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MOPSO TABANLI LQG SERVO KONTROL YAKLAŞIMI İLE ARAÇ ÜZERİNDE KONUMLU TERS SARKACIN KONTROLÜ

Year 2022, , 418 - 433, 03.09.2022

Ali Fazıl Uygur

https://doi.org/10.17780/ksujes.1133786

Abstract

Araç üzerinde konumlu Ters Sarkaç, çeşitli kontrol yöntemlerinin uygulanması ve performanslarının karşılaştırılması adına, akademik anlamda yaygın olarak kullanılmaktadır. Kararsız ve lineer olmayan yapıdaki Ters Sarkaç, sistem bozucuları ve ölçüm gürültüleri karşısında, duyarlı ve kırılgan yapıdadır. Bozuculara ve sensör ölçüm gürültüsüne maruz kalmak, kontrol sistemlerinin performansını olumsuz anlamda etkilemekte ve kontrol kalitesinin düşmesine sebep olmaktadır. Bahsedilen problem karşısında, çözüm olarak başvurulan yöntemlerden biri de Kalman Filtresi ile LQR kontrolün kombinasyonu olan ve Lineer Quadratic Gaussian (LQG) olarak bilinen kontrol tasarım yöntemidir.

Bu çalışmada, sistem bozucularına ve sensör gürültüsüne maruz kalan, araç üzerinde konumlu Ters Sarkaç için, sarkacı üzerinde taşıyan araç, verilen bir referansı takip ederken, sarkacın da bu esnada kararsız olan dik denge konumunu koruması istenmektedir. Sistem bozucuları ve sensör gürültüleri Gaussian Beyaz Gürültü olarak seçilmişlerdir, Referans takibi sağlamak ve denge noktası civarında kararlılığı sürdürmek adına, LQG servo kontrol yaklaşımı benimsenmiştir. Kullanılacak olan kontrolcünün, kontrol gereksinimlerini en iyi şekilde karşılaması bakımından, performansının optimize edilmesi icap eder. Bu maksatla, LQG servo kontrolcü bünyesindeki LQI bloğu için performans ölçütü ağırlık matrislerinin, Çok Amaçlı Parçacık Sürü Optimizasyonu Algoritması (MOPSO) yardımıyla optimizasyonu gerçekleştirilmiştir.

