Multiobjective control/structure design optimization in the presence of practical constraints

The purpose of this research is to examine true multiobjective control/structure pareto optimization in the presence of practical constraints. The practical constraints that are addressed in this thesis are: (1) limiting the maximum time response of the output, (2) reduced order controllers. The purpose is also to examine the benefits of combined optimization when these practical constraints are included in the control synthesis. To perform the investigation, a new methodology was developed for combined optimization. This uses a new control law parameterization which chooses the closed loop covariance matrix as controller design variables. This parameterization allows the control design to be cast in the same form as the structural optimization design problem, i.e. a nonlinear constrained optimization problem. A number of independent design constraints are closed form and gradients can be found analytically to aid the nonlinear minimization. Two sets of design examples were used in this study. The first series minimizes control effort with the structure fixed. The second set of studies minimizes both control effort and total structural mass to find a pareto optimal solution. For all of the examples examined, the controller objectives are much more sensitive to the control variables than to the structural variables. Also, including the structural optimization in the combined problems does not substantially change the structural mass. This suggests that any benefit of simultaneous optimization of the controller and the structure may be mitigated by local minima in the numerical search. It was also found that minimizing control effort without constraining the closed loop eigenvalues or damping ratios can cause the resulting closed loop system to have substantially less damping than the initial closed loop system