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Shock and Vibration
Volume 20 (2013), Issue 6, Pages 1049-1063

The Rigid-Flexible Robotic Manipulator: Nonlinear Control and State Estimation Considering a Different Mathematical Model for Estimation

André Fenili

Universidade Federal do ABC (UFABC), CECS/Aerospace Engineering Av. dos Estados, 5001 – Bloco B, Sala 936 – Santo André/SP – CEP 09210 580, Brazil

Received 7 November 2013; Accepted 7 November 2013

Copyright © 2013 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this paper the author investigates the angular position and vibration control of a nonlinear rigid-flexible two link robotic manipulator considering fast angular maneuvers. The nonlinear control technique named State-Dependent Riccati Equation (SDRE) is used here to achieve these aims. In a more realistic approach, it is considered that some states can be measured and some states cannot be measured. The states not measured are estimated in order to be used for the SDRE control. These states are all the angular velocities and the velocity of deformation of the flexible link. A SDRE-based estimator is used here. Not only different initial conditions between the system to be controlled (here named "real" system) and the estimator but also a different mathematical model is considered as the estimation model in order to verify the limitations of the proposed state estimation and control techniques. The mathematical model that emulates the real system to be controlled considers two modes expansion and the estimation model considers only one mode expansion. The results for the different approaches are compared and discussed.