The comparisons of minimum-energy control of the mass-spring-damper system

The definition of performance index for mechanical minimum energy is employed to the mass-spring-damper (MSD) system with specified final states and time numerically. There are four approaches are compared in this paper. First, the traditional minimum control effort (MCE) with Hamiltonian function is applied to the MSD system. Secondly, the optimal control (OC) by riccati equation approach is implemented. Thirdly, the optimal control with exact solution (OCES) approach is employed and exact solution is obtained by manuscript. Finally, a minimum-energy control (MEC) approach based on the simplest controller of proportional-integral-derivative (PID) controller is utilized by particle swarm optimization (PSO) approach. The control parameters of PID controller can be searched and selected by PSO to minimize control energy for the MSD system. From numerical results, the MEC approach can obtain the minimum energy with specified final state and time. In short, this paper has successfully demonstrated differential characters for the four optimal approaches. The comparisons of numerical results with the definition of control energy, the MEC approach with evaluation PSO optimization approach can obtain the minimum-energy control for the MSD system.