Polynomial Chaos Expansion-Based Robust Multi-Objective Control of Hydraulic Turbine-Regulating Systems Under Hydro-Mechanical Uncertainties

Hydraulic turbine-regulating systems (HTRSs) require advanced robust control strategies to ensure grid frequency stability and prevent mechanical wear under severe non-stationary conditions. This paper presents an original polynomial chaos expansion (PCE)-based robust control framework, designed to address hydro-mechanical uncertainties in HTRSs. Initially, a deterministic multi-objective optimization utilizing the integral of time-weighted absolute error (ITAE) and the integral of the square control signal (ISC) is executed via the multi-objective imperialist competitive algorithm (MOICA) to establish nominal fractional-order proportional-integral-derivative (FOPID) controller parameters. Subsequently, a PCE-based Sobol sensitivity analysis demonstrates that these nominal designs suffer from severe performance variability under real-world parameter drift. To overcome this limitation, a comprehensive four-dimensional robust multi-objective optimization framework is formulated to simultaneously minimize both expected values and standard deviations of tracking errors and control efforts. By integrating generalized PCE surrogate moment evaluations directly within the MOICA optimization loop, the proposed architecture effectively suppresses dynamic performance variance without requiring computationally expensive Monte Carlo simulations. Numerical evaluations confirm that the proposed PCE-MOICA-tuned robust FOPID controller achieves a substantial 57% to 91% reduction in performance variability compared to traditional deterministic baselines and established literature methodologies, including NSGA-II and MOHHO-optimized controllers.