Optimal design of reduced-order observers with specified eigenvalues and performance measurement of minimizing estimation errors using evolutionary optimization
A new method is proposed in this paper which designs a reduced-order observer of a non-observable-form-based dynamical system such that: (i) the eigenvalues are specified to satisfy desired convergence performance, (ii) a full-rank condition is satisfied, and (iii) a quadratic performance measuremen...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SAGE Publishing
2019-06-01
|
| Series: | Journal of Low Frequency Noise, Vibration and Active Control |
| Online Access: | https://doi.org/10.1177/1461348419830226 |
| _version_ | 1818402218450092032 |
|---|---|
| author | Fu-I Chou Ming-Yang Cheng |
| author_facet | Fu-I Chou Ming-Yang Cheng |
| author_sort | Fu-I Chou |
| collection | DOAJ |
| description | A new method is proposed in this paper which designs a reduced-order observer of a non-observable-form-based dynamical system such that: (i) the eigenvalues are specified to satisfy desired convergence performance, (ii) a full-rank condition is satisfied, and (iii) a quadratic performance measurement of the deviation of the estimates from the actual states is minimized so as to reduce the large error occurring during the transient period of observation. The proposed approach combines the merits of both the orthogonal functions approach and evolutionary optimization. By solving a Sylvester equation, the proposed optimal design method can not only be used to design the reduced-order observer of a non-observable-form-based dynamical system, but also can avoid the shortcomings of approaches already existing in relevant literatures. Two examples are given to demonstrate the effectiveness and efficiency of the proposed new optimization method on the performance of state estimations. From the demonstrative examples, it can be seen that the estimated state errors asymptotically converge quickly to zero. In addition, the performance measurement values based on the proposed optimal design approach are apparently much lower than those based on the existing nonoptimal design method. |
| first_indexed | 2024-12-14T08:04:52Z |
| format | Article |
| id | doaj.art-eccc9624b4b54d6f98a3827aa7c9892c |
| institution | Directory Open Access Journal |
| issn | 1461-3484 2048-4046 |
| language | English |
| last_indexed | 2024-12-14T08:04:52Z |
| publishDate | 2019-06-01 |
| publisher | SAGE Publishing |
| record_format | Article |
| series | Journal of Low Frequency Noise, Vibration and Active Control |
| spelling | doaj.art-eccc9624b4b54d6f98a3827aa7c9892c2022-12-21T23:10:14ZengSAGE PublishingJournal of Low Frequency Noise, Vibration and Active Control1461-34842048-40462019-06-013810.1177/1461348419830226Optimal design of reduced-order observers with specified eigenvalues and performance measurement of minimizing estimation errors using evolutionary optimizationFu-I ChouMing-Yang ChengA new method is proposed in this paper which designs a reduced-order observer of a non-observable-form-based dynamical system such that: (i) the eigenvalues are specified to satisfy desired convergence performance, (ii) a full-rank condition is satisfied, and (iii) a quadratic performance measurement of the deviation of the estimates from the actual states is minimized so as to reduce the large error occurring during the transient period of observation. The proposed approach combines the merits of both the orthogonal functions approach and evolutionary optimization. By solving a Sylvester equation, the proposed optimal design method can not only be used to design the reduced-order observer of a non-observable-form-based dynamical system, but also can avoid the shortcomings of approaches already existing in relevant literatures. Two examples are given to demonstrate the effectiveness and efficiency of the proposed new optimization method on the performance of state estimations. From the demonstrative examples, it can be seen that the estimated state errors asymptotically converge quickly to zero. In addition, the performance measurement values based on the proposed optimal design approach are apparently much lower than those based on the existing nonoptimal design method.https://doi.org/10.1177/1461348419830226 |
| spellingShingle | Fu-I Chou Ming-Yang Cheng Optimal design of reduced-order observers with specified eigenvalues and performance measurement of minimizing estimation errors using evolutionary optimization Journal of Low Frequency Noise, Vibration and Active Control |
| title | Optimal design of reduced-order observers with specified eigenvalues and performance measurement of minimizing estimation errors using evolutionary optimization |
| title_full | Optimal design of reduced-order observers with specified eigenvalues and performance measurement of minimizing estimation errors using evolutionary optimization |
| title_fullStr | Optimal design of reduced-order observers with specified eigenvalues and performance measurement of minimizing estimation errors using evolutionary optimization |
| title_full_unstemmed | Optimal design of reduced-order observers with specified eigenvalues and performance measurement of minimizing estimation errors using evolutionary optimization |
| title_short | Optimal design of reduced-order observers with specified eigenvalues and performance measurement of minimizing estimation errors using evolutionary optimization |
| title_sort | optimal design of reduced order observers with specified eigenvalues and performance measurement of minimizing estimation errors using evolutionary optimization |
| url | https://doi.org/10.1177/1461348419830226 |
| work_keys_str_mv | AT fuichou optimaldesignofreducedorderobserverswithspecifiedeigenvaluesandperformancemeasurementofminimizingestimationerrorsusingevolutionaryoptimization AT mingyangcheng optimaldesignofreducedorderobserverswithspecifiedeigenvaluesandperformancemeasurementofminimizingestimationerrorsusingevolutionaryoptimization |