Distributed delay input shaper design by optimizing smooth kernel functions

The aim of this paper is the development of a general class of input shapers with distributed time delay which leads to retarded spectral properties. The design of the shaper is formulated as a multi-objective optimization problem, where response time and robustness, expressed in terms of residual vibrations, are the main objectives. As a part of the optimization formulation, common requirements for input shapers such as non-decreasing step response and unity steady state gain are considered in the design. Moreover, additional optional requirements, such as smoothness of a step response, jerk and even jounce limits can be added to optimization procedure. The resulting problem can be solved using convex optimization techniques. Several illustrative examples are presented in comparison with classical input shaping techniques. Finally, implementation aspects are discussed. The paper is accompanied by an implementation in MATLAB, including a user-friendly interface for the interactive shaper design.