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Aktif Süspansiyon Sistemleri Kontrolünde Ters Optimal Kontrol Yaklaşımı

Yıl 2026, Cilt: 16 Sayı: 1, 73 - 82, 31.01.2026

Lütfi Ulusoy , Sadık Kıvanç Süngü , İbrahim Eksin , Müjde Güzelkaya

Öz

Bu çalışmada da aktif süspansiyon sisteminin konfor ve sürüş güvenliği isterlerini karşılamak amacıyla ters optimal kontrol temelli yeni bir tasarım yaklaşımı önerilmiştir. Ters Optimal Kontrol (TOK) yaklaşımı, geleneksel optimal kontrol yaklaşımının aksine önceden belirlenmiş bir maliyet fonksiyonu için uygun kontrol kuralını hesaplama problemi değil; önceden belirlenmiş olan bir kontrol kuralının minimum yaptığı maliyet fonksiyonunu bulma problemidir. Çalışmada çeyrek araç modeli kullanılmış ve TOK yaklaşımıyla kararlı, maliyet-etkin ve gerçek zamanda uygulanabilir bir kontrolör tasarlanmıştır. Tasarlanan kontrolör, yine durum geri beslemeli bir kontrolör olan Doğrusal Kuadratik Regülatör (DKR) ile karşılaştırılmış ve bu kontrolöre alternatif olabileceği gösterilmiştir.

Anahtar Kelimeler

Kontrol Lyapunov Fonksiyonu Doğrusal sistemler Ters Optimal Kontrol Aktif Süspansiyon Sistemi Durum Geri Beslemeli Kontrol Doğrusal Kuadratik Regulator

