Stable inversion of LPTV systems with application in position-dependent and non-equidistantly sampled systems |
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Authors: | Jurgen van Zundert Tom Oomen |
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Affiliation: | Control Systems Technology Group, Department of Mechanical Engineering, Eindhoven University of Technology , Eindhoven, The Netherlands |
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Abstract: | Many control applications, including feedforward and learning control, involve the inverse of a dynamical system. For nonminimum-phase systems, the response of the inverse system is unbounded. For linear time-invariant (LTI), nonminimum-phase systems, a bounded, noncausal inverse response can be obtained through an exponential dichotomy. For generic linear time-varying (LTV) systems, such a dichotomy does not exist in general. The aim of this paper is to develop an inversion approach for an important class of LTV systems, namely linear periodically time-varying (LPTV) systems, which occur in, e.g. position-dependent systems with periodic tasks and non-equidistantly sampled systems. The proposed methodology exploits the periodicity to determine a bounded inverse for general LPTV systems. Conditions for existence are provided. The method is successfully demonstrated in several application cases, including position-dependent and non-equidistantly sampled systems. |
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Keywords: | Stable inversion dichotomy linear time-varying systems linear periodically time-varying systems tracking control |
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