Multi-objective optimal design of an optimal fuzzy fractional order PID controller for fractional order hydraulic turbine regulating system

Abstract

The hydraulic turbine regulating system (HTRS) is a crucial component of the energy dispatch of hydropower plants. To achieve precise control of the HTRS output speed under variable working conditions, this paper explores the benefits of multi-objective optimization in the control field. A multi-objective optimization problem is established for an optimal fuzzy fractional order PID (OFFOPID) controller, tailored for fractional order HTRS working under both unload and load conditions. By introducing fractional order calculus operators and specifically optimizing the gains, rule bases, and membership functions, the OFFOPID controller enhances the traditional fuzzy PID controller and provides greater flexibility. In this multi-objective optimization problem, steady-state error (SSE), integral square error (ISE), and overshoot percentage (OP) are selected as the objective functions to ensure precise control accuracy, rapid response, and smooth transient behavior. To obtain the optimal Pareto frontier, the Pareto local search-nondominated sorting genetic algorithm III (PLS-NSGAIII) is proposed, with hybrid coding for population individuals specific to the OFFOPID framework. In this algorithm, the improved individual selection, crossover, and mutation operators enhance global search, while individual local search, conducted based on Pareto optimality, improves local search capabilities. Experiments show that the OFFOPID controller provides rapid and accurate responses for highly inertial HTRS, outperforming traditional controllers. Compared to three other multi-objective optimization algorithms on benchmark test functions and HTRS applications, the PLS-NSGAIII achieves lower GD and IGD values and higher HV values, demonstrating its effectiveness in solving HTRS problem.