Adaptive step size numerical algorithm for fractional order control systems

Abstract

For fractional order control systems, fast and accurate numerical algorithm is the key step in real-time control and simulation. Although the short memory method (SMM) and the constant weight memory method (CWMM) accelerate the computation speed through the choice and approximation of the historical information of the fractional differential operator, the computation precision decreases with the increase of time. The CWMM is affected by input function and the error range is large. Considering the limitation of fixed step size discretization (FSSD) of fractional differential operator, a variable step size discretization (VSSD) scheme is utilized. According to the local error obtained by the step-doubling technique, the iterative step size is adjusted adaptively. The algorithm not only can achieve good accuracy, uniform error, but also fast calculation speed, which provides a feasible way for the numerical calculation of state space description of fractional order control system. Finally, the reliability of the algorithm is verified by an example.