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AĞIRLIK MATRİSLERİNİN 3-SD HELİKOPTERİN DDRD TABANLI KONTROL METODU ÜZERİNE ETKİLERİ

Year 2021, Volume: 9 Issue: 3, 588 - 605, 01.09.2021
https://doi.org/10.36306/konjes.863012

Abstract

Durum Değişkenine Bağlı Riccati Denklemi (DDRD) tekniği, verilen ikinci dereceden bir maliyet fonksiyonunu en aza indirecek şekilde doğrusal olmayan bir sistem sınıfı için optimale yakın bir kontrol kanunu sağlar. Doğrusal olmayan sistem (DOS) matrisleri her zaman anında hesaplanıp, DOS doğrusal ve zamanla değişmeyen bir sistem olarak ele alınabilir ve ilgili optimal kontrol problemi her anda Doğrusal Kuadratik Regülatör (DKR) problemi olarak tanımlanabilir. Bu nedenle, DKR'nin ağırlık matrisleri, DDRD denetleyicisi vasıtasıyla kapalı çevrim sistemin geçici zaman cevabını şekillendirmede önemli bir rol oynamaktadır. Bu çalışmada, üç serbestlik dereceli (3-SD) deney helikopterinin pozisyon kontrolü için DDRD tabanlı bir optimal kontrolcü tasarlandı. Deneyler, helikopterin geçici zaman cevabı üzerindeki etkilerini değerlendirilmek için farklı ağırlık matrisleriyle tekrarlandı. Deneylerin ilk aşamasında, ağırlık matrisleri sabit gerçek elemanlı köşegen matris olarak seçildi. DDRD metoduyla kontrol edilen helikopterin durumlarıyla ilişkili köşegen elemanlar, bu durumların geçici zaman cevaplarını nasıl etkilediğini incelemek için değiştirildi. İkinci aşamada, ağırlık matrisleri durum bağımlı olarak seçildi. Her iki aşamadaki deneysel sonuçların kıyaslaması, durum bağımlı ağırlık matrislerinin yerleşme zamanı ve kalıcı durum hatası gibi geçici zaman cevabının özelliklerini iyileştirme yeteneğine daha fazla sahip olduklarını ortaya çıkartmaktadır.

Supporting Institution

Türk Havacılık ve Uzay Sanayii A.Ş.

