Control of a Nonlinear System Using the Saturation Phenomenon

In this paper, a theoretical investigation of nonlinear vibrations of a 2 degrees of freedom system when subjected to saturation is studied. The method has been especially applied to a system that consists of a DC motor with a nonlinear controller and a harmonic forcing voltage. Approximate solutions are sought using the method of multiple scales. It is shown that the closed-loop system exhibits different response regimes. The nature and stability of these regimes are studied and the stability boundaries are obtained. The effects of the initial conditions on the response of the system have also been investigated. Furthermore, the second-order solution is presented and the corresponding results are compared with those of the first-order solution. It is shown that by increasing the amplitude of the excitation voltage, the higher-order term in the solution becomes significant and causes a drift in the response. In order to verify the obtained theoretical results, they are compared with the corresponding numerical results. Good agreement between the two sets of results is observed.