Parameter Identification of Fractional Order Systems Using a Hybrid of Bernoulli Polynomials and Block Pulse Functions

Block pulse functions (BPFs) are piecewise constant and not sufficiently smooth. Therefore, their accuracy is limited when it comes to identifying the parameters of fractional order systems (FOSs). This in turn means that BPFs are incapable of offering highly accurate parameter identification results. However, using a great number of BPFs would significantly increase the dimension of the operational matrix and thereby adds to the computational complexity and burden. To overcome this problem, we present here a hybrid function method for identifying FOSs. The method utilizes a hybrid of Bernoulli polynomials and block pulse functions (HBPBPFs) as the base functions to approximate input and output signals. The fractional integral operational matrix of HBPBPFs is derived and used to convert an FOS to an algebraic system. The parameters of the FOS are successfully identified by minimizing the mean square error between the output of the true system and that of the algebraic representation of the FOS. The simulation experiment verifies that our proposed HBPBPFs method is effective and can generate more accurate identification results than existing BPFs methods.