Keywords

Ters Sarkaç LQG Servo Kontrolcü Kalman Filtresi MOPSO

References

  • Abdollahzadeh, H., Atashgar, K., & Abbasi, M. (2016). Multi-objective opportunistic maintenance optimization of a wind farm considering limited number of maintenance groups. Renewable Energy, 88(April), 247–261. Retrieved from https://doi.org/10.1016/j.renene.2015.11.022
  • Ashok Kumar, M., & Kanthalakshmi, S. (2018, August 1). H∞tracking control for an inverted pendulum. JVC/Journal of Vibration and Control. SAGE Publications Inc. Retrieved from https://doi.org/10.1177/1077546317750977
  • Bǎlan, R., Mǎtieş, V., & Stan, S. (2005). A solution of the inverse pendulum on a cart problem using predictive control. In IEEE International Symposium on Industrial Electronics (Vol. I, pp. 63–68). Institute of Electrical and Electronics Engineers Inc. Retrieved from https://doi.org/10.1109/ISIE.2005.1528889
  • Chawla, I., Chopra, V., & Singla, A. (2019). Robust LQR Based ANFIS Control of x-z Inverted Pendulum. Proceedings - 2019 Amity International Conference on Artificial Intelligence, AICAI 2019, 818–823. Retrieved from https://doi.org/10.1109/AICAI.2019.8701333
  • Irfan, S., Mehmood, A., Razzaq, M. T., & Iqbal, J. (2018). Advanced sliding mode control techniques for Inverted Pendulum: Modelling and simulation. Engineering Science and Technology, an International Journal, 21(4), 753–759. Retrieved from https://doi.org/10.1016/j.jestch.2018.06.010
  • Li, W., Ding, H., & Cheng, K. (2012). An investigation on the design and performance assessment of double-PID and LQR controllers for the inverted pendulum. In Proceedings of the 2012 UKACC International Conference on Control, CONTROL 2012 (pp. 190–196). Retrieved from https://doi.org/10.1109/CONTROL.2012.6334628
  • Mahmoodabadi, mj, Taherkhorsandi, m., Talebipour, m., & Castillo-Villar, kk. (2015). Adaptive robust PID control subject to supervisory decoupled sliding mode control based upon genetic algorithm optimization. Transactions of the Institute of Measurement and Control, 37(4), 505–514. Retrieved from https://doi.org/10.1177/0142331214543295
  • Mishra, S. K., & Chandra, D. (2014). Stabilization and Tracking Control of Inverted Pendulum Using Fractional Order PID Controllers. Journal of Engineering (United Kingdom), 2014. Retrieved from https://doi.org/10.1155/2014/752918
  • Morimoto, H. (1990). Adaptive LQG Regulator via the Separation Principle. IEEE Transactions on Automatic Control, 35(1), 85–88. Retrieved from https://doi.org/10.1109/9.45150
  • Roose, A. I., Yahya, S., & Al-Rizzo, H. (2017). Fuzzy-logic control of an inverted pendulum on a cart. Computers and Electrical Engineering, 61, 31–47. Retrieved from https://doi.org/10.1016/j.compeleceng.2017.05.016
  • Saifizul, A. A., Zainon, Z., Abu Osman, N. ., Azlan, C. A., & Ibrahim, U. F. . U. (2006). Intelligent Control for Self-erecting Inverted Pendulum Via Adaptive Neuro-fuzzy Inference System. American Journal of Applied Sciences, 3(4), 1795–1802. Retrieved from https://doi.org/10.3844/ajassp.2006.1795.1802
  • Singh, K., Nema, S., & Padhy, P. K. (2014). Modified PSO based PID sliding mode control for inverted pendulum. In 2014 International Conference on Control, Instrumentation, Communication and Computational Technologies, ICCICCT 2014 (pp. 722–727). Institute of Electrical and Electronics Engineers Inc. Retrieved from https://doi.org/10.1109/ICCICCT.2014.6993054
  • Soltanpour, M. R., Khooban, M. H., & Khalghani, M. R. (2016). An optimal and intelligent control strategy for a class of nonlinear systems: Adaptive fuzzy sliding mode. JVC/Journal of Vibration and Control, 22(1), 159–175. Retrieved from https://doi.org/10.1177/1077546314526920
  • Suzuki, Y., Nomura, T., Casadio, M., & Morasso, P. (2012). Intermittent control with ankle, hip, and mixed strategies during quiet standing: A theoretical proposal based on a double inverted pendulum model. Journal of Theoretical Biology, 310, 55–79. Retrieved from https://doi.org/10.1016/j.jtbi.2012.06.019
  • Vinodh Kumar, E., & Jerome, J. (2013). Robust LQR controller design for stabilizing and trajectory tracking of inverted pendulum. In Procedia Engineering (Vol. 64, pp. 169–178). Elsevier Ltd. Retrieved from https://doi.org/10.1016/j.proeng.2013.09.088
  • Welch, G., & Bishop, G. (2006). An Introduction to the Kalman Filter. In Practice, 7(1), 1–16. Retrieved from https://doi.org/10.1.1.117.6808
  • Yu, L. H., & Jian, F. (2014). An inverted pendulum fuzzy controller design and simulation. In Proceedings - 2014 International Symposium on Computer, Consumer and Control, IS3C 2014 (pp. 557–559). IEEE Computer Society. Retrieved from https://doi.org/10.1109/IS3C.2014.151
  • Zamani, M., Karimi-Ghartemani, M., Sadati, N., & Parniani, M. (2009). Design of a fractional order PID controller for an AVR using particle swarm optimization. Control Engineering Practice, 17(12), 1380–1387. Retrieved from https://doi.org/10.1016/j.conengprac.2009.07.005