Kaynakça

  • [1] “ISO 2631,” Guide for the evaluation of human exposure to whole-body vibration. 1978.
  • [2] S. M. Savaresi, C. Poussot-Vassal, C. Spelta, O. Sename, and L. Dugard, Semi-active suspension control design for vehicles. Elsevier, 2010.
  • [3] H. Pang, Y. Chen, J. Chen, and X. Liu, “Design of LQG Controller for Active Suspension without Considering Road Input Signals,” Shock and Vibration, vol. 2017, pp. 1–13, Feb. 2017, doi: 10.1155/2017/6573567.
  • [4] R. Vatankhah, M. Rahaeifard, and A. Alasty, “Vibration control of vehicle suspension system using adaptive critic-based neurofuzzy controller,” in 2009 6th International Symposium on Mechatronics and its Applications, 2009, pp. 1–6. doi: 10.1109/ISMA.2009.5164809.
  • [5] A. Alleyne and J. K. Hedrick, “Nonlinear adaptive control of active suspensions,” IEEE transactions on control systems technology, vol. 3, no. 1, pp. 94–101, 1995.
  • [6] J.-S. Lin and I. Kanellakopoulos, “Nonlinear design of active suspensions,” IEEE Control Systems Magazine, vol. 17, no. 3, pp. 45–59, 1997, doi: 10.1109/37.588129.
  • [7] A. J. Barr and J. I. Ray, “Control of an active suspension using fuzzy logic,” in Proceedings of IEEE 5th International Fuzzy Systems, 1996, vol. 1, pp. 42–48.
  • [8] J. Wu, “A simultaneous mixed LQR/H∞ control approach to the design of reliable active suspension controllers,” Asian Journal of Control, vol. 19, no. 2, pp. 415–427, 2017.
  • [9] Z. Liu, C. Luo, and D. Hu, “Active suspension control design using a combination of LQR and backstepping,” in 2006 Chinese Control Conference, 2006, pp. 123–125.
  • [10] T. H. S. Abdelaziz and M. Valášek, “STATE DERIVATIVE FEEDBACK BY LQR FOR LINEAR TIME-INVARIANT SYSTEMS,” IFAC Proceedings Volumes, vol. 38, no. 1, pp. 435–440, Jan. 2005, doi: 10.3182/20050703-6-CZ-1902.00934.
  • [11] L. S. Pontryagin, v. G. Boltyankii, R. V. Gamkrelizde, and E. F. Mischenko, The Mathematical Theory of Optimal Processes. New York: Interscience Publishers, Inc, 1962.
  • [12] R. Bellman, “Dynamic programming,” RAND CORP SANTA MONICA CA, SANTA MONICA CA, 1956.
  • [13] S. E. Dreyfus and R. Bellman, Applied dynamic programming. Princeton University Press, 1962.
  • [14] B. D. O. Anderson and J. B. Moore, “Optimal control: linear quadratic methods.” Prentice-Hall, Inc., 1990.
  • [15] F. L. Lewis, D. Vrabie, and V. L. Syrmos, Optimal control. John Wiley & Sons, 2012.
  • [16] P. Moylan and B. Anderson, “Nonlinear regulator theory and an inverse optimal control problem,” IEEE Transactions on Automatic Control, vol. 18, no. 5, pp. 460–465, 1973.
  • [17] R. Sepulchre, M. Jankovic, and P. v Kokotovic, Constructive nonlinear control. Springer Science & Business Media, 2012.
  • [18] R. E. Kalman, “When is a linear control system optimal?,” 1964.
  • [19] B. Molinari, “The stable regulator problem and its inverse,” IEEE Transactions on Automatic Control, vol. 18, no. 5, pp. 454–459, 1973.
  • [20] N. Kawasaki and E. Shimemura, “Determining quadratic weighting matrices to locate poles in a specified region,” Automatica, vol. 19, no. 5, pp. 557–560, 1983.
  • [21] T. Fujii and M. Narazaki, “A complete optimality condition in the inverse problem of optimal control,” SIAM journal on control and optimization, vol. 22, no. 2, pp. 327–341, 1984.
  • [22] D. Mehdi, M. Darouach, and M. Zasadzinski, “Discrete time lq design from the viewpoint of the inverse optimal regulator,” Optimal Control Applications and Methods, vol. 15, no. 3, pp. 205–213, 1994.
  • [23] M. Krstic and P. Tsiotras, “Inverse optimal stabilization of a rigid spacecraft,” IEEE Transactions on Automatic Control, vol. 44, no. 5, pp. 1042–1049, 1999.
  • [24] D. Hrovat, “Survey of Advanced Suspension Developments and Related Optimal Control Applications,” Automatica, vol. 33, no. 10, pp. 1781–1817, Oct. 1997, doi: 10.1016/S0005-1098(97)00101-5.
