ROBUST CONTROL DESIGN BY NUMERICAL OPTIMIZATION APPLIED TO HYDROELECTRIC TURBINES UNDER PARAMETRIC UNCERTAINTIES

Roberto Canonico¹; Fabrizio Leonardi¹

¹ FEI

doi:10.20906/CPS/COB-2015-0208

Resumo

This work proposes the use of numerical optimization technique based on direct transcription for the robust design of the control system for hydroelectric turbines under parametric uncertainties. The controller design for this type of application involves physical and operational constraints. The usual control design techniques typically do not explicitly incorporate constraints in the formulation of the problem resulting in a trial and error design. By means of optimization is possible to formulate a controller design problem that explicitly takes into account the constraints. For this purpose normally one may use the shooting optimization technique that is based on the integration of differential equations of the model but it may have convergence difficulties due to its typical sensitivity to initial estimates of the parameters. In this work we apply direct transcription technique where the system dynamics are included as constraints to the optimization problem. The technique dilutes the errors due to the quality of the initial estimate over the discretization nodes, usually implying smaller convergence issues. The problem of robustness was included in the design framework by adding a fixed number of models to the optimization problem that can represent the uncertainties span. Although the proposed method might be extended to nonlinear systems, in this application it was used a linear deviation model suggested in the literature for the configuration of a single generator unit connected to an isolated system. The proposed method can be extended to other kinds of controllers but, since it is usual in practical applications, the PID controller was employed here. The constraints considered are the maximum displacement and speed of the actuator and other operating limits such as the maximum inverse response amplitude of mechanical power in a maneuver for changing the operating condition. The numerical results suggest that the proposed framework is well suited to the robust control design of hydroelectric turbine sys

Palavras-chave: Numerical Optimization; Direct Transcription; Hydraulic Turbines Governors