Uncertainty modeling and predicting the probability of stability and performance in the manufacture of dynamic systems

In this work, a method for determining the reliability of dynamic systems is discussed. Using statistical information on system parameters, the goal is to determine the probability of a dynamic system achieving or not achieving frequency domain performance specifications such as low frequency tracking error, and bandwidth. An example system is considered with closed loop control. A performance specification is given and converted into a performance weight transfer function. The example system is found to have a 20% chance of not achieving the given performance specification. An example of a realistic higher order system model of an electro hydraulic valve with spring feedback and position measurement feedback is also considered. The spring rate and viscous friction are considered as random variables with normal distributions. It was found that nearly 6% of valve systems would not achieve the given frequency domain performance requirement. Uncertainty modeling is also considered. An uncertainty model for the hydraulic valve systems is presented with the same uncertain parameters as in the previous example. However, the uncertainty model was designed such that only 95% of plants would be covered by the uncertainty model. This uncertainty model was applied to the valve control system example in a robust performance test.