Model Reference Input Shaping Using Quantitative Feedforward-Feedback Controller

Input shaping convolutes the reference signal with a sequence of impulses, whose amplitudes and timings are designed to produce a shaped reference that avoids exciting lightly-damped modes to reduce residual vibration from a quick movement. The input shaper can be made robust to uncertain mode parameters by adding more impulses, which delays the reference signal, resulting in longer move time. Instead of using more impulses, in this paper, a feedforward-feedback control system, based on the quantitative feedback theory, is placed in the loop to match the closed-loop system, with uncertain plant, to a known reference model. The feedforward-feedback system handles the uncertainty, so the input shaper, placed outside the loop, needs not be robust. The closed-loop system emphasizes on selected frequencies and reduces the cost of feedback. It is shown that the proposed feedforward-feedback system is less conservative than the pure-feedback system. Other sources of vibration such as external disturbances and noise can be handled by the feedforward-feedback system as well. Simulation shows that the proposed technique can withstand large plant uncertainty with fast move time when compared to traditional robust input shaper