Robust controller design for LPV systems with saturating actuators

Gain-scheduling control is one of the most popular nonlinear control method which gathers the simple structure of linear controllerstogether with the global effectiveness of the nonlinear controllers. Hence, this method has been widely and successfully applied infields ranging from chemical process control to aerospace systems. Gain-scheduling is also a very powerful method for control of linear parameter varying (LPV) systems. There are two main methods to compute a linear parameter varying model for the plant.Historically, the most common approach is based on Jacobian linearization of the nonlinear plant about a family of equilibriumpoints, also called operating points or set points. Another approach is quasi-LPV scheduling, in which the plant dynamics are rewritten to disguise nonlinearities. In this approach, time-varying parameters are mostly used as scheduling variables. Therefore, quasi-LPV approach gives us very good opportunity to use efficient and well-known linear control techniques over nonlinear plants without any negligences.Linear Matrix Inequalities are generally used to find adequate controllers for LPV systems. However, their solutions are expected to be conservative since they mostly provide sufficient conditions. It is well known that the provided solutions are mostly tight. To overcome this problem, in this work, an extended Polya relaxation technique has been developed. This extended Polya relaxation is necessary for systematic reduction of conservatism that can be actually shown to be asymptotically exact.Main purpose of this thesis is to solve the design problem of mixed L2, H2 gain-scheduling nonlinear state feedback controller for Linear Parameter Varying (LPV) systems subjected to actuator saturations and L2 bounded disturbances. First, a new formulation of H2 controllers has been presented based on the Homogeneous Polynomial Parameter Dependent (HPPD)representation. Then a systematic procedure has been presented to generate a sequence of LMI conditions of increasing precision for obtaining a sub-optimal L2, H2 state-feedback controller for LPV systems subject to actuator saturations and L2 bounded disturbances. The presented method utilizes the modified sector condition for actuator saturation formalization and HPPD matrix representation.Finally, the efficiency of the proposed approach has been presented through the control of an inverted pendulum system which has been modeled by quasi-LPV modeling technique.