Closed-loop time response analysis of irrational fractional-order systems with numerical Laplace transform technique

Irrational transfer function has been widely used in modelling and identification. But time response analysis of systems with irrational transfer functions is hard to be achieved in comparison with the rational ones. One of the main reasons is that irrational transfer function generally has infinite poles or zero. In this paper, the closed-loop time response of fractional-system with irrational transfer function is analyzed based on numerical inverse Laplace transform. The numerical solutions and stability evaluation of irrational fractional-order systems are presented. Several examples of fractional-order systems with irrational transfer functions are shown to verify the effectiveness of the proposed algorithm in both time and frequency domain analysis. The MATLAB codes developed to solve the fractional differential equations using numerical Laplace transform are also provided. The results of this paper can be used on analysis and design of control system described by irrational fractional-order or integer-order transfer function.