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The pure integrating process model with dead-time is inherently an unstable open-loop system. This paper presents a 2-DOF (2-degree of freedom) PID controller, based on the direct synthesis (DS) method, to improve the set-point tracking and load disturbance rejection performance for the pure integrating processes with time delays (PIPTD) models. The 2-DOF PID controller consists of a linear PID controller for rejecting the load disturbance in regulatory response and a set-point filter for relieving the overshoot in servo response. The DS method is based on comparing the desired closed-loop characteristic equation with the closed-loop characteristic equation, consisting of plant and PID controller. The adjustment parameter is only one desired time constant, with the roots of the desired characteristic equation placed at the same location, and the desired time constant was expressed as a function of the maximum magnitude of the sensitivity function (MS), for providing convenience in the selection of the desired time constant. The proposed controller is simulated by applying it to three other processes and comparing it with conventional methods, to demonstrate its effectiveness and applicability.

Design of Linear PID Controller for Pure Integrating Systems with Time Delay Using Direct Synthesis Method