Abstract
This paper deals with an exact state space dynamic model for manipulators with flexible links. We use the Bernoulli-Euler beam equations to derive a frequency domain matrix transfer function. This transfer function is then used to compute the Laplace transform of the state vector as a function of the lateral position along a single link manipulator. The problem of optimal end point control of the beam is then addressed. A sixth-order state space model is derived for the manipulator and the controller is based on this model. Several control laws are studied for this model. Next, the manipulator is modeled as eighth order but the control law based on the sixth-order model is retained. We then estimate the six states from the output of the eighth-order model and feed these states back to the controller to derive the control torque used to drive the manipulator. A filter is introduced to compensate for spillover. The results are very satisfactory, and are illustrated by simulated case studies.
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Pal, S., Stephanou, H.E. & Cook, G. Optimal control of a single-link flexible manipulator. J Intell Robot Syst 2, 187–199 (1989). https://doi.org/10.1007/BF00238688
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DOI: https://doi.org/10.1007/BF00238688