding model variable structure will be presented , and it is applied in the model achieved by identifications, adopting the method of fuzzy control system approximating equivalent control and designing switching controller based on fuzzy control gain dynamic regulation, could inhabit the buffeting existing in sliding model variable structure control. Simulation results show that performance of an electrohydraulic servo oil film stiffness control system is improved significantly for hydrostatic center frame based on fuzzy sliding model variable structure controller, which can’t only effectively inhabit buffeting, reduce steady-state error, but also has strong robustness for uncertainties of structure parameter. Index Terms—hydrostatic center frame; electro-hydraulic servo system; oil film stiffness; model identification; sliding model variable structure; semi-physical simulation
I. INTRODUCTION As the key component for heavy NC horizontal boring lathe, hydrostatic center frame was used for supporting heavy or extra heavy long thin shaft type and rotor type work pieces, whose performance had a direct effect on the machining quality and operation efficiency of heavy NC horizontal boring lathe [1-4]. With the continuous improvement for machining accuracy and efficiency of a heavy NC machine tool, improving the stiffness of hydrostatic center frame was very important and urgent. Oil film thickness was a key influencing factor of oil film stiffness; therefore this thesis adopted reasonable oil supply control system for improving the ability which oil film thickness could adapt it to the changes of external conditions. This method could make hydrostatic center frame be of regulating oil film thickness, and attain the objective of improving stiffness and steady state of hydrostatic center frame. Currently, oil film thickness control system of hydrostatic center frame adopted open-loop control; proportional pump supplied constant flow pressure oil for the oil chamber of a bearing block by oil separators. Oil film thickness changed continuously resulting from
© 2013 ACADEMY PUBLISHER doi:10.4304/jnw.8.6.1322-1328
external load, cutting force, thermal effect, surface roughness, which could make oil film thickness deviate from the optimal value, reduce the stiffness of hydrostatic center frame, and have an impact on the mechanical precision and quality of a machine tool. In recent years, research for active control system in hydrostatic center frame had been new development and research directions, and electro-hydraulic servo control technology was widely used in a variety of CNC machining equipments because of its fast response speed and high control precision, strong anti-jamming capability, etc. However, electro-hydraulic servo system was a typical nonlinear system, there were uncertainties, time variation, outside interference and cross-coupling interference, so anti-interference ability of the system was poor, and the overshoot was large [5-8]. So this paper carries on an active control research for hydrostatic center frame based on oil film bearing mechanism and electro-hydraulic servo control technology, proposes a complex control algorithm of sliding mode variable structure based on fuzzy control ,which combines fuzzy control and sliding mode variable structure to form a composite control for electrohydraulic servo control system of hydrostatic center frame oil film, in which the sliding mode control is used to overcome imprecision and disturbance of the system model, and fuzzy systems is designed taking switching function and its change rate as the input variables, which makes the equivalent controller design not depend on system mathematical model, dynamic adjustment control gain of fuzzy system could weaken the buffeting, and give full play to both advantages . The research results which are of innovation and significance are summarized as follows: Firstly, build the mathematics model of an active control system in hydrostatic center frame; Secondly, carry on model identification for oil film control of two-channel electro-hydraulic servo system; Thirdly, design the fuzzy sliding model variable structure controller for active control system in hydrostatic center frame. Finally, carry on simulation and analysis. Simulation results show that this method coordinates the conflict between chattering reduction and high steadystate precision, maintaining the resisting disturbance of sliding mode control ,and the system is of better dynamic characteristic and steady-state performance compared with conventional sliding mode variable structure control,
