Proximate Time-Optimal Control of a Harmonic Oscillator

This paper considers near-time-optimal setpoint tracking of a second-order oscillator. First, the time-optimal setpoint tracking feedback law is derived by recasting the problem as a regulator problem in the error coordinates with shifted control limits. This result is used to construct a derated approximation of the optimal control. Initially, the control law is derived as a regulator controller. This result is then extended to include setpoint tracking. Global stability is proven for the setpoint tracking controller in the zero-damping case. A scaling method is developed, which allows an efficient implementation of the control laws using a single lookup table. Both the damped and undamped controllers are validated experimentally.