A fundamental study of loop shaping on H∞ control designs by fractional order calculus

This paper deals with the design of fractional order control (FOC), in which controllers described by differential equations of non-integer orders. The purpose of this paper is to take advantage of the introduction of the control parameters and satisfy additional specifications of design, ensuring a robust performance of the controlled system with respect to gain variations and noise. A method for tuning the controller is proposed in this paper to fulfill five different design specifications. The specifications about gain crossover frequency and phase margin are readily satisfied, together with the damping property of the time response of the controlled system is not deteriorated. Simulation results are given to illustrate the effectiveness of this method.