Hamiltonian-based minimum-energy trajectory planning and tracking control for a motor-table system: part I minimum-energy methods in trajectory planning

In this paper, we propose the minimum energy control input based on Hamiltonian strategy for the motor-table system. The energy equation of the motor-table system contains of the input energy, dissipation energy, potential energy and output energy, and includes electrical and mechanical energies. The methods of the minimum control effort (MCE), minimum input energy control (MIEC), minimum dissipation energy control (MDEC) and trapezoidal trajectory energy control are compared for the motor-table system. From the numerical results, we can find that the MIEC and MDEC approaches can obtain the same minimum input energy. Traditionally, the MCE approach was regarded as the minimum energy control in the previous study. However, we have demonstrated that the MCE approach is not the minimum energy control in this paper.