System Modeling and Controller Design in the Presence of Nonlinear Distortions

The aim of this paper is to provide an experimental examination of the application of linear system identification techniques in the design of linear model-based controllers for systems suffering nonlinear distortions. The study is conducted on an analog electrical circuit, which simulates a nonlinear mechanical resonating system. Parametric linear models are estimated from measurements taken using random-phase multisines. Furthermore, a full nonlinear model is estimated for the system. Initially, the estimated linear models and the nonlinear model are compared in terms of their performance in simulating the system dynamics. This is followed by the design of linear optimal controllers for the system based on the different models, and the performance obtained from the controllers based on the nonlinear model is set as the benchmark. It is shown that although the performance of the linear models estimated from the random multisine measurements is poor in terms of the simulation error when compared to that of the nonlinear model, it closely matches the performance of the nonlinear model in terms of controller design