Effect Of Uncertain Parameters On Controllability Of Vibration Control Systems

In practical engineering problems, the theories of the design and analysis of structures are always established on the basis of the definite mathematics models. However, there are always uncertain factors in the structural engineering practices, such as the inaccuracy of the measurement, the complexity of the structures or errors in manufacture, etc. When the structures are large and complex, the combination of the uncertainty can have some effect on the systems. Therefore, it is necessary to design and analyze the structures with uncertain models directly.The uncertainty can be described as following three kinds: 1.physical uncertainty. It is correlated to load, material and geometrical size. Generally speaking, the change of working conditions and the errors in manufacturing or installation can bring this kind of uncertainty. 2.statistical uncertainty. Nowadays, probability statistical methods are used in solving uncertainty. But because there is no enough statistic information, samples cannot represent all the system information. 3.model uncertainty. During structural analysis and design, the models are constructed between the inputs, including load, geometric size and plastic modules, and the outputs, the displacement, stress and strain. Even beside the physical uncertainty, there are uncertainties in modeling such as the theoretical simplifying and unknown boundary conditions. The vibration control problems are very important in engineering and the deterministic one has been well developed. The closed-loop control systems are defined as following: the real-time control is applied to the controlled objects according to the state of the objects to obtain the requirement in advance.The method to research the vibration control problems of the system with uncertain parameters is developed at present dissertation. The equations of the system with uncertain parameters are divided into two parts, the deterministic part and the uncertain part. The deterministic part is used to investigate the vibration control problem, for example, it is can be used to design the feedback control law. Then the uncertain part is used to determine the effects of the uncertain parameters on the actual uncertain system. For repeated eigenvalue systems, the modal controller of single-input system cannot stabilize the repeated eigenvalues. In order to stabilize the uncontrolled eigenvalues, we present a multi-stage procedure to design the feedback controller of the system with repeated eigenvalues. The singular value decomposition (SVD) of input matrix in the modal subspace is used to estimate and measure the controllability. By using perturbation theory, the effects to controllability of the uncertain parameters can be presented.