Dynamics and control of mechanical systems in partly specified motion

The paper presents a systematic formulation for the dynamic analysis and synthesis of control of mechanical systems in partly specified motion. The motion specifications are modelled as program constraints on a controlled system, and the control that ensure their realization is determined. It is shown that program constraints may be realized by tangent control reactions with respect to the program constraint manifold, and this yields a very specific structure of the governing equations of the problem. The equations arise as DAEs, and the index of the DAEs may considerably exceed three. Index five and index 2n + 1 DAEs that describe control problems in mechanics are reported as illustrations. A method for analyzing the system motion consistent with the constraints and, based on the solution, synthesizing the program control is developed and applied to solve the mentioned case studies.