Integrating systems with time delay are found in modeling of liquid level systems, liquid storage tanks, boilers, batch chemical reactors and bottom level control of a distillation column. There also exist Processes such as aerospace control system, vertical take-off air place (Filatov et al, 1996), DC motors
and high speed disk drives (Liu et al., 2004). Oxygen control in fed batch fragmental fungal fermentation reactors (Bodizs et a1.2007) whose dynamics show the characteristics of double integrating types.
There are number of methods available in the literature for designing PID controllers for pure integrating with time delay. They are: methods based on stability criteria (Ziegler Nichols, 1942; Tyreus and Luyben, 1992; Chidambaram, 1994; Poulin and Pomerleau, 1999; Luyben, 1996; Wang and Cluette, 1997; Kookos et al., 1999; Wang and Cai, 2002 ;), optimization method (Visioli, 2001; Zhang et al., 1999), IMC method (Rivera et al., 1986; Chien and Fruehauf, 1990; Skogestad, 2003), two degree Freedom Controller (Sung and Lee, 1996), modified smith predictor method for large time delay (Matausek and Micic, 1999; Majhi and Atherton, 1999) and direct synthesis method (Seshagiri Rao and Chidambaram, 2008).
Generally when a PID Controller is designed for a process, it is designed to give best performance for the regulatory problem. The same PID is used for a servo problem which leads to a large overshoot for integrating and unstable systems. The overshoot is reduced by set point weighted PID controller. Many of the commercial PID controllers have the set point weighted PID action. However, the method for the Selection of set point weighting parameter is not given for integrating and unstable systems.
Therefore, the present work is intended to calculate set point weighting parameter for integrating Systems, double integrating systems and unstable/stable FOPTD(First Order Plus Time Delay) systems with an integrator using numerical optimization of ISE (Integral Square Error), IAE (Integral Absolute Error), ITAE (Integral Time weighted Absolute Error) using MATLAB and simulink
It is also proposed to extend the equating coefficient method (Padma Sree and Chidambaram, 2004) for the calculation of set point weighting parameter for unstable systems to the above mentioned systems and Compare the servo performance with numerical optimization methods.
Simulations on various transfer function models of integrating system with time delay, double integrating system with time delay and stable/unstable FOPTD system with an integrator show that both the methods give improved performance with less ISE, IAE and ITAE values when compared with the conventional PID controller and the conventional PID controller with a set point filter (Lee et al., 1999).