Project Number

DKTM/2015/07

References

  • Arican, A.C., Ozcan, S., Kocagil, B.M., Guzey, U.M., Copur, E.H., Salamci, M.U., “Linear and Nonlinear Optimal Controller Design for a 3 DOF Helicopter”, 19th International Carpathian Control Conference, Szilvasvarad, Hungary, 185-190, 28-31 Mayıs 2018.
  • Babaei, N., Salamci, M.U., 2015, “Personalized Drug Administration for Cancer Treatment Using Model Reference Adaptive Control”, Journal of Theoretical Biology, Vol. 371, pp. 24-44.
  • Babaei, N., Salamci, M.U., 2018, “Controller Design for Personalized Drug Administration in Cancer Therapy: Successive Approximation Approach”, Optimal Control Applications and Methods, Vol. 39, No. 2, pp. 682-719.
  • Batmani,, Y., Khaloozadeh H., 2013, “Optimal Chemotherapy in Cancer Treatment: State Dependent Riccati Equation Control and Extended Kalman Filter”, Optimal Control Applications and Methods, Vol. 34, ss. 562-577.
  • Bilgin, N., Salamci, M.U., “Sliding Mode Control Design for Nonlinear Systems without Reaching Phase and Its Applications to A Flexible Spacecraft”, ASME 2014 12th Biennial Conference on Engineering Systems Design and Analysis, Copenhagen, Denmark, 1-9, 25-27 Haziran 2014.
  • Bogdanov, A., Carlsson, M., Harvey, G., Hunt, J., Kieburtz, D., van der Merwe, R., & Wan, E., “State- Dependent Riccati Equation Control of a Small Unmanned Helicopter”, AIAA Guidance, Navigation, and Control Conference and Exhibit, Austin, Texas, 11-14 Ağustos 2003.
  • Çimen, T., “State-Dependent Riccati Equation (SDRE) Control: A Survey”, Proceedings of the 17th World Congress the International Federation of Automatic Control, Seoul, Korea, 3761-3775, 6-11 Temmuz 2008.
  • Çimen, T., 2010, “Systematic and Effective Design of Nonlinear Feedback Controllers via the State- Dependent Riccati Equation (SDRE) Method”, Annual Reviews in Control, Vol. 34, No. 1, pp. 32- 51.
  • Çimen, T., 2012, “Survey of State-Dependent Riccati Equation in Nonlinear Optimal Feedback Control Synthesis”, Journal of Guidance, Control and Dynamics, Vol. 35, No. 4, pp. 1025-1047.
  • Copur, E.H., Arican, A.C., Ozcan, S., Salamci, M.U., 2019, “An Update Algorithm Design Using Moving Region of Attraction for SDRE Based Control Law”, Journal of The Franklin Institute, Vol. 356, No. 15, pp. 8388-8413.
  • Das, R.R., Elumalai, V.K., Subramanian R.G., Kumar, K.V.A., 2018, “Adaptive Predator–Prey Optimization for Tuning of Infinite Horizon LQR Applied to Vehicle Suspension System”, Applied Soft Computing, Vol. 72, pp. 518-526.
  • Durmaz, B., Özgören, M.K., Salamci, M.U., 2012, “Sliding Mode Control for Non-linear Systems with Adaptive Sliding Surfaces”, Transactions of the Institute of Measurement and Control, Vol. 34, No. 1, pp. 56-90.
  • Halbe, O., Hajek, M., 2019, “Online Waypoint Trajectory Generation Using State-Dependent Riccati Equation”, Journal of Guidance, Control, and Dynamics, Vol. 42, No. 12, pp. 2687-2693.
  • Ishutkina, M.A., 2004, Design and Implementation of a Supervisory Safety Controller for a 3-DOF Helicopter, Yüksek Lisans Tezi, Massachusetts Institute of Technology, Department of Aeronautics and Astronautics, Cambridge, Massachusetts, USA.
  • İtik, M, Salamcı, M.U., Banks S.P., 2010, “SDRE optimal control of drug administration in cancer treatment”, Turkish Journal of Electrical Engineering Computer Sciences, Vol. 18, No. 5, pp. 715-729.
  • Kara, F., Salamci, M.U., 2017, “Model Reference Adaptive Sliding Surface Design for Nonlinear Systems”, IEEE Transactions on Industry Applications, Vol. 54, No. 1, pp. 611-624.
  • Kocagil B.M., Ozcan S., Arican A.C., Guzey U. M., Copur E.H., Salamci M.U., “MRAC of a 3-DoF Helicopter with Nonlinear Reference Model”, 26th Mediterranean Conference on Control and Automation, Zadar, Croatia, 278-283, 19-22 Temmuz 2018.
  • Kocagil, B.M., Ozcan, S., Arican, A.C., Guzey, U.M., Copur, E.H., Salamci, M.U., “Adaptive Control of a 3 DoF Helicopter with Linear and Nonlinear Reference Models”, 6th International Conference on Control Engineering & Information Technology, Istanbul, Turkey, 1-6, 25-27 Ekim 2018.
  • Korayem, M.H., Nekoo, S.R., 2015, “Finite-time state-dependent riccati equation for time-varying nonaffine systems: rigid and flexible joint manipulator control”, ISA Transactions, Vol. 54, pp. 125-144.
  • Kukreti, S., Kumar, M., Cohen, K., “Genetically Tuned LQR Based Path Following for UAVs under Wind Disturbance”, International Conference on Unmanned Aircraft Systems, Arlington, VA, 267-274, 7-10 Haziran 2016.
  • Mani, G., Sivaraman, N., Sanjeevikumar, P., 2018, “Particle Swarm Optimization-Based Closed-Loop Optimal State Feedback Control for CSTR”, Advances in Systems, Control and Automation, Editör: Konkani A., Bera R., Paul S., Springer, Singapore, 469-479.
  • Miyamoto, K., Shec J., Satod D., Yasuo, N., 2018, “Automatic Determination of LQR Weighting Matrices for Active Structural Control”, Engineering Structures, Vol. 174, pp. 308-321.
  • Nath K., Dewan L., “Heuristic Optimization Based Choice of LQR Weighting Matrices for A Rotary Inverted Pendulum”, IEEE International Conference on Recent Trends in Electrical, Control and Communication, Chennai, India, 269-274, 20-22 Mart 2018.
  • Qin., Sun H., 2018, “State Dependent Riccati Equation Based Rotor-Side Converter Control for Doubly Fed Wind Generator”, IEEE Access, Cilt 6, pp. 27853-27863.
  • Salamci, M.U., Gökbilen, B., 2007, “SDRE Missile Autopilot Design Using Sliding Mode Control with Moving Sliding Surfaces”, IFAC Proceedings Volumes, Vol. 40, No. 7, pp. 768-773.
  • Stansbery, D.T., Cloutier, J.R., “Position and Attitude Control of a Spacecraft Using the State-Dependent Riccati Equation Technique”, Proceedings of the American Control Conference, Chicago, Illinois, 1867-1871, June 2000.
  • Vaddi, S., Menon, P.K., Ohlmeyer, E. J., 2009, ” Numerical State-Dependent Riccati Equation Approach for Missile Integrated Guidance Control”, Journal of Guidance, Control, and Dynamics, Vol. 32, No. 2, pp. 699-703.
  • Voos, H., "Nonlinear state-dependent Riccati equation control of a quadrotor UAV”, 2006 IEEE International Conference on Control Applications, Munich, Germany, 2547-2552, October 2006.
  • Xin, M., Balakrishnan, S., “State Dependent Riccati Equation Based Spacecraft Attitude Control”, 40th AIAA Aerospace Sciences Meeting & Exhibit, Reno, Nevada, USA, 1-7, 14-17 Ocak 2002.

