Flexible-Link Manipulators: Dynamic Analysis and Advanced Control Strategies

  • R. BoucettaEmail author
  • S. Hamdi
  • S. Bel Hadj Ali
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 270)


This chapter contains advanced studies in dynamic modelling and nonlinear control strategies applied to flexible-link robotic manipulators increasingly in demand in many fields such as industrial domain, medical intervention, and space exploitation. Taking into consideration the flexibility effect, Hamilton’s principle and Euler–Lagrange equations are associated to determine a highly nonlinear and coupled dynamic model. Therefore, the main control goals are to reach a perfect trajectory tracking without vibration impact. That is why, PD, Fuzzy, and gain scheduling Fuzzy PD controllers are applied to a rigid-flexible two links manipulator and then compared in terms of robustness and vibration minimization. A stability study is accomplished using the candidate function of Lyapunov. To improve performances, a robust Fractional Order Fuzzy PD (FOFPD) controller is developed by using non-integer order differentiator operators in the fuzzy PD controller. The gains of the FOFPD are normalized with the Particle Swarm Optimization (PSO) algorithm. The small gain theorem is used to establish the sufficient condition for bounded input-bounded output (BIBO) stability in closed-loop. Simulation results are introduced for each case of control to discuss reached performances.


Rigid-flexible manipulator Dynamic model PD control Fuzzy control Fractional order fuzzy control Particle Swarm Optimization 



This work was supported by the Ministry of the Higher Education and Scientific Research in Tunisia.


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Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.Physics Department, Sciences Faculty of SfaxUniversity of SfaxSfaxTunisia
  2. 2.MACS Laboratory, National Engineering School of GabesUniversity of GabesGabesTunisia
  3. 3.Preparatory Institute of Tunis El ManarUniversity of Tunis El ManarTunisTunisia

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