CONTROL OF THE INVERTED PENDULUM ON A CART WITH THE MOPSO-BASED LQG SERVO CONTROL APPROACH

Year 2022, , 418 - 433, 03.09.2022

Ali Fazıl Uygur

https://doi.org/10.17780/ksujes.1133786

Abstract

The Inverted Pendulum, located on the vehicle, is widely used in the academic sense for the application of various control methods and comparison of their performance. An unstable and non-linear Inverted Pendulum is sensitive and fragile to system disturbances and measurement noises. Exposure to disturbances and sensor measurement noise adversely affects the performance of control systems and causes a decrease in control quality. One of the methods used as a solution to the mentioned problem is the control design method known as Linear Quadratic Gaussian (LQG), which is a combination of Kalman Filter and LQR control.

In this study, for the Inverted Pendulum located on the vehicle, which is exposed to system disturbances and sensor noise, while the vehicle carrying the pendulum follows a given reference, the pendulum is required to maintain its unstable vertical equilibrium position. System disturbances and sensor noises are chosen as Gaussian White Noise. LQG servo control approach is adopted to provide reference tracking and maintain stability around the balance point. It is necessary to optimize the performance of the controller to be used in order to best meet the control requirements. For this purpose, the performance criterion weight matrices for the LQI block within the LQG servo controller have been optimized with the help of the Multi-Objective Particle Swarm Optimization Algorithm (MOPSO).

