Fuzzy finite-frequency output feedback control for nonlinear active suspension systems with time delay and output constraints

Abstract

• The T-S fuzzy method is used to approximate the nonlinear uncertain dynamics. • A finite frequency control criterion is formulated based on the Lyapunov theory. • A parallel-distributed compensation strategy is used in the fuzzy SOF controller. This paper investigates the problem of fuzzy finite-frequency output feedback control for nonlinear active suspension systems with time delay and output constraints. Firstly, as the physical suspension systems always exist the phenomenon of sprung and un-sprung mass variation and time delay, the Takagi-Sugeno (T-S) fuzzy model is adopted to represent the nonlinear uncertain active suspension system with uncertainties and time delay. Secondly, since the human body is much more sensitive to vertical vibrations between 4 and 8 Hz, a finite-frequency control criterion is formulated for the controller deign with consideration of time delay and output constraints. Other mechanical constraints such as suspension travel, tire dynamic deflection and actuator saturation are also considered. Thirdly, on a practical point of view, not all the states are online measurable. Hence, a novel fuzzy static output feedback (SOF) controller is proposed by applying the parallel-distributed compensation (PDC) scheme. The sufficient conditions for deriving the fuzzy SOF controller are obtained in terms of linear matrix inequalities (LMIs). Finally, numerical simulations on a quarter-car suspension model are conducted to validate the effectiveness and applicability of the proposed fuzzy SOF controller.