New analytical design of the Smith predictor controller for high-order systems

Abstract

In this paper, a new analytical Smith predictor (SP) controller design method is proposed for industrial and chemical high-order systems. Firstly, by using the integral-squared-error (ISE) performance specification, the ideally optimal SP controller is analytically derived according to the nominal high-order plant model, which inevitably results in the high-order controller. Then the analytical controller reduction formulae based on the mathematical Maclaurin and Padé expansions are proposed to duplicate it in the form of a low-order controller such as the proportional-integral-derivative (PID). Hence, the difficulty of controller implementation in practice is significantly relieved without pitiful system performance degradation in comparison with many existing methods. At the same time, the control system robust stability is analysed. Accordingly, the on-line tuning rule of the single adjustable parameter of the proposed controller is provided to cope with the actual system uncertainties. Finally, several illustrative simulation examples are included to demonstrate the effectiveness of the proposed method.