Effect of past History on Transient Response of a Closed Loop System with Fractional PI Controller

Correct initialization plays an important role in solving a fractional differential system. However, the problem of non-zero initialization in a control system consisting of a fractional PI/PID controller is not given proper attention by many authors. This paper attempts to solve this problem by using the Infinite state approach and show the effect of initialization on the transient response of a closed loop system with fractional PI controller. The idea is demonstrated through simulation results based on the fractional integrator method which clearly shows that unless and until proper initialization is incorporated, using a superior fractional PI/PID controller to improve the transient response of the system is incomplete.

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