Optimal Control of Servo Actuators with Flexible Load and Coulombic Friction

Feedback control and optimal control techniques are discussed for servo actuators that are widely used in micro-electro-mechanical systems (MEMS) technology of manufacturing. A typical servo actuator is the voice-coil motor used for actuating micro machine tool axes, bonding machines and hydraulic/pneumatic valve drives. State-of-the-art feedback control techniques are deficient with regard to high precision positioning and process duration. To improve on this deficiency, optimal control techniques are applied to a dynamical model of servo drives. Since Coulombic friction is modeled as sign function depending on the sign of the velocity, the optimal control problem belongs to the class of nonsmooth optimization problems. Time-optimal controls are computed for a variety of control bounds. It is shown that time-optimal controls are of bang-bang type and reduce transfer times considerably. Switching times are optimized directly by appropriate nonlinear programming methods. Optimal controls are studied under state constraints that limit deviations in positions and velocities of the slider and load mass. The goal of reducing such deviations can also be achieved by energy-optimal controls with larger transfer times. Real-time implementations of the computed optimal control signals indicate an excellent agreement between predicted trajectories and experimental results.