Effects of Weighting Matrices on SDRE Based Control Method of 3-DoF Helicopter

Year 2021, Volume: 9 Issue: 3, 588 - 605, 01.09.2021
https://doi.org/10.36306/konjes.863012

Abstract

State Dependent Riccati Equation (SDRE) technique enables a suboptimal control law for a class of nonlinear systems such that it minimizes a given quadratic cost function. A nonlinear system is treated as a linear system by being computed its nonlinear matrices at each instant of time and the optimal control problem of interest can be defined as a Linear Quadratic Regulator (LQR) problem in each instant.
Therefore, the weighting matrices of LQR play an important role in shaping the transient time response of the closed-loop system by means of SDRE controller. In this study, a SDRE based optimal controller was designed for controlling the position of a 3 DOF laboratory helicopter. The experiments were repeated with different weighting matrices to evaluate their effects on the transient time response of the helicopter. In the first phase of the experiments, the weighting matrices were selected such that form diagonal matrix with constant real elements. The diagonal elements corresponding to the states of the helicopter controlled by SDRE method were changed to explore how affect the transient time responses of these states. In the second phase, the weighting matrices were selected to be state-dependent. The comparison of the experimental results in both phases reveal that the state dependent weighting matrices have more capabilities of enhancing transient time response specifications such as settling time and steady-state error.

Project Number

DKTM/2015/07

References

  • Arican, A.C., Ozcan, S., Kocagil, B.M., Guzey, U.M., Copur, E.H., Salamci, M.U., “Linear and Nonlinear Optimal Controller Design for a 3 DOF Helicopter”, 19th International Carpathian Control Conference, Szilvasvarad, Hungary, 185-190, 28-31 Mayıs 2018.
  • Babaei, N., Salamci, M.U., 2015, “Personalized Drug Administration for Cancer Treatment Using Model Reference Adaptive Control”, Journal of Theoretical Biology, Vol. 371, pp. 24-44.
  • Babaei, N., Salamci, M.U., 2018, “Controller Design for Personalized Drug Administration in Cancer Therapy: Successive Approximation Approach”, Optimal Control Applications and Methods, Vol. 39, No. 2, pp. 682-719.
  • Batmani,, Y., Khaloozadeh H., 2013, “Optimal Chemotherapy in Cancer Treatment: State Dependent Riccati Equation Control and Extended Kalman Filter”, Optimal Control Applications and Methods, Vol. 34, ss. 562-577.
  • Bilgin, N., Salamci, M.U., “Sliding Mode Control Design for Nonlinear Systems without Reaching Phase and Its Applications to A Flexible Spacecraft”, ASME 2014 12th Biennial Conference on Engineering Systems Design and Analysis, Copenhagen, Denmark, 1-9, 25-27 Haziran 2014.
  • Bogdanov, A., Carlsson, M., Harvey, G., Hunt, J., Kieburtz, D., van der Merwe, R., & Wan, E., “State- Dependent Riccati Equation Control of a Small Unmanned Helicopter”, AIAA Guidance, Navigation, and Control Conference and Exhibit, Austin, Texas, 11-14 Ağustos 2003.
  • Çimen, T., “State-Dependent Riccati Equation (SDRE) Control: A Survey”, Proceedings of the 17th World Congress the International Federation of Automatic Control, Seoul, Korea, 3761-3775, 6-11 Temmuz 2008.
  • Çimen, T., 2010, “Systematic and Effective Design of Nonlinear Feedback Controllers via the State- Dependent Riccati Equation (SDRE) Method”, Annual Reviews in Control, Vol. 34, No. 1, pp. 32- 51.
  • Çimen, T., 2012, “Survey of State-Dependent Riccati Equation in Nonlinear Optimal Feedback Control Synthesis”, Journal of Guidance, Control and Dynamics, Vol. 35, No. 4, pp. 1025-1047.
  • Copur, E.H., Arican, A.C., Ozcan, S., Salamci, M.U., 2019, “An Update Algorithm Design Using Moving Region of Attraction for SDRE Based Control Law”, Journal of The Franklin Institute, Vol. 356, No. 15, pp. 8388-8413.
  • Das, R.R., Elumalai, V.K., Subramanian R.G., Kumar, K.V.A., 2018, “Adaptive Predator–Prey Optimization for Tuning of Infinite Horizon LQR Applied to Vehicle Suspension System”, Applied Soft Computing, Vol. 72, pp. 518-526.
  • Durmaz, B., Özgören, M.K., Salamci, M.U., 2012, “Sliding Mode Control for Non-linear Systems with Adaptive Sliding Surfaces”, Transactions of the Institute of Measurement and Control, Vol. 34, No. 1, pp. 56-90.
  • Halbe, O., Hajek, M., 2019, “Online Waypoint Trajectory Generation Using State-Dependent Riccati Equation”, Journal of Guidance, Control, and Dynamics, Vol. 42, No. 12, pp. 2687-2693.
  • Ishutkina, M.A., 2004, Design and Implementation of a Supervisory Safety Controller for a 3-DOF Helicopter, Yüksek Lisans Tezi, Massachusetts Institute of Technology, Department of Aeronautics and Astronautics, Cambridge, Massachusetts, USA.
  • İtik, M, Salamcı, M.U., Banks S.P., 2010, “SDRE optimal control of drug administration in cancer treatment”, Turkish Journal of Electrical Engineering Computer Sciences, Vol. 18, No. 5, pp. 715-729.
