Tuning Three-Term Controllers for Integrating Processes with both Inverse Response and Dead Time

Most industrial processes respond to the actions of a feedback controller by moving the process variable in the same direction as the control effort. However, there are some interesting exceptions where the process variable first drops, then rises after an increase in the control effort. This peculiar behaviour that is well known as “inverse response”, is due to the non-minimum phase zeros appearing in the process transfer function and representing part of the process dynamics. Second order dead-time inverse response process models (SODT-IR) are used to represent the dynamics of several chemical processes (such as level control loops in distillation columns and temperature control loops in chemical reactors), as well as the dynamics of PWM based DC-DC boost converters in industrial electronics. In the extant literature, there is a number of studies regarding the design and tuning of three-term controllers for SOPD-IR processes (Chen et al, 2005, 2006; Chien et al, 2003; Luyben, 2000; Padma Sree & Chidambaram, 2004; Scali & Rachid, 1998; Waller & Nygardas, 1975; Zhang et al, 2000). On the other hand, integrating models with both inverse response and dead-time (IPDT-IR models) was found to be suitable for a variety of engineering processes, encountered in the process industry. The common examples of such processes are chemical reactors, distillation columns and, especially, level control of the boiler steam drum. In recent years, identification and tuning of controllers for such process models has not received the appropriate attention as compared to other types of inverse response processes, although some very interesting results have been reported in the literature (Gu et al, 2006; Luyben, 2003; Shamsuzzoha & Lee, 2006; Srivastava & Verma, 2007). In particular, the method reported by (Luyben, 2003) determines the integral time of a series form PID controller as a fraction of the minimum PI integral time, while the controller proportional gain is obtained by satisfying the specification of +2 dB maximum closed-loop log modulus, and the derivative time is given as the one maximizing the controller gain. In the work proposed by (Gu et al, 2006), PID controller tuning for IPDT-IR processes is performed based on H∞ optimization and Internal Model Control (IMC) theory. In the work