Abstract
In the feedback control robotic systems, the repetitive control method has a high control performance for the track or elimination of the periodic signals. The promotion of the plug-in type configuration of the controller broadens the application range and applicability of the control method. In this article, a novel design algorithm based on the steady-state residual convergence ratio of the repetitive control system is proposed to improve the performance of the stabilized platform to resist the periodic perturbation. The basic structure and stable condition of the plug-in type repetitive control method are first introduced by applying the small gain theorem and the stability theorem for time-lag systems. Then the analysis of the convergence rate is utilized in constructing the basic index of the design algorithm of a plug-in type repetitive control system based on a steady-state residual convergence ratio. The parameters of the designed controller are checked by the validity condition of the plug-in type repetitive control system, and a simulation example is given to verify the effectiveness of the design algorithm. The article provides basic design guidelines and schemes for the design of the periodic disturbance suppression performance of the feedback control system. In the final physical prototype experiment, the prospective steady-state residual convergence ratio is basically achieved within the allowable range of error.
Highlights
Repetitive control is a useful servo design tool for systems that are surrounded by periodic disturbances
Perturbation– rejection experiments are designed to realize the certification of the simulation example and to explore the effectiveness of the design algorithm based on the index of the steady-state residual convergence ratio
Based on the comprehensive analysis, it can be concluded that the steady-state residual convergence ratio of 0.376% in the physical prototype experiment has achieved a great deal of reach of the design index of 0.02%, and the correctness and validity of the design algorithm of the plug-in type repetitive control system (PITR) based on the steady-state residual convergence ratio can be verified basically
Summary
Repetitive control is a useful servo design tool for systems that are surrounded by periodic disturbances. The shortcoming of the harsh condition for the stabilization in the standard repetitive controller appears in the actual system, but the frequency of periodic signals that the control system needs to track or suppress does not need to reach infinity To solve this problem, some scholars try to set a low-pass filter before the delay module so that the undesired high-frequency components are cut off to improve the repetitive controller.[23] The improved method is analyzed in detail and its exponential stabilization condition is given to extend this method to a multivariable control system.[1] The improved repetitive controller is called a plug-in type repetitive controller (abbreviated as PITRC) for it can be inserted into the control loop without affecting the performance of the original controller.
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