Feedback Linearizing Model Predictive Control for Nonlinear Systems with Input Constraints

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研究生：	李玉芬 Peeraya Pongpanyaporn
論文名稱：	Feedback Linearizing Model Predictive Control for Nonlinear Systems with Input Constraints Feedback Linearizing Model Predictive Control for Nonlinear Systems with Input Constraints
指導教授：	郭永麟 Yong-Lin Kuo
口試委員:	蘇順豐 Shun-Feng Su 蔡明忠 Ming-Jong Tsai 楊振雄 Cheng-Hsiung Yang 郭永麟 Yong-Lin Kuo
學位類別：	碩士 Master
系所名稱：	工程學院 - 自動化及控制研究所 Graduate Institute of Automation and Control
論文出版年：	2020
畢業學年度：	108
語文別：	英文
論文頁數：	107
中文關鍵詞：	模型預測控制、反饋線性化、Laguerre函數、輸入約束、非線性系統
外文關鍵詞：	Model predictive control, Feedback linearization, Laguerre functions, Input constraints, Nonlinear system
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上一筆

模型預測控制(MPC)是工業領域中廣泛使用的控制方案，用於解決機器的輸
入約束；但是，採用此種方法會需要大量的運算時間。為了減少模型預測控制的處
理時間，提高模型預測控制的控制性能，本文提出了將模型預測控制，反饋線性化
(Feedback linearization, FL)和 Laguerre 函數組合應用於輸入約束非線性系統的方法。
反饋線性化是一種眾所周知的方法，用於將非線性系統轉換為線性系統，簡化系統
模型的複雜度，同時應用 Laguerre函數透過估計控制訊號來減少計算時間，並使用
Lyapunov函數進行系統穩定性分析。另外，此方法適用於單輸入單輸出(SISO)和多
輸入多輸出(MIMO)非線性系統;為了評估控制性能，在 SISO 和 MIMO 的情況下都
進行了本文所提出的控制方法與其他文獻控制方法之間的比較。根據模擬結果，本
文所提出的方法可以有效減少運算時間，同時有效地處理輸入約束，並且比其他文
獻所採用的控制方法有更佳的效果。

The model predictive control (MPC) is a widely used control scheme in the industry to tackle with the input constraints of machines; however, this approach consumes huge computational time. To reduce processing time and enhance the control performances of the model predictive control, this thesis presents the combination of the model predictive control, the feedback linearization, and the Laguerre functions applying on the nonlinear systems with input constraints. The feedback linearization (FL) is a well-known method for converting a nonlinear to a linear system in order to obtain a less complicated system while the Laguerre functions are applied for decreasing computational time by estimating the control signal. A stability analysis is presented using the Lyapunov function. In addition, the proposed method is generalized for both single-input single-output (SISO) and multiple-input multiple-output (MIMO) nonlinear systems. To evaluate the control performances, the comparisons between the proposed control scheme and other similar control schemes in the literature review are illustrated in both SISO and MIMO cases. According to the results, the proposed method consumes less computational time while it effectively handles input constraints and performs better than other observed control schemes.

ABSTRACT .................................................................... i
ACKNOWLEDGMENT .............................................................. iii
TABLE OF CONTENTS ........................................................... iv
LIST OF FIGURES ............................................................. vii
LIST OF TABLES .............................................................. xi
CHAPTER 1: INTRODUCTION ..................................................... 1
1 Background .............................................................. 1
2 Literature Review........................................................ 2
3 Motivation and objective ................................................ 4
4 Methodology ............................................................. 5
5 Contributions............................................................ 5
6 Thesis outline .......................................................... 5
CHAPTER 2: LINEAR-LIKE FORMULATIONS OF NONLINEAR SYSTEMS .................... 7
1 Feedback linearization (FL) ............................................. 7
1.1 Input-state feedback linearization (ISFL) ............................. 8
1.2 Input-output feedback linearization (IOFL) ............................ 9
2 State-dependent Riccati equation (SDRE) ................................. 10
3 Takagi–Sugeno fuzzy model (TSF) ........................................ 11
4 Comparisons of the three linear-like structures ......................... 12
CHAPTER 3: FEEDBACK LINEARIZING MODEL PREDICTIVE CONTROL  WITH INPUT CONSTRAINTS FORMULATIONS ................................................................ 13
1 Problem description ..................................................... 13
2 Laguerre functions ...................................................... 13
3 Feedback linearizing model predictive control for nonlinear systems with input constraints ................................................................. 14
4 Hildreth’s quadratic programming ....................................... 21
5 Stability analysis ...................................................... 23
CHAPTER 4: ILLUSTRATIVE EXAMPLES ............................................ 26
1 Example I: Flexible-joint mechanism ..................................... 26
1.1 Problem description.................................................... 26
1.2 Controller design ..................................................... 27
1.2.1 Feedback linearizing model predictive control (the proposed method) . 27
1.2.2 Feedback linearization and linear quadratic tracking (FL + LQT)...... 33
1.2.3 State-dependent Riccati equation (SDRE) ............................. 35
1.2.4 Takagi–Sugeno fuzzy model and model predictive control (TSF + MPC) . 37
1.3 Simulation results .................................................... 39
1.3.1 Parameter tuning .................................................... 39
1.3.2 The proposed method with input constraints........................... 45
1.3.3 The comparisons between the proposed method and other methods mentioned in the literature review ....................................................... 47
2 Example II: Two-link robot arm .......................................... 59
2.1 Problem description.................................................... 59
2.2 Controller design ..................................................... 60
2.2.1 Feedback linearizing model predictive control (the proposed method) . 60
2.2.2 Feedback linearization and linear quadratic tracking (FL + LQT)...... 68
2.2.3 State-dependent Riccati equation (SDRE) ............................. 69
2.2.4 Takagi–Sugeno fuzzy model and model predictive control (TSF + MPC) . 72
2.3 Simulation results .................................................... 76
2.3.1 Parameter tuning .................................................... 76
2.3.2 The proposed method with input constraints........................... 85
2.3.3 The comparisons between the proposed method and other methods mentioned in the literature review ....................................................... 88
CHAPTER 5: CONCLUSIONS AND FUTURE WORKS ..................................... 101
1 Conclusions ............................................................. 101
2 Future works ............................................................ 102
REFERENCES .................................................................. 103
APPENDIX .................................................................... 107 
                                