Keywords

Inverted Pendulum LQG Servo Controller Kalman Filter MOPSO

References

  • Abdollahzadeh, H., Atashgar, K., & Abbasi, M. (2016). Multi-objective opportunistic maintenance optimization of a wind farm considering limited number of maintenance groups. Renewable Energy, 88(April), 247–261. Retrieved from https://doi.org/10.1016/j.renene.2015.11.022
  • Ashok Kumar, M., & Kanthalakshmi, S. (2018, August 1). H∞tracking control for an inverted pendulum. JVC/Journal of Vibration and Control. SAGE Publications Inc. Retrieved from https://doi.org/10.1177/1077546317750977
  • Bǎlan, R., Mǎtieş, V., & Stan, S. (2005). A solution of the inverse pendulum on a cart problem using predictive control. In IEEE International Symposium on Industrial Electronics (Vol. I, pp. 63–68). Institute of Electrical and Electronics Engineers Inc. Retrieved from https://doi.org/10.1109/ISIE.2005.1528889
  • Chawla, I., Chopra, V., & Singla, A. (2019). Robust LQR Based ANFIS Control of x-z Inverted Pendulum. Proceedings - 2019 Amity International Conference on Artificial Intelligence, AICAI 2019, 818–823. Retrieved from https://doi.org/10.1109/AICAI.2019.8701333
  • Irfan, S., Mehmood, A., Razzaq, M. T., & Iqbal, J. (2018). Advanced sliding mode control techniques for Inverted Pendulum: Modelling and simulation. Engineering Science and Technology, an International Journal, 21(4), 753–759. Retrieved from https://doi.org/10.1016/j.jestch.2018.06.010
  • Li, W., Ding, H., & Cheng, K. (2012). An investigation on the design and performance assessment of double-PID and LQR controllers for the inverted pendulum. In Proceedings of the 2012 UKACC International Conference on Control, CONTROL 2012 (pp. 190–196). Retrieved from https://doi.org/10.1109/CONTROL.2012.6334628
  • Mahmoodabadi, mj, Taherkhorsandi, m., Talebipour, m., & Castillo-Villar, kk. (2015). Adaptive robust PID control subject to supervisory decoupled sliding mode control based upon genetic algorithm optimization. Transactions of the Institute of Measurement and Control, 37(4), 505–514. Retrieved from https://doi.org/10.1177/0142331214543295
  • Mishra, S. K., & Chandra, D. (2014). Stabilization and Tracking Control of Inverted Pendulum Using Fractional Order PID Controllers. Journal of Engineering (United Kingdom), 2014. Retrieved from https://doi.org/10.1155/2014/752918
  • Morimoto, H. (1990). Adaptive LQG Regulator via the Separation Principle. IEEE Transactions on Automatic Control, 35(1), 85–88. Retrieved from https://doi.org/10.1109/9.45150
  • Roose, A. I., Yahya, S., & Al-Rizzo, H. (2017). Fuzzy-logic control of an inverted pendulum on a cart. Computers and Electrical Engineering, 61, 31–47. Retrieved from https://doi.org/10.1016/j.compeleceng.2017.05.016
  • Saifizul, A. A., Zainon, Z., Abu Osman, N. ., Azlan, C. A., & Ibrahim, U. F. . U. (2006). Intelligent Control for Self-erecting Inverted Pendulum Via Adaptive Neuro-fuzzy Inference System. American Journal of Applied Sciences, 3(4), 1795–1802. Retrieved from https://doi.org/10.3844/ajassp.2006.1795.1802
  • Singh, K., Nema, S., & Padhy, P. K. (2014). Modified PSO based PID sliding mode control for inverted pendulum. In 2014 International Conference on Control, Instrumentation, Communication and Computational Technologies, ICCICCT 2014 (pp. 722–727). Institute of Electrical and Electronics Engineers Inc. Retrieved from https://doi.org/10.1109/ICCICCT.2014.6993054
  • Soltanpour, M. R., Khooban, M. H., & Khalghani, M. R. (2016). An optimal and intelligent control strategy for a class of nonlinear systems: Adaptive fuzzy sliding mode. JVC/Journal of Vibration and Control, 22(1), 159–175. Retrieved from https://doi.org/10.1177/1077546314526920
  • Suzuki, Y., Nomura, T., Casadio, M., & Morasso, P. (2012). Intermittent control with ankle, hip, and mixed strategies during quiet standing: A theoretical proposal based on a double inverted pendulum model. Journal of Theoretical Biology, 310, 55–79. Retrieved from https://doi.org/10.1016/j.jtbi.2012.06.019
  • Vinodh Kumar, E., & Jerome, J. (2013). Robust LQR controller design for stabilizing and trajectory tracking of inverted pendulum. In Procedia Engineering (Vol. 64, pp. 169–178). Elsevier Ltd. Retrieved from https://doi.org/10.1016/j.proeng.2013.09.088
  • Welch, G., & Bishop, G. (2006). An Introduction to the Kalman Filter. In Practice, 7(1), 1–16. Retrieved from https://doi.org/10.1.1.117.6808
  • Yu, L. H., & Jian, F. (2014). An inverted pendulum fuzzy controller design and simulation. In Proceedings - 2014 International Symposium on Computer, Consumer and Control, IS3C 2014 (pp. 557–559). IEEE Computer Society. Retrieved from https://doi.org/10.1109/IS3C.2014.151
  • Zamani, M., Karimi-Ghartemani, M., Sadati, N., & Parniani, M. (2009). Design of a fractional order PID controller for an AVR using particle swarm optimization. Control Engineering Practice, 17(12), 1380–1387. Retrieved from https://doi.org/10.1016/j.conengprac.2009.07.005
There are 18 citations in total.

Details

Primary Language Turkish
Subjects Electrical Engineering
Journal Section Electrical and Electronics Engineering
Authors

Ali Fazıl Uygur 0000-0002-1049-4927

Publication Date September 3, 2022
Submission Date June 21, 2022
Published in Issue Year 2022

Cite

APA Uygur, A. F. (2022). MOPSO TABANLI LQG SERVO KONTROL YAKLAŞIMI İLE ARAÇ ÜZERİNDE KONUMLU TERS SARKACIN KONTROLÜ. Kahramanmaraş Sütçü İmam Üniversitesi Mühendislik Bilimleri Dergisi, 25(3), 418-433. https://doi.org/10.17780/ksujes.1133786