Abstract

The present study proposes a novel proportional-integral-derivative (PID) control design method in discrete time. In the proposed method, a PID controller is designed for first-order plus dead-time (FOPDT) systems so that the prescribed robust stability is accomplished. Furthermore, based on the control performance, the relationship between the servo performance and the regulator performance is a trade-off relationship, and hence, these items are not simultaneously optimized. Therefore, the proposed method provides an optimal design method of the PID parameters for optimizing the reference tracking and disturbance rejection performances, respectively. Even though such a trade-off design method is being actively researched for continuous time, few studies have examined such a method for discrete time. In conventional discrete time methods, the robust stability is not directly prescribed or available systems are restricted to systems for which the dead-time in the continuous time model is an integer multiple of the sampling interval. On the other hand, in the proposed method, even when a discrete time zero is included in the controlled plant, the optimal PID parameters are obtained. In the present study, as well as the other plant parameters, a zero in the FOPDT system is newly normalized, and then, a universal design method is obtained for the FOPDT system with the zero. Finally, the effectiveness of the proposed method is demonstrated through numerical examples.

Highlights

  • Proportional-integral-derivative (PID) [1,2,3,4,5,6,7,8,9] control has few tuning parameters: proportional gain, integral time, and derivative time, and its structure is simple

  • Using the ZN method, the PID parameters are decided based on the step response trajectory so that the tracking performance is optimized

  • Robust PID control systems are designed in the discrete time domain [16,17], the stability margin cannot be prescribed

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Summary

Introduction

Proportional-integral-derivative (PID) [1,2,3,4,5,6,7,8,9] control has few tuning parameters: proportional gain, integral time, and derivative time, and its structure is simple. PID control has been widely used in industry, and numerous tuning methods have been proposed. In the model-based approach, optimal tracking and robust stability are achieved. As a simple model-based optimal design method, Ziegler and Nichols proposed the step response method (ZN method) [10]. Using the ZN method, the PID parameters are decided based on the step response trajectory so that the tracking performance is optimized. Robust control designs have been proposed [13,14]. Robust stability is obtained, but the tracking performance is not optimized. Robust PID control systems are designed in the discrete time domain [16,17], the stability margin cannot be prescribed

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