Robustness Analysis Of Closed-loop Systems With Uncertain Parameters Using Interval Method

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.There are several mathematical models in present researches or applications about uncertain structural analysis, such as stochastic model, fuzzy model, convex model and interval one etc. Due to the diversity and complexity of the uncertain parameters, it is impossible to apply one uncertain model to all kinds of problems. We have to select the better ones for each specific problem. For instance, although the stochastic one has been developed well, it is difficult to use in the following two cases: (1) no more data can be given to obtain the statistical character; (2) the parameters disagree the random mechanism. For...