To improve the servo response of the system, a set point weighted Proportional Integral and Derivative (PID) controller is used. Two methods of calculating set point weighting parameter is proposed for integrating systems with time delay in this paper. First method is based on numerical optimization of Integral Square Error (ISE), Integral Absolute Error (IAE) and Integral Time Weighted Absolute Error (ITAE) for the closed loop servo problem. Second method is the extension of equating coefficient method for integrating systems. A simulink block diagram is generated using the process transfer function and the PID controller with set point weighting parameter which is updated by a MATLAB program using lsqnonlin/fminunc routines with ISE/IAE/ITAE as the objective functions. Optimum set point weighting parameter is obtained by minimizing these objective functions numerically. In the equating coefficient method, set point weighting parameter is obtained by matching the corresponding coefficients of s in the numerator with that of the denominator of the closed loop transfer function. The above set point weighted PID controllers are applied to various transfer function models and nonlinear models of integrating systems to show the efficiency of the proposed set point weighted PID controllers.

A PID controller is required for the stabilization of any process at its set point. In general, PID controllers are to be designed to give no overshoot. Generally when a PID controller is designed for a process, it is designed to give best performance for a regulatory problem. The same PID is used for the servo problem which sometimes leads to a large overshoot. Large overshoot indicates that the controlled variable changes very widely causing damage to the process. Therefore, set point weighted PID controller (Eitelberg, 1987; Hippe et al., 1989; and Park et al., 1998) is used to keep the operating/controlled variable in limits with less/no overshoot with faster servo response. PID controllers can be used along with a set point filter which gives no overshoot. This is equivalent to make set point weighting parameter equal to zero (Jung et al., 1999; Lee et al., 2000; and Astrom and Hagglund, 2004). But the response is very sluggish. Chidambaram (2000) has proposed a value of 0.4 for set point weighting parameter for integrating systems. Wang and Cai (2002) have proposed tuning formulae for set point weighted PID controller for stable First Order Plus Time Delay (FOPTD) system with an integrator. They have used a phase margin and gain margin of 60º and 3 respectively. Sravanthi and Padma Sree (2006) have proposed numerical optimization method to calculate set point weighting parameter for integrating systems. Seshagiri Rao et al. (2007) and Uma et al. (2010) have also used a value of 0.4 (Chidambaram, 2000) for set point weighting parameter to improve servo performance of the integrating systems.

Many of the commercial PID controllers have the set point weighted PID action. However, the method for the selection of the set point weighting parameter is not given in the literature for pure integrating, double integrating systems with time delay and stable/unstable FOPTD with an integrator. For integrating systems with time delay, the overshoot in the servo response is larger than that of the stable systems. Hence, there is a need for a method to calculate the set point weighting parameter for these systems. Therefore, the present work is intended to calculate the set point weighting parameter for such systems.

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