Abstract
This paper is concerned with the design of a PID-based repetitive control strategy for a strictly proper plant with requirements of high-precision tracking performance for periodic signals and good rejecting performance for an external disturbance with a finite frequency range. The PID-based controller consists of a PID controller and a repetitive controller connected in series, and its control parameters are optimized to meet the performance requirements. First, utilizing Youla–Kucera Parameterization, the necessary and sufficient conditions for the existence of the PID-based repetitive controller are derived. Second, from the requirements of the control performance and the analysis of the sensitivity function, the description of the PID-based repetitive controller is deduced. Third, the design of PID control parameters depends on the stability of closed-loop system and the attenuation performance. By introducing an arbitrarily small relaxation variable and applying the $H_\infty $ control method, the design problem is transformed into a generalized eigenvalue minimization problem (GVEP) under linear matrix inequality (LMI) constraints. In addition, the largest cutoff frequency in the repetitive controller is also achieved by solving a GVEP. Finally, simulations are applied to examine the validity and efficacy of the proposed method.
Highlights
In the periodic production process, the application of repetitive control to obtain high-precision tracking performance has achieved remarkable results
Most research results only focus on the reference input tracking performance, disturbance rejection performance, or passive disturbance attenuation performance when the period time of the disturbance is equal to the period time of reference input for passive disturbances [7]
This paper proposes a design method for an optimal PID-based repetitive controller of a strictly proper plant to simultaneously track a periodic signal and reject disturbances
Summary
In the periodic production process, the application of repetitive control to obtain high-precision tracking performance has achieved remarkable results. For some external disturbance signals with unknown or unmeasured period time, the application of higher-order repetitive controllers can help to improve the disturbance rejection performance [3]–[6]. A high-order repetitive controller can improve the attenuation performance for unknown or time-varying period frequency components and guarantee a good tracking performance for known periodic signals [12]. High-precision tracking properties for periodic signals and to consider an external disturbance with frequency components that differ from that of the reference input. To track the periodic signals for a strictly proper plant with high control precision, the modified repetitive controller is adopted, and the optimal low-pass filter needs to be determined [14]. This paper proposes a design method for an optimal PID-based repetitive controller of a strictly proper plant to simultaneously track a periodic signal and reject disturbances. Numerical examples illustrate the validity of the developed design method in this paper
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