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which is fit for effective control of active control system of hydrostatic center frame. II. PROPOSED SCHEME There were two electro-hydraulic position servo synchronous control subsystems in oil film control system of hydrostatic center frame ,and each subsystem separately had electro-hydraulic servo valve, hydraulic cylinder with two rods, displacement sensor, variable, servo amplifier as well as other accessories, etc. Hydraulic pump station and data collection as well as computer control system were shared by two subsystems. Shaft type machining work pieces installed on spindle and bearing block was connected by hydrostatic oil film of oil chamber, separate hydraulic pump supply oil for a controllable oil chamber and the flow of each oil chamber were equal. Hydrostatic oil film gap was formed between a work piece and a bearing block, which was of higher stiffness; the oil film played the role including bearing and rotation lubrication. when a work piece produced deformation or vibration because of external load and bearing block produced displacement, and because of force deformation or thermal wedge disturbance, eddy measures oil film thickness changed, and gave the feedback to computer, completed control algorithm, produced control signal, control current signal of electro-hydraulic servo valve was regulated by power amplifier, driving hydraulic cylinder moved according to requirements to regulate swashplate angle of variable pump, automatic regulation of variable pump flow could meet the flow changes needs of variable control oil chamber in real time, which ensured that oil film gap kept invariant under the best condition, and achieved automatic regulation of oil film thickness, working principal of hydrostatic center frame was shown as Fig. 1. Active control system of hydrostatic center frame was composed by electro-hydraulic position power mechanism with two-way valve controlled cylinder as well as variable pump, etc. The overall system performance largely depended on the characteristic of electro-hydraulic position servo mechanism. According to hydraulic control theory, we could conduct mathematical model of electro-hydraulic position servo system with single channel, simplified transfer function was as: Ka Kv Kq K f (1) G= 2 2ζ k s s 2 2ζ v s( 2 + s + 1)( 2 + s + 1)
ωk ωk ωv ωv where K a was proportional gain of a servo amplifier, K v was flow gain of hydraulic servo value, K q was flow gain
of
hydraulic
servo
cylinder; K f
was
voltage-
displacement proportional component of displacement sensor; ωk was natural frequency of hydraulic cylinder; ζ k was damping ratio of hydraulic cylinder; ωv was natural frequency of electro-hydraulic servo value; ζ v was damping ratio of servo value. © 2013 ACADEMY PUBLISHER
P0
shaft part
h
P1
bearing block
displacement transducer
hydraulic cylinder
U0
P2 variable pump
Uf amplifer
Q2
Q1
Ps
Electro-hydraulic servo valve
Figure 1. Controllable oil chamber diagram of hydrostatic center frame
The relationship of hydraulic cylinder and pump swash plate angle was expressed as: X P ( s )= R ⋅ θ（） s (2) where R was rotation radius of swash plate. Flow equation of variable pump could be expressed as without considering leakage (3) Q( s ) = nK BQθ ( s ) where n
was motor speed; K BQ was discharge
coefficient. Transfer function of variable pump flow and hydraulic cylinder displacement synthesizing (2) and (3). θ ( s ) Q( s ) nK BQ Q( s) (4) Gb ( s ) = = ⋅ = X p ( s) X p (s) θ (s) R III. MODEL VERIFICATION BASED ON MATLAB Mathematical model of electro-hydraulic servo control single-channel system of hydrostatic center frame oil film was of explicit model structure and order, but model parameters was time-variant and uncertain, model identification was based on servo system test and achieved the measured input and output data, the necessary data processing and computing were added, this was a process eliminating the mathematical model equal to measured system [9-10]. We could introduce the collected input and output data using system identification toolbox of MATLAB, the collected input and output data set was carried on filter , averaging and removing trend as well as other pretreatments,we could achieve input and output data
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[11-12]. Pretreated input and output data set was divided into generating model segment and verifying the model segment, where one part was used for model identification of working data and the other part was used for validation data, then generating model segment data was input into identification algorithm,mathematical model was achieved after identifications. Identification model was adopted ARX model and state space model, two-channel open-loop transfer function through transformation arrangement was as: 5.07 s + 6054 G1 ( s ) = 3 s + 22.3s 2 + 5650 s (5) 4.57 s + 5725 G ( s ) = 2 s3 + 22.5s 2 + 5453s Correctness of open-loop transfer function achieved by identification need verification [13-15]. In order to verify the accurate degree of the model identification, we designed the PID position closed loop control system in off-line condition, the simulation program was showed as Fig.4. The position-type digital PID algorithm of the controller was as follows: k
u (k= ) K p e(k ) + K i ∑ e( j ) + K d [e(k ) − e(k − 1)]
(b) Figure 3. Validation of identification model sine response
a) was the model identification test comparison of first channel) was the model identification test comparison of second channel, curve 1 stood for the output of identification model, curve 2 stood for the output of identification experiment, output curve of identification model and output curve of identification experiment fit well according to Fig. 3, variable experiments under different conditions all illustrated the credibility of identification model.
