Algebraic IDA-PBC for Polynomial Systems with Input Saturation: An SOS-based Approach
##plugins.themes.bootstrap3.article.main##
Resumen
Abstract: The necessity to deal with partial differential equations (PDEs) and the dissipation condition are the mainadversities in the application of Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC). Recently,an algebraic solution of IDA-PBC has been explored for a class of affine polynomial systems by using sum of squares(SOS) and semidefinite programming (SDP). In this work, we extend the previous method by incorporating actuatorsaturation (AS) and two minimization objectives in the SDP. Our results are validated on two polynomial systems.
Descargas
Descargas
Detalles del artículo
Citas
Astolfi, A., Chhabra, D., and Ortega, R. (2002a). Asymptotic Stabilization of Some Equilibria of an Underactuated Underwater Vehicle. Systems & Control Letters, 45:193-206.
Astolfi, A. and Ortega, R. (2001). Energy-Based Stabilization of Angular Velocity of Rigid Body in Failure Configuration. Journal of Guidance, Control, and Dynamics, 25(1):184-187.
Astolfi, A., Ortega, R., and Sepulchre, R. (2002b). Stabilization and Disturbance Attenuation of Nonlinear Systems Using Dissipativity Theory. European Journal of Control, 8(5):408-431.
Åström, K. J., Aracil, J., and Gordillo, F. (2008). A family of smooth controllers for swinging up a pendulum. Automatica, 44(7):1841-1848.
Batlle, C., Dòria-Cerezo, A., Espinosa-Pérez, G., and Ortega, R. (2007). Simultaneous interconnection and damping assignment passivity-based control: Two practical examples. In Lagrangian and Hamiltonian Methods for Nonlinear Control 2006, pages 157-169. Springer.
Batlle, C., Doria-Cerezo, A., and Ortega, R. (2004). Power flow control of a doubly-fed induction machine coupled to a flywheel. In International Conference on Control Applications, volume 2, pages 1645-1650.
Borja, P., Cisneros, R., and Ortega, R. (2016). A constructive procedure for energy shaping of port-Hamiltonian systems. Automatica, 72(1):230-234.
Boyd, S., El Ghaoui, L., Feron, E., and Balakrishnan, V. (1994). Linear Matrix Inequalities in System and Control Theory, volume 15. SIAM studies in Applied Mathematics.
Castaños, F. and Gromov, D. (2016). Passivity-Based Control of Implicit Port-Hamiltonian Systems with Holonomic Constraints. Systems & Control Letters, 94(1):11-18.
Cieza, O. B. and Reger, J. (2018). IDA-PBC for Polynomial Systems : An SOS-based Approach. In IFAC Conference on Modelling,Identification and Control of Nonlinear Systems (MICNON), pages 366-371.
Delgado, S. and Kotyczka, P. (2014). Overcoming the Dissipation Condition in Passivity-based Control for a class of mechanical systems. In IFAC World Congress, pages 11189-11194.
Donaire, A., Mehra, R., Ortega, R., Satpute, S., Romero, J. G., Kazi, F., and Singh, N. M. (2016a). Shaping the Energy of Mechanical Systems Without Solving Partial Differential Equations. IEEE Transactions on Automatic Control, 61(4):1051-1056.
Donaire, A., Ortega, R., and Romero, J. G. (2016b). Simultaneous Interconnection and Damping Assignment Passivity-based Control of Mechanical Systems Using Generalized Forces. Systems & Control Letters, 94(1):118-126.
Escobar, G., Ortega, R., and Sira-Ramírez, H. (1999). Output Feedback Global Stabilization of a Nonlinear Benchmark System Using a Saturated Passivity Based Controller. IEEE Transactions on Control Systems Technology, 7(2):289-293.
Fujimoto, K., Sakurama, K., and Sugie, T. (2001). Trajectory tracking control of port-controlled Hamiltonian systems and its application to a magnetic levitation system. In Conference on Decision and Control, pages 3388-3393.
Fujimoto, K. and Sugie, T. (2001). Canonical transformation and stabilization of generalized Hamiltonian systems. Systems & Control Letters, 42(9):217-227.
Gómez-Estern, F. and Van der Schaft, A. (2004). Physical Damping in IDA-PBC Controlled Underactuated Mechanical Systems. European Journal of Control, 10(5):451-468.
Hu, T. and Lin, Z. (2001). Control Systems with Actuator Saturation: Analysis and Design. Birkhäuser.
Ichihara, H. (2009). Optimal Control for Polynomial Systems Using Matrix Sum of Squares Relaxations. IEEE Transactions on Automatic Control, 54(5):1048-1053.
Ichihara, H. (2013). A Convex Approach to State Feedback Synthesis for Polynomial Nonlinear Systems with Input Saturation. SICE Journal of Control, Measurement, and System Integration, 6(3):186-193.
Jennawasin, T., Kawanishi, M., Narikiyo, T., and Lin, C.-L. (2012). An Improved Stabilizing Condition for Polynomial Systems with Bounded Actuators: An SOS-Based Approach. In IEEE International Symposium on Intelligent Control (ISIC), pages 258-263. IEEE.
