DC MOTORA UYGULANAN LQR KONTROLCÜ İÇİN AĞIRLIK MATRİSLERİNİN NSGA-II TABANLI ÇOK AMAÇLI OPTİMİZASYONU
Abstract
LQR kontrol yaklaşımıyla, Lineer Zamanla Değişmeyen bir sistemin kararlılığının temin edilmesi yanında, sisteme uygulanacak geri besleme kazancına, karesel bir performans ölçütünün minimizasyonu yoluyla ulaşılıyor olması, bu kontrol yaklaşımını, kapalı çevrim sistemden beklenen performansı şekillendirme kabiliyetine sahip kılmaktadır. Bu noktada, minimize edilecek karesel performans ölçütünün ya da maliyet fonksiyonunun, içerdiği ağırlık matrisleri üzerinden, amaca uygun biçimde oluşturulması kontrolcü performansı bakımından önem arz etmektedir. O yüzden, LQR kontrolcünün tasarımında kullanılan ağırlık matrislerinin optimizasyonu, kontrolcüden beklenen çoklu performans amaçları doğrultusunda gerçekleştirilmelidir. Bu durum çok amaçlı bir optimizasyon problemini doğurmaktadır. Karesel maliyet fonksiyonunun ağırlık matrisleri, optimizasyon yapılmaksızın, deneme yanılma, kutup atama gibi klasik yöntemler yardımıyla ayarlanabilir olsa da bu durum yorucu ve zaman alıcı olabilmektedir. Bu zorluğun üstesinden gelebilmek adına, çeşitli çok amaçlı optimizasyon tekniklerinden istifade edilmesi mümkündür.
Yapılan bu çalışma kapsamında, LQR tabanlı optimal DC motor kontrolü amaçlanmıştır. LQR kontrolcü için söz konusu karesel maliyet fonksiyonuna dair Q ve R ağırlık matrisi parametrelerinin ayarlanması gerekmektedir. Çok amaçlı optimizasyon tekniklerinden biri olan ve Non-Dominated Sorted Genetic Algorithm (NSGA-II) olarak bilinen optimizasyon algoritması yardımıyla ilgili parametreler ayarlanmıştır. Elde edilen optimum parametreler kullanılarak sentezlenen LQR kontrolcünün sistem üzerindeki performans bulguları, simülasyon sonuçları ile sunulmuştur.
References
- Al-Mahturi, Ayad, and Herman Wahid. 2017. “Optimal Tuning of Linear Quadratic Regulator Controller Using a Particle Swarm Optimization for Two-Rotor Aerodynamical System.” International Journal of Electronics and Communication Engineering 11(2):196–202. doi: 10.5281/zenodo.1128899.
- Ata, Baris, and Ramazan Coban. 2015. “Artificial Bee Colony Algorithm Based Linear Quadratic Optimal Controller Design for a Nonlinear Inverted Pendulum.” International Journal of Intelligent Systems and Applications in Engineering 3.
- Athans, M. 1966. “The Status of Optimal Control Theory and Applications for Deterministic Systems.” IEEE Transactions on Automatic Control 11(3):580–96. doi: 10.1109/TAC.1966.1098353.
- Bottura, C. P., and J. V Da Fonseca Neto. 1999. “Parallel Eigenstructure Assignment via LQR Design and Genetic Algorithms.” Pp. 2295–99 vol.4 in Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251). Vol. 4.
- Hassani, Kaveh, and Won Sook Lee. 2014. “Optimal Tuning of Linear Quadratic Regulators Using Quantum Particle Swarm Optimization.” International Conference of Control, Dynamic Systems, and Robotics (59):1–8.
- HG Kamil. 2015. “Intelligent Model-Based Control of Complex Three-Link Mechanisms.” (April). Lewis, Frank L. 1986. Optimal Control. New York: Wiley.
- Li, Yong, Jianchang Liu, and Yu Wang. 2008. “Design Approach of Weighting Matrices for LQR Based on Multi-Objective Evolution Algorithm.” Proceedings of the 2008 IEEE International Conference on Information and Automation, ICIA 2008 (2):1188–92. doi: 10.1109/ICINFA.2008.4608180.