(6)
j =0
IV. CONTROL STRATEGY
The hardware-in-the-loop of the PID controller was carried out under the on-line simulation environment, which was showed in Fig. 2. Given the same sine wave signals, we recorded the identification model and the experimental test response curves respectively. The result was shown in Fig.3. The response curves were almost coincident, showing that the identification model and the identification method were right.
Figure 2. Program graph of hardware-in-the-loop simulation
(a)
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A. Fuzzy Sliding Model Variable Structure Control The article gave a fuzzy sliding model complex control strategy integrating sliding model control theory and fuzzy control theory, which could inhibit the buffeting of sliding model variable structure system effectively, guarantee stability of system and extend the application further. The design of sliding model variable structure controller mainly included two problems. Firstly, we chose the switching function s ( x) , designed the switching surface, and kept the sliding motion under the condition of good stability and dynamic quality. Then, we determined the control law u ± ( x) , which satisfied the reachable condition of the sliding model motions and made sliding model bund on the switching surface. If the design of the switching function s ( x) and the control law u ± ( x) were finished, the sliding model control system would be established completely. The electro-hydraulic servo system of oil film control of hydrostatic center frame used an adjustable gain sliding model control. In order to decrease the effect of the buffeting on the accuracy and the stability of the system control, we used the fuzzy system to adjust sliding model gain system on line adaptively, which ensured the quick response of the system, decreased buffeting effectively, soften the control signal, this could achieve robust stability of variation range of inertial parameters and external disturbance, and assured the accuracy of the tracking performance. The fuzzy sliding model variable structure control of oil film control system of hydrostatic center frame was shown as Fig. 4.
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u
vs
u
electro-hydraulic position servo system
-
product
+
eq
fuzzy sliding model control variable
e
d
u
removing fuzzy
x
fuzzy
switching function
d / dt
s
fuzzy control rule
fuzzy
d / dt d / dt
removing fuzzy
fuzzy control rule
s
x
Figure 4. Structure principle diagram of fuzzy sliding control system
B. Fuzzy Sliding Mode Controller Using the fuzzy system to approach the equivalent control, the fuzzy sliding model controller based on the equivalent control was established. At first, we transferred the control object from tracking error e to sliding model function s .Then, when the controlled system was more than second order ,the control input in ordinary controller should be expressed as e, e, , e( n −1) , which was multi-dimensional expression. But in the fuzzy sliding model controller, it could be expressed as ( s, s) , which was always two-dimensional. That decreased the number of the fuzzy rules and simplified the structure of fuzzy control system. In the fuzzy system of equivalent control, we took s and s as the input, and quantized them though the factor of quantization K s and K s′ .The fuzzy set of s and
{ NB, NM , NS , Z 0, PS , PM , PB} universe of discourse was {−3, −2, −1, 0,1, 2,3} . s
was
,
the
We defined the fuzzy set of the output ueq as { NL, NB, NM , NS , Z 0, PS , PM , PB, PL} , the universe of discourse as {−0.8, −0.6, −0.4, −0.2, 0, 0.2, 0.4, 0.6, 0.8} . The design rule of the fuzzy control law was that: if s and s were large positive values, ss was also large positive value. In order to get the rapid decrease of ss ,it was necessary to control the input in a various large positive range .When ss was negative, the system was under the expected working condition and the control various is 0.If s and s were large negative value, ss was large positive value, it was necessary to control the input in a various large negative to get rapid decrease of ss ,the control rule was shown as Table I. TABLE I. THE FUZZY MODEL OF EQUIVALENT CONTROL
s NB NM NS ZO
s NB NL NL NB NM
NM NL NL NM NS
NS NB NB NM NS
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ZO NM NS NS ZO
PS NS ZO ZO PS
PM NS ZO PS PM
PB ZO ZO PS PM
PS PM PB
NS NS ZO
ZO NS ZO
ZO ZO PS
PS PS PM
PM PM PB
PB PB PB
PB PB PL
