THÔNG TIN TÀI LIỆU
MINISTRY OF EDUCTION AND TRAINING MINISTRY OF TRANSPORT HO CHI MINH CITY UNIVERSITY OF TRANSPORT TA VAN PHUONG Dissertation Abstract Designing Adaptive Tracking Controller For Non-Linear MIMO Systems Using CMAC Major: Automation and Control Engineering Code: 9520216 Instructor 1: Assoc.Prof Dang Xuan Kien Instructor 2: Dr Ngo Thanh Quyen Ho Chi Minh City, March 2019 Abstract Designing control system for non-linear MIMO systems has attracted many researchers for the recent decades Due to the complex characteristics, defining the dynamic model of the non-linear MIMO systems are invaluable for the practical applications Therefore, the model-based controllers cannot satisfy the desired performances To cope with this problem, many advanced controllers have been studied and applied for the non-linear MIMO systems such as Particle Swarm Optimization (PSO), Fuzzy Logic Controller (FLC), Neural Network (NN), Fuzzy Neural Network, and so on By using these adaptive and intelligent controllers, the performances have been achieved for the practical applications However, there exists disadvantages and shortcomings that need to be improved such as online learning problems, selection number of fuzzy rules, number of neurons and layers, the robustness of the system in the presence of disturbances, noise, and uncertainties, and so on This thesis has proposed the CMAC, the recurrent CMAC, the redundant recurrent CMAC, and the robust recurrent cerebellar model articulation control system (RRCMACS) for the non-linear MIMO systems to achieve the desired performances such as good tracking responses, stability, robustness, disturbances attenuation, and noise rejection The main contributions of this dissertation are presented in Chapter 2, Chapter 3, and Chapter In Chapter 2, a traditional Cerebellar Model Articulation Controller is represented to show the superior properties of the CMAC to different intelligent controllers Chapter presents the factors affecting the learning capability and efficiency of the CMAC and then some innovative solutions are proposed to enhance the performance and the learning effectiveness of the CMAC Besides improving the CMAC, the redundant solution is also proposed to maintain continuously the controling and supervising process A combination between the RCMAC and the robust controller to form the robust RCMAC to achieve not only good tracking response but also attenuate significantly the effects of the external disturbances, and sensor noise is shown in Chapter With this combination, the stability and robustness of the control system are remarkably improved during operation Along with the main theorems, the experimental results were also provided to prove the effectiveness of the proposed solutions Page Chapter 1: INTRODUCTION OF NON-LINEAR MIMO SYSTEM AND PROPOSED CONTROL SYSTEM 1.1 Introduction of the non-linear MIMO systems and research problems Most of the practical systems are non-linear systems the non-linear features of the system may come from the effects of dead-zone, hysteresis, saturation, friction coefficients, cross-coupling, uncertainties, disturbances, and noises [1]-[5] Due to the effects of the non-linear characteristics, the dynamic model of the practical systems cannot be completely obtained Therefore, they must be considered in designing the control systems From the point of view in designing control system, model-based controllers cannot achieve desired performances for the non-linear MIMO systems [6]-[15] To cope with the the non-linear characteristics and the uncertainties of the system, Fuzzy Logic Controller (FLC) [16]-[23], Sliding Mode Controller (SMC) [24]-[30], neural network (NN) [31]-[39] have been developed for the non-linear system to achieve desired performances However, these controllers still exist shotcomings as flows The performance of the FLC depended utterly on the selection of fuzzy sets and the number of rules However, there are not a specific method that ensure the optimal selections of fuzzy sets and rules for the controllers so far To achieve good performance of the FLC for the practical applications, the fuzzy sets and rules were mostly selected by trial and error For the SMC, the chattering phenomena affects long life and responses of the actuators, the selection of the boundary of uncertainties is a trade-off between the stability and the chattering phenomena The NNs remain several shortcomings such as all weights in the structure of the neural network are updated each learning cycle, this is unsuitable for the problems requiring real-time learning; the selection of the number of neurons and hidden layers to achieve good performances is very difficult in the practical applications Along with the development of the NNs, Cerebellar Model Articulation Controller (CMAC) having the learning structure similar