Improving the performance of linear controllers through nonlinear perturbations: Applications to one-dimensional systems

Linear control techniques have been widely used for controlling both linear and nonlinear systems. In this paper we show the design of a kind of nonlinear controllers starting from the standard procedure for designing linear controllers by pole placement. After the linear controller is designed, we add a nonlinear term with the aim to improve the system performance together with the significant decrease of the control effort. The methodology is developed through an example corresponding to a one-dimensional system. The stability and control effort are proved in analytical way and the performance of the system is tested numerically and analytically.