  • [25] W. Sun, H. Gao, and P. Shi, Advanced control for vehicle active suspension systems, vol. 204. Springer, 2020.
  • [26] F. E. Veldpaus, I. Besselink, W. J. E. Evers, and A. J. C. Schmeitz, “An active suspension system,” 2007.
  • [27] F. Ornelas, E. N. Sanchez, and A. G. Loukianov, “Discrete-time nonlinear systems inverse optimal control: A control Lyapunov function approach,” in Proc. IEEE Int. Conf. on Control Applications (CCA), 2011, pp. 1431–1436.
  • [28] R. A. Freeman and J. A. Primbs, “Control Lyapunov functions: New ideas from an old source,” in Proceedings of 35th IEEE Conference on Decision and Control, 1996, vol. 4, pp. 3926–3931.
  • [29] R. A. Freeman and P. V. Kokotovic, Robust Nonlinear Control Design: State-Space and Lyapunov Techniques, Springer, 2008.
  • [30] T. Fujii, “A new approach to the LQ design from the viewpoint of the inverse regulator problem,” IEEE Transactions on Automatic Control, vol. 32, no. 11, pp. 995–1004, 1987.
  • [31] R. E. Kalman, “When is a linear control system optimal?,” Journal of Basic Engineering, vol. 86, no. 1, pp. 51–60, 1964.
  • [32] W. Li, E. Todorov, and D. Liu, “Inverse optimality design for biological movement systems,” IFAC Proceedings Volumes, vol. 44, no. 1, pp. 9662–9667, 2011.
  • [33] E. N. Sanchez and F. Ornelas-Tellez, Discrete-Time Inverse Optimal Control for Nonlinear Systems, Boca Raton, FL: CRC Press, 2017
  • [34] R. Sepulchre, M. Jankovic, and P. V. Kokotovic, Constructive Nonlinear Control, Springer, 2012.
  • [35] K. Sugimoto, “Partial pole placement by LQ regulators: An inverse problem approach,” IEEE Transactions on Automatic Control, vol. 43, no. 5, pp. 706–708, 1998.
  • [36] F. Ornelas-Tellez, E. N. Sanchez, A. G. Loukianov, and J. J. Rico, “Robust inverse optimal control for discrete-time nonlinear system stabilization,” European Journal of Control, vol. 20, no. 1, pp. 38–44, 2014.
  • [37] M. Almobaied, I. Eksin, and M. Güzelkaya, “A new inverse optimal control method for discrete-time systems,” in Proc. 12th Int. Conf. on Informatics in Control, Automation and Robotics (ICINCO), vol. 1, Colmar, France: IEEE, Jul. 21–23, 2015, pp. 275–280.
  • [38] M. Almobaied, I. Eksin, and M. Guzelkaya, “Inverse optimal controller based on extended Kalman filter for discrete-time nonlinear systems,” Optimal Control Applications and Methods, vol. 39, no. 1, pp. 19–34, Jan. 2018.
  • [39] L. Ulusoy, M. Güzelkaya, and İ. Eksin, “Fusion of inverse optimal and model predictive control strategies,” Transactions of the Institute of Measurement and Control, vol. 42, no. 6, pp. 1122–1134, Nov. 2019, doi: 10.1177/0142331219884803.
  • [40] A. Al-Tamimi, F. L. Lewis, and M. Abu-Khalaf, “Discrete-time nonlinear HJB solution using approximate dynamic programming: Convergence proof,” IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), vol. 38, no. 4, pp. 943–949, 2008
  • [41] L. Ulusoy, M. Güzelkaya, and İ. Eksin, “Inverse optimal control approach to model predictive control for linear system models,” in 2017 10th International Conference on Electrical and Electronics Engineering (ELECO), 2017, pp. 823–827.
  • [42] C. E. Shannon, “Communication in the presence of noise,” Proceedings of the IRE, vol. 37, no. 1, pp. 10–21, 1949.
  • [43] O. K. Erol, and I. Eksin, . A new optimization method: big bang–big crunch. Advances in engineering software, 37(2), 106-111, 2006.
  • [44] J. Apkarian and A. Abdossalami, “Quanser Active Suspension Experiment Labarotory Guide,” 2013.
  • [45] Quanser Inc., Active Suspension Datasheet, Markham, ON, Canada: Quanser Inc., 2013. [Online]. Available: https://www.quanser.com/wp-content/uploads/2017/03/Active-Suspension-Datasheet.pdf. [Accessed: Dec. 23, 2025]
  • [46] Quanser Inc., Active Suspension – User Manual, Copyright © 2012 Quanser Inc. [Online]. Available: https://www.scribd.com/document/803093859/Active-Suspension-User-Manual. [Accessed: Dec. 23, 2025].

