A Simple Fuzzy PI Control of Dual-Motor Driving Servo System

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1 MATEC Web of Conferences 04, 0006 (07) DOI: 0.05/ matecconf/ IC4M & ICDES 07 A Simle Fuzzy PI Control of Dual-Motor Driving Servo System Haibo Zhao,,a, Chengguang Wang 3 Engineering Technology Research Center of Otoelectronic Aliance, Tongling University, Tongling Anhui, 4406, China Deartment of Electrical Engineering, Tongling University, Tongling Anhui, 4406, China 3 Sichuan Institute of Aerosace System Engineering, Chengdu Sichuan, 6000, China Abstract. Aiming at the control roblem of dual-motor driving servo system, in order to avoid the comlicated numerical calculation of comlicated control algorithm, we resented a simle fuzzy PI controller for the first time. Firstly, we exlained system control rincile. In view of the shortcomings of current-error negative feedback, we used seed-error negative feedback synchronous driving control strategy. Then we theoretically analyzed dual-motor synchronous driving system in detail. We roosed the conditions of dual-motor driving servo system synchronous oeration for ste signal and ram signal, resectively. Finally, we resented a simle fuzzy PI controller, by combining fuzzy controller with PI controller. We analyzed the fuzzy PI control system and found it was stable. We considered two cases in simulation tests comaring fuzzy PI control with PI control. Simulation results show that fuzzy PI control has better adatability than conventional PI control, validating the effectiveness and efficiency of the roosed control strategy. Introduction Dual-motor driving servo system is widely used in military, civilian and other occasions. Many scholars have studied it. In [, ], the mechanical model of the rotary kiln drive as well as the develoment of an aroriate laboratory simulating system were resented. Exerimental results roved that gear faults can be identified by monitoring the motor hase current as well as the frequency sectrum of this current. In [3], the dynamic model of dual-motor driving system was given, using switching toeque control, simulation results showed that system has good osition control recision. In [4], simulation model based on the adative full-order flux observer and torque sensor vector control was established to observe or test variety of system dynamic resonse directly. However, all the above mentioned results have used more comlicated intelligent control strategy. Fuzzy control algorithm has a high maturity and has been widely used in many occasions. Quang Hieu Ngo, et al. [5] resented a fuzzy sliding mode control strategy for container cranes. Simulation results illustrated the efficiency of the roosed control law. Chun-Yan Wang, et al. [6] rovided a common adative fuzzy smooth dynamic controller for a class of uncertain switched nonlinear systems. Its effectiveness and feasibility were demonstrated by both a numerical examle and a chemical system. Do Wan Kim, et al. [7] resented a new direct discrete-time design methodology of a Corresonding author : hayzhaohaibo@6.com The Authors, ublished by EDP Sciences. This is an oen access article distributed under the terms of the Creative Commons Attribution License 4.0 (htt://creativecommons.org/licenses/by/4.0/).

2 MATEC Web of Conferences 04, 0006 (07) DOI: 0.05/ matecconf/ IC4M & ICDES 07 a robust samled-data fuzzy controller for a class of nonlinear systems. The simulation results for the samled-data deth control of AUV convincingly illustrated the effectiveness of the develoed techniques. Xiaojie Su, et al. [8] resented a T-S model-based fuzzy controller design aroach for electromagnetic susension systems. The T-S fuzzy model was firstly alied to reresent the nonlinear electromagnetic susension systems. Numerical simulation on an electromagnetic susension system was erformed to validate the effectiveness of the roosed aroach. From [5-8], we can see that fuzzy control is rarely used alone, and is usually used in conjunction with other control methods. Fuzzy control is introduced into the logical reasoning, has strong adative ability and a good control effect on comlex system, but searate fuzzy control cannot fundamentally eliminate steadystate error, control recision is low [9]. Conventional PI control rincile is simle, easy to imlement, has been widely used in industrial rocess control. But the coefficient setting of roortion and integral is a very troublesome thing, reasonable PI arameters are usually determined online by exerienced technical ersonnel. In the case of the control object s time variant, a set of fixed PI arameters cannot meet the requirements of system. Fuzzy PI control algorithm is formed by combining fuzzy control with conventional PI control. In recent years, a simle fuzzy PI control has rarely been used in dual-motor driving servo system. Hence, it is imerative to study the fuzzy PI control of dual-motor driving servo system. This algorithm can not only achieve recise control, but also has strong adatability. It can automatically modify the control arameters of PI according to the changes of the environment. This aer is organized as follows: system modeling is given in Section. System control rincile is resented in Section 3. The theoretic analysis of dual-motor synchronous driving system is given in Section 4. Section 5 resents the design of fuzzy PI controller. Simulation analysis in Section 6 to show the effectiveness of fuzzy PI control strategy. Section 7 concludes this aer. System Control Princile Since the system is a dual-motor driving mode, it must be ensured that the seeds of the two motors are synchronous. In the ideal case, if the two motors are the same, for the same command signal, the outut seeds must be the same. However, due to the discrete characteristic of motors and other comonents, even if the same tag arameters of comonents, the actual arameters cannot be comletely consistent. Therefore, it is necessary to solve the roblem of dual-motor synchronous driving, otherwise there will be a so-called servo fight henomenon. The existing method is to use current-error negative feedback, which can achieve the synchronous driving of two motors by the balanced control of current. Because the motor arameters cannot be comletely consistent, even if the consistent motor current may not be able to achieve the same seed, and the effect of synchronous driving must be based on the seed synchronization. In view of the shortcomings of current-error negative feedback, we use seed-error negative feedback synchronous driving control strategy. Inut signal R G Gc Driver Driving motor Driving motor seed outut G c Driver Driven motor Driven motor seed outut G Figure. Control block diagram of dual-motor synchronous driving. As is shown in Fig., take one of the motors as driving motor, retaining its seed loo, the other is driven motor, disconnecting the seed loo. For each motor, the inut current instruction is a comosite signal of the basic current given signal and seed-error feedback signal. And the seederror negative feedback signals of two motors are equal, but the olarities are oosite.

