Increasing Robustness of Input Shaping Method to Parametric Uncertainties and Time-Delays

Abstract

The input shaping technique has proven to be highly effective in reducing or eliminating residual vibration of flexible structures. The exact elimination of the residual vibration via input shaping depends on the amplitudes and instants of utilized impulses. However, systems always have parametric uncertainties, which can lead to performance degradation. Furthermore, input shaping method does not deal with vibration excited by external disturbances and time-delays. In this paper, a closed-loop input shaping control scheme is developed for uncertain flexible structure and uncertain time-delay flexible structure .systems. The algorithm is based on the sliding mode control and H^l¡x techniques. This scheme guarantees closed-loop system stability, and yields good performance and robustness in the presence of parametric uncertainties, time-delays and external disturbances as well. Also, it is shown that increasing the robustness to parametric uncertainties and time-delays does not lengthen the duration of the impulse sequence. Numerical examples are presented to verify the theoretical analysis.

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

“…Then the input shaped reference model (70) and the input shaped uncertain time-delay flexible structure system (71) are transformed into the controllable canonical form. The input shaped uncertain time-delay flexible structure system (71) in the controllable canonical form can be expressed as T s = 0.001 s is applied in (72), and the state observer is given in (20). Following the designing procedures in the above section, the proposed controller is given by the following steps.…”

“…Consider the discrete-time uncertain time-delay flexible structure system (18). If the state observer (20), the sliding surfaces (23) and (37), the control law (59) with (47), (60), the weight update (49) with (53) and bias update (50) with (54) are used, and there exist matrices K and S 2 such that the eigenvalues of the matrix U mc þ C mc ðS 2 C mc Þ À1 S 2 þ C mc K are within the unit circle in the Z-plane, then the output estimation error decreases asymptotically to zero and the model error achieves a very small ultimate boundedness.…”

“…The sliding surface in term of e h (l) is defined as follows: ð23:bÞ where S 1 e R 1Ân is a constant full rank matrix and is chosen such that S 1 C mc is nonsingular, and the observer gain matrix L 2 R nÂv is defined in (20). Also, it is assumed that the matrix S 1 satisfies…”

“…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 [19], an active vibration control using optimized modified acceleration feedback is developed for vibration reduction. In [20], a closed-loop input shaping control scheme is developed for uncertain flexible structure and uncertain time-delay flexible structure systems. In [21], a feedback controller with an adaptive input shaper is developed for single-link flexible manipulators.…”