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The controlling parameter tuning of the hydraulic turbine governing system (HTGS) is always deduced under single operating condition and is not suitable for the changeable operating conditions of the hydraulic turbine. For this purpose, multiobjective optimization problem of fractional order PID (FOPID) controller for HTGS is constructed through the consideration of no-load disturbance and on-load disturbance operation conditions, where the performance indicators of integral time absolute error (ITAE) under both operation conditions are employed as the objective functions. To achieve the optimum, the multiobjective version of newly proposed Harris hawks optimization (MOHHO) is established to solve the optimization issue. Additionally, hybrid strategies which include Latin hypercube sampling initialization, modified differential evolution operator, and mutation operator are coupled into MOHHO (HMOHHO) to promote the global searching capability. Simultaneously, the linear model of rabbit energy within MOHHO is replaced with a nonlinear one to further enhance the searching capacity. Subsequently, the effectiveness and superiority of the proposed HMOHHO are verified by several multiobjective UF and ZDT test problems. Finally, the practical application and contrastive analysis ascertain that the constructed multiobjective problem of FOPID controller is suitable for HTGS under changeable operating conditions, and the proposed HMOHHO is effective in solving the issue.

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Multiobjective Optimal Control of FOPID Controller for Hydraulic Turbine Governing Systems Based on Reinforced Multiobjective Harris Hawks Optimization Coupling with Hybrid Strategies