Inverse Optimal Control Approach for Active Suspension System Control

Yıl 2026, Cilt: 16 Sayı: 1, 73 - 82, 31.01.2026

Lütfi Ulusoy , Sadık Kıvanç Süngü , İbrahim Eksin , Müjde Güzelkaya

Öz

In this study, a new inverse optimal control–based design approach is proposed to satisfy the comfort and driving safety requirements of an active suspension system. Unlike the conventional optimal control approach, the Inverse Optimal Control (IOC) method does not solve the problem of computing an appropriate control law for a predefined cost function; instead, it seeks the cost function that is minimized by a given control law. A quarter-car model is employed, and a stable, cost-effective, and real-time applicable controller is designed using the IOC approach. The designed controller is compared with a Linear Quadratic Regulator, which is also a state-feedback controller, and it is demonstrated that the proposed approach can serve as a viable alternative to the LQR controller.

Anahtar Kelimeler

Control Lyapunov Function Linear Systems Inverse Optimal Control Active Suspension System State Feedback Control Linear Quadratic Regulator

Kaynakça

  • [1] “ISO 2631,” Guide for the evaluation of human exposure to whole-body vibration. 1978.
  • [2] S. M. Savaresi, C. Poussot-Vassal, C. Spelta, O. Sename, and L. Dugard, Semi-active suspension control design for vehicles. Elsevier, 2010.
  • [3] H. Pang, Y. Chen, J. Chen, and X. Liu, “Design of LQG Controller for Active Suspension without Considering Road Input Signals,” Shock and Vibration, vol. 2017, pp. 1–13, Feb. 2017, doi: 10.1155/2017/6573567.
  • [4] R. Vatankhah, M. Rahaeifard, and A. Alasty, “Vibration control of vehicle suspension system using adaptive critic-based neurofuzzy controller,” in 2009 6th International Symposium on Mechatronics and its Applications, 2009, pp. 1–6. doi: 10.1109/ISMA.2009.5164809.
  • [5] A. Alleyne and J. K. Hedrick, “Nonlinear adaptive control of active suspensions,” IEEE transactions on control systems technology, vol. 3, no. 1, pp. 94–101, 1995.
  • [6] J.-S. Lin and I. Kanellakopoulos, “Nonlinear design of active suspensions,” IEEE Control Systems Magazine, vol. 17, no. 3, pp. 45–59, 1997, doi: 10.1109/37.588129.
  • [7] A. J. Barr and J. I. Ray, “Control of an active suspension using fuzzy logic,” in Proceedings of IEEE 5th International Fuzzy Systems, 1996, vol. 1, pp. 42–48.
  • [8] J. Wu, “A simultaneous mixed LQR/H∞ control approach to the design of reliable active suspension controllers,” Asian Journal of Control, vol. 19, no. 2, pp. 415–427, 2017.
  • [9] Z. Liu, C. Luo, and D. Hu, “Active suspension control design using a combination of LQR and backstepping,” in 2006 Chinese Control Conference, 2006, pp. 123–125.
  • [10] T. H. S. Abdelaziz and M. Valášek, “STATE DERIVATIVE FEEDBACK BY LQR FOR LINEAR TIME-INVARIANT SYSTEMS,” IFAC Proceedings Volumes, vol. 38, no. 1, pp. 435–440, Jan. 2005, doi: 10.3182/20050703-6-CZ-1902.00934.
  • [11] L. S. Pontryagin, v. G. Boltyankii, R. V. Gamkrelizde, and E. F. Mischenko, The Mathematical Theory of Optimal Processes. New York: Interscience Publishers, Inc, 1962.
  • [12] R. Bellman, “Dynamic programming,” RAND CORP SANTA MONICA CA, SANTA MONICA CA, 1956.
  • [13] S. E. Dreyfus and R. Bellman, Applied dynamic programming. Princeton University Press, 1962.
  • [14] B. D. O. Anderson and J. B. Moore, “Optimal control: linear quadratic methods.” Prentice-Hall, Inc., 1990.
  • [15] F. L. Lewis, D. Vrabie, and V. L. Syrmos, Optimal control. John Wiley & Sons, 2012.
  • [16] P. Moylan and B. Anderson, “Nonlinear regulator theory and an inverse optimal control problem,” IEEE Transactions on Automatic Control, vol. 18, no. 5, pp. 460–465, 1973.
  • [17] R. Sepulchre, M. Jankovic, and P. v Kokotovic, Constructive nonlinear control. Springer Science & Business Media, 2012.
  • [18] R. E. Kalman, “When is a linear control system optimal?,” 1964.
  • [19] B. Molinari, “The stable regulator problem and its inverse,” IEEE Transactions on Automatic Control, vol. 18, no. 5, pp. 454–459, 1973.
  • [20] N. Kawasaki and E. Shimemura, “Determining quadratic weighting matrices to locate poles in a specified region,” Automatica, vol. 19, no. 5, pp. 557–560, 1983.
  • [21] T. Fujii and M. Narazaki, “A complete optimality condition in the inverse problem of optimal control,” SIAM journal on control and optimization, vol. 22, no. 2, pp. 327–341, 1984.