3 MATEC Web of Conferences 04, 0006 (07) DOI: 0.05/ matecconf/ IC4M & ICDES 07 Where G C is seed loo controller(tye-pi), G and G are transfer functions between servo motor, and resective current loo. G C is fuzzy PI controller, R is seed inut signal. and are seed outut of motor and, resectively. In a dynamic rocess, if the two motor s seeds are not synchronous, after seed-error was linear amlified, feedback to the two motors current given end resectively as auxiliary inut. Because the current loo resonse is much faster than the seed loo resonse, the seed-error signal is introduced into the current given end to inhibit the two motors seed out of synchronization as soon as ossible. So when the seed of motor is faster than the seed of motor, the given inut of motor will slightly decrease on the basis of basic current, and the given inut of motor will increase and vice versa. 3 Theoretic Analysis of Dual-Motor Synchronous Driving System Dual-motor synchronous driving control block diagram, as shown in fig.. Using Mason formula, we can solve the transfer function between and R W () s GG C+ GGG CGC GY - R_ CL () Rs () D D= + G G + G G + G G + G G GG where C C C C C Similarly, the transfer function between and R W () s GCG+ GG GCGC GY - R_ CL Rs () D () Then the transfer function between and R W() s - W () s GC( G G) = Rs () D- (3) From Eq. (), we can see that when the two motors are exactly the same, namely G = G, regardless of the inut signal, regardless of whether there is a seed-error negative feedback or not, 0, the two motors seed must be synchronized(assume there is no disturbance). Eqs. (), (), (3) are close loo transfer functions, the equivalent oen-loo transfer functions of the unit feedback are GY - R_ CL GCG(+ GCG) GY - R_ - GY - R_ CL + GCG+ GCG (4) GY - R_ CL GCG(+ GCG) GY - R_ - GY - R_ CL + GCG+ GCG+ GCG- GCG (5) GDY- R_ CL Gc ( G- G) GDY- R- - GDY- R_ CL + GCG+ GCG+ GCG+ GCGCGG (6) From fig., we can get the transfer function between current loo and servo motor as follows: KMKITIs KM GI () s 3 Cs Cs Cs 3 DM DL (7) Where, C LT J LT J, C RTJ RTJ LTD LTD KTJ KTJ, I m I L I m I L I M I L I I m I I L C RTD RTD KTD KTD J J K KT For convenience of analysis, let 3 I M I L I I M I I L m L M I 3

