Model-Matching Fractional-Order Controller Design Using AGTM/AGMP Matching Technique for SISO/MIMO Linear Systems

A new two-stage method is proposed for the model-matching fractional-order (FO) controller (FOC) design for the single-input single-output (SISO) / multiple-input multiple-output (MIMO) linear systems. A streamlined procedure for the selection of reference model M(s), based on a linear quadratic regulator (LQR) with integral action (LQRI) is presented. Since the proposed M(s) is designed using the optimal control theory, the designed output-feedback closed-loop system can be termed as a suboptimal one. Formulation of M(s) incorporates the time-domain characteristics, and the optimal interaction desired to be present in the designed closed-loop system. The developed controller design procedure also works with a user-specified M(s). In the first stage of the controller design, a higher-order controller K(s) which makes the closed-loop system exactly equal to the M(s) is obtained. In the second stage, K(s) is approximated to a FOC or an integer-order (IO) controller (IOC) C(s) with the aim of matching a certain number of approximate generalized time moments (AGTMs) and/or approximate generalized Markov parameters (AGMPs) of K(s) to those of C(s) at a set of frequency points in the s-plane. The simulation and experimental validation of the proposed approach are performed by the design and implementation of the controller for an IO MIMO plant with time-delays. The controller design algorithm is also illustrated based on the user-defined reference model for a FO MIMO plant with time-delays taken from the literature. The obtained results show that the FOC results in better performance compared with its IO counterpart.