Optimal Sample-Error/Ripple Tradeoff for Sampled-Data Systems with Harmonic Disturbances

Although a digital controller operating in a sampled-data control system has access to the sampled error signal, the intersample behavior (ripple) is relevant to the overall performance. This paper thus investigates the tradeoff between the sample error and ripple for a system with a lightly damped mode and harmonic disturbance. The approach is based on an approximate expression for the harmonic-steady-state response of the closed-loop system. Numerical optimization of the ripple provides an optimal tradeoff between the peak sample error and peak ripple. Fast sampling as well as the effect of modal folding and disturbance aliasing are considered.