4 MATEC Web of Conferences 04, 0006 (07) DOI: 0.05/ matecconf/ IC4M & ICDES 07 ms + n ms + n G =, G 3 = 3 as + bs + cs + d as + bs + cs + d (8) KP s+ KI KPs+ KI GC =, GC = s s Where, m, m, n, n, a, a, b, b, c, c, d and d are all greater than zero, KI 0, when using roortional feedback K I 0, when using roortional integral feedback K I 0, substitute Eq.(8) into Eqs.(4), (5) and (6) resectively, we get: 4 3 ( ms n)( KP ski)( Cs Cs Cs 3 Cs 4 nk I) GY R_ s( C5s C6s C7s C8s C9s C0s CsKInd KInd) 4 3 ( msn )( KP ski)( Cs C3s C4s C5s nk I) GY R_ (9) s( C6s C7s C8s C9s C0s Cs CsKInd KInd KInd KInd ) 4 3 s( KP ski)( C3s C4s C5s C6snd nd) G YR C7s C8s C9s C30s C3s C3s C33s C34sKIKInn where, C i ( i =,,3,,34) are olynomial coefficients. There are two cases in Eq. (9):. K I ¹ 0, KInd KInd KInd KInd 0 In this case, numerator constant term coefficient of GY - R_ is not equal to zero, constant term coefficient in denominator bracket is also not equal to zero, so GY - R_ is tye- system, GY - R_ is also tye- system, the system can be synchronized for ste signal; if it also meets nd nd, the above two systems outut all exist steady-state error, but the steady-state error is equal, so the two systems can still be synchronized.. K I ¹ 0, KInd KInd KInd KInd 0 In this case, GY - R_ is still tye- system, GY - R_ is at least tye- system. The two systems can be synchronized for ste signal, but cannot be synchronized for ram signal. From the above analysis, we can see that dual-motor can be synchronized for ste signal when K ¹, dual-motor could be synchronized for ram signal only when it meets: I 0 I 0 K ¹, KInd KInd KInd KInd 0 and nd nd. 4 Design of Fuzzy PI Controller System control block diagram is shown in Fig.. Figure. System control block diagram. System control block diagram is shown in figure. The fuzzy PI controller use error e and error change ec as inut. The control scheme is to find out the fuzzy relation between the two arameters of PI and e, ec firstly, the two arameters of PI can be modified online by continuous testing of e and ec, so as to meet the different control arameter requirements for different e and ec, making the 4

5 MATEC Web of Conferences 04, 0006 (07) DOI: 0.05/ matecconf/ IC4M & ICDES 07 controlled object has a good dynamic and static erformance. 4. Determination of Inut and Outut Variables The seed error e of dual-motor and the change rate ec of seed error are as the inut of fuzzy controller, correction arameters k and ki are as the outut of fuzzy controller, then PI regulator outut arameters k and k i are shown in Eq.(0). k k k, ki ki ki (0) where k and k i are setting values. 4. Determination of Membershi Function Fuzzy subsets of fuzzy controller inut and outut variables are e, ec, k and ki resectively. Linguistic value of each variable is [large negative, medium negative, small negative, zero, small ositive, medium ositive, large ositive] denoted by [,,,,,, ], discourse domain is integer in [-6, 6]. Taking into account the sensitivity, stability, robustness and the coverage degree of discourse domain, the membershi function curve of each fuzzy subset is selected by triangle shae, shown in Fig. 3. (a) Membershi function of e and ec (b) Membershi function of k and ki Figure 3. Membershi function curve. 4.3 Fuzzy Control Rules The core of fuzzy control design is the determination of fuzzy control rules, and the selection of control rules is directly related to the erformance of system. From the above arameters setting rincile, through the fuzzy reasoning and exerimental correction, we get the fuzzy control rules of and ki are shown in Table. k ec e Table. Fuzzy control rules / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / 4.4 Stability of Fuzzy PI Control System 5

6 MATEC Web of Conferences 04, 0006 (07) DOI: 0.05/ matecconf/ IC4M & ICDES 07 In section 3, we have analyzed the stability conditions of PI control system in detail. In a conventional PI control system, if the linear PI controller is relaced by the nonlinear fuzzy PI controller, then the stability of the resulting control system remains unchanged [0]. Thus the stability conditions of fuzzy PI control system are the same as the PI control system. In the following simulation analysis, fuzzy PI control system is stable. 5 Simulation Exeriment Simulation block diagram is shown in Fig. 4: Figure 4. Simulation block diagram of fuzzy PI control. Where, PID Controller is seed regulator, Transfer Fun is transfer function between driving motor and its current loo, Transfer Fun is transfer function between driven motor and its current loo, the inut and outut of simulation block diagram are seed given signal and dual-motor seed error resectively. According to reference[], we get: 8.738s 6750 GI () s () s s 50s0.85 let G () s GI () s In the following simulation, system arameters are chosen as follows: ke 600, kec 666.7, ku.5, k.3, ki. PID controller arameter is chosen as follows:k=5.6,ki=.6 ) In order to satisfy the equation: KInd KInd KInd KInd 0 () let 8.738s 6700 G () s (3) s s 50s0.896 Thus, we get n 6750, n 6700, d 0.85, d and substituted into eq.(), after simlification, we obtain 95KI 95KI. Figure 5. Seed error of dual-motor tracking ram signal 000t(mil/s). Figure 6. Seed error of dual-motor tracking ste signal 500mil. 6