to the human brain Page has been studied from the 1970s [40] The CMAC has been developing and incorporating for the complex non-linear MIMO systems because of its superior properties such as fast learning, good generation capability, and simple computation [41]-[46] The effectiveness of the CMACs rather than NNs has been proved in the practical applications [47]-[48] In the recent works, the wavelet function and recurrent technique were utilized to improve learning capability and dynamic response of the CMAC [49]-[51] Although the above studies achieved good results in designing the controller to cope with the high non-linear MIMO systems both in simulation and experiment, however, the robustness of the system in the presence of the disturbances and noise were not fully taken into account After studying the papers relating to the CMAC, the author proposed a new methodology to design a control system for the non-linear MIMO system basing on the Cerebellar Model Articulation Controller with the following characteristics i) The control system is not dependence on the dynamic model Meanwhile, the stability and convergence error of the system can be obtained in case the model cannot be exactly defined ii) The control system has dynamic response capability and avoid the local minimization during operation iii) The control system can deal with uncertainties, disturbances, and change in parameters of the system to have good tracking response iv) The control system has redundant capability which maintains continuously the control and supervisory process v) The control system guarantees the stability and robustness of the system in the presence of the uncertainties, disturbances, and noise 1.2 Outline of the Dissertation This dissertation is divided into five chapters Chapter mentions about the non-linear MIMO system, scientific researches relating to the non-linear system control, neccessory problems to research and proposed control system Structure of the traditional Cerebellar Model Articulation Controller (CMAC) and its applications are shown in Chapter Chapter points out the shortcomings of the traditional CMAC and proposes innovative solutions to enhance the performances of the CMAC The factors affect the robustness Page and the robust CMAC designing are provided in detail in Chapter Finally, the conclusion and future works are delivered in Chapter Along with the representation of research problems by theory, the simulation and experimental results are also included to prove the effectiveness and merit of the proposesd control system The organization of this dissertation is expressed in Fig 1.1 as follows Chapter Introduction of Non-linear System and Proposed Control System Chapter Cerebellar Model Articulation Controller Chapter Improved Cerebellar Model Articulation Controller Controlller CMAC Chapter Robust Cerebellar Model Articulation Controller Chapter Conclusion and Future Works Figure 1.1: Organization of the dissertation Page 1.3 MIMO non-linear system including uncertainties In general, the dynamic equation of MIMO non-linear systems including uncertainties, disturbances, and noise is described as flows x n = F0 (x) + ΔF( x) + (G (x) + ΔG (x))u + dn(x) F0 (x) + G (x)u UD(x) (1.1) y = x where y = x [x1 , x , , x no ]T R x [x T , x T , , x (n -1)T ]T R n is u [u1 , u , , u no ]T R no no is the the system system output vector, state is the control input vector, F0 (x) R vector, n o n in the nomial non-linear function, G (x) R no no is nomial gain matrix, ΔF(x) and n n n n ΔG(x) are change in parameter of the F0 (x) R o , and G (x) R o o dn(x) = [dn1 ,dn , ,dn o ]T R respectively disturbances and noise, no stands for UD(x) F(x) + G(x)u + dn(x) is external lumped uncertainties, disturbances, and noise The objective of the control system synthesis is that the output signals x can not only track the desired trajectories xd R but also satisfy the robust performance in the presence no of the uncertainties, disturbances, and noise 1.4 The proposed control system For the high-order system, the sliding error manifold was defined [2],[29]-[30] to reduce the order of variables during designing and computating the control system The sliding error manifold has the following form S en-1 + Ke (1.2) Therein, e xd x and e e, e, , en-1 are the tracking error and error T vector of the system, respectively Derivative both sides of S and combination with the dynamic equation (1.1), yields Page S en + Ke = xnd - xn + K(e) = x nd - Fo (x) - G o (x)u - UD(x) + K(e) (1.3) In case the nominal functions Fo (x) R no x n , Go1 (x) R no xno , and the lumped of external disturbances, uncertainties, and noise UD(x) are exactly known, an ideal sliding mode (ISM) controller is designed to guarantee the stability of the system as follows [49],[52]-[53] (1.4) uISM Go1 (x) xdn - Fo (x) UD(x) K(e) + ηsgn(S) However, for