A Comprehensive Optimization of PD^μ Controller Design for Trade-off of Energy and System Performance

This paper investigates the optimal trade-off between the system performance and control energy consumption for different settings of the control parameters \({k_P}, {k_D}, {\mu }\) and \(P{D^{\mu }}\) controller design, and a comprehensive optimization method is proposed to obtain the optimal \(P{D^{\mu }}\) controller. Detailed correlation analysis between the control performance and energy consumption is presented. The method is applied to the control of a ball-beam system, and the simulation results confirm that the proposed method is practically useful in the analysis and design of the \(P{D^{\mu }}\) controller.