  • Kara, F., Salamci, M.U., 2017, “Model Reference Adaptive Sliding Surface Design for Nonlinear Systems”, IEEE Transactions on Industry Applications, Vol. 54, No. 1, pp. 611-624.
  • Kocagil B.M., Ozcan S., Arican A.C., Guzey U. M., Copur E.H., Salamci M.U., “MRAC of a 3-DoF Helicopter with Nonlinear Reference Model”, 26th Mediterranean Conference on Control and Automation, Zadar, Croatia, 278-283, 19-22 Temmuz 2018.
  • Kocagil, B.M., Ozcan, S., Arican, A.C., Guzey, U.M., Copur, E.H., Salamci, M.U., “Adaptive Control of a 3 DoF Helicopter with Linear and Nonlinear Reference Models”, 6th International Conference on Control Engineering & Information Technology, Istanbul, Turkey, 1-6, 25-27 Ekim 2018.
  • Korayem, M.H., Nekoo, S.R., 2015, “Finite-time state-dependent riccati equation for time-varying nonaffine systems: rigid and flexible joint manipulator control”, ISA Transactions, Vol. 54, pp. 125-144.
  • Kukreti, S., Kumar, M., Cohen, K., “Genetically Tuned LQR Based Path Following for UAVs under Wind Disturbance”, International Conference on Unmanned Aircraft Systems, Arlington, VA, 267-274, 7-10 Haziran 2016.
  • Mani, G., Sivaraman, N., Sanjeevikumar, P., 2018, “Particle Swarm Optimization-Based Closed-Loop Optimal State Feedback Control for CSTR”, Advances in Systems, Control and Automation, Editör: Konkani A., Bera R., Paul S., Springer, Singapore, 469-479.
  • Miyamoto, K., Shec J., Satod D., Yasuo, N., 2018, “Automatic Determination of LQR Weighting Matrices for Active Structural Control”, Engineering Structures, Vol. 174, pp. 308-321.
  • Nath K., Dewan L., “Heuristic Optimization Based Choice of LQR Weighting Matrices for A Rotary Inverted Pendulum”, IEEE International Conference on Recent Trends in Electrical, Control and Communication, Chennai, India, 269-274, 20-22 Mart 2018.
  • Qin., Sun H., 2018, “State Dependent Riccati Equation Based Rotor-Side Converter Control for Doubly Fed Wind Generator”, IEEE Access, Cilt 6, pp. 27853-27863.
  • Salamci, M.U., Gökbilen, B., 2007, “SDRE Missile Autopilot Design Using Sliding Mode Control with Moving Sliding Surfaces”, IFAC Proceedings Volumes, Vol. 40, No. 7, pp. 768-773.
  • Stansbery, D.T., Cloutier, J.R., “Position and Attitude Control of a Spacecraft Using the State-Dependent Riccati Equation Technique”, Proceedings of the American Control Conference, Chicago, Illinois, 1867-1871, June 2000.
  • Vaddi, S., Menon, P.K., Ohlmeyer, E. J., 2009, ” Numerical State-Dependent Riccati Equation Approach for Missile Integrated Guidance Control”, Journal of Guidance, Control, and Dynamics, Vol. 32, No. 2, pp. 699-703.
  • Voos, H., "Nonlinear state-dependent Riccati equation control of a quadrotor UAV”, 2006 IEEE International Conference on Control Applications, Munich, Germany, 2547-2552, October 2006.
  • Xin, M., Balakrishnan, S., “State Dependent Riccati Equation Based Spacecraft Attitude Control”, 40th AIAA Aerospace Sciences Meeting & Exhibit, Reno, Nevada, USA, 1-7, 14-17 Ocak 2002.
There are 29 citations in total.

Details

Primary Language Turkish
Subjects Engineering
Journal Section Research Article
Authors

Engin Hasan Çopur 0000-0003-0837-1255

Project Number DKTM/2015/07
Publication Date September 1, 2021
Submission Date January 17, 2021
Acceptance Date May 10, 2021
Published in Issue Year 2021 Volume: 9 Issue: 3

Cite

IEEE E. H. Çopur, “AĞIRLIK MATRİSLERİNİN 3-SD HELİKOPTERİN DDRD TABANLI KONTROL METODU ÜZERİNE ETKİLERİ”, KONJES, vol. 9, no. 3, pp. 588–605, 2021, doi: 10.36306/konjes.863012.