Abstract
This paper presents an integrated methodology for optimal design and control of nonlinear flexible mechanical systems, including minimum time problems. This formulation is implemented in an optimum design code and it is applied to the nonlinear behavior dynamic response. Damping and stiffness characteristics plus control driven forces are considered as decision variables. A conceptual separation between time variant and time invariant design parameters is presented, this way including the design space into the control space and considering the design variables as control variables not depending on time. By using time integrals through all the derivations, design and control problems are unified. In the optimization process we can use both types of variables simultaneously or by interdependent levels. For treating minimum time problems, a unit time interval is mapped onto the original time interval, then treating equally time variant and time invariant problems. The dynamic response and its sensitivity are discretized via space-time finite elements, and may be integrated either by at-once integration or step-by-step. Adjoint system approach is used to calculate the sensitivities.
Highlights
Structures and flexible mechanical systems, by one hand, as well as optimal design and optimal control, by another hand, have been traditionally treated with separated formulations
This paper presents an integrated methodology for optimal design and control of nonlinear flexible mechanical systems
In order to implement it, one uses: (i) a nonlinear structural finite element technique to model large displacements, referring all the quantities to an inertial frame and using stress and strain measures that are invariant with the rigid body motion [7]; (ii) a conceptual separation between time variant and time invariant design parameters, this way including the design space into the control space and considering the design variables as control variables not depending on time
Summary
Structures and flexible mechanical systems, by one hand, as well as optimal design and optimal control, by another hand, have been traditionally treated with separated formulations. Numerical methods for the solution of optimum control problems are divided into two major approaches: methods based on the Pontryagin’s maximum principle and direct methods. The former ones need considerable preparatory work to derive the adjoint differential equations and are very sensitive to the initial estimate of the control variables and to the integration of adjoint differential equations. This paper presents an integrated methodology for optimal design and control of nonlinear flexible mechanical systems. For minimum time problems there is no way of checking the sensitivities by finite differences comparison In this case one needs to compare them with closed form solutions. The response analysis and corresponding DSA are implemented in the interactive optimal design code OPTIMISE in order to use optimality criteria or nonlinear programming optimization runs
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