the complex high non-linear systems, the external disturbances, uncertainties, and noise UD(x) can’t be defined, measured or estimated exactly in practical applications Consequently, the u ISM can’t satisfy the stability and robust performance of the system To cope with the drawbacks of the model-based controllers, many modern controllers have been developed such as Fuzzy Logic Controller (FLC), Sliding Mode Controller (SMC), Neural Networks (NNs), and Cerebellar Model Articulation Controller (CMAC) [17-51] Although the above studies achieved impressive results in designing the controllers to cope with the high non-linear MIMO systems, the dynamic response and robust specifics of the system in the presence of the uncertainties were not totally mentioned In this research, a robust recurrent cerebellar model articulation control system (RRCMACS) is proposed for the non-linear MIMO system Therein, the RCMAC is designed to imitate the ideal controller to minimize error surface and the H robust controller is designed to attenuate the effects of the uncertainties acting on the system to achieve the robustness performance of the system during operation The total control system is described in (1.7) and a block diagram of the RRCMACS is depicted in Fig 1.2 (1.7) uRRCMACS = u ISM - u RC - u RCMAC Page xd n uISM = G -1 (x) xd - Fo (x) - UD(x) + K(e) - ηsgn(S) η w , η m , ησ , η w r xd + x- e S Learning Rules en-1 + Ke u ISM + ˆ σ, ˆ m, ˆ w ˆr w, - MIMO Nonlinear System RCMAC UD(x ) u RCMAC S Robust Controller u RC - + u RRCMACS Figure 1.2: Block diagram of the proposed control system The block diagram of the proposed control system includes three main control parts as follows The ideal sliding mode controller is used when the uncertainties are exactly known The RCMAC is the main controller, it is used to learn the uncertainties, UD(x) to minimize the error sliding surface, S With the selection of the appropriate learning rate, the error sling surface will tend to zero by learning capability of the RCMAC The robust controller u RC guarantees the robustness of the system in the presence of the uncertainties during operation Page Chapter 2: THE CEREBELLAR MODEL ARTICULATION CONTROLLER (CMAC) 2.1 Introduction to the CMAC Cerebellar model articulation controller (CMAC) is a neural network model proposed by Albus [54]–[56] The CMAC with its fast learning and good generation capability has been studied and implemented to identify and control the non-linear systems [57]-[59] Based on its superior properties, the CMAC is unnecessary to require much prior knowledge of the system Consequently, it can be considered as an intelligent controller that suits many practical non-linear systems [60]-[61] The superior properties of the CMAC to NNs were proved in the references [62]-[64] 2.1.1 Block diagram of the proposed control system and Structure of the CMAC The CMAC with its fast learning and good generalization capability places an important role in learning the unknown uncertainties, UD(x) to minimize the error sliding surface The block diagram of the proposed control system is depicted in Fig 2.1 and the structure of the CMAC is shown in Fig 2.2 The controller includes input space S , association memory space A , receptive field space R , weight memory space, and output spaces O The signal propagation in the CMAC is presented as follows [48], [65] Page xd n uISM = G -1 (x) xd - Fo (x) - UD(x) + K(e) - ηsgn(S) η w , η m , ησ xd + S e x- Learning Rules e n -1 + Ke u ISM + ˆ σ ˆ m, ˆ w, - MIMO Nonlinear System CMAC UD(x ) u CMAC S Compensator Controller ηB u CC - + u CMACS Figure 2.1: Block diagram of the proposed control system using CMAC Input Space S Association MeReceptive mory Space A Field Space R Weight Memory Space W Output Space O O1 S1 μ1k bik w1k w jk Sn i μ ik Layer nk Figure 2.2: The structure of the CMAC Page Oj motion stage powered by the linear piezoelectric motor (LPM) was reused to investigate the stability and robustness of the system The dynamic equation of LPM including hysteresis and stiffness behavior was described in references [2] and [50] 4.4.2.2 The simulation parameters and simulation result The initial parameters are the same with the RCMAC The impacts of uncertainties, external disturbances, and noise, UD(x) is generated by a random signal with mean=5 and variance=5 Sample time = 0.01s The simulation results of the robust cerebellar model articulation controller due to periodic step commands are shown in Fig 4.12 for the Xaxis and Fig 4.13 for the Y-axis The Fig 4.14 and Fig 4.15 illustrates the simulation results of the robust cerebellar model articulation controller due to sinusoidal command in the Xaxis and the Y-axis, respectively Figure 4.12: Tracking response of the robust cerebellar model articulation controller due to step command in the X-axis Page 44 