Inverse signal shapers in effective feedback architecture

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

“…Since the matrices L and S 1 can be designed such that the matrix U 2 À LC mc is stable, it is obvious that the state estimation error dynamics (22) in the quasi-sliding mode is stable. The proof is completed.…”

“…First, it will show that the quasi-sliding mode of the sliding surface r 1 (l) is achieved. From (47)-(58), it can be seen that the state estimation error dynamics (22) in the quasi-sliding mode can be achieved as the control law (47) and the weight update (49) with (53) and bias update (50) with (54) are applied. From Theorem 1, the state estimation error dynamics (22) in the quasi-sliding mode is asymptotically stable if there exist matrices L and S 1 such that the eigenvalues of the matrix U 2 À LC mc are within the unit circle in the Z-plane.…”

“…In [21], a feedback controller with an adaptive input shaper is developed for single-link flexible manipulators. In [22], an inverse shaper in the feedback configuration is developed for the vibration reduction. However, these methods assumed that all states of systems are available and are developed in continuous-time systems.…”

“…(23.a) and r 1 (l) = 0, it leads to e 1 ðlÞ ¼ ÀS 1 e h ðlÞ:ð29ÞSubstituting (29) into (28), the equivalent control(28) can be expressed as u eq ðlÞ ¼ ðS 1 C mc Þ À1 S 1 U mc e h ðlÞ À ðS 1 C mc Þ À1 S 1 e h ðlÞ þ f ðlÞ: ð30Þ Substituting (30) into(22), the state estimation error dynamics(22) in the quasi-sliding mode can be obtained as e h ðl þ 1Þ ¼ ðU 2 À LC mc Þe h ðlÞ;…”

Spectral design of output feedback controllers for systems pre-compensated by input shapers∗∗The presented research has been supported by the Czech Science Foundation under the project No. 13–06962S, by the Programme of Interuniversity Attraction Poles of the Belgian Federal Science Policy Office(IAP P6–DYSCO), by OPTEC, the Optimization in Engineering Center of the KU Leuven, and the project G.0712.11N and G.0717.11N of the Research Foundation –Flanders (FWO).

“…Following the preliminary results in Vyhlidal et al (2013a), the novel and for the given task entirely efficient feedback loop architecture has been proposed in Vyhlidal et al (2015b), including both simulation and experimental verification, see also Vyhlidal et al (2014) for the double mode compensation task. The method, which will be addressed in the following preliminary section in more detail, is based on including an inverse shaper to the feedback The first objective of the paper is to demonstrate the applicability of the inverse shaper to a more complex system utilizing output feedback from all the available (measured) outputs in a multi-degree of freedom mechanical system.…”