Linear Feedback Control of Position and Contact Force for a Nonlinear Constrained Mechanism

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Abstract
A feedback control problem for a constrained mechanism is formulated and solved. The mechanism is controlled by forces applied to the mechanism which 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 constraint force on the mechanism. The control objective is to achieve accurate and robust local regulation of the motion of the mechanism and of the constraint force on the mechanism. Derivation of a suitable control law is significantly complicated by the nonclassical nature of the differential-algebraic model of the constrained system and by the nonlinear characteristics of the model. The control design approach involves use of a certain nonlinear transformation which leads to a set of decoupled differential-algebraic equations; classical control design methodology can be applied to these latter equations. An example of a planar mechanism is studied in some detail, for two different regulation objectives. Specific control laws are developed using the described methodology. Comparisons are made with a closed loop system, where the control law is derived without proper consideration of the constraint force. Computer simulations are presented to demonstrate the several closed-loop properties.

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