(A) study on the gain scheduling in a linear parameter varying system

Abstract

Since every system in real world is nonlinear, gain scheduling control is one of the typical methods which has been used very successfully in many applications. It is based on the linear parameter varying (LPV) system whether it is from the Jacobian linearization around the equilibrium manifold or quasi-linearization through re-definition of the parameters. This dissertation is concerned with the gain scheduling controller for this LPV system. Two different methods to design a gain scheduling controller for LPV system are proposed. The first one is the interpolation method among the pre-designed controllers at each specified operating point and the second one is direct design method of parameter dependent controller. A generalized interpolating method to guarantee the stability at intermediate points among the controllers designed at each specified operating point is proposed. The proposed method is to design the parameter dependent controller by interpolating Q factor in $RH_∞$ space. Since $RH_∞$ space is a ring, the weighted sum of the Q factors of the controllers also belongs to $RH_∞$ space. As a result, the design problem can be reduced to the problem of choosing the weights. Some specific weights for single-input single-output (SISO) system are suggested and extended a little bit to multi-input multi-output (MIMO) system. For this kind of interpolating controller, some properties like sensitivity function are also investigated. Finally, using the lyapunov function, it is shown that this kind of parameter varying controller can guarantee the overall stability for slow varying scheduling variables as well. On the other hands, the direct design methods of a parameter dependent $H_∞$ controller for LPV system are developed. Sufficient conditions for existence of the controller guaranteeing the stability and some performance level for LPV system, could be given in convex optimization problem. But, because of the dependence on the varying parameters, construct...