Input Shaping Design and Multi-Objective Optimization for Residual Vibration Control of Flexible Systems

This thesis proposes a robust command-shaping approach to suppress residual vibrations that arise during fast and precise positioning of flexible mechanical/robotic systems. The approach integrates a Cycloid–Ramp–Ramped Versine (CPRVPR)-based smooth reference profile with zero-vibration (ZV, ZVD, ZVDD) input shapers. The generated pre-commands are optimized using two complementary multi-objective formulations. In the first design framework, the Vibrating Particle System (VPS) algorithm is employed. By incorporating the robustness constraints of the Extra-Insensitive (EI) shaper, the robustness–travelling time trade-off is enhanced through improving the efficiency of insensitivity, yielding the final command profile. In the second design framework, a Genetic Algorithm (GA) is used to fully eliminate residual vibration at selected vibration frequencies, while constraining the residual vibration below a 10% threshold in the regions between these frequencies. The proposed methods are experimentally validated on a Quanser pendulum-type crane setup. The resulting sensitivity curves and sensitivity surfaces demonstrate insensitivity against parameter uncertainties. Comparative evaluations with 15 widely used shapers indicate meaningful improvements in robustness and overall performance. Unlike classical input shapers (e.g., ZV, ZVD, ZVDD, EI, 2H-EI, 3H-EI, MISZV, and MISZVD) that rely on impulse sequences, the proposed approaches generate smooth motion profiles. Consequently, demands for sudden acceleration and braking are reduced, helping to mitigate excessive stress, wear, and fatigue in actuators and mechanical components, and providing a solution suitable for industrial applications.