On the Use of the Udwadia-Kalaba Equations for the Nonlinear Control of a Generalized Van Der Pol-Duffing Oscillator

Abstract

In this paper, a new method for controlling nonlinear mechanical systems is proposed. The methodology developed in this work is based on the use of the Udwadia-Kalaba equations in conjunction with the modern techniques of optimal control. The Udwadia-Kalaba equations represent an effective method for solving forward and inverse dynamics problems in the same analytical framework. On the other hand, the optimal control method is used in this work in combination with the inverse dynamic approach based on the Udwadia-Kalaba equations in order to obtain a nonlinear tracking controller. The mechanical system considered in this paper for performing numerical experiments is a nonlinear oscillator which includes in a generalized form the Van der Pol model for the system damping and the Duffing model for the system stiffness. The numerical results presented in this paper demonstrate the effectiveness of the method developed in this investigation.