Robust Control Design to the Furuta System under Time Delay Measurement Feedback and Exogenous-Based Perturbation
Abstract
:1. Introduction
- (a)
- Design of a nonlinear state-feedback stabiliser for nonlinear systems with random time delays, Lipschitz nonlinearities and parametric uncertainties.
- (b)
- Satisfaction of the asymptotic stabilisation based on Lyapunov–Krasovskii stability theory and LMI approach.
- (c)
- The proposed method is rather straightforward and there is no complexity in the employment of this technique.
- (d)
- Application of the offered method on an experimental device, to prove the efficiency of the method.
2. Notation
3. Robust Delay-Dependent Control Design
- is the state variable.
- is the time delay.
- A, , B, E, C, and are real matrices of appropriate dimensions.
- is the external perturbation.
- is the control input.
- is the output variable.
- is the internal or virtual variable.
4. Random Time Delay Realization
4.1. Nonlinear System Equations
4.2. Formulation
4.3. Random Time Delay Algorithm
Algorithm 1: Algorithm of the random time delay on the measurements. |
Initialise xn, xm, r (xn = 0.1, xm = 0, r = 3.7, d1 = 0.23, d2 = 0.45) do xm = r·xn·(1 − xn) if (xm > 0.5) d = d1 else d = d2 endif xn = xm end do |
5. Experimental Results
6. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Pujol-Vazquez, G.; Mobayen, S.; Acho, L. Robust Control Design to the Furuta System under Time Delay Measurement Feedback and Exogenous-Based Perturbation. Mathematics 2020, 8, 2131. https://doi.org/10.3390/math8122131
Pujol-Vazquez G, Mobayen S, Acho L. Robust Control Design to the Furuta System under Time Delay Measurement Feedback and Exogenous-Based Perturbation. Mathematics. 2020; 8(12):2131. https://doi.org/10.3390/math8122131
Chicago/Turabian StylePujol-Vazquez, Gisela, Saleh Mobayen, and Leonardo Acho. 2020. "Robust Control Design to the Furuta System under Time Delay Measurement Feedback and Exogenous-Based Perturbation" Mathematics 8, no. 12: 2131. https://doi.org/10.3390/math8122131
APA StylePujol-Vazquez, G., Mobayen, S., & Acho, L. (2020). Robust Control Design to the Furuta System under Time Delay Measurement Feedback and Exogenous-Based Perturbation. Mathematics, 8(12), 2131. https://doi.org/10.3390/math8122131