Nonconservative control design for robustly stable structural dynamic systems
Kozodoy, Dmitry A.
Spanos, Pol D.
Doctor of Philosophy
This dissertation considers a general concept of nonconservative measures of dynamic system performance via a consistent approach in terms of signal and system norms and suggests an appropriate iterative procedure for reduction of conservatism in the design of active structural control systems. This reduction is accomplished by introducing two modified variants of the H$\sb2$-norm leading to less conservative system performance criteria than the conventional H$\sb2$-norm-based performance indices. These modifications make both the stochastic and the deterministic control design specifications less conservative and, at the same time, retain all the benefits of the standard H$\sb2$-norm. In view of model uncertainties, the standard H$\sb2$-method alone (as, virtually, all existing control strategies) may lead to arbitrarily small stability margins. On the contrary, the modern H$\sb\infty$-control method can handle the robust stability problem but cannot guarantee an admissible nominal performance. In the context of robustly stable control design, the dissertation considers the general mixed H$\sb2$/H$\sb\infty$-control problem that is stated as a reduction of the H$\sb2$-norm of one transfer function under a constraint in terms of the H$\sb\infty$-norm of another transfer function. As a solution for this problem, the dissertation introduces a new H$\sb2$/H$\sb\infty$ nested control synthesis which combines the advantages of the both standard control methods. An important practical application of the nested control synthesis to active structural control design, such as control for an optimal H$\sb2$-norm-based performance with guaranteed robust stability, is considered. An iterative algorithm which incorporates a less conservative H$\sb2$-norm-based performance measure into the nested synthesis is introduced. The H$\sb2$/H$\sb\infty$ nested synthesis employs the idea of Youla parametrization of all H$\sb2$-suboptimal controllers. The state-space formulae of a parametrized controller can be obtained in terms of the solutions of two modified Riccati equations. In the new formulation the explicit state-space formulae of the full parametrization are specially derived for the most general case when the traditionally accepted simplifying assumptions are relaxed.
Applied mechanics; Civil engineering