Multi-Objective Optimal Feedback Controls for Under-Actuated Dynamical System
- PDF / 1,607,794 Bytes
- 8 Pages / 612.284 x 810.709 pts Page_size
- 63 Downloads / 197 Views
Multi-Objective Optimal Feedback Controls for Under-Actuated Dynamical System QIN Zhichang 1∗ (
),
XIN Ying 2,3 (
ê )
), SUN Jianqiao 4 (
(1. School of Transportation and Vehicle Engineering, Shandong University of Technology, Zibo 255000, Shandong, China; 2. School of Mechanical Engineering, Tianjin University of Technology, Tianjin 300384, China; 3. Tianjin Key Laboratory for Advanced Mechatronic System Design and Intelligent Control, Tianjin University of Technology, Tianjin 300384, China; 4. School of Engineering, University of California Merced, CA 95343, USA)
© Shanghai Jiao Tong University and Springer-Verlag GmbH Germany, part of Springer Nature 2020 Abstract: This paper presents a study of optimal control design for a single-inverted pendulum (SIP) system with the multi-objective particle swarm optimization (MOPSO) algorithm. The proportional derivative (PD) control algorithm is utilized to control the system. Since the SIP system is nonlinear and the output (the pendulum angle) cannot be directly controlled (it is under-actuated), the PD control gains are not tuned with classical approaches. In this work, the MOPSO method is used to obtain the best PD gains. The use of multi-objective optimization algorithm allows the control design of the system without the need of linearization, which is not provided by using classical methods. The multi-objective optimal control design of the nonlinear system involves four design parameters (PD gains) and six objective functions (time-domain performance indices). The Hausdorff distances of consecutive Pareto sets, obtained in the MOPSO iterations, are computed to check the convergence of the MOPSO algorithm. The MOPSO algorithm finds the Pareto set and the Pareto front efficiently. Numerical simulations and experiments of the rotary inverted pendulum system are done to verify this design technique. Numerical and experimental results show that the multi-objective optimal controls offer a wide range of choices including the ones that have comparable performance to the linear quadratic regulator (LQR) control. Key words: multi-objective optimal control, under-actuated system, particle swarm optimization (PSO), rotary inverted pendulum CLC number: O 232 Document code: A
Nomenclature Barm — Viscous damping coefficient of arm Bp — Viscous damping coefficient of pendulum g— Gravity constant larm — Rotary arm length from pivot to center of mass lp — Distance from pivot to center of mass Lp — Full length of pendulum Jarm — Rotary arm moment of inertia about pivot Jp — Pendulum moment of inertia about pivot Kg — Total gearbox ratio Km — The back electromotive force constant
0 Introduction Feedback controls are applied to various engineering systems. Many design or tuning methods for feedReceived date: 2018-04-13 Foundation item: the National Natural Science Foundation of China (Nos. 11572215 and 11702162), and the Natural Science Foundation of Shandong Province (No. ZR2018LA009) ∗E-mail: [email protected]
Kt — Motor torque constant marm , mp — Rotary arm mass, pendulum mass
Data Loading...
