| For successful development of smart structural systems to control structural vibration, the actuator/sensors should be configured at locations giving maximum control effectiveness, and the synthesized controller has to be robust for uncertainties such as uncertain parameters and saturating actuators. In addition, the designed controller should have a lower order in order to simplify the hardware implementation. Different control methods are presented in this thesis to satisfy these requirements. The optimal placement of actuator/sensors is determined by a two-step approach requiring no large computational effort. In this approach, two easily calculated criteria are first used to select a set of candidate locations of actuator/sensors, from which the optimal placement is then chosen based on the control performance of each configuration of actuator/sensors. The uncertainties in structural systems are modelled as unstructured uncertainties, and parametric uncertainties in natural frequencies and damping ratios. Three analysis methods, based on the integral quadratic constraint (IQC) theory, the general Popov criterion, and parameter-dependent Lyapunov functions, are proposed for analyzing the stability and different control performances of smart structural systems with parametric uncertainties. They are able to provide much less conservative analysis results than many available methods. Two of the analysis methods are further extended to design a multi-objective controller with robust stability and performance. By using IQC multipliers and Lyapunov functions, two methods are proposed for testing the stability and the performance deterioration of smart structural systems with saturating actuators. The robustness of the controller for actuator saturation is improved by a control approach based on the circle criterion. The lower-order controller is obtained by a frequency-weighted controller reduction method, which gives minimal reduction error. Based on the frequency distribution of the full-order controller, the weighting function is chosen to preserve the control performance. Alternatively, the lower-order controller is directly synthesized by approximating the nonconvex synthesis conditions as a convex minimization problem. All these analysis and control methods are represented in terms of linear matrix inequalities (LMIs), and thus can be easily implemented by efficient LMI algorithms. |
