Design of Adaptive Robust Controller for Second-Order Non-affine Systems with Input Saturation

In this paper, two techniques are introduced to transform an uncertain second-order non-affine system under input saturation to an equivalent affine model. First, this affine model is obtained using the linearization technique with respect to the system inputs. In the case of the system being non-differentiable or its derivative with respect to the input being zero, this technique cannot be used. Then, to cope with this problem, an average dynamical model is suggested using the Filippov’s model and the pulse width modulation. Afterward, an adaptive sliding mode controller is designed to overcome the approximation errors appeared in this transformation and inherent system uncertainties. Stability analysis is also derived using the Lyapunov theory. Ultimately, the capability of the proposed method is shown through MATLAB simulations.