Adaptive command shaping using genetic algorithms for vibration control of a single-link flexible manipulator

This paper presents investigations into the design of an adaptive command-shaping technique using genetic algorithms (GAs) for vibration control of a single-link flexible manipulator. Designing a command shaper requires a priori knowledge about the damping ratio and natural frequency of the system. A single-link flexible manipulator experimental setup is considered in this work. This is a high order, nonlinear and single-input multi-output system with infinite number of modes each with different damping ratios. For such a complex system, it is very difficult to design an effective command shaper. An adaptive command shaper based on GAs can provide a good solution. The open loop response due to bang-bang signal shows that the main flexible modes of the system lie within 100 Hz with significant peaks at about 13, 35 and 65Hz causing much of the vibration. GA is used to determine the optimum amplitudes and corresponding time-locations of impulses in the proposed multi-mode three impulse and four impulse input shapers. For flexible manipulators, rise time and end point vibration are in conflict since the faster the motion, the larger the level of vibration. Multi-objective GAs with fitness technique is used to find optimal set of solutions which trade-off between these conflicting objectives. The effectiveness of the proposed technique is assessed in terms of vibration suppression and response time. Moreover, a comparative assessment of the performance of the technique with the standard input shaper and to the system response with unshaped bang-bang input is presented.