Takagi–Sugeno Observer Design for Remaining Useful Life Estimation of Li-Ion Battery System Under Faults
Abstract
:1. Introduction
- Analytical: they are based on the analytical RC models of the battery system. Most of these approaches inherit a common drawback that the underlying RC parameters are constant. Thus, it is beneficial to develop an approach that is able to settle the above problem assuming that RC parameters can vary in a given feasible set.
- Data-driven: they are based on soft computing techniques like fuzzy logic [22] and neural networks [23] or a combination of them. They also inherit a common drawback that a large amount of training and validation data is required. Indeed, the quality of such methods relies solely on the quality of data. Another drawback is that the models valid for a given battery system cannot be directly used for another one. This is caused by the fact that the models being using model merely the observed input–output relation while their parameters do not have any physical meaning.
2. Battery System
3. Observer Design
- 1.
- There exist and such that
- 2.
- There exist , and such that
- Step 0:
- Set the internal state of the observer initial conditions , while .
- Step 1:
- Determinate and based on Equations (17) and (18).
- Step 2:
- Set and move to Step 1.
4. Illustrative Example
- Step 0:
- Set covariance matrix , where is a sufficiently large positive contort. Moreover, set initial parameter vector and .
- Step 1:
- Calculate:
- Step 2:
- Update parameter vectorSet and move to Step 1.
5. Concluding Remarks
Author Contributions
Funding
Conflicts of Interest
Appendix A
References
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0 | 0.18777 | 0.016782 | 0.10044 | 574.2 | 935.5 |
0.083 | 0.15643 | 0.019272 | 0.041271 | 492.44 | 2225.1 |
0.167 | 0.15797 | 0.018844 | 0.040802 | 494.31 | 2226 |
0.25 | 0.16243 | 0.018733 | 0.040952 | 487.87 | 2272.6 |
0.33 | 0.16355 | 0.018036 | 0.040065 | 512.41 | 2209.8 |
0.417 | 0.15656 | 0.018058 | 0.039243 | 519.19 | 2190.4 |
0.5 | 0.16255 | 0.01858 | 0.039791 | 498.86 | 2189.8 |
0.583 | 0.15325 | 0.018479 | 0.039945 | 498.46 | 2239.7 |
0.667 | 0.16402 | 0.018512 | 0.040019 | 489.93 | 2294.8 |
0.75 | 0.15714 | 0.019181 | 0.039949 | 500.61 | 2424.3 |
0.833 | 0.15489 | 0.019026 | 0.040046 | 502.43 | 2420 |
0.917 | 0.15324 | 0.019026 | 0.040046 | 502.43 | 2420 |
1 | 0.15996 | 0.016109 | 0.043569 | 593.18 | 2224.4 |
Proposed Novel Observer | Lyapunov-Based Observer | |
---|---|---|
(mV) | 2.4 | 5.2 |
(mV) | 0.319 | 26.8 |
(%) | 0.058 | 4.6 |
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Kukurowski, N.; Pazera, M.; Witczak, M. Takagi–Sugeno Observer Design for Remaining Useful Life Estimation of Li-Ion Battery System Under Faults. Electronics 2020, 9, 1537. https://doi.org/10.3390/electronics9091537
Kukurowski N, Pazera M, Witczak M. Takagi–Sugeno Observer Design for Remaining Useful Life Estimation of Li-Ion Battery System Under Faults. Electronics. 2020; 9(9):1537. https://doi.org/10.3390/electronics9091537
Chicago/Turabian StyleKukurowski, Norbert, Marcin Pazera, and Marcin Witczak. 2020. "Takagi–Sugeno Observer Design for Remaining Useful Life Estimation of Li-Ion Battery System Under Faults" Electronics 9, no. 9: 1537. https://doi.org/10.3390/electronics9091537