Probabilistic Parameter Uncertainty Analysis of Single Input Single Output Control Systems

The current standards for handling uncertainty in control systems use interval bounds for definition of the uncertain parameters. This approach gives no information about the likelihood of system performance, but simply gives the response bounds. When used in design, current methods of m-analysis and can lead to overly conservative controller design. With these methods, worst case conditions are weighted equally with the most likely conditions. This research explores a unique approach for probabilistic analysis of control systems. Current reliability methods are examined showing the strong areas of each in handling probability. A hybrid method is developed using these reliability tools for efficiently propagating probabilistic uncertainty through classical control analysis problems. The method developed is applied to classical response analysis as well as analysis methods that explore the effects of the uncertain parameters on stability and performance metrics. The benefits of using this hybrid approach for calculating the mean and variance of responses cumulative distribution functions are shown. Results of the probabilistic analysis of a missile pitch control system, and a non-collocated mass spring system, show the added information provided by this hybrid analysis.

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