Optimal Feedforward Preview Control by FIR Filters

The paper presents a new method for designing an optimal feedforward preview controller for asymptotically stable single-input single-output (SISO) systems. We conduct an optimization based on an impulse response representation of the system's dynamics for a chosen control horizon. This leads to an optimal deconvolution that proactively exploits the reference or disturbance signal's preview information to calculate the control input for a desired output. In order to extend this deconvolution to arbitrarily long input signals, we show that, under certain circumstances, a finite impulse response (FIR) filter can be build from it. This filter can be seen as the system's optimized inverse, which also applies to non-minimum phase systems. Since optimization is done offline, the resulting filter is computationally inexpensive and easily implemented. Its effectiveness is shown by applying the proposed method to a sample system.