Modeling and control of complex mechanical systems.

摘要

The focus of this dissertation is the modeling and control of complex mechanical systems. First, constrained coordinates are used to obtain the equations of motion of complex systems in differential-algebraic form. Elasticity of components comprising the mechanical system, such as beams and beam-like structures are considered. In addition to transverse deformation, we also include both components of axial deformation, axial stretch and shortening of the projection, into the models. We analyze the impact of both components of axial deformation on the model accuracy and provide guidelines which component of axial deformation to include as a function of various parameters. Then we consider the design of a control law for systems described in differential-algebraic form. Therefore, we extend the original pointwise optimal control law so that it can be applied on systems with constrains. We prove that pointwise optimal control stabilizes the system. In robustness analysis, we provide estimates for the steady state errors of the system response. In addition, we present useful guidelines for choosing values for weighting matrices that are used in the control law.