[1] L.P. Wang, Model predictive control system design and implementation using MATLAB, London: Springer-Verlag London Limited, 2009.
[2] F. Allgower and A. Zheng, Nonlinear model predictive control, vol. 26, Washington D.C.: Springer Basal AG, 2000.
[3] J. Rua and L.O. Nord, "Optimal control of flexible natural gas combined cycles with stress monitoring : Linear vs nonlinear model predictive control," Appl. Energy, vol. 265, no. c, article number: 114820, 2020.
[4] G.X. Bai, Y. Meng, L. Liu, W.D. Luo, and Q. Gu, "Review and comparison of path tracking based on model predictive control," Electron., vol. 8, no. 10, article number: 1077, 2019.
[5] M.W. Zhang, Z.X. Lin, H.Y. Huang, and T.H. Zhang, "Design and verification of model predictive control for micro-turboshaft engine," Adv. Mech. Eng., vol. 11, no. 12, pp. 1-16, 2019.
[6] L. Guang, "Nonlinear model predictive control of a wave energy converter based on differential flatness parameterisation," Int. J. Control, vol. 90, no. 1, pp. 68-77, 2017.
[7] E. Nuss, M. Wick, J. Andert, J. De Schutter, M. Diehl, D. Abel, and T. Albin, "Nonlinear model predictive control of a discrete-cycle gasoline-controlled auto ignition engine model: Simulative analysis," Int. J. Engine Res., vol. 20, no. 10, pp. 1025-1036, 2019.
[8] J.J.E. Slotine and W.P. Li, Applied nonlinear control, New Jersey: Prentice-Hall, Inc., 1991.
[9] A. Owczarkowski, D. Horla, and J. Zietkiewicz, "Introduction of feedback linearization to robust LQR and LQI control - Analysis of results from an unmanned bicycle robot with reaction wheel," Asian J. Control, vol. 21, no. 2, pp. 1028-1040, 2019.
[10] S.L. Zhao, H.L. An, D.B. Zhang, and L.C. Shen, "A new feedback linearization LQR control for attitude of quadrotor," the 13th International Conference on Control, Automation, Robotics & Vision, Singapore, 10-12 December 2014.
[11] F. Yakub and Y. Mori, "Comparative study of autonomous path-following vehicle control via model predictive control and linear quadratic control," P. I. Mech. Eng. D-J Aut., vol. 229, no. 12, pp. 1695-1714, 2015.
[12] A. Devanshu, M. Singh, and N. Kumar, "Sliding mode control of induction motor drive based on feedback linearization," IETE J. Res., vol. 66, no. 2, pp. 256-269, 2018.
[13] S.X. Hou and J.T. Fei, "Robust adaptive fuzzy control of a three-phase active power filter based on feedback linearization," Turk. J. Electr. Eng. Co., vol. 25, no. 1, pp. 126-139, 2017.
[14] B. Xu, X.P. Liu, H.Q. Wang, and Y.C. Zhou, "Event-triggered control for nonlinear systems via feedback linearisation," Int. J. Control, 2020 (DOI: 10.1080/00207179.2020.1730008).
[15] K. Zhou, M. Ai, D.Y. Sun, N.Z. Jin, and X.G. Wu, "Field weakening operation control strategies of PMSM based on feedback linearization," Energies, vol. 12, no. 23, article number: 4526, 2019.
[16] S.F. Yang, P. Wang, and Y. Tang, "Feedback linearization-based current control strategy for modular multilevel converters," IEEE Trans. Power Electron., vol. 33, no. 1, pp. 161-174, 2018.
[17] S. Kilicaslan, "Tracking control of elastic joint parallel robots via state-dependent Riccati equation," Turk. J. Elec. Eng. & Comp. Sci., vol. 23, no. 2, pp. 522-538, 2015.
[18] M.H. Korayem, N.Y. Lademakhi, and S.R. Nekoo, "Application of the statedependent Riccati equation forflexible-joint arms: Controller and estimator design," Optim. Contr. Appl. Met., vol. 39, no. 2, pp. 792-808, 2018.
[19] N. Vafamand, M.H. Asemani, A. Khayatiyan, M.H. Khooban, and T. Dragicevic, "TS fuzzy model-based controller design for a class of nonlinear systems including nonsmooth functions," IEEE Trans. Syst. Man Cybern. Syst., vol. 50, no. 1, pp. 233244, 2020.
