Hybrid control scheme for robust tracking of two-link flexible manipulator (Q5915505)

The reduction of the manipulator component weight allows the manipulator to move faster and carry heavier loads. But it makes the links relatively longer leading to the so-called flexural effects, which are inherent in light-weight slender manipulators. Caused by flexural effects, the uncertainty increases, adding complexity to the system model, and thus the controller synthesis for flexible manipulators becomes a very complex problem for engineers. Here, in order to describe the flexural effect, eigenfunctions of the clamped-free uniform beam are used. The nonlinear equations of motion are derived by means of Lagrange's method when the kinetic energy and potential energy include the flexural components. The coupling interactions between the rigid motions and the flexural modes reduce the positioning accuracy of the manipulator. Therefore it is first of all necessary to separate the rigid body and flexible systems and design a controller for a rigid system which governs the gross motion by means of the control of joint angles. The gross motion of the flexible links does not drive the flexible vibrations to zero. So the next step in designing the control system is to reduce the flexural vibrations. The authors consider two control schemes: the composite control scheme and the hybrid control scheme. The first one uses the governing signal to reduce the flexural effect by means of a special block after a variable structure controller is used to generate its commands. The second one generates its commands, taking into account a summary signal of the gross rigid body position and flexural vibrations simultaneously. As it is shown, the second scheme is more robust and has high accuracy.