Abstract
This paper presents a comprehensive dynamic modeling of a flexible link manipulator by using Hamilton's principle. The model is formulated by considering the flexible arm as a Timoshenko beam model. Hence, the shear, bending as well as rotational inertia effect of the manipulator are all taken into account in the dynamic formulation. In order to obtain a comprehensive dynamic model, the gravitational effect, which is missing in most of the flexible manipulator dynamic models, is also included in the formulation. Then, an efficient motion and force controller design method utilizing root contour analysis is proposed. With the proposed method the multi controller gains of the position/force controller for the flexible manipulator can be chosen analytically, as opposed to the method of trial and error used conventionally for selecting manipulator controller gains. The tuning process of these controllers' gains proves the simplicity of gains selection. And the motion/force simulation results verify the effectiveness of the controllers. The simulation results also show that the derived control scheme, which is based on a linear control system analysis, can drive the highly non-linear flexible arm to achieve the desired position and force satisfactorily.
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