PID-Like Controller Tuning for Second-Order Unstable Dead-Time Processes

Several processes encountered in various fields of engineering exhibit an inherently unstable behaviour coupled with time delays. To approximate the open loop dynamics of such systems for the purpose of designing controllers, many of these processes can be satisfactorily described by unstable transfer function models. The most widely used models of this type is the unstable first order plus dead-time (UFOPDT) and the unstable second order plus dead-time (USOPDT) transfer function models, which take into account dead times that might appear in the model, due to measurement delay or due to the approximation of higher order dynamics of the process, by a simple transfer function model. Research on tuning methods of two or three-term controllers for unstable dead-time processes has been very active in the last 20 years. The most widely used feedback schemes for the control of such processes are the Proportional-Integral-Differential (PID) controller with set-point filter (Jung et al, 1999; Lee et al, 2000), the Pseudo-Derivative Feedback (PDF) or I-PD controller (Paraskevopoulos et al, 2004), and the Proportional plus Proportional– Integral–Derivative (P-PID) controller (Jacob & Chidambaram, 1996; Park et al, 1998). These control schemes are identical in practice, provided that the parameters of the controllers and of the pre-filters needed in some cases are selected appropriately. Controller tuning for unstable dead-time processes has been performed according to several methods, the most popular of them being various modifications of the Ziegler-Nichols method (De Paor & O’ Malley, 1989; Venkatashankar & Chidambaram, 1994; Ho & Xu, 1998), several variations of the direct synthesis tuning method (Jung et al, 1999; Prashanti & Chidambaram, 2000; Paraskevopoulos et al, 2004; Padma Sree & Chidambaram, 2004), the ultimate cycle method (Poulin & Pomerleau, 1997), the pole placement method (Clement & Chidambaram, 1997), the method based on the minimization of various integral criteria, the Internal Model Control (IMC) tuning method (Rotstein & Lewin, 1991; Lee et al, 2000; Yang et al, 2002; Tan et al, 2003), the optimization method (Jhunjhunwala & Chidambaram, 2001; Visioli, 2001), the two degrees of freedom method (Huang & Chen, 1997; Liu et al, 2005; Shamsuzzoha et al, 2007), etc. (see the work (O’Dwyer, 2009), and the references cited therein). Moreover, due to the wide practical acceptance of the gain and phase margins (GPM) in characterizing system robustness, some tuning methods for unstable dead-time models, based on the satisfaction of GPM specifications, have also been reported (Ho & Xu, 1998; Fung et al, 1998;