Energy-saving trajectory planning by using Fourier sine series and tracking control for a mechatronic elevator system

In this paper, Lagrangian method is proposed to formulate dynamic model for a mechatronic elevator system, which includes mechanical and electrical parts. Lagrange equations, i.e. the torque balance equation and voltage balance equation, are derived from the kinetic energy, potential energy and virtual work of the mechatronic system. From the dynamic equations, the energy balance equation is obtained including electromagnetic energy, electrical dissipation energy, mechanical kinetic energy, mechanical dissipation energy, and the mechanical potential energy. The minimum-energy trajectory by using Fourier sine series (FSS) and power series are found by real-coded genetic algorithm. From simulation results, it is found that FSS with less order can find the minimum input energy more quickly than the power series. The four-degree (4-D) FSS trajectory is given as a reference one for the adaptive tracking control. It is found that the proposed adaptive controller has good tracking performance for the 4-D FSS angular displacement and velocity.