  • [22] D. Mehdi, M. Darouach, and M. Zasadzinski, “Discrete time lq design from the viewpoint of the inverse optimal regulator,” Optimal Control Applications and Methods, vol. 15, no. 3, pp. 205–213, 1994.
  • [23] M. Krstic and P. Tsiotras, “Inverse optimal stabilization of a rigid spacecraft,” IEEE Transactions on Automatic Control, vol. 44, no. 5, pp. 1042–1049, 1999.
  • [24] D. Hrovat, “Survey of Advanced Suspension Developments and Related Optimal Control Applications,” Automatica, vol. 33, no. 10, pp. 1781–1817, Oct. 1997, doi: 10.1016/S0005-1098(97)00101-5.
  • [25] W. Sun, H. Gao, and P. Shi, Advanced control for vehicle active suspension systems, vol. 204. Springer, 2020.
  • [26] F. E. Veldpaus, I. Besselink, W. J. E. Evers, and A. J. C. Schmeitz, “An active suspension system,” 2007.
  • [27] F. Ornelas, E. N. Sanchez, and A. G. Loukianov, “Discrete-time nonlinear systems inverse optimal control: A control Lyapunov function approach,” in Proc. IEEE Int. Conf. on Control Applications (CCA), 2011, pp. 1431–1436.
  • [28] R. A. Freeman and J. A. Primbs, “Control Lyapunov functions: New ideas from an old source,” in Proceedings of 35th IEEE Conference on Decision and Control, 1996, vol. 4, pp. 3926–3931.
  • [29] R. A. Freeman and P. V. Kokotovic, Robust Nonlinear Control Design: State-Space and Lyapunov Techniques, Springer, 2008.
  • [30] T. Fujii, “A new approach to the LQ design from the viewpoint of the inverse regulator problem,” IEEE Transactions on Automatic Control, vol. 32, no. 11, pp. 995–1004, 1987.
  • [31] R. E. Kalman, “When is a linear control system optimal?,” Journal of Basic Engineering, vol. 86, no. 1, pp. 51–60, 1964.
  • [32] W. Li, E. Todorov, and D. Liu, “Inverse optimality design for biological movement systems,” IFAC Proceedings Volumes, vol. 44, no. 1, pp. 9662–9667, 2011.
  • [33] E. N. Sanchez and F. Ornelas-Tellez, Discrete-Time Inverse Optimal Control for Nonlinear Systems, Boca Raton, FL: CRC Press, 2017
  • [34] R. Sepulchre, M. Jankovic, and P. V. Kokotovic, Constructive Nonlinear Control, Springer, 2012.
  • [35] K. Sugimoto, “Partial pole placement by LQ regulators: An inverse problem approach,” IEEE Transactions on Automatic Control, vol. 43, no. 5, pp. 706–708, 1998.
  • [36] F. Ornelas-Tellez, E. N. Sanchez, A. G. Loukianov, and J. J. Rico, “Robust inverse optimal control for discrete-time nonlinear system stabilization,” European Journal of Control, vol. 20, no. 1, pp. 38–44, 2014.
  • [37] M. Almobaied, I. Eksin, and M. Güzelkaya, “A new inverse optimal control method for discrete-time systems,” in Proc. 12th Int. Conf. on Informatics in Control, Automation and Robotics (ICINCO), vol. 1, Colmar, France: IEEE, Jul. 21–23, 2015, pp. 275–280.
  • [38] M. Almobaied, I. Eksin, and M. Guzelkaya, “Inverse optimal controller based on extended Kalman filter for discrete-time nonlinear systems,” Optimal Control Applications and Methods, vol. 39, no. 1, pp. 19–34, Jan. 2018.
  • [39] L. Ulusoy, M. Güzelkaya, and İ. Eksin, “Fusion of inverse optimal and model predictive control strategies,” Transactions of the Institute of Measurement and Control, vol. 42, no. 6, pp. 1122–1134, Nov. 2019, doi: 10.1177/0142331219884803.
  • [40] A. Al-Tamimi, F. L. Lewis, and M. Abu-Khalaf, “Discrete-time nonlinear HJB solution using approximate dynamic programming: Convergence proof,” IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), vol. 38, no. 4, pp. 943–949, 2008
  • [41] L. Ulusoy, M. Güzelkaya, and İ. Eksin, “Inverse optimal control approach to model predictive control for linear system models,” in 2017 10th International Conference on Electrical and Electronics Engineering (ELECO), 2017, pp. 823–827.
  • [42] C. E. Shannon, “Communication in the presence of noise,” Proceedings of the IRE, vol. 37, no. 1, pp. 10–21, 1949.
  • [43] O. K. Erol, and I. Eksin, . A new optimization method: big bang–big crunch. Advances in engineering software, 37(2), 106-111, 2006.
  • [44] J. Apkarian and A. Abdossalami, “Quanser Active Suspension Experiment Labarotory Guide,” 2013.
  • [45] Quanser Inc., Active Suspension Datasheet, Markham, ON, Canada: Quanser Inc., 2013. [Online]. Available: https://www.quanser.com/wp-content/uploads/2017/03/Active-Suspension-Datasheet.pdf. [Accessed: Dec. 23, 2025]
  • [46] Quanser Inc., Active Suspension – User Manual, Copyright © 2012 Quanser Inc. [Online]. Available: https://www.scribd.com/document/803093859/Active-Suspension-User-Manual. [Accessed: Dec. 23, 2025].
Toplam 46 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Konular Elektrik Mühendisliği (Diğer)
Bölüm Araştırma Makalesi
Yazarlar