Figure 4.13: Tracking response of the robust cerebellar model articulation controller due to step input in the Y-axis Figure 4.14: Tracking response of the robust cerebellar model articulation controller due to sinusoidal input in the X-axis Page 45 Figure 4.15: Tracking response of the robust cerebellar model articulation controller due to sinusoidal input in the Y-axis The simulation results showed that the RRCMACS obtained the stability and robustness in the presence of uncertainties, external disturbances, and noise at t1 = 235s to t = 245s and t = 465s to t = 475s for both periodic step and sinusoidal inputs The performances of the control system is better as the prescribed attenuation levels of the H robust controller are smaller 4.4.2.3 Conclusion In this chapter, the robust solutions are proposed for the non-linear MIMO system to achieve the stability and robustness in the presence of uncertainties, external disturbances, and noise, UD(x) The robust solutions include µ_Synthesis method and the H robust controller The µ_Synthesis method mainly focused on finding the control parameters to achieve the robustness under the effects of disturbances, noise, and change in the nominal coefficients The µ_Synthesis method does not mention much tracking responses of the system The H robust controller is combined with the RCMAC Therein, the RCMAC is utilized to imitate the ideal sliding mode controller to minimize Page 46 the error sliding manifold, and the H robust controller aims to attenuate the effects of uncertainties, external disturbance, and noise to the prescribed attenuation level The simulation results of the micro-motion stage base powered by the LPM proved the effectiveness of the proposed control system In addition, the UD(x) stands for the inherent complex properties of the non-linear MIMO systems Therefore, the proposed control system can handle other non-linear MIMO systems The future works will improve the control algorithm and hardware equipments to show the effectiveness of the H robust controller in real time Chapter 5: CONCLUSION AND FUTURE WORKS 5.1 Conclusion This thesis has proposed the CMAC, the recurrent CMAC, redundant recurrent cerebellar model articulation controller, and the robust recurrent cerebellar model articulation control system (RRCMACS) for the non-linear MIMO systems to achieve desired performances In particular, the non-linear MIMO systems are represented in the general framework Therein, the factors affecting the stability and robustness of the system such as dead-zone, hysteresis, backlash, saturation, friction coefficients, cross-coupling, uncertainties, disturbances, noises, and non-linear characteristics are taken into consideration in designing the control system The proposed control system is designed to achieve desired performances such as good command following, stability, robustness, disturbances attenuation, noise rejection and, continuously the control and supervisory process maintenance The main contributions of this dissertation are presented in Chapter 2, Chapter 3, and Chapter In Chapter 2, the traditional Cerebellar Model Articulation Controller is introduced to show the superior properties of the CMAC to different intelligent controllers such as Fuzzy Logic, Neural Network The structure of the CMAC, signal propagation, selection cost function, and learning algorithm are described as well Experimental results are provided to verify the effectiveness of the CMAC Besides, the limitations of the traditional CMAC are analyzed in detail Page 47 The factors affecting the learning capability and efficiency of the CMAC is pointed out in Chapter and then the innovative solutions are implemented to enhance the performances of the CMAC In particular, the Wavelet function and recurrent network technique are incorporated into the CMAC to improve learning ability and dynamic response for the controller A long with improving the CMAC, the redundant solution is also proposed in this chapter to maintain the continuously control and supervisory process With two control stations are used to operate concurrently Whenever one station gets faults, the other will quickly take over control the system Therefore, the operation of the control system is guaranteed continuously Beside representating theory, the experimental results are also provided to show the effectiveness of the proposed control system Chapter presented a combination between the CMAC and the robust controller to form the robust CMAC to achieve not only good tracking response but also attenuate the effects of the external disturbances and sensor noise The experimental results show the stability and robustness of the control system in the presence of the uncertainties 5.2 Future works Although this study obtained some good results, designing the controller for the uncertain non-linear