Evaluation strategies of fractional order controllers discretization methods

To solve the difficulties of the discretization and application of fractional order controllers (FOC), evaluation strategies of digital realization of FOC are investigated. The realization principle and process of various discretization methods are discussed. One position control system is introduced as the objective controlled by FOC. Based on Mittag-Leffler function, the fractional order control system with full memory length is adopted as evaluation criterion, and an approximation performance function of discretization methods is proposed. Analyzing the time domain error and approximation performance, the investigation to various discretization methods is carried out comparatively in detail. The result verifies that the discrete model with power series direct discretization method requires 100 memory length to obtain the better approximation, while one with continued fraction direct discretization method requires only 10 order. Thus the continued fraction direct discretization method is preferable to digital realization of fractional order control algorithms in engineering applications.