Mechanical structure optimization in minimum-time motion control of flexible bodies

Abstract

This paper considers the problem of minimum-time motion control of a flexible body for which the dynamic properties can be optimized within a structural design. This allows a matching of modal characteristics to a control task such that reductions in time-of-motion can be achieved compared with unoptimized designs. The problem formulation is based on an elastic structure undergoing a motion task with specified boundary conditions and subject to limits on actuation forces. A numerical method for calculating minimum-time control input solutions based on an iterative construction of the reachable set is first considered. A structural optimization approach is further developed based on continuity properties of the solution set, these admitting a first order perturbation analysis from which an optimization of system design parameters can be achieved. A selection of numerical case studies are presented involving single and multi-mode structures. Possibilities for realization of the approach using variable stiffness/deformable structures are discussed and results from a linear motion stage with tunable-stiffness flexible armature presented that demonstrate the potential benefits.