All the control rules were designed according to ss , so the control system of fuzzy sliding model was stable. At last, the fuzzy output was quantized exactly though Product inference engine, Gaussian fuzzifier and center average defuzzifier. C. Design of switching controller The product between switching function and derivative ss was taken as the input variable and the control gain k as the output variable in the fuzzy system with the control gain adjustment. The input ss was quantized though the factor of quantization K ss , and the output k was quantized by the factor of proportionality K k . We defined the input of fuzzy controller ss and the fuzzy set of language value of k as { NB, NM , NS , ZO, PS , PM , PB} , the universe of discourse as {−3, −2, −1, 0,1, 2,3} . The fuzzy rule should satisfy the existence and the accessibility requirement, it needed not only ensure the rapidity that the moving point approaches the switching surface, but also decreased the effect of buffeting .we took the large gain value when far from the sliding model surface, similarly took the lower value when near the surface. The fuzzy control rule of control gain k was shown as table II. ss k
TABLE II. FUZZY RULE TABLE OF CONTROL GAIN NB NM NS ZO PS PM
PB
NB
PB
NM
NS
ZO
PS
PM
V. SIMULATIONS The simulation was an important method of analyzing and studying the system, we could verify the correctness of theoretical analysis and design, simulate the operation process of an actual system, analyze the variety law between system characteristics and parameters, describe the state and characteristics, explore whether the design
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equivalent fuzzy sliding controller 1
Set value Fuzzy gain switching controller 1
Controlled object of main channel
Display Equivalent fuzzy sliding controller 1
fuzzy gain switching controller 1
Controlled object of synchronous channel
Figure 5. MATLAB/ Simulink simulation model
result could meet a design requirement or not, and study whether the control method would improve and increase the system or not [16-17]. Consequently, the simulation was as important as an experiment, and which could avoid complexities resulting from the actual experiment, and completed the simulations that could not be realized by an experiment, which could visually analyze the dynamic performance and steady state performance quickly. This thesis realized the modeling and simulation of hydrostatic center frame control system based on software MATLAB. A. Simulation Model Oil film control electro-hydraulic servo system of hydrostatic center frame was of nonlinear, and its uncertainty of parameters as well as outside disturbance, etc. A lot of parameters changed with working condition and temperature, that was main parameters of oil film control electro-hydraulic servo system of hydrostatic center frame might be uncertain, so we adopted model identification value to replace these parameters, and designed the system control target. When lots of uncertainties existed in system parameters, system output signal y tracked desired signal r. According to basic principle of oil film control of hydrostatic center frame, we used fuzzy sliding model control based on control gain fuzzy control to build MATLAB/ Simulink simulation model with two-channel under MATLAB7.4, and the simulation model were shown as Fig.5.B Simulation results analysis According to pole assignment and parameters uncertainty ranges of identification model in oil film control system as well as existence and accessibility of sliding model ,we set switching parameter of sliding model as = C1 8000, = C2 900 ,in equivalent fuzzy controller, quantization factors of variable s were K s = 0.0005 , K 's = 0.00001 ,scale factor of output
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control variable ueq was K u = 25 ;gain regulating fuzzy controller, quantization factor of variable ss was K ss = 0.0000005 ,scale factor of control gain k was K k = 1.7 .For oil film control electro-hydraulic position servo system of hydrostatic center frame with twochannel, traditional PID control and fuzzy sliding variable structure control with constant gain control as well as fuzzy sliding variable structure control with fuzzy regulating gain control were implemented, then simulations were carried out, unit was input as instruction signal, at the same time, disturbance signal y = 0.1sin 2π t mm was implemented under latter two conditions .simulation results were shown from Fig 6 to Fig 8. Where, a) was step response diagram of oil film thickness, curve 1 stood for input signal, curve 2 and 3 were respectively path curve of oil film thickness in oil chamber located in the first channel and second channel) was track error diagram, curve 1 and 2 were respectively track error path curve of oil film thickness in oil chamber located in the first channel and second channel.
