Predictive PID Control of Non-Minimum Phase Systems

Control engineers have been aware of non-minimum phase systems showing either undershoot or time-delay characteristics for some considerable time (Linoya & Altpeter, 1962; Mita & Yoshida, 1981; Vidyasagar, 1986; Waller & Nygardas, 1975). A number of researchers that addressed this problem from a predictive control point of view mainly followed one of two approaches: a classical (non-optimal) predictive approach or a modern optimisation based predictive approach (Johnson & Moradi, 2005). The common characteristic of all these approaches is that they are model-based. Predictive control allows the controller to predict future changes in the output signal and to use this prediction to generate a desirable control variable. The classical predictive controllers that are most widely considered include the Smith predictor structure and the internal model control (IMC) structure (Katebi & Moradi, 2001; Morari & Zafiriou, 1989; Tan et al., 2001). Modern predictive controllers consider generalised predictive control (GPC) or model-based predictive control (MPC) structures (Johnson & Moradi, 2005; Miller et al., 1999; Moradi et al., 2001; Sato, 2010). The performance of a PID controller degrades for plants exhibiting non-minimum phase characteristics. In order for a PID controller to deal with non-minimumphase behaviour, some kind of predictive control is required (Hägglund, 1992). Normally the derivative component of the PID controller can be considered as a predictive mechanism, however this kind of prediction is not appropriate when addressing non-minimum phase systems. In such a case the PI control part is retained and the prediction is performed by an internal simulation of plant inside the controller. This chapter starts with a quick review of the system-theoretic concept of a pole and zero and then draws the relationship to non-minimum phase behaviour. The relationship between the undershoot response and time-delay response will be discussed using Padé approximations. Classical and modern predictive PID control approaches are considered with accompanying examples. The main contribution of the chapter is to illustrate the context and categories of predictive PID control strategies applied to non-minimum phase systems by: