Çeşitli Test Senaryoları ile Ters Sarkaca Uygulanan Açık Model Öngörümlü Kontrol Tekniği Üzerinde Gürültü ve Bozucu Bastırma Performans Değerlendirmesi

Öz

Uygulama kolaylığı nedeniyle kontrolör tasarımı için yaygın olarak kullanılan bir test ortamı olan araba üzerinde ters sarkaç (IPC) sistemi, doğrusal olmayan ve düşük harekete geçirilmiş özellikleri ile farklı alanlarda uygulama imkânına sahiptir. Bu çalışmada, açık MPC kontrol yönteminin, iki test durumu ve analiz yaklaşımları kullanılarak gürültü ve bozuculara karşı performansı incelenmiştir. Ayrıntılı senaryolarda farklı yörünge takibi, bozucu ve gürültü durumları dikkate alınmıştır. Sayısal uygulamalar, Matlab®/Simulink®'in model öngörülü kontrol araç kutusu tarafından gerçekleştirilmiştir. Kontrolcünün avantajları ve dezavantajları, zaman alanı spesifikasyonları açısından tartışılmıştır.

Anahtar Kelimeler

• IPC
• Açık MPC
• Bozucu bastırma
• Gürültü azaltma

Noise and Disturbance Rejection Performance Evaluation on Explicit Model Predictive Control Technique Applied to Inverted Pendulum with Various Test Scenarios

Öz

An inverted pendulum on a cart (IPC) system, which is a widely used test environment for controller design due to ease of applicability, has the opportunity to be applied in different fields with nonlinear and under-actuated characteristics. In this study, the performance of the explicit MPC control method has been examined against the noise and disturbances by using two test cases and analysis approaches. Different trajectory tracking, disturbance, and noise situations have been taken into account in the elaborated scenarios. The numerical applications have been performed by the model predictive control toolbox of Matlab®/Simulink®. The advantages and drawbacks of the controller have been discussed in terms of time-domain specifications.

Anahtar Kelimeler

• IPC
• Explicit MPC
• Disturbance rejection
• Noise attenuation

Kaynakça

1. 1. Tedrake, R., 2022. Underactuated Robotics: Algorithms for Walking, Running, Swimming, Flying, and Manipulation (Course Notes for MIT 6.832).
2. 2. Kalman, R. E. 1960. Contribution to the Theory of Optimal Control, Bull. Soc. Math. Mex, 102–119.
3. 3. Kumar E., V., Jerome, J. 2013 Robust LQR Controller Design for Stabilizing and Trajectory Tracking of Inverted Pendulum, Procedia Eng., 64, 169–178.
4. 4. Eide, R., Egelid, P.M., Stamsø, A., Karimi, H. R., 2011. LQG Control Design for Balancing an Inverted Pendulum Mobile Robot, Intell. Control Autom., 02(02), 160–166.
5. 5. Askari, M., Mohamed, H.A.F., Moghavvemi, M., Yang, S. S., 2009. Model Predictive Control of an Inverted Pendulum, 2009 Int. Conf. Tech. Postgraduates (TECHPOS 2009), Kuala Lumpur, 6, 1-4.
6. 6. Boubaker, O., 2013. The Inverted Pendulum Benchmark in Nonlinear Control Theory: A Survey, Int. J. Adv. Robot. Syst., 10(5), 233.
7. 7. Baciu, A., Lazar, C., 2021. Data Driven Control for Swing-up and Stabilization of an Inverted Pendulum System. 2021 29th Mediterr. Conf. Control Autom. (MED 2021), 1155–1160.
8. 8. Mills, A., Wills, A., Ninness, B., 2009. Nonlinear Model Predictive Control of an Inverted Pendulum. 2009 American Control Conference, St. Loise, 2335–2340.

9. 9. Bemporad, A., Borrelli, F., Morari, M., 2002. Model Predictive Control Based on Linear Programming-The Explicit Solution, IEEE Trans. Automat. Contr., 47(12), 1974–1985.
10. 10. Bemporad, A., 2019. Explicit Model Predictive Control. Encycl. Syst. Control, 1–7,.
11. 11. Jaiwat, P., Ohtsuka, T., 2014. Real-Time Swing-up of Double Inverted Pendulum by Nonlinear Model Predictive Control. 2014 5th Int. Symp. Adv. Control Ind. Process., Hirosima, 290–295.
12. 12. Patne, V., Ingole, D., Sonawane, D., 2020. FPGA Implementation Framework for Explicit Hybrid Model Predictive Control, IFAC- PapersOnLine, 53(1), 362–367. 13. Tian, X., Peng, H., Zhou, F., Peng, X., 2019. RBF-ARX Model-based Fast Robust MPC Approach to an Inverted Pendulum, ISA Transactions, 93, 255–267.
13. 14. Verhoek, C., Abbas, H. S., Tóth, R., Haesaert, S., 2021. Data-Driven Predictive Control for Linear Parameter-Varying Systems, IFAC- PapersOnLine, 54(8), 101–108.
14. 15. Ozgur, H.E., Ozbek, N.S., Sarigecili, M.I., 2022. Assessment of Lqr and Explicit Mpc Methods for an Inverted Pendulum on a Cart System. 2022 MAS 16th International European Conference on Mathematics, Engineering, Natural & Medical Sciences, Mardin, 225–234.
15. 16. Franklin, G.F., Powell, J., Emami-Naeini, A., Sanjay, H.S., 2015. Feedback Control of Dynamic Systems (7/E Global Edition), Pearson Education Ltd.
16. 17. CTMS Michigan University, "Inverted Pendulum: System Modeling.”, https://ctms. engin.umich.edu//. (Accessed 12.04.2022).