7 MATEC Web of Conferences 04, 0006 (07) DOI: 0.05/ matecconf/ IC4M & ICDES 07 Figure 7. Seed error of dual-motor tracking ste signal 000mil. Figure 8. Seed error of dual-motor tracking ste signal 500mil. ) In order to satisfy the equation: KInd KInd KInd KInd 0 (4) nd nd, let and 8.738s 6700 G () s (5) s s 50s we can get n 6750, n 6700, d 0.85, d and substituted into Eq.(4), after simlification, we get K I 0. Figure 9. Seed error of dual-motor tracking ram signal 000t(mil/s). Figure 0. Seed error of dual-motor tracking ste signal 500mil. Figure. Seed error of dual-motor Figure. Seed error of dual-motor tracking ste signal 000mil. tracking ste signal 500mil. From Fig. 5 to Fig., we can see that when the inut is a ram signal, seed-error feedback controller using fuzzy PI comared with PI, the former start u rocess is better, reducing the overshoot and oscillation frequency. In the condition of inut ste signal amlitude changes, the seed error of dual-motor changes slightly when using fuzzy PI control, but the seed error of dual-motor changes greatly when using PI control, so the fuzzy PI controller has stronger robustness than PI controller. 6 Conclusion Aiming at the dual-motor driving servo system, a simle fuzzy PI controller was resented for the first time. The conventional PI control system has a large overshoot, and the ure fuzzy control cannot eliminate the steady-state error due to its structure. In this aer, the two control methods are 7

8 MATEC Web of Conferences 04, 0006 (07) DOI: 0.05/ matecconf/ IC4M & ICDES 07 combined, namely fuzzy PI control, simulation results show that the fuzzy PI control not only has better dynamic and static quality, but also has better adatability [-5] than conventional PI control, which can significantly imrove the control erformance of system, validating the efficacy of the roosed control strategy. This aer rovides a reference for the further research of dual-motor driving servo system. Acknowledgment This work was suorted by National Natural Science Foundation of China(No ), Nature Science Foundation in Anhui Province of China(No MF30), Natural Science Research Key Project of Universities in Anhui Province of China (No.KJ05A97), the Engineering Technology Research Center of Otoelectronic Aliance in Anhui Province of China, Sichuan Institute of Aerosace System Engineering in Sichuan Province of China. The authors confirm that this article content has no conflicts of interest. References. I. X. Bogiatzidis, E. D. Mitronikas, A. N. Safacas, Investigation of backlash henomena aearing in a twin AC cement kiln drive, 9th International Conference on Electrical Machines, 00, -6.. I. X. Bogiatzidis, A. N. Safacas, Vibration analysis and backlash identification of a twin AC drive for a cement kiln, 5th IET International Conference on Power Electronics, Machines and Drives, 00, L. F. Sun, Research on motion characteristic and anti-backlash control of dual-motor system, The Outstanding Master s Degree Thesis of Northeastern University, June H. Z. Zhu, W. X. Song, Y. Dong, Modeling and simulation of coaxial connected dual-motor drive system, Electric Mach. Control Al. 40() (03) Q. H. Ngo, N. P. Nguyen, C. N. Nguyen, Fuzzy sliding mode control of container cranes, Int. J. Control, Autom. Syst. 3() (05) C. Y. Wang, X. H. Jiao, Observer-based adative arbitrary switching fuzzy tracking control for a class of switched nonlinear systems, Int. J. Control, Autom. Syst. 3(4) (05) D. W. Kim, H. J. Lee, M. H. Kim, Robust samled-data fuzzy control of nonlinear systems with arametric uncertainties: Its alication to deth control of autonomous underwater vehicles, Int. J. Control, Autom. Syst. 0(6) (05) X. J. Su, X. Z. Yang, P. Shi, Fuzzy control of nonlinear electromagnetic susension systems, Mechatron. 4(4) (04) H. Ying, S. William, J. B. James, Fuzzy control theory: a nonlinear case, Automatica, 6(3) (990) G. R. Chen, H. Ying, Stability analysis of nonlinear fuzzy PI control systems, The Third International Conference on Industrial Fuzzy Control and Intelligent Systems, 993, H. B. Zhao, X. H. Zhou, Research of fuzzy PI control of dual-motors driving servo system, Journal of Chaohu College, (3) (009) Y. M. Jia, H. Kokame J. Lunze, Simultaneous adative decouling and model matching control of a fluidized bed combustor for sewage sludge, IEEE T. Control Syst. Technol. (4) (003) S. J. Yoo, Distributed adative consensus tracking of a class of networked non-linear systems with arametric uncertainties, IET Control Theor. Al. 7(7) (03) B. Yao, C. X. Hu, L. Lu, Adative Robust Precision Motion Control of a High-Seed Industrial Gantry With Cogging Force Comensations, IEEE T. Control Syst. Technol. 9(5) (0) S. Y. Xu, Further results on adative robust control of uncertain time-delay systems, IET Control Theor. Al. (5) (008)