Inverted pendulum with linear synchronous motor swing up using boundary value problem

Anotace: Research in the field of underactuated systems shows that control algorithms which take the natural dynamics of the system’s underactuated part into account are more energy-efficient than those utilizing fully-actuated systems. The purpose of this paper to apply the two-degrees-of-freedom (feedforward/feedback) control structure to design a swing-up manoeuver that involves tracking the desired trajectories so as to achieve and maintain the unstable equilibrium position of the pendulum on the cart system. The desired trajectories are obtained by solving the boundary value problem of the internal system dynamics, while the optimal state-feedback controller ensures that the desired trajectory is tracked with minimal deviations. The proposed algorithm is verified on the simulation model of the available laboratory model actuated by a linear synchronous motor, and the resulting program implementation is used to enhance the custom Simulink library Inverted Pendula Modeling and Control, developed by the authors of this paper.