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Design a pre-compensator to guarantee the finiteness of integral performance indices in fractional-order control systems

It is known that due to the existence of non-exponential modes in the step response of a fractional-order control system having zero steady-state error, integral performance indices of such a system may be unbounded. In the present study, a pre-compensator is designed to guarantee the boundedness of different integral performance indices (such as the integral of absolute error (IAE), the integral of squared error (ISE), the integral of time multiplied absolute error (ITAE), the integral of time multiplied squared error (ITSE), and the integral of squared of time multiplied error (ISTE)) in fractional-order control systems. Using this pre-compensator can improve the convergence rate of the step responses of fractional-order control systems. Numerical simulation results are presented to show the usefulness of the proposed method.