Performant design of an input shaping prefilter via embedded optimization

Traditional input shaping filters are linear mappings between the reference input and the system input. These filters are often unnecessarily conservative with respect to input and output bounds if multiple references with different amplitudes are applied. This conservatism is due to the off-line computation of the prefilter. This paper presents an on-line input prefilter design approach to overcome this conservatism. The resulting prefilters are called predictive prefilters because the on-line design is based on the model predictive control (MPC) framework. By theoretical considerations, simulation results and experimental results, it is shown that this new prefilter is at least as good as traditional prefilters, and can result in substantial gains in settling time. Tests show that a 30 % decrease in settling time is possible in a classical application.