Critically damped stabilization of inverted-pendulum systems using continuous-time cascade linear model predictive control

Abstract In this paper, a cascade continuous-time linear MPC controller with 7 well defined parameters is proposed to stabilize the inverted pendulum system around the desired equilibrium points. The proposed controller scheme is composed of two MPC controllers in cascade. These controllers are tuned so as to obtain a doubly critically damped behavior for the inner and outer loops. Explicit generalized expressions of the MPC controller parameters in relation to the inverted pendulum characteristics and the chosen horizon time parameter with the robustness analysis of the controlled system are given to facilitate the controller design for a wide class of inverted pendulum systems. Simulation results show that the MPC controller is compared favorably to the well known parallel two-PID control scheme.

[1]  C.W. Anderson,et al.  Learning to control an inverted pendulum using neural networks , 1989, IEEE Control Systems Magazine.

[2]  Jia-Jun Wang,et al.  Simulation studies of inverted pendulum based on PID controllers , 2011, Simul. Model. Pract. Theory.

[3]  Xiaoou Li,et al.  A systematic tunning method of PID controller for robot manipulators , 2011, 2011 9th IEEE International Conference on Control and Automation (ICCA).

[4]  Karl Johan Åström,et al.  GLOBAL STABILIZATION OF THE INVERTED PENDULUM USING MODEL PREDICTIVE CONTROL , 2002 .

[5]  Scott A. Bortoff,et al.  Robust Swing-Up Control for a Rotational Double Pendulum , 1996 .

[6]  Dinesh Chandra,et al.  Stabilization and Tracking Control of Inverted Pendulum Using Fractional Order PID Controllers , 2014 .

[7]  Katsuhisa Furuta,et al.  Swinging up a pendulum by energy control , 1996, Autom..

[8]  Liuping Wang,et al.  Model Predictive Control System Design and Implementation Using MATLAB , 2009 .

[9]  N. Ono,et al.  Attitude control of a triple inverted pendulum , 1984 .

[10]  Jianqiang Yi,et al.  Upswing and stabilization control of inverted pendulum system based on the SIRMs dynamically connected fuzzy inference model , 2001, Fuzzy Sets Syst..

[11]  Peter J. Gawthrop,et al.  Intermittent Predictive Control of an Inverted Pendulum , 2006 .

[12]  Olfa Boubaker,et al.  The Inverted Pendulum Benchmark in Nonlinear Control Theory: A Survey , 2013 .

[13]  Markus Schöberl,et al.  Applications of energy based control methods for the inverted pendulum on a cart , 2009, Robotics Auton. Syst..

[14]  Boris Tovornik,et al.  Swinging up and stabilization of a real inverted pendulum , 2006, IEEE Transactions on Industrial Electronics.

[15]  Kazunobu Yoshida,et al.  Swing-up control of an inverted pendulum by energy-based methods , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[16]  Dongkyoung Chwa,et al.  Orbital Stabilization of Inverted-Pendulum Systems via Coupled Sliding-Mode Control , 2009, IEEE Transactions on Industrial Electronics.

[17]  Dongkyoung Chwa,et al.  Swing-Up and Stabilization Control of Inverted-Pendulum Systems via Coupled Sliding-Mode Control Method , 2009, IEEE Transactions on Industrial Electronics.

[18]  Brett Ninness,et al.  Nonlinear model predictive control of an inverted pendulum , 2009, 2009 American Control Conference.

[19]  Rong-Jong Wai,et al.  Adaptive stabilizing and tracking control for a nonlinear inverted-pendulum system via sliding-mode technique , 2006, IEEE Trans. Ind. Electron..

[20]  Amit Patra,et al.  Swing-up and stabilization of a cart-pendulum system under restricted cart track length , 2002, Syst. Control. Lett..

[21]  S. Joe Qin,et al.  A survey of industrial model predictive control technology , 2003 .

[22]  Su-Yong Shim,et al.  Swing-up control for an inverted pendulum with restricted cart rail length , 2009 .

[23]  K. Furuta,et al.  Computer control of a double inverted pendulum , 1978 .

[24]  Rey-Chue Hwang,et al.  A self-tuning PID control for a class of nonlinear systems based on the Lyapunov approach , 2002 .

[25]  Barjeev Tyagi,et al.  Optimal Control of Nonlinear Inverted Pendulum System Using PID Controller and LQR: Performance Analysis Without and With Disturbance Input , 2014, Int. J. Autom. Comput..