Dynamics of multi-link flexible manipulators are highly nonlinear. Furthermore, the vibrational frequencies of these manipulators are configuration-dependent. Therefore, any feedforward or feedback algorithm has to deal with these frequency variations. In this paper, an inner-loop nonlinear controller based on feedback linearization of O(1) dynamics derived from an asymptotic expansion is utilized. It is shown that this control scheme significantly reduces the frequency variations due to the geometric configuration of the arm and cancels some of the nonlinearities due to Coriolis and centripetal effects. The advocated control law is compared and contrasted to an independent joint-based PD controller. However, since the aforementioned controllers are joint-based control schemes, significant vibrations are still induced at the end-effector. To this end, these control schemes are augmented with an input preshaper for vibration suppression. The objective is to preshape the reference input signals so that a vibration free output is achieved. The input preshaping scheme is shown to be effective when the plant dynamics are linear and time-invariant. These assumptions do not hold for the multi-link flexible manipulators as alluded to above. Application of an inner-loop nonlinear control to cancel some of the nonlinearities and to reduce configuration dependence of structural frequencies enhances the performance of the advocated input preshaping scheme or any other outer-loop linear control design. Experimental and simulation results for a two-link flexible manipulator are provided to validate the effectiveness of the advocated controllers.
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