Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-22T17:07:02.977Z Has data issue: false hasContentIssue false
  • English
  • Français

Robust Stable Limit Cycle Generation in Multi-Input Mechanical Systems

Published online by Cambridge University Press:  29 January 2021

Tahereh Binazadeh Open the ORCID record for Tahereh Binazadeh [Opens in a new window]  and
Mahsa Karimi
Tahereh Binazadeh*
Affiliation:
Department of Electrical and Electronic Engineering, Shiraz University of Technology, Shiraz, Iran E-mail: [email protected]
Mahsa Karimi
Affiliation:
Department of Electrical and Electronic Engineering, Shiraz University of Technology, Shiraz, Iran E-mail: [email protected]
*
*Corresponding author. E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Summary

This paper proposes a robust controller for the generation of stable limit cycles in multi-input mechanical systems subjected to model uncertainties. The proposed idea is based on Port-Controlled Hamiltonian (PCH) model and energy-based control by considering the Hamiltonian function as the Lyapunov function. For this purpose, first, a nominal controller is designed by shaping the energy function of the system according to the structure of the desired limit cycle. Then, an additional robustifying control term is designed based on the integral sliding mode method with the selection of an appropriate sliding surface. Finally, computer simulations for two practical case studies are provided to confirm the effectiveness of the proposed controller in the generation of stable limit cycles in the presence of uncertainties.

