ANALYTICAL DESIGN OF CGPC-BASED PID CONTROLLERS FOR COMMONLY ENCOUNTERED ENGINEERING SYSTEMS

Abstract

The traditional PID controllers have continued to be the most widely implemented control technique in the industries for many years because of its structural simplicity and its transparent tuning rules. In this work, an analytical design method for PID controllers based on continuous generalized predictive control (CGPC) law is proposed. The design method consists of two steps. The first step entails tuning a CGPC system to obtain a satisfactory closed-loop response. Thereafter a truncated Maclaurin series is employed to approximate the designed CGPC law.  Four simulation examples are used to demonstrate the effectiveness of the proposed method. The four examples used are the commonly encountered engineering systems which range from a first order plus time delay system, a second order plus time delay system, a third order system and a non-minimum phase system which has been known to be very problematic to control. The simulation results obtained showed that the proposed CGPC-based PID controllers provided good set-point tracking and disturbance rejection and compared favourably well with PID controllers designed by Ziegler-Nichols and Direct-Synthesis methods. The controllers are also found to be robust as indicated by the small values of computed sensitivity peak.