Design of a novel state-feedback robust $$H_2/H_{\infty }$$ sliding-mode controller for a hydraulic turbine governing system

This paper presents a novel state-feedback robust sliding-mode controller (SFRSMC) based on a mixed <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:msub><mml:mi>H</mml:mi> <mml:mn>2</mml:mn></mml:msub> <mml:mo>/</mml:mo> <mml:msub><mml:mi>H</mml:mi> <mml:mi>∞</mml:mi></mml:msub> </mml:mrow> </mml:math> approach to enhance the control performance of hydraulic turbine governing systems (HTGS) with complex conduit systems under external load disturbances and control signal uncertainties. A state-space model incorporating the dynamic responses of the HTGS is developed. The SFRSMC is designed using the sliding-mode equivalent control principle, with a disturbance observer to estimate and mitigate unknown disturbances. To balance robustness and optimality, mixed <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:msub><mml:mi>H</mml:mi> <mml:mn>2</mml:mn></mml:msub> <mml:mo>/</mml:mo> <mml:msub><mml:mi>H</mml:mi> <mml:mi>∞</mml:mi></mml:msub> </mml:mrow> </mml:math> linear matrix inequalities (LMIs) are utilized to determine the critical performance sliding matrix via an auxiliary feedback control method. The effectiveness of the proposed control scheme is validated through time-domain simulations under various operating scenarios, including different parameter variations of the HTGS.