An Extended Experimental Study on Control of Unstable and Non-Minimum Phase Plants With the Cascaded Form of a Fractional Order Compensator

Abstract

With the advent and emergence of calculus with fractional order (FO), the generalized form of the integer order (IO) has created significant advancement in the field of control. The real time systems represented by the FO models are more accurate enough developing improved performance in contrast to the classical IO one. In this context, the area is still deficient of methodical design algorithms with the different available structures of the FO compensators to control the various types of any unstable and non-minimum phase (NMP) Linear Time Invariant (LTI) plants. There is dearth of detailed analytical and experimental work on the cascaded form of this FO lead compensator in the available literatures. The cascaded structure of the non-integer order compensator is therefore employed here through classical control theory to exhibit the simplified design method in frequency domain explicitly through numerical studies and MATLAB simulation results. These FO compensators with its non-integer order helps one to add the required exact magnitude and phase to the plant to be compensated at a particular frequency thus leading to the unique solution of the desired compensator parameters. This proposition has been further extended to compensate a highly non-linear unstable NMP Cart-Inverted Pendulum System. Experimental results have been appended in support of the method explained to show the applicability of this study in control system design.