C.1 Relay Tuning of Integrating Plus FOPTD Systems

The most used dynamic model for chemical engineering process is the FOPTD model. In many cases, time constant is very large; in some cases, dead time is the dominant one. In the literature, industrial examples of large time constants are reported by McNeill and Sacks (1969) for distillation and by Westerlund et al. (1980) for cement production. Some of the processes such as heating boilers, liquid storage tanks and batch chemical reactors are examples of integrating processes in industrial and chemical plants (Liu et al., 2005)

Zhang et al. (1999) proposed PID controller design method for integrating process with dead time and time constant. Kwak et al. (1997) proposed an online identification and autotuning method for integrating process. Kookos et al. (1999) proposed online PI controller tuning for integrating/dead time processes. Tian and Gao (1999) proposed a control scheme for integrating process with dominant time delay. The proposed scheme consist of a local proportional feedback to pre-stablize the process, a proportional controller for set-point tracking and a PD controller for load disturbance rejection. Huzmezan et al. (2002) designed a PID controller based on adaptive predictive control strategy to handle integrating type processes with large time constant. An industrial example of temperature control of a process that involves the heating and cooling of a batch reactor is studied.

C.2 Improved Analysis of Relay Tuning

The transfer function model for the integrating plus FOPTD system is given by Kp exp(-Ds)/[s(τs + 1)].