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Multi-level optimization techniques for designing digital input shapers

Input shaping decreases residual vibration in flexible systems by filtering the reference command with a sequence of impulses known as the input shaper. Input shaping techniques have been proven highly successful on a large class of computer-controlled systems. While some shapers may be determined in closed form, often a nonlinear optimization is needed to create the desired shaper. This paper proposes a multi-level optimization approach for creating digital shapers. Creating input shapers in the digital domain leads to linear constraint equations, so the difficulties of nonlinear optimization are avoided. Furthermore, the multiple levels of optimization allow for both primary and secondary design constraints to be optimized.