[20] W.L. Yang, W.T. Zhang, D.Z. Xu, and W.X. Yan, "Fuzzy model predictive control for 2-DOF robotic arms," Assem. Autom., vol. 38, no. 5, pp. 568-575, 2018.
[21] Y.L. Kuo and I.E.C. Resmi, "Model predictive control based on a Takagi–Sugeno fuzzy model for nonlinear systems," Int. J. Fuzzy Syst., vol. 21, no. 2, pp. 556-570, 2018.
[22] Z. Lendek, T.M. Guerra, R. Babuska, and B.D. Schutter, Stability analysis and nonlinear observer design using Takagi-Sugeno fuzzy models, Berlin: SpringerVerlag Berlin Heidelberg, 2010.
[23] K. Guemghar, B. Srinivasan, Ph. Mullhaupt, and D. Bonvin, "Analysis of cascade structure with predictive control and feedback linearisation," IET Control Theory A., vol. 152, no. 3, pp. 317-324, 2005.
[24] J. Shi and A.G. Kelkar, "Feedback linearization based generalized predictive control of Jupiter icy moons orbiter," J. Dyn. Syst. Meas. Control, vol. 131, no. 1, article number: 011003, 2009.
[25] G.N. Lou, W. Gu, W.X. Sheng, X.H. Song, and F. Gao, "Distributed model predictive secondary voltage control of islanded microgrids with feedback linearization," IEEE Access, vol. 6, pp. 50169-50178, 2018.
[26] T.F. Orchi, T.K. Roy, M.A. Mahmud, and A.M.T Oo, "Feedback linearizing model predictive excitation controller design for multimachine power systems," IEEE Access, vol. 6, pp. 2310-2319, 2018.
[27] J.J. Hu, X.M. Xu, and K.Y. Zhu, "Arm exoskeleton based on model predictive control with input/output feedback linearization," J. Med. Imaging Health Inform., vol. 3, no. 3, pp. 432-439, 2013.
[28] X.F. Bao, N. Kirsch, A. Dodson, and N. Sharma, "Model predictive control of a feedback-linearized hybrid neuroprosthetic system with a barrier penalty," J. Comput. Nonlinear Dyn., vol. 14, no. 10, article number: 101009, 2019.
[29] W. Liao, M. Cannon, and B. Kouvaritakis, "Constrained MPC using feedback linearization on SISO bilinear systems with unstable inverse dynamics," Int. J. Control, vol. 78, no. 9, pp. 638-646, 2005.
[30] S. Mohammed, P. Poignet, P. Fraisse, and D. Guiraud, "Toward lower limbs movement restoration with input-output feedback linearization and model predictive control through functional electrical stimulation," Control. Eng. Pract., vol. 20, no. 2, pp. 182-195, 2012.
[31] G. Clowes, "Choice of the time-scaling factor for linear system approximations using orthonormal Laguerre functions," IEEE Trans. Automat. Contr., vol. 10, no. 4, pp. 487-489, 1965.
[32] A. Eskandarpour and I. Sharf, "A constrained error-based MPC for path following of quadrotor with stability analysis," Nonlinear Dyn., vol. 99, no. 2, pp. 899-918, 2020.
[33] A. Zhang, I.G. Ramirez-Alpizar, K.G. Esclasse, O. Stasse, and K. Harada, "Humanoid walking pattern generation based on model predictive control approximated with basis functions," Adv. Robot., vol. 33, no. 9, pp. 454–468, 2019.
[34] C.M. Abdissa and K.T. Chong, "Stabilization and voltage regulation of the buck DCDC converter using model predictive of Laguerre functions," Stud. Inform. Control., vol. 26, no. 3, pp. 315-324, 2017.
[35] E.B. Erdem and A.G. Alleyne, "Design of a class of nonlinear controllers via state dependent Riccati equations," IEEE Trans. Control Syst. Technol., vol. 12, no. 1, pp. 133-137, 2004.
[36] K. Tanaka and H.O. Wang, Fuzzy control systems design and analysis: A linear matrix inequality approach, New York: John Wiley & Sons, Inc., 2001.
[37] D.G. Luenberger, Optimization by vector space methods, New York: John Wiley & Sons, Inc., 1969.
[38] [Online]. Available: https://www.mathworks.com/help/robust/ref/feasp.html.
[39] D.S. Naidu, Optimal control systems, Florida: CRC Press LLC, 1940.

全文公開日期 2025/08/11 (校內網路)
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