Affiliations: Instituto Superior Técnico, Departamento de
Engenharia Mecânica, Av. Rovisco Pais, 1049-001 Lisboa, Portugal | Escola Superior de Tecnologia de Setúbal, Campus
do IPS, 2914-508 Setúbal, Portugal
Abstract: A sensitivity analysis and multicriteria control optimization
formulation is derived for mechanical systems. This formulation is implemented
into an interactive optimum design code and it is applied to optimize
protection systems for the prevention of injuries. The limiting isolation
capabilities of the systems are determined. The effect of pre-acting control is
investigated. Control forces as well as the time at which the control should
act before the instant of impact are considered as design variables. The same
idea used by the authors in previous articles for minimum time control problems
is applied here to find the preview time. Dynamic response index, maximum
acceleration, rattlespace, or maximum power of the resisting force among others
can be used as performance criteria. In order to handle the multicriteria
problem, both the reduced feasible region method and a min-max upper bound
method are utilized. The adjoint system approach is used to calculate the
sensitivities. The dynamic response of the systems and its sensitivity are
discretized via space-time finite elements. The equations of motion and the
sensitivity equations are integrated at-once as it is typical for the static
response. This way, displacement, velocity or acceleration control conditions
can be imposed easily at any point in time. Also, adjoint system response is
obtained without needing primary response memorization. Mathematical
programming is used for the optimal control process.
Keywords: Optimum control, preview control, multicriteria, space-time finite elements
