Optimal Tracking Control of Motion Systems

Tracking control of motion systems typically requires accurate nonlinear friction models, especially at low speeds, and integral action. However, building accurate nonlinear friction models is time consuming, friction characteristics dramatically change over time, and special care must be taken to avoid windup in a controller employing integral action. In this paper a new approach is proposed for the optimal tracking control of motion systems with significant disturbances, parameter variations, and unmodeled dynamics. The ‘desired’ control signal that will keep the nominal system on the desired trajectory is calculated based on the known system dynamics and is utilized in a performance index to design an optimal controller. However, in the presence of disturbances, parameter variations, and unmodeled dynamics, the desired control signal must be adjusted. This is accomplished by using neural network based observers to identify these quantities, and update the control signal on-line. This formulation allows for excellent motion tracking without the need for the addition of an integral state. The system stability is analyzed and Lyapunov based weight update rules are applied to the neural networks to guarantee the boundedness of the tracking error, disturbance estimation error, and neural network weight errors. Experiments are conducted on the linear axes of a mini CNC machine for the contour control of two orthogonal axes, and the results demonstrate the excellent performance of the proposed methodology.