Jennawasin, T., Narikiyo, T., and Kawanishi, M. (2010). An improved SOS-based stabilization condition for uncertain polynomial systems. In SICE Annual Conference 2010, pages 3030- 3034.
Li, H., Wang, X., and Tian, T. (2010). The performance research of induction motor systems controlled by the IDA-PBC method and its speed sensorless implementation. In International Conference on Electrical Machines and Systems (ICEMS), pages 680-683.
Li, J., Liu, Y., Li, C., and Chu, B. (2013). Passivity-based nonlinear excitation control of power systems with structure matrix reassignment. Information, 4(3):342-350.
Macchelli, A. (2002). Port Hamiltonian systems: A unified approach for modeling and control finite and infinite dimensional physical systems. Ph.d. dissertation, University of Bologna.
Macchelli, A. (2014). Passivity-Based Control of Implicit Port- Hamiltonian Systems. SIAM Journal on Control and Optimization, 52(4):2422-2448.
Macchelli, A., Melchiorri, C., Secchi, C., and Fantuzzi, C. (2003). A variable structure approach to energy shaping. In European Control Conference (ECC), pages 1309-1314.
Nunna, K., Sassano, M., and Astolfi, A. (2015). Constructive Interconnection and Damping Assignment for Port-Controlled Hamiltonian Systems. IEEE Transaction on Automatic Control, 60(9):2350-2361.
Ortega, R. and García-Canseco, E. (2004). Interconnection and Damping Assignment Passivity-Based Control: A Survey. European Journal of Control, 10(5):432-450.
Papachristodoulou, A., Anderson, J., Valmorbida, G., Prajna, S., Seiler, P., and Parrilo, P. A. (2016). SOSTOOLS: Sum of squares optimization toolbox for MATLAB. User’s guide.
Parrilo, P. A. (2000). Structured Semidefinite Programs and Semialgebraic Geometry Methods in Robustness and Optimization. PhD thesis, California Institute of Technology.
Petrovi´c, V., Ortega, R., and Stankovi´c, A. M. (2001). Interconnection and damping assignment approach to control of PM synchronous motors. IEEE Transactions on Control Systems Technology, 9(6):811-820.
Renton, C., Teo, Y. R., Donaire, A., and Perez, T. (2012). Active control of car suspension systems using IDA-PBC. In Australian Control Conference, pages 361-366.
Romero, J. G., Donaire, A., Ortega, R., and Borja, P. (2017). Global Stabilisation of Underactuated Mechanical Systems via PID Passivity-Based Control. In IFACWorld Congress, pages 9577- 9582.
Sepulchre, R., Jankovi´c, M., and Kokotovi´c, P. V. (1997). Constructive nonlinear control. Springer.
Sprangers, O., Lopes, G. A. D., and Babuska, R. (2015). Reinforcement learning for port-Hamiltonian systems. IEEE Transactions on Cybernetics, 45(5):1017-1027.
Sun, W., Lin, Z., and Wang, Y. (2009). Global Asymptotic and Finite-gain L2 Stabilization of Port-Controlled Hamiltonian Systems Subject to Actuator Saturation. In American Control Conference (ACC), pages 1894-1898.
Valmorbida, G., Tarbouriech, S., and Garcia, G. (2013). Design of polynomial control laws for polynomial systems subject to actuator saturation. IEEE Transactions on Automatic Control, 58(7):1758-1770.
Viola, G., Ortega, R., Banavar, R., Acosta, J. A., and Astolfi, A. (2007). Total Energy Shaping Control of Mechanical Systems: Simplifying the Matching Equations Via Coordinate Changes. IEEE Transactions on Automatic Control, 52(6):1093-1099.
Wei, A. and Yuzhen, W. (2010). Stabilization and HÂ¥ control of nonlinear port-controlled Hamiltonian systems subject to actuator saturation. Automatica, 46(12):2008-2013.
Wibowo, B. S., Trilaksono, B. R., and Syaichu-Rohman, A. (2014). HÂ¥ Control of Polynomial Fuzzy Systems: A Sum of Squares Approach. Journal of Engineering and Technological Sciences, 46(2):152-169.
Xue, L. and Zhiyong, G. (2017). Control of Underactuated Bridge Cranes: A Simplified IDA-PBC Approach. In 11th Asian Control Conference (ASCC), pages 717-722.
Yu, A. G.-R. and Wang, B. S.-M. (2013). Polynomial Fuzzy Control of an Inverted Pendulum System by Sum-of-Squares Approach. In IEEE International Symposium on Next-Generation Electronics (ISNE), pages 236-239. IEEE.
Zhu, Y., Zhao, D., Yang, X., and Zhang, Q. (2018). Policy Iteration forHÂ¥ Optimal Control of Polynomial Nonlinear Systems via Sum of Squares Programming.
Barra lateral del artículo
Barra lateral del artículo
