This paper proposes a control design strategy for LPV systems subject to additive disturbances in the presence of actuator saturation and state constraints. LMI conditions are derived in order to simultaneously compute an LPV controller and an anti-windup gain that ensures the boundedness of the trajectories, considering that the disturbances belong to a given admissible set. The disturbance attenuation is addressed via an H ∞ constraint. Besides, state constraints (corresponding to the local validity of the LPV model and system structural limits) are always assured. The theoretical results are applied to a quarter-car model rewritten in the LPV framework where the passivity constraint is recast to the saturation one. The interest of the provided methodology is emphasized by simulations. I. INTRODUCTIONIn the last years, many studies have focused on the control of saturated (in states, control inputs...) systems which are present in almost real applications. For a system with input saturation, there is usually an inconsistency between the states of the plant and those of the controller because of the saturated actuator between the system control input and the controller output. This effect, usually called windup, dramatically degrades the closed-loop performances or even worse causes the system instability. To preserve the consistency, the input to controller needs to be changed by an appropriate signal, which is provided by a called antiwindup compensator. Usually, when a system is subject to actuator saturation, two main issues arise: the guarantee of stability (global or local) and the minimization of the performance degradation. There are two methods to solve these problems: two-step and one-step design. The traditional two-step method first designs a linear controller without considering the input saturation effect and then add an anti-windup compensator to minimize the adverse effects of control input saturation on closed-loop performance [1], [2]. For the one step approach, the controller and an antiwindup compensator (static in general) are simultaneously computed [3], [4]. It can be noticed that the control design with input saturation is a nonlinear problem. However, many solutions have been proposed to model the saturation effect in such a way that the problem can be treated within a linear framework, for example: the polytopic differential inclusion
This tutorial paper aims at presenting two methodologies to deal with the semi-active suspension control problem, in the framework of Linear Parameter Varying (LPV) systems.
Abstract-This paper presents a new solution for the semiactive suspension control problem. First, a quarter vehicle model equipped with a semi-active damper is reformulated in the LPV framework using the nonlinear static semi-active damper model. This formulation allows to turn the control problem with dissipativity constraint into that with input saturation. Then the damper force saturation is taken into account in an original LPV fashion. This leads to the definition of a new LPV model with two parameters which is handled in a polytopic way. The H∞ control design for polytopic systems is then applied. The interest of the provided methodology is emphasized by simulations on a nonlinear vehicle model.
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