Constraint-following Servo Control Design for Mechanical Systems

A mechanical system is required to obey a set of constraints. The tools to accomplish this performance requirement are a set of servo controls; that is, the servo controls are to generate the appropriate constraint force. In this article, the servo control design problem for constraint-following is thoroughly discussed. The problem is formulated as an algebraic setting in which a second order constraint is adopted. The control is a solution to the problem, whose projection to a subspace is used to ensure conformation to the constraint. The complete solution to this problem is provided in analytical form. It is shown that the environmentally constrained system simply adopts the minimum form of the complete solution. The setting presented here helps to broaden the scope of traditional Lagrangian mechanics.