Multimodel Robust Control for Hydraulic Turbine

The paper deals with the multimodel and robust control system design and their combination based on structure. Controller design will be done in the frequency domain with nominal performance specified by phase margin. Hydraulic turbine model is analyzed as system with unstructured uncertainty, and robust stability condition is included in controller design. Multimodel and robust control approaches are presented in detail on hydraulic turbine model. Control design approaches are compared and used for derivation of new approaches which combine advantages of both. 1. Introduction When hydraulic turbine power control is considered, the water inertia effect is a factor that makes it difficult to maintain stability under isolated operation or to have fast response in case of load change in the whole operational range. Nonlinear models of hydraulic turbine control systems are needed in those cases where the turbine power varies in the whole range. The turbine model parameters vary significantly with the unpredictable load variations. Such nonlinearities make the controller design a nontrivial task due to the fact that a controller designed for specific operating conditions may not perform well under different loads [1]. This fact leads to the adaptive [2] or hybrid control algorithms. There are several approaches to model hybrid systems [3]. In a model of a large class of hybrid systems, [4] is considered as discrete event system and continuous dynamic modeled by differential or difference equation. Such models are used to formulate a general stability analysis and controller synthesis framework for hybrid systems. Results for modeling and stability analysis of hybrid systems have been presented in [3, 5, 6]. In this paper, we follow the class of hybrid system known as switched systems [7]. In this paper, hybrid control, often denoted by multimodel control, will be used. Several switching algorithms will be compared to show how the switching speed affects performance and stability. Well-known robust control method will be presented as a control solution which ensures stability on whole operating range, but with lower performance. Combination of multimodel control and robust control which ensure stability and good performance will be presented on numerical example of nonlinear hydraulic turbine model. 2. Preliminaries and Problem Formulation Consider nonlinear system as uncertain system described by set of transfer functions and controller in standard configuration: where , , and are output, control, and set-point variables of system, respectively; is the