Control System Design Using Improved Newton-Raphson Method and Optimal Linear Model of Nonlinear Equations

Model reference techniques are successfully used in many control system designs. particularly in the field of model reference adaptive control systems. In this paper for a linear single-input, single-output time-invariant system, a method for modeling transfer functions of reference model using the basic performance specifications is presented. A set of non-linear equations is constructed from the definitions of the performance specifications and the unknown coefficients of a transfer function. Improved Newton-Raphson method and optimal linear model are applied to solve the non-linear equations. The proposed method constructs approximate representations of the desired transfer functions to ensure more rapid convergence of the numerical method. First, improved Newton-Raphson method is developed. Second. a optimal linearization technique is explained to obtain optimal linear model of nonlinear equations. Finally, simulation with four specifications is carried out to obtain a second-order transfer function model and demonstrate our method.