Improving Track Performance by Combining Padé-Approximation-Based Preview Repetitive Control and Equivalent-Input-Disturbance

Improving Track Performance by Combining Padé-Approximation-Based Preview Repetitive Control and Equivalent-Input-Disturbance

25 February 2024 | Yong-Hong Lan, Jia-Yu Zhao
This paper proposes a method for improving the tracking performance of continuous-time uncertain systems by combining Padé-approximation-based preview repetitive control (POPRC) with equivalent-input-disturbance (EID). The method first constructs a delay-free state-space representation of the modified repetitive control (MRC) system using the Padé-approximation method. Then, an augmented dynamic system incorporating the output of the MRC system is established. By introducing a quadratic performance index, the POPRC problem is transformed into a linear quadratic regulation problem of the augmented dynamic system. To ensure the robustness of the closed-loop system in the presence of external disturbances, the standard EID technique is combined with the POPRC law using the Separation Theorem. The stability of the overall control system is proved using the small-gain theorem. A simplified POPRC law with EID is obtained for the original system. Simulation results are presented to illustrate the effectiveness and robustness of the controller. Preview control (PC) is an effective method for improving the tracking control performance of a system by using future information from the reference/disturbance signals. Repetitive control (RC) is an effective method for tracking periodic reference/disturbance signals. The combination of PC and RC is called preview repetitive control (PRC). In previous studies, PRC was first designed for position control of DC servo motor. To further enhance the robustness of the control system, sliding mode PRC was investigated and applied to the position control system of the logical disk manager. Subsequently, an observer-based PRC law for uncertain discrete-time systems was presented. However, the PRC laws proposed in these works include time-delay compensation terms, which can potentially reduce the robustness and steady-state tracking accuracy of the control system. In addition, it is challenging to prove the controllability and observability of the systems with relative degree greater than zero before using LQR technology. Based on these observations, in this paper, we will concern the POPRC with EID design problem of continuous time uncertain systems. The main contributions are as follows: (1) By using Padé-approximation method, we first attempt to rewrite state-space representation of MRC system into a delay free one. This helps the controllability and observability conditions of the linear quadratic regulator (LQR) theory degrade to the original system. Furthermore, it enhances the robustness and improves the steady-state tracking accuracy of the control system. (2) An augmented dynamic system is constructed by incorporating the output vector of the MRC, state feedback and error integration. Then, the regulator problem of non-delay augmented systems is solved, and the optimal PRC law of the original system is derived. (3) The feedback control is improved by integrating an active disturbance rejection part, and the analysis and the design of the system are straightforward.This paper proposes a method for improving the tracking performance of continuous-time uncertain systems by combining Padé-approximation-based preview repetitive control (POPRC) with equivalent-input-disturbance (EID). The method first constructs a delay-free state-space representation of the modified repetitive control (MRC) system using the Padé-approximation method. Then, an augmented dynamic system incorporating the output of the MRC system is established. By introducing a quadratic performance index, the POPRC problem is transformed into a linear quadratic regulation problem of the augmented dynamic system. To ensure the robustness of the closed-loop system in the presence of external disturbances, the standard EID technique is combined with the POPRC law using the Separation Theorem. The stability of the overall control system is proved using the small-gain theorem. A simplified POPRC law with EID is obtained for the original system. Simulation results are presented to illustrate the effectiveness and robustness of the controller. Preview control (PC) is an effective method for improving the tracking control performance of a system by using future information from the reference/disturbance signals. Repetitive control (RC) is an effective method for tracking periodic reference/disturbance signals. The combination of PC and RC is called preview repetitive control (PRC). In previous studies, PRC was first designed for position control of DC servo motor. To further enhance the robustness of the control system, sliding mode PRC was investigated and applied to the position control system of the logical disk manager. Subsequently, an observer-based PRC law for uncertain discrete-time systems was presented. However, the PRC laws proposed in these works include time-delay compensation terms, which can potentially reduce the robustness and steady-state tracking accuracy of the control system. In addition, it is challenging to prove the controllability and observability of the systems with relative degree greater than zero before using LQR technology. Based on these observations, in this paper, we will concern the POPRC with EID design problem of continuous time uncertain systems. The main contributions are as follows: (1) By using Padé-approximation method, we first attempt to rewrite state-space representation of MRC system into a delay free one. This helps the controllability and observability conditions of the linear quadratic regulator (LQR) theory degrade to the original system. Furthermore, it enhances the robustness and improves the steady-state tracking accuracy of the control system. (2) An augmented dynamic system is constructed by incorporating the output vector of the MRC, state feedback and error integration. Then, the regulator problem of non-delay augmented systems is solved, and the optimal PRC law of the original system is derived. (3) The feedback control is improved by integrating an active disturbance rejection part, and the analysis and the design of the system are straightforward.
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[slides and audio] Improving Track Performance by Combining Pad%C3%A9-Approximation-Based Preview Repetitive Control and Equivalent-Input-Disturbance