Embedded Optimization for Input Shaping

Traditional input shaping filters are linear mappings between reference input and 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 its offline design and linear mapping. This paper presents an online input prefilter design approach to overcome this conservatism. The resulting prefilters are called predictive prefilters because the online 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 common input shaping application.