Robust Control and Model and Controller Reduction of Linear Parameter Varying Systems

In this paper we develop and demonstrate a Linear Parameter Varying (LPV) stabilisation technique. The method systematically obtains a controller of a gain-scheduling nature that exhibits a certain level of robustness and performance for the LPV system. We propose a global approach to simultaneously design a robust controller as well as devise a procedure which uses the solution to the controller problem to both reduce the order of the plant and the order of the controller The balancing method suggested has been proven to be suitable for both stable and unstable plants and the truncation procedure is shown to be directly related to the closed-loop performance level obtained. The solution employs convex optimisation solvers. To illustrate the design method, an unstable, high order, parameter driven Tokamak design example is presented where the aim is to robustly stabilise the plant as it varies along operating points.