MIMO system still remains gaps for future research Therefore, there are several opening problems that should be concerned in future works as follows In this thesis, the robustness of the system was only focused on the controller instead of for all the system Consequently, the stability and robustness for all inputs-outputs of the system should be mentioned in the future research The number of the layers of the CMAC did not automatically structured It means that the number of the layers will increase in case the sliding error surfaces is increment and vice versa Therefore, the learning effectiveness of the controller in real time is not optimal In future works, these properties need to consider completely The global optimization problem is not solved completely in this dissertation For that reason, it should be investigated more in the future studies Page 48 Published papers [1] Ta Van Phuong, Đong Van Huong, Ngo Thanh Quyen, “Adaptive tracking control for non-linear MIMO system using Self-Wavelet Cerebellar Model Articulation Controller”, Journal of Transportation Science and Technology, No 22, February 2017 [2] Ta Van Phuong, Nguyen Quoc Tan, Nguyen Thanh Luan, Ta Minh Giang, Ly Thanh Hung, “Deal with uncertainty systems using intelligent control methods”, Journal of Technical Education Science, ISSN 1859-1272, No.49, Steptember 2018 [3] Ta Van Phuong, Dong Van Huong, Ngo Thanh Quyen, “Designing a adaptive tracking adapting to the Fuzzy-Neural network for the 2-DOF Helicopter system”, Journal of Science and Technology, The University of Danang, ISSN 1859-1531, No.9, 2016 [4] Dang Xuan Kien, Ta Van Phuong, Nguyen Truong Phi, “Analysis and Design for Twin Rotor MIMO System using µ_Synthesis”, The 4th Vietnam International Conference and Exhibition on Control and Automation (VCCA-2017), Vietnamese, Ho Chi Minh, December 2017 [5] Van-Phuong Ta, Xuan-Kien Dang, Thanh-Quyen Ngo, “Adaptive Tracking Control Based On Cerebellar Model Articulation Controller for Non-linear Systems”, IEEE International Conference On Systems Science and Engineering (ICSSE 2017), July 2017 [6] Van-Phuong Ta, Xuan-Kien Dang, Van-Huong Dong, Viet-Dung Do “Designing Dynamic Positioning System Based on H∞ Robust Recurrent Cerebellar Model Articulation Controller ”, 4th International Conference on Green Technology and Sustainable Development, GTSD 2018, IEEE December 2018 [7] Xuan-Kien Dang, Van-Phuong Ta, Thanh-Danh Nguyen, “Designing Robust Controller For Twin Rotor MIMO System”, ICIC Express Letters, Part B: Applications, ICIC International, ISSN 2185-2766, (Sopus) October 2018 [8] Van-Phuong Ta, Xuan-Kien Dang, “Pressure Tank Stability Control System Using Recurrent Cerebellar Model Articulation Controller”, ICIC Express Letters, Part B: Applications, ICIC International, ISSN 2185-2766, (Sopus) Accepted November 2018 Page 49 [9] Van-Phuong Ta, Xuan-Kien Dang, “Improved Wavelet Cerebellar Model Articulation Controller For Precision Positioning Of PiezoDriven Stage”, Advanced Control, Automation and Robotics, IOP Conf Series: Materials Science and Engineering 383, (Sopus), 2018 [10] Van-Phuong Ta, Xuan-Kien Dang, Van-Lam Nguyen, Van-Thu Nguyen “Designing Dynamic Positioning System Based on Robust Recurrent Cerebellar Model Articulation Controller ”, 19th Annual General Assembly – AGA 2018, International Association of Maritime Universities, Bacelonar, October 2018 [11] Van-Phuong Ta, Xuan-Kien Dang, “An Innovative Recurrent Cerebellar Model Articulation Controller For Piezo-Driven Micromotion Stage”, International Journal of Innovative Computing, Information and Control (ISI), Volume 14, Number 4, August 2018 [12] T.Q Ngo, T.V Phuong, “Robust Adaptive Self-Organizing Wavelet Fuzzy CMAC Tracking Control for Deicing Robot Manipulator”, International Journal of Computers Communication & Control, (SCIE) August 2015 [13] Xuan-Kien Dang and Van-Phuong Ta, “Robust Recurrent Cerebellar Model Articulation Controller for Non-linear MIMO systems”, International Journal of Advanced Computer Science and Applications: IJACSA (ISI ), ISSN 2156-5570 , Vol 10, No 3, 2019 [14] Xuan-Kien Dang, Ta Van Phuong, Xuan-Phuong Nguyen, Viet-Dung Do, “Control Dynamic Positioning System Using Wavelet Cerebellar Model Articulation Controller”, Asia Maritime and Fisheries Universities Forum, November 2017 [15] Van-Phuong Ta, Xuan-Kien Dang, “Redundant Recurrent Cerebellar Model Articulation Control System for Industrial Applications”, Journal of Electrical Engineering and Technology, ISSN: 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of the CMAC and the RCMAC due to periodic... thesis has proposed the CMAC, the recurrent CMAC, the redundant recurrent CMAC, and the robust recurrent cerebellar model articulation control system (RRCMACS) for the non-linear MIMO systems to achieve
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