Robust Model Predictive Control Paradigm for Automatic Voltage Regulators against Uncertainty Based on Optimization Algorithms
Abstract
:1. Introduction
- A new robust control strategy is introduced for the AVR to handle the parameters uncertainty issue and voltage variations.
- The stability of the perturbed AVR system is proved according to derived frequency-domain constraints using the Hermite–Biehler theorem during the design of MPC.
- The factors of the MPC are tuned based on an intelligent algorithm named AOA rather than the trial-and-error methods.
- A developed figure of demerit objective function is introduced to handle the decreasing of the response settling time and the voltage maximum overshoot simultaneously.
- The system response confirms the robustness characteristic of the developed AOA-based robust MPC against the variations of the voltage and the parameters’ uncertainty compared with other techniques.
2. Description of AVR System
- The output voltage from the measuring device
- The terminal voltage of the generator
- The exciter voltage
- The amplifier voltage.
2.1. Formulation of AVR for MPC
2.2. Obtaining the Control Law of MPC
3. Robust MPC Formulation
4. Arithmetic Optimization Algorithm Overview
4.1. Exploration Stage
4.2. Exploitation Stage
5. Results and Discussion
Algorithm 1. The pseudo-code of the main steps to design the robust MPC based on AOA |
1: Initialize AOA technique 2: Confirm the frequency domain constraints 3: Run the AVR system with MPC 4: Determine the FoD function in Equation (31) 5: while (current iteration < iterationmax) 6: Perform the searching procedure of AOA technique 7: Confirm the frequency domain constraints 8: Run the AVR system with MPC 9: Determine the FoD function in Equation (31) 10: Select the minimum value of the FoD index 11: Update the solutions of AOA population 12: end while 13: Print the best gains of the MPC 14: Stop |
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Controller Type | Controller Gains | FoD Value |
---|---|---|
ABC-based PID | kp = 1.6524, ki = 0.4083, kd = 0.3654 | 1.5844 |
NSGA-II-based PID | kp = 2.7666, ki = 0.4991, kd = 0.5008 | 1.1335 |
MOEO-based PID | kp = 0.8503, ki = 0.7473, kd = 0.3874 | 0.3895 |
FSA-based PID | kp = 0.6450, ki = 0.4730, kd = 0.2550 | 0.0805 |
Multi-objective PID | kp = 0.612, ki = 0.463, kd = 0.2 | 0.0878 |
Proposed AOA based robust MPC | Ts = 0.012, C = 4, P = 30, rw = 0.01, qw = 1 | 0.0574 |
Controller Type | ts (s) | Mo (%) | umax (p.u) |
---|---|---|---|
ABC-based PID | 3.0939 | 24.9592 | 38.19 |
NSGA-II-based PID | 1.9894 | 40.5778 | 52.85 |
MOEO-based PID | 0.8995 | 6.6678 | 39.59 |
FSA-based PID | 0.4417 | 1.0460 | 23.14 |
Multi-objective PID | 0.4783 | 1.5164 | 20.61 |
Proposed AOA based robust MPC | 0.2444 | 1.2862 | 13.52 |
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Elsisi, M.; Tran, M.-Q.; Hasanien, H.M.; Turky, R.A.; Albalawi, F.; Ghoneim, S.S.M. Robust Model Predictive Control Paradigm for Automatic Voltage Regulators against Uncertainty Based on Optimization Algorithms. Mathematics 2021, 9, 2885. https://doi.org/10.3390/math9222885
Elsisi M, Tran M-Q, Hasanien HM, Turky RA, Albalawi F, Ghoneim SSM. Robust Model Predictive Control Paradigm for Automatic Voltage Regulators against Uncertainty Based on Optimization Algorithms. Mathematics. 2021; 9(22):2885. https://doi.org/10.3390/math9222885
Chicago/Turabian StyleElsisi, Mahmoud, Minh-Quang Tran, Hany M. Hasanien, Rania A. Turky, Fahad Albalawi, and Sherif S. M. Ghoneim. 2021. "Robust Model Predictive Control Paradigm for Automatic Voltage Regulators against Uncertainty Based on Optimization Algorithms" Mathematics 9, no. 22: 2885. https://doi.org/10.3390/math9222885
APA StyleElsisi, M., Tran, M.-Q., Hasanien, H. M., Turky, R. A., Albalawi, F., & Ghoneim, S. S. M. (2021). Robust Model Predictive Control Paradigm for Automatic Voltage Regulators against Uncertainty Based on Optimization Algorithms. Mathematics, 9(22), 2885. https://doi.org/10.3390/math9222885