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Striking developments have taken place in feedback control theory after the evolution of the fractional-order (FO) control concept. However, for large-scale (high-order) systems, these well-established FO techniques become rigorous and lead to an infeasible solution. To overcome this issue, this paper proposes a three-fold control policy. The first step finds the optimal reduced-order (low-order) model using Big-Bang, Big-Crunch (BB–BC) optimisation algorithm. Based on the obtained reduced model, the control structure is formulated in the internal model control (IMC) framework. The controller acquires a PID form followed by an additional term and FO integrator. Unlike the FO-PID controller which demands five tuning parameters, the proposed controller requires only two tuning parameters whose evaluation is done on the basis of user specified gain crossover frequency and phase margin. To substantiate the design approach, a detailed simulation study has been carried out, in which the problems of tracking control, disturbance rejection, and time-delay compensation are illustrated.

Fractional-order IMC controller for high-order system using reduced-order modelling via Big-Bang, Big-Crunch optimisation