Elimination of Hard-Nonlinearities Destructive Effects in Control Systems Using Approximate Techniques

Many of the physical phenomena, such as friction, backlash, drag, etc., which appear in mechanical systems are inherently nonlinear and have destructive effects on the control system behavior. Generally, they are modeled by hard nonlinearities. In this paper, two different methods are proposed to cope with the effects of hard nonlinearities which exist in various models of friction. Simple inverted pendulum on a cart (SIPC) is considered as a test bed system, as well. In the first technique, a nonlinear optimal controller based on the approximate solution of Hamilton-Jacobi-Bellman (HJB) partial differential equation (PDE) is designed for the system and finally, an adaptive anti disturbance technique is proposed to eliminate the friction destructive effects. In the second one, three continuous functions are used to approximate hard nonlinearities when they are integrated into the system model. These techniques are compared with each other using simulations and their effectiveness is shown.