- Mobayen, S., A. Rabiei, M. Moradi, and B. Mohammady. 2011. “Linear Quadratic Optimal Control System Design Using Particle Swarm Optimization Algorithm.” International Journal of Physical Sciences 6(30):6958–66. doi: 10.5897/IJPS11.726.
- Nise, N. S. 2007. Control Systems Engineering. Wiley.
NSGA-II BASED MULTI-OBJECTIVE OPTIMIZATION OF WEIGHT MATRICES FOR LQR CONTROLLER APPLIED TO DC MOTOR
Abstract
In addition to ensuring the stability of a Linear Time Invariant system with the LQR control approach, the fact that the feedback gain to be applied to the system is achieved by minimizing a quadratic performance criterion makes this control approach capable of shaping the performance expected from a closed-loop system. At this point, it is important in terms of controller performance to create the quadratic performance criterion or cost function to be minimized, over the weight matrices it contains, in accordance with the purpose. Therefore, the optimization of the weight matrices used in the design of the LQR controller should be carried out in line with the multiple performance objectives expected from the controller. This situation creates a multi-objective optimization problem. Although the weight matrices of the quadratic cost function can be adjusted with the help of classical methods such as trial and error, pole assignment, without optimization, this can be tiring and time consuming. In order to overcome this difficulty, it is possible to benefit from various multi-objective optimization techniques.
Within the scope of this study, LQR-based optimal DC motor control is aimed. For the LQR controller, the Q and R weight matrix parameters of the square cost function need to be adjusted. Relevant parameters are adjusted with the help of the optimization algorithm known as Non-Dominated Sorted Genetic Algorithm (NSGA-II), which is one of the multi-purpose optimization techniques. By using the optimum parameters obtained, the performance findings of the synthesized LQR controller on the system are presented with simulation results.
References
- Al-Mahturi, Ayad, and Herman Wahid. 2017. “Optimal Tuning of Linear Quadratic Regulator Controller Using a Particle Swarm Optimization for Two-Rotor Aerodynamical System.” International Journal of Electronics and Communication Engineering 11(2):196–202. doi: 10.5281/zenodo.1128899.
- Ata, Baris, and Ramazan Coban. 2015. “Artificial Bee Colony Algorithm Based Linear Quadratic Optimal Controller Design for a Nonlinear Inverted Pendulum.” International Journal of Intelligent Systems and Applications in Engineering 3.
- Athans, M. 1966. “The Status of Optimal Control Theory and Applications for Deterministic Systems.” IEEE Transactions on Automatic Control 11(3):580–96. doi: 10.1109/TAC.1966.1098353.
- Bottura, C. P., and J. V Da Fonseca Neto. 1999. “Parallel Eigenstructure Assignment via LQR Design and Genetic Algorithms.” Pp. 2295–99 vol.4 in Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251). Vol. 4.
- Hassani, Kaveh, and Won Sook Lee. 2014. “Optimal Tuning of Linear Quadratic Regulators Using Quantum Particle Swarm Optimization.” International Conference of Control, Dynamic Systems, and Robotics (59):1–8.
- HG Kamil. 2015. “Intelligent Model-Based Control of Complex Three-Link Mechanisms.” (April). Lewis, Frank L. 1986. Optimal Control. New York: Wiley.
- Li, Yong, Jianchang Liu, and Yu Wang. 2008. “Design Approach of Weighting Matrices for LQR Based on Multi-Objective Evolution Algorithm.” Proceedings of the 2008 IEEE International Conference on Information and Automation, ICIA 2008 (2):1188–92. doi: 10.1109/ICINFA.2008.4608180.
- Mobayen, S., A. Rabiei, M. Moradi, and B. Mohammady. 2011. “Linear Quadratic Optimal Control System Design Using Particle Swarm Optimization Algorithm.” International Journal of Physical Sciences 6(30):6958–66. doi: 10.5897/IJPS11.726.
- Nise, N. S. 2007. Control Systems Engineering. Wiley.
Details
| Primary Language | Turkish |
|---|---|
| Subjects | Electrical Engineering |
| Journal Section | Electrical and Electronics Engineering |
| Authors | |
| Publication Date | September 3, 2022 |
| Submission Date | June 2, 2022 |
| Published in Issue | Year 2022 |