Feedback Control of Position and Contact Force for a Two-Dimensional Mechanism Constrained to a Given Planar Contour

The planar motion of a two dimensional mechanism is constained so that one point on the mechanism moves along a specified contour; it is assumed that the motion of the mechanism is controlled by planar forces applied to the mechanism. These control forces are to be adjusted according to a linear control law, based on feedback of the positions and velocities of the mechanism and feedback of the contact force between the mechanism and the constraining contour. The control objective is to achieve accurate and robust regulation of the motion of the mechanism and of the contact force. For each of two specific regulation objectives, a linear control law is derived and the resulting closed loop resonses are characterized. Derivation of a suitable control law is significantly complicated by the nonclassical nature of the differential-algebraic model of the constrained system; the control design methodology is facilitated by use of certain nonlinear transformations that are explicitly exhibited. A comparison is made with a closed loop system, where the control law is derived by designing independent control loops for each degree of freedom, ignoring the coupling that occurs through the contact force. Computer simulations are presented to demonstrate the several closed loop properties.