a)
Step response curve of oil film thickness
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b) Track error curve of oil film thickness
b) Track error curve of oil film thickness
Figure 6. Oil film depth step responses curve of classical PID control
Figure 8. Oil film depth step responses curve of fuzzy-regulating gain FSM control
It was known from Fig. 6, under noninterference, oil film control system of hydrostatic center frame achieved track of oil film thickness for unit-step response within 1.7s, at the same time. Slight oscillation appeared and steady-state performance was not very good, but basically kept better control precision.
a) Step response curve of oil film thickness
a)
Track error curve of oil film thickness
Figure 7. Oil film depth step responses curve of constant gain FSM control
a) Step response curve of oil film thickness
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It was known from Fig.7 and Fig.8,when adopting fuzzy sliding variable structure control with constant gain control, because we chose bigger control gain value(k=50), system response speed was fast, for unitstep response, complete track of oil film thickness was implemented within 0.5s, but accompanying with bigger buffeting ,steady-state performance of system was poor. when adopting fuzzy sliding variable structure control with fuzzy regulating gain control ,fuzzy regulation was chosen to carry on online controlling switching gain, control gain eliminates interference term of control system as far as possible under sliding model reaching, at the same time, response speed of oil film control system was also fast, complete track of oil film thickness was implemented within 0.5s for unit-step response, and buffeting greatly reduced, which was beneficial to improvement of system steady-state accuracy in oil film control electro-hydraulic position servo system of hydrostatic center frame. According to simulation results, fuzzy sliding model variable structure control strategy was of faster response speed, short regulation time and excellent steady-state performance compared with traditional PID control, steady position sliding output was still achieved when system was subject to disturbance and parameter changes, which reduced steady state error. Therefore, this strategy was fit for electro-hydraulic servo control system of oil film in hydrostatic center frame considering dynamic performance, and it could achieve excellent control characteristic, which was of strong application value. VI. CONCLUSION This paper brought a scheme about electro-hydraulic servo active control of hydrostatic center frame, and control flow adopting controllable oil chamber with multi-channel, improved oil film stiffness of hydrostatic center frame. Model identification and verification were carried on for electro-hydraulic position servo system; we designed controller taking transfer function achieved by identification and carried on simulation by Simulink. Simulation results showed that the controller could not only effectively inhabit buffeting and reduce steady-state error, but also had strong robustness for the structure parameter uncertainty.
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ACKNOWLEDGMENTS This work was supported by Science Technology Item of Heilongjiang Provincial Education Department (No. 12521125) and Youth Foundation of Harbin University of Science and Technology (No. P20110067)
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REFERENCES [1] Jiang Gui Yun. Study on design theory for hybrid Bearings based on hydraulic servo control. Chongqing: Chongqing University, 2009:11-152. [2] Han Gui Hua Research on Hydrostatic Thrust Bearing Oil Film Control of Heavy NC Lathe, harbin: Harbin University of Science and Technology, 2009. [3] Shao Junpeng, Yang Xiaodong, Zhou Limin. Numerical Simulation of Integrated Deformation of Heavy Hydrostatic Thrust Bearing and Experimental Research. 2009 International Conference on Intelligent HumanMachine Systems and Cybernetics, Hangzhou, Zhejiang, China, 2009:45-48. [4] Shao J. P, Li H. M. Study on Flow ability of the Gap Oil Film of the Multi-oil Pad Hydrostatic Bearing with Variable Viscosity. IEEE Computer Society. 