Lütfi Ulusoy 0000-0002-8180-6270

Sadık Kıvanç Süngü

İbrahim Eksin

Müjde Güzelkaya

Gönderilme Tarihi 19 Kasım 2025
Kabul Tarihi 16 Ocak 2026
Yayımlanma Tarihi 31 Ocak 2026
Yayımlandığı Sayı Yıl 2026 Cilt: 16 Sayı: 1

Kaynak Göster

APA Ulusoy, L., Süngü, S. K., Eksin, İ., & Güzelkaya, M. (2026). Aktif Süspansiyon Sistemleri Kontrolünde Ters Optimal Kontrol Yaklaşımı. EMO Bilimsel Dergi, 16(1), 73-82. https://izlik.org/JA99NL56LC
AMA 1.Ulusoy L, Süngü SK, Eksin İ, Güzelkaya M. Aktif Süspansiyon Sistemleri Kontrolünde Ters Optimal Kontrol Yaklaşımı. EMO Bilimsel Dergi. 2026;16(1):73-82. https://izlik.org/JA99NL56LC
Chicago Ulusoy, Lütfi, Sadık Kıvanç Süngü, İbrahim Eksin, ve Müjde Güzelkaya. 2026. “Aktif Süspansiyon Sistemleri Kontrolünde Ters Optimal Kontrol Yaklaşımı”. EMO Bilimsel Dergi 16 (1): 73-82. https://izlik.org/JA99NL56LC.
EndNote Ulusoy L, Süngü SK, Eksin İ, Güzelkaya M (01 Ocak 2026) Aktif Süspansiyon Sistemleri Kontrolünde Ters Optimal Kontrol Yaklaşımı. EMO Bilimsel Dergi 16 1 73–82.
IEEE [1]L. Ulusoy, S. K. Süngü, İ. Eksin, ve M. Güzelkaya, “Aktif Süspansiyon Sistemleri Kontrolünde Ters Optimal Kontrol Yaklaşımı”, EMO Bilimsel Dergi, c. 16, sy 1, ss. 73–82, Oca. 2026, [çevrimiçi]. Erişim adresi: https://izlik.org/JA99NL56LC
ISNAD Ulusoy, Lütfi - Süngü, Sadık Kıvanç - Eksin, İbrahim - Güzelkaya, Müjde. “Aktif Süspansiyon Sistemleri Kontrolünde Ters Optimal Kontrol Yaklaşımı”. EMO Bilimsel Dergi 16/1 (01 Ocak 2026): 73-82. https://izlik.org/JA99NL56LC.
JAMA 1.Ulusoy L, Süngü SK, Eksin İ, Güzelkaya M. Aktif Süspansiyon Sistemleri Kontrolünde Ters Optimal Kontrol Yaklaşımı. EMO Bilimsel Dergi. 2026;16:73–82.
MLA Ulusoy, Lütfi, vd. “Aktif Süspansiyon Sistemleri Kontrolünde Ters Optimal Kontrol Yaklaşımı”. EMO Bilimsel Dergi, c. 16, sy 1, Ocak 2026, ss. 73-82, https://izlik.org/JA99NL56LC.
Vancouver 1.Ulusoy L, Süngü SK, Eksin İ, Güzelkaya M. Aktif Süspansiyon Sistemleri Kontrolünde Ters Optimal Kontrol Yaklaşımı. EMO Bilimsel Dergi [Internet]. 01 Ocak 2026;16(1):73-82. Erişim adresi: https://izlik.org/JA99NL56LC

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