Robustness analysis of feedback linearisation and LQR control on quarter-car model with cubic nonlinearity

The nonlinear behaviour of suspension elements is crucial when vehicles encounter large road inputs. These nonlinearities lead to performance degradation of active suspension systems. Feedback linearisation (FBL) is an efficient technique for nonlinear systems, whereas it may have a drawback when the nonlinearities are not well estimated and/or their parameters are varying or uncertain. Hence, the robustness of FBL for active suspension systems is investigated. In this work, the quarter-car model has a suspension spring with a cubic nonlinearity. The presented design is based on the combination of FBL and LQR controller. The LQR controller is preferred owing its ability to define an objective function that takes into consideration the active suspension performance specifications. To assess the performance and robustness of the proposed controller, simulations are carried out on two types of road profiles. They demonstrate the robustness of the FBL with LQR controller against uncertain nonlinear suspension stiffness.