Parametric identification of fractional-order nonlinear systems

Abstract

This work presents a new method for the identification of fractional-order nonlinear systems from time domain data. A parametric identification technique for integer-order systems using multiple trials is generalized and adapted for identification of fractional-order nonlinear systems. The time response of the system to be identified by two different harmonic excitations are considered. An initial value of the fractional-order term is assumed. Other system parameters are identified for each of the trial data by finding the pseudo-inverse of an equivalent algebraic system. A termination criterion is specified in terms of the error between identified values of system parameters from the two trials. If the error in system parameters does not fall in the specified tolerance, the value of the fractional-order term is varied using gradient descent method and identification is carried out until convergence. The validity of the proposed algorithm is demonstrated by applying it to fractional-order Duffing, van der Pol and van der Pol–Duffing oscillators. Numerical simulations show that the exact and identified parameters are in very close agreement. Comparison of the time taken for identification by the proposed method and those which define error in terms of time response shows the effectiveness of the method. Furthermore, the validity of the proposed method for identification of chaotic fractional-order systems is demonstrated by showing that the identified values are independent of signal time length used.