Regular Papers

International Journal of Control, Automation and Systems 2022; 20(4): 1063-1075

Published online April 2, 2022

https://doi.org/10.1007/s12555-021-0121-1

© The International Journal of Control, Automation, and Systems

Continuous-time Nonlinear Robust MPC for Offset-free Tracking of Piece-wise Constant Setpoints with Unknown Disturbance

Abbas Zamani* and Hossein Bolandi

Iran University of Science & Technology

Abstract

This paper develops a novel robust tracking predictive controller for continuous-time nonlinear systems capable to deal with changing setpoints and unknown non-additive bounded disturbance. The sudden changes in a setpoint and/or existence of disturbance may lead to feasibility and stability issues if a stabilizing terminal constraint-based predictive controller is used. The robust tracking MPC presented in this paper extends the artificial reference-based nonlinear MPC for continuous-time systems and disturbance rejection. Closed-loop input-to-state stability and recursive feasibility of the optimization problem are guaranteed by tightening the terminal region, input constraint, and appropriate terminal cost function. An explicit formula that specifies the bound of sampling time interval is also introduced. We show that the proposed controller can reach an offset-free tracking if the disturbance is slowly time varying. However, in the case of non-slowly varying disturbance, a specific bound on tracking error will be guaranteed using an appropriate disturbance observation error based Lyapunov function. The satellite attitude control system simulation results are provided to show the efficiency of the proposed controller.

Keywords Continuous-time MPC, nonlinear systems, recursive feasibility, robust control.

Article

Regular Papers

International Journal of Control, Automation and Systems 2022; 20(4): 1063-1075

Published online April 1, 2022 https://doi.org/10.1007/s12555-021-0121-1

Copyright © The International Journal of Control, Automation, and Systems.

Continuous-time Nonlinear Robust MPC for Offset-free Tracking of Piece-wise Constant Setpoints with Unknown Disturbance

Abbas Zamani* and Hossein Bolandi

Iran University of Science & Technology

Abstract

This paper develops a novel robust tracking predictive controller for continuous-time nonlinear systems capable to deal with changing setpoints and unknown non-additive bounded disturbance. The sudden changes in a setpoint and/or existence of disturbance may lead to feasibility and stability issues if a stabilizing terminal constraint-based predictive controller is used. The robust tracking MPC presented in this paper extends the artificial reference-based nonlinear MPC for continuous-time systems and disturbance rejection. Closed-loop input-to-state stability and recursive feasibility of the optimization problem are guaranteed by tightening the terminal region, input constraint, and appropriate terminal cost function. An explicit formula that specifies the bound of sampling time interval is also introduced. We show that the proposed controller can reach an offset-free tracking if the disturbance is slowly time varying. However, in the case of non-slowly varying disturbance, a specific bound on tracking error will be guaranteed using an appropriate disturbance observation error based Lyapunov function. The satellite attitude control system simulation results are provided to show the efficiency of the proposed controller.

Keywords: Continuous-time MPC, nonlinear systems, recursive feasibility, robust control.

IJCAS
July 2024

Vol. 22, No. 7, pp. 2055~2340

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eISSN 2005-4092
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