TY - JOUR
T1 - B-spline-decomposition-based output tracking with preview for nonminimum-phase linear systems
AU - Wang, Haiming
AU - Kim, Kyongsoo
AU - Zou, Qingze
N1 - Funding Information:
This work was supported by the NSF CAREER grant CMMI-1066055 . The material in this paper was partially presented at the 2012 American Control Conference (ACC12), June 27–29, 2012, Montréal, Canada. This paper was recommended for publication in revised form by Associate Editor Abdelhamid Tayebi under the direction of Editor Toshiharu Sugie.
PY - 2013/5
Y1 - 2013/5
N2 - This article proposes a B-spline-decomposition-based approach to output tracking with preview for nonminimum-phase (NMP) systems. It has been shown that when there exists a finite (in time) preview of future desired trajectory, precision output tracking of NMP systems can be achieved by using the preview-based stable-inversion technique. The performance of this approach, however, can be sensitive to system dynamics uncertainty, and the computation involved can be demanding. We propose to address these challenges by integrating the notion of trajectory decomposition with the iterative learning control (ILC) technique. Particularly, the B-splines are used to construct a library of output elements and the corresponding input elements a priori, and the ILC techniques are used to obtain the input elements for precision tracking of the output elements. During the tracking with preview, the previewed future desired trajectory is decomposed by using the output elements, and the input is synthesized by using the corresponding input elements with chosen pre- and post-actuation times. The required pre-/post-actuation times are quantified based on the stable-inversion theory. The use of B-splines substantially reduces the number of output elements in the library, and the decomposition-synthesis occurs only at time instants separated by the difference between the preview time and pre-actuation time. The proposed approach is illustrated through a simulation study of nanomanipulation application using a NMP piezo actuator model.
AB - This article proposes a B-spline-decomposition-based approach to output tracking with preview for nonminimum-phase (NMP) systems. It has been shown that when there exists a finite (in time) preview of future desired trajectory, precision output tracking of NMP systems can be achieved by using the preview-based stable-inversion technique. The performance of this approach, however, can be sensitive to system dynamics uncertainty, and the computation involved can be demanding. We propose to address these challenges by integrating the notion of trajectory decomposition with the iterative learning control (ILC) technique. Particularly, the B-splines are used to construct a library of output elements and the corresponding input elements a priori, and the ILC techniques are used to obtain the input elements for precision tracking of the output elements. During the tracking with preview, the previewed future desired trajectory is decomposed by using the output elements, and the input is synthesized by using the corresponding input elements with chosen pre- and post-actuation times. The required pre-/post-actuation times are quantified based on the stable-inversion theory. The use of B-splines substantially reduces the number of output elements in the library, and the decomposition-synthesis occurs only at time instants separated by the difference between the preview time and pre-actuation time. The proposed approach is illustrated through a simulation study of nanomanipulation application using a NMP piezo actuator model.
KW - B-spline
KW - Iterative learning control
KW - System inversion
KW - Trajectory-decomposition
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U2 - 10.1016/j.automatica.2013.01.044
DO - 10.1016/j.automatica.2013.01.044
M3 - Article
AN - SCOPUS:84876670552
SN - 0005-1098
VL - 49
SP - 1295
EP - 1303
JO - Automatica
JF - Automatica
IS - 5
ER -