Optimal determination of feedback controller parameters conditioned on probabilistic dynamic loadings

Abstract

A chance constrained optimization model is presented for determining dynamic control parameters for active members within structural designs. To begin, a dynamic model of a structure with linear displacement and velocity control at every member is developed. The optimal feedback control parameters are determined by minimizing the levels of each control parameter conditioned on the probability that displacements at any time do not exceed pre-specified maxima. The actual displacements at any point are calculated by solving the governing equations of motion subject to a given excitation which is expressed in terms of random variables. Structural response constraints, originally expressed as probability statements, are transformed into deterministic equivalent constraints using the cumulative distribution of the random force variables. The optimization model is solved using a Monte-Carlo simulation in which the objective is to minimize the control feedback parameters for each member. An example is presented using a single mode model of a one-bay, one-story frame subject to a probabilistic point force to illustrate the performance of the optimization model. The technique presented here may be used to aid engineers in locating active members within structural designs and provide a measure of the probable dynamic performance of the structure.