Multi-criteria optimisation design of shapers with piece-wise equally distributed time-delay

The paper presents an optimisation based method to parametrize input shapers with time delays of piece-wise-equal distribution. The design respects the two key requirements on the shaper performance that are the prompt response time and the robustness represented by residual vibration functions, which are however conflicting criteria as a rule. Thus, the optimisation task is solved as a constrained multi-objective problem where the constraints respect the additional requirements on the shaper performance such as a non-decreasing step response or zero residual function at some frequency points. The result is a Pareto front that shows a trade-off between the two main requirements. Next to the presentation of the results in an example, a user friendly shaper-design tool is presented.