Keywords

Stable oscillationRobust limit cycleMulti-input mechanical systemsUncertaintiesEnergy shaping, PCH modelIntegral sliding mode
Type
Article
Information
Robotica , Volume 39 , Issue 7 , July 2021 , pp. 1316 - 1327
Copyright
© The Author(s), 2021. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ren, J., McIsaac, K. A. and Patel, R. V., “Modified Newton’s method applied to potential field-based navigation for nonholonomic robots in dynamic environments,” Robotica 26(1), 117–127 (2008).CrossRefGoogle Scholar
Hashimoto, S., Naka, S., Sosorhang, U. and Honjo, N., “Generation of optimal voltage reference for limit cycle oscillation in digital control-based switching power supply,” J. Energy Power Eng. 6(4), 623–628 (2012).Google Scholar
Teplinsky, A. and Feely, O., “Limit Cycles in a MEMS oscillator,” IEEE Trans. Syst, Circuits. Express Briefs, II 55(9), 882–886 (2008).Google Scholar
Dizaji, A. F., Sepiani, H. A., Ebrahimi, F., Allahverdizadeh, A. and Sepiani, H. A., “Schauder fixed point theorem based existence of periodic solution for the response of Duffing’s oscillator,” J. Mech. Sci. Technol. 23(8), 2299–2307 (2009).CrossRefGoogle Scholar
Garofalo, G. and Ott, C., “Energy based limit cycle control of elastically actuated robots,” IEEE Trans. Automat. Control 62(5), 1164–1176 (2017).CrossRefGoogle Scholar
Garofalo, G., Ott, C. and Albu-Schäffer, A., “Orbital stabilization of mechanical systems through semidefinite Lyapunov functions,” IEEE American Control Conference (ACC), Washington, DC (2013) pp. 5735–5741.Google Scholar
Binazadeh, T. and Hakimi, A. R., “Adaptive generation of limit cycles in a class of nonlinear systems with unknown parameters and dead-zone nonlinearity”, Int. J. Syst. Sci. 51(15), 3134–3145 (2020).CrossRefGoogle Scholar
Hakimi, A. R. and Binazadeh, T., “Sustained oscillations in MIMO nonlinear systems through limit cycle shaping,” Int. J. Robust Nonlinear Control 30(2), 587–608 (2020).CrossRefGoogle Scholar
Geyer, H., Seyfarth, A. and Blickhan, R., “Compliant leg behavior explains basic dynamics of walking and running,” Proc. R. Soc. B 273, 2861–2867 (2006).CrossRefGoogle Scholar
McGeer, T., “Passive dynamic walking,” Int. J. Robot Res. 9, 62–82 (1990).CrossRefGoogle Scholar
Binazadeh, T., “Finite-time tracker design for uncertain nonlinear fractional-order systems,” J. Comput. Nonlinear Dyn. 11(4), 041028 (2016).Google Scholar
Binazadeh, T. and Bahmani, M., “Robust time-varying output tracking control in the presence of actuator saturation,” Trans. Inst. Meas. Control 40(1), 61–70 (2018).CrossRefGoogle Scholar
Azhdari, M. and Binazadeh, T., “Adaptive robust tracker design for nonlinear sandwich systems subject to saturation nonlinearities,” Robotica 1–16, in press (2020), doi: 10.1017/S0263574720000508.Google Scholar
Zarei, F. and Shafiei, M. H., “On event-triggered tracking for non-linear SISO systems via sliding mode control,” IMA J. Math. Control Inform. 37(1), 105–119, (2020).Google Scholar
Haddad, W. M. and Chellaboina, V., Nonlinear Dynamical Systems and Control: A Lyapunov-Based Approach (Princeton University Press, Princeton, 2008).Google Scholar
Hakimi, A. R. and Binazadeh, T., “Inducing sustained oscillations in a class of nonlinear discrete time systems,” J. Vib. Control 24(6), 1162–1170 (2018).CrossRefGoogle Scholar
Hakimi, A. R. and Binazadeh, T., “Limit cycle synchronization of nonlinear systems with matched and unmatched uncertainties based on finite-time disturbance observer”. Circuits Syst. Signal Proc. 38(12), 5488–5507 (2019).CrossRefGoogle Scholar
Shiriaev, A., Perram, J. W. and de Wit, C. C., “Constructive tool for orbital stabilization of underactuated nonlinear systems: Virtual constraints approach,” IEEE Trans. Automat. Control 50(8), 1164–1176 (2005).CrossRefGoogle Scholar
Aguilar-Ibanez, C., Martinez, J. C., de Jesus Rubio, J. and Suarez-Castanon, M. S., “Inducing sustained oscillations in feedback-linearizable single-input nonlinear systems,” ISA Trans. 54, 117–124 (2015).CrossRefGoogle ScholarPubMed
Oliveira, N. M. F., Kienitz, K. H. and Misawa, E. A., “A describing function approach to the design of robust limit-cycle controllers,” Nonlinear Dyn. 67(1), 357–363 (2012).CrossRefGoogle Scholar
Hakimi, A. R. and Binazadeh, T., “Robust generation of limit cycles in nonlinear systems: Application on two mechanical systems,” J. Comput. Nonlinear Dyn. 12(4), 041013 (2017).CrossRefGoogle Scholar
Hakimi, A. R. and Binazadeh, T., “Generation of stable oscillations in uncertain nonlinear systems with matched and unmatched uncertainties,” Int. J. Control 92(1), 163–174 (2019).CrossRefGoogle Scholar
Hakimi, A. R. and Binazadeh, T., “Generation of stable and robust limit cycle in the uncertain nonlinear systems using sliding mode controller,” Tabriz J. Electr. Eng. 47(2), 481–489 (2017).Google Scholar
Hakimi, A. R. and Binazadeh, T., “Robust limit cycle generation in nonlinear dynamical systems with nominal performance recovery,” J. Comput. Nonlinear Dyn. 14(11), 114501-1–114501-4 (2019).Google Scholar
Hakimi, A. R., ad Binazadeh, T., “Robust limit cycle control in a class of nonlinear discrete-time systems,” Int. J. Syst. Sci. 49(15), 3108–3116 (2018).CrossRefGoogle Scholar
Valentinis, F., Donaire, A. and Perez, T., “Energy-based motion control of a slender hull unmanned underwater vehicle,” Ocean Eng. 104, 604–616 (2015).CrossRefGoogle Scholar
Yang, S. and Xian, B., “Energy-based nonlinear adaptive control design for the quadrotor UAV system with a suspended payload,” IEEE Trans. Ind. Electron., 67(3), 2054–2064 (2019).Google Scholar
Maschke, B. M. and van der Schaft, A. J., “Port-controlled Hamiltonian systems: Modelling origins and system theoretic properties,” IFAC Proc. Vol. 25(13), 359–365 (1992).CrossRefGoogle Scholar
Karimi, M. and Binazadeh, T., “Energy-based Hamiltonian approach in H ∞ controller design for n-degree of freedom mechanical systems,” Syst. Sci. Control Eng. 7(1), 264–275 (2019).CrossRefGoogle Scholar
Komijani, H., Masoumnezhad, M., Zanjireh, M. M. and Mir, M., “Robust hybrid fractional order proportional derivative sliding mode controller for robot manipulator based on extended grey wolf optimizer,” Robotica 38(4), 605–616 (2020).CrossRefGoogle Scholar
Shiravani, F. and Shafiei, M. H.. “Robust output regulation via sliding mode control and disturbance observer: Application in a forced Van Der Pol chaotic oscillator,” J. Dyn. Syst. Meas. Control 139(9), 091015-1–091015-6 (2017).CrossRefGoogle Scholar
Herrmann, G., Jalani, J., Mahyuddin, M. N., Khan, S. G. and Melhuish, C., “Robotic hand posture and compliant grasping control using operational space and integral sliding mode control,” Robotica 34(10), 2163–2185 (2016).CrossRefGoogle Scholar
Castaños, F. and Fridman, L., “Analysis and design of integral sliding manifolds for systems with unmatched perturbations,” IEEE Trans. Automat. Control 51(5), 853–858 (2006).CrossRefGoogle Scholar
Khalil, H. K., Nonlinear, Control (Upper Saddle River, Prentice Hall, 2015).Google Scholar
Binazadeh, T., Karimi, M. and Tavakolpour-Saleh, A. R., “Robust control approach for handling matched and/or unmatched uncertainties in port-controlled Hamiltonian systems,” IET Cyber-Syst. Robot. 1(3), 73–80, (2019).CrossRefGoogle Scholar
Ortega, R., Loria, A., Nicklasson, P. J. and Sira-Ramirez, H., Passivity-based Control of Euler-Lagrange Systems (Springer, London, 1998).CrossRefGoogle Scholar
Binazadeh, T. and Shafiei, M. H., “Output tracking of uncertain fractional-order nonlinear systems via a novel fractional-order sliding mode approach,” Mechatronics 23(7), 888–892 (2013).CrossRefGoogle Scholar
Mohammadpour, S. and Binazadeh, T., “Observer-based synchronization of uncertain chaotic systems subject to input saturation,” Trans. Inst. Meas. Control 40(8), 2526–2535 (2018).CrossRefGoogle Scholar
Jafari, E. and Binazadeh, T., “Low-conservative robust composite nonlinear feedback control for singular time-delay systems,” J. Vib. Control in press, (2020), doi: 10.1177/1077546320953736.CrossRefGoogle Scholar
Ge, S. S. and Harris, C. J., Adaptive Neural Network Control of Robotic Manipulators (World Scientific, Singapore, 1998).CrossRefGoogle Scholar