Robust Adaptive Control of Residual Vibration in Point-to-Point Motion of Flexible Bodies

Abstract

Input Shaping is a widely used method of suppressing residual vibrations in point-to-point motion of flexible bodies. It is easy to implement and gives good results if the dynamics of the system are known accurately. However, it is not very robust to system parameter variations. Early methods of increasing the robustness incurred a large time penalty. Hence attempts were made to apply adaptive control to increase the robustness of the shaper. These methods met with varying degrees of success. In this paper, we propose a new adaptive control scheme which is effective in increasing the robustness of the shaper, even in the presence of additive noise in the system output. It is also able to handle sudden changes in the plant parameters. The performance of the system in the presence of high-order unmodelled dynamics is also studied and found to be satisfactory.

Discrete-time dynamic output feedback input shaping control of vibration in uncertain time-delay flexible structures

“…It follows from (32), (17), (20) and (26) that the model error system can be expressed as e m ðl þ 1Þ ¼ U mc e m ðlÞ þ C mc uðlÞ þ Le y ðlÞ þ C mc uðlÞ þ C mc gðlÞ;…”

“…In [16], an adaptive input shaper is explored for providing robustness to parameter uncertainties by tuning the shaper to the flexible mode frequencies. In [17], a new adaptive control scheme is developed to increase the robustness of the shaper, even in the presence of additive noise in the system output. In [18], a comparative assessment of hybrid control schemes is presented for vibration suppression and end-point trajectory tracking of a flexible robot manipulator.…”

Closed‐loop input shaping control of vibration in flexible structures using discrete‐time sliding mode

“…Consider a flexible structure system with parameter uncertainties 14. The uncertain flexible structure system and the nominal system are expressed as P o ( s ) = 1/( s 2 + 0.4 s + 1) and P n ( s ) = 1/( s 2 + 0.84 s + 6), respectively.…”

“…An adaptive input shaper providing robustness to parameter uncertainties by tuning the shaper to the flexible mode frequencies is explored by Cutforth and Pao 12. Some schemes of increasing the robustness of shaper without adding more impulses to the shaper are presented by Pai and Sinha 13 and Dharne and Jayasuriya 14. However, these methods are developed in continuous‐time systems.…”

Robust input shaping control for multi-mode flexible structures

“…Pai and Sinha [18] developed a scheme of increasing the robustness of shaper without adding more impulses to the shaper. Dharne and Jayasuriya [19] proposed a method to improve the robustness of the input shaping method without incurring the time penalties associated with extra impulse additions. Ahmad et al [20] presented a comparative assessment of hybrid control schemes for vibration suppression and end-point trajectory tracking of a flexible robot manipulator.…”