2009International Conference on Intelligent HumanMachine Systems and Cybernetics, HangZhou, 2009:15-18. [5] WANG Zhan-Linn. Modern electricity hydraulic servo control . Beijing: Beijing University of Aeronautics Astronautics Press, 2005. [6] LI Hong-ren. Hydraulic control system .Beijing: National Defense Industry Press, 1981. [7] WU Bo. Research on flight simulator motion platform control system based on quantitative feedback theory .Harbin:Harbin Institute of Industry,2007. [8] Jianying Li,Junpeng Shao, Zhongwen Wang and Guihua Han. Study of the electro-hydraulic load simulator based on double servo valve concurrent control. Proceedings of 9th International Conference on Electronic Measurement and Instruments ICEMI2009, Beijing, China, 2009 36993795. [9] SHAO Jun-peng, WANG Zhong-wen, LI Jian-ying, et al. Rule Self-tuning Fuzzy-PID Controller of Electrohydraulic Position servo system . Journal of Central South University: Science and Technology, 2010, 41(3): 960-965. [10] Zhongwen Wang,Junpeng Shao,Jianying Lin and Guihua Han. Research on Controller Design and Simulation of Electro-hydraulic Servo System. ICMA2009. Changchun, China, 2009 380-385. [11] HAN Gui-hua, CHEN Li-hua, SHAO Jun-peng. Study of fuzzy PID controller for industrial steam turbine governing system//ISCIT 2005—International Symposium on Communications and Information Technologies 2005, Proceedings. Beijing, 2005: 1228-1232. [12] XUE Ding-yu, CHEN Yang-quan. System simulink and application based on MATLAB/Simulink. Beijing: Tsinghua University Press, 2002: 404−416. [13] SHAO Jun-peng, WANG Zhong-wen, LI Jian-ying, et al Model Identification and Nonlinear Control of Electro-
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hydraulic Position Servo System. Mechanical Science and Technology for Aerospace Engineering, 2010,29(4) 488492. Sihai Zheng, Layuan Li, Yong Li,A QoS Routing Protocol for Mobile Ad Hoc Networks Based on Multipath, Journal of Networks, Vol. 7, No. 4, pp.691-698, 2012 Shoujia Wang, Wenhui Li, Ying Wang, Yuanyuan Jiang, Shan Jiang, Ruilin Zhao,An Improved Difference of Gaussian Filter in Face Recognition, Journal of Multimedia, Vol. 7, No. 6, pp.429-433, 2012 Tao Gao, Ping Wang, Chengshan Wang, Zhenjing Yao, Feature Particles Tracking for Moving Objects, Journal of Multimedia, Vol. 7, No. 6, pp. 408-414, 2012 N.El RAchkidy, A.Guitton, M. Misson, ”Pivot Routing Improves Wireless Sensor Networks Performance” Journal of Networks, Vol. 7, pp. 962-71, June 2012.
Zhongwen Wang, was born in Anhui province of China in August 15th, 1979, Doctor of Engineering, graduated from Harbin University of Science and Technology in April 2011 and majored in mechanical, manufacturing and automation ; he mainly researched in hydrostatic bearing, numerical control technology and electro-hydraulic servo control. He worked as an assistant in Harbin University of Science and Technology from July in 2003 to July in 2005,and he has worked as a professional teacher in Rongcheng College of Harbin University of Science and Technology since 2011. Ruizhen Duan, was born in Nei Monggol, China in October 23th, 1981, Master of Engineering, graduated from Harbin University of Science and Technology in April 2008 and majored in control theory and control engineering; she mainly researched in automatic control theory and industrial process control. She worked as an engineer in Huawei Technologies Co., Ltd. from April in 2008 to June in 2010, and she has worked as a professional teacher in Rongcheng College of Harbin University of Science and Technology since 2010. Xiaoqiu Xu, who was born in Heilongjiang province of China in May 29th, 1986, Master of Engineering, graduated from Harbin University of Science and Technology in April 2012 and majored in mechanical and electronic engineering; she mainly researched in hydrostatic bearing and numerical control technology. She has worked as a professional teacher in Rongcheng College of Harbin University of Science and Technology since 2012.
