State observers for the time discretization of a class of impulsive mechanical systems
In this work, we investigate the state observer problem for linear mechanical systems with a single unilateral constraint, for which neither the impact time instants nor the contact distance is explicitly measured. We propose to attack the observer problem by transforming and approximating the origi...
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| Published in | International journal of robust and nonlinear control Vol. 32; no. 12; pp. 6667 - 6683 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
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Bognor Regis
Wiley Subscription Services, Inc
01.08.2022
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| ISSN | 1049-8923 1099-1239 1099-1239 |
| DOI | 10.1002/rnc.6168 |
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| Abstract | In this work, we investigate the state observer problem for linear mechanical systems with a single unilateral constraint, for which neither the impact time instants nor the contact distance is explicitly measured. We propose to attack the observer problem by transforming and approximating the original continuous‐time system by a discrete linear complementarity system (LCS) through the use of the Schatzman–Paoli scheme. From there, we derive a deadbeat observer in the form of a linear complementarity problem. Sufficient conditions guaranteeing the uniqueness of its solution then serve as observability conditions. In addition, the discrete adaptation of an existing passivity‐based observer design for LCSs can be applied. A key point in using a time discretization is that the discretization acts as a regularization, that is, the impacts take place over multiple time steps (here two time steps). This makes it possible to render the estimation error dynamics asymptotically stable. Furthermore, the so‐called peaking phenomenon appears as singularity within the time discretization approach, posing a challenge for robust observer design. |
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| AbstractList | In this work, we investigate the state observer problem for linear mechanical systems with a single unilateral constraint, for which neither the impact time instants nor the contact distance is explicitly measured. We propose to attack the observer problem by transforming and approximating the original continuous‐time system by a discrete linear complementarity system (LCS) through the use of the Schatzman–Paoli scheme. From there, we derive a deadbeat observer in the form of a linear complementarity problem. Sufficient conditions guaranteeing the uniqueness of its solution then serve as observability conditions. In addition, the discrete adaptation of an existing passivity‐based observer design for LCSs can be applied. A key point in using a time discretization is that the discretization acts as a regularization, that is, the impacts take place over multiple time steps (here two time steps). This makes it possible to render the estimation error dynamics asymptotically stable. Furthermore, the so‐called peaking phenomenon appears as singularity within the time discretization approach, posing a challenge for robust observer design. |
| Author | Leine, Remco I. Preiswerk, Pascal V. |
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| CitedBy_id | crossref_primary_10_1109_TSMC_2024_3388026 crossref_primary_10_1016_j_ijcce_2022_12_001 crossref_primary_10_1109_TCE_2023_3278299 crossref_primary_10_1016_j_arcontrol_2022_12_002 |
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| SubjectTerms | Discretization impacts linear complementarity systems Mechanical systems nonsmooth systems Observability (systems) peaking phenomenon Regularization State observers unilateral constraints |
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| Title | State observers for the time discretization of a class of impulsive mechanical systems |
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