The robustness of H-infinity control
| dc.contributor.advisor | Braae, Martin | en_ZA |
| dc.contributor.author | Marques, Fausto | en_ZA |
| dc.date.accessioned | 2016-01-02T04:19:37Z | |
| dc.date.available | 2016-01-02T04:19:37Z | |
| dc.date.issued | 1999 | en_ZA |
| dc.description | Bibliography : leave 111. | en_ZA |
| dc.description.abstract | Modern control theory generates controllers of a high order. Since these controllers inherently require elaborate circuits or algorithms for implementation, there is always the possibility that the implemented controller will differ from the designed controller by a certain degree. Furthermore, the control engineer might want to tweak the controller in practice and will therefore deliberately adjust the parameters of the nominal controller. The key factor is that the controller although perturbed from the nominal controller, will still stabilize the closed loop system. The greater this perturbation can be without destabilizing the closed loop system, the more robust the controller is. Keel et al, in their paper entitled "Robust, Fragile or Optimal?" (1997), made a statement that the controllers generated by H-infinity design methods are fragile. A norm was introduced called the parametric stability margin, to serve as a measure of this robustness. A fragile controller is defined as a controller that is very sensitive to changes in its controller coefficients and any small change from the nominal controller will result in closed loop instability. This type of controller will have a very small parametric stability margin. This parametric stability margin is defined as a radius in parameter space in which the controller will be stable in closed loop. If the norm of the perturbation exceeds this margin in parameter space, then the closed loop system will become unstable. A real plant was chosen as a means to test the claims of Keel et al. The plant is a simple "robot arm", a non-linear second order system. The non-linearity creates both open loop stable and unstable regions for control. A controller was designed for this plant using H-infinity techniques. This controller would form the basis for testing the claims of Keel et al. When this controller was analysed using the parametric stability margin, it was predicted to be fragile or stated differently: very small changes in the controller coefficients would destabilize the closed loop system. However, closer scrutiny revealed that this sensitivity was only concentrated on the leading coefficients in the numerator and denominator of the controller. Furthermore, the relative size of the perturbations on these coefficients was far in excess of 1000% of the original coefficient. The designed controller was implemented successfully in practice using a digital implementation. Even a perturbed version of 200% of the controller coefficients stabilized the closed loop system. It was then discovered that it was possible to create a perturbation with a norm greater than the parametric stability margin that would still stabilize the closed loop system. A similar perturbation could also be constructed for the examples presented by Keel et al in their paper (1997). The resulting conclusion was that the H-infinity techniques actually generate rather robust controllers. Provided that the perturbations on the leading controller coefficients are kept below the destabilizing value, the other coefficients can be perturbed to a very large degree. This destabilizing value is given by the perturbation vector at the parametric stability margin. This perturbation will place some closed loop poles on the stability boundary of the region of interest. | en_ZA |
| dc.identifier.apacitation | Marques, F. (1999). <i>The robustness of H-infinity control</i>. (Thesis). University of Cape Town ,Faculty of Engineering & the Built Environment ,Department of Electrical Engineering. Retrieved from http://hdl.handle.net/11427/16094 | en_ZA |
| dc.identifier.chicagocitation | Marques, Fausto. <i>"The robustness of H-infinity control."</i> Thesis., University of Cape Town ,Faculty of Engineering & the Built Environment ,Department of Electrical Engineering, 1999. http://hdl.handle.net/11427/16094 | en_ZA |
| dc.identifier.citation | Marques, F. 1999. The robustness of H-infinity control. University of Cape Town. | en_ZA |
| dc.identifier.ris | TY - Thesis / Dissertation AU - Marques, Fausto AB - Modern control theory generates controllers of a high order. Since these controllers inherently require elaborate circuits or algorithms for implementation, there is always the possibility that the implemented controller will differ from the designed controller by a certain degree. Furthermore, the control engineer might want to tweak the controller in practice and will therefore deliberately adjust the parameters of the nominal controller. The key factor is that the controller although perturbed from the nominal controller, will still stabilize the closed loop system. The greater this perturbation can be without destabilizing the closed loop system, the more robust the controller is. Keel et al, in their paper entitled "Robust, Fragile or Optimal?" (1997), made a statement that the controllers generated by H-infinity design methods are fragile. A norm was introduced called the parametric stability margin, to serve as a measure of this robustness. A fragile controller is defined as a controller that is very sensitive to changes in its controller coefficients and any small change from the nominal controller will result in closed loop instability. This type of controller will have a very small parametric stability margin. This parametric stability margin is defined as a radius in parameter space in which the controller will be stable in closed loop. If the norm of the perturbation exceeds this margin in parameter space, then the closed loop system will become unstable. A real plant was chosen as a means to test the claims of Keel et al. The plant is a simple "robot arm", a non-linear second order system. The non-linearity creates both open loop stable and unstable regions for control. A controller was designed for this plant using H-infinity techniques. This controller would form the basis for testing the claims of Keel et al. When this controller was analysed using the parametric stability margin, it was predicted to be fragile or stated differently: very small changes in the controller coefficients would destabilize the closed loop system. However, closer scrutiny revealed that this sensitivity was only concentrated on the leading coefficients in the numerator and denominator of the controller. Furthermore, the relative size of the perturbations on these coefficients was far in excess of 1000% of the original coefficient. The designed controller was implemented successfully in practice using a digital implementation. Even a perturbed version of 200% of the controller coefficients stabilized the closed loop system. It was then discovered that it was possible to create a perturbation with a norm greater than the parametric stability margin that would still stabilize the closed loop system. A similar perturbation could also be constructed for the examples presented by Keel et al in their paper (1997). The resulting conclusion was that the H-infinity techniques actually generate rather robust controllers. Provided that the perturbations on the leading controller coefficients are kept below the destabilizing value, the other coefficients can be perturbed to a very large degree. This destabilizing value is given by the perturbation vector at the parametric stability margin. This perturbation will place some closed loop poles on the stability boundary of the region of interest. DA - 1999 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 1999 T1 - The robustness of H-infinity control TI - The robustness of H-infinity control UR - http://hdl.handle.net/11427/16094 ER - | en_ZA |
| dc.identifier.uri | http://hdl.handle.net/11427/16094 | |
| dc.identifier.vancouvercitation | Marques F. The robustness of H-infinity control. [Thesis]. University of Cape Town ,Faculty of Engineering & the Built Environment ,Department of Electrical Engineering, 1999 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/16094 | en_ZA |
| dc.language.iso | eng | en_ZA |
| dc.publisher.department | Department of Electrical Engineering | en_ZA |
| dc.publisher.faculty | Faculty of Engineering and the Built Environment | |
| dc.publisher.institution | University of Cape Town | |
| dc.subject.other | Electrical Engineering | en_ZA |
| dc.title | The robustness of H-infinity control | en_ZA |
| dc.type | Master Thesis | |
| dc.type.qualificationlevel | Masters | |
| dc.type.qualificationname | MSc | en_ZA |
| uct.type.filetype | Text | |
| uct.type.filetype | Image | |
| uct.type.publication | Research | en_ZA |
| uct.type.resource | Thesis | en_ZA |
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