A method of frequency domain error modeling to predict the probability of stability and performance of dynamic systems with parametric uncertainty

Abstract

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] In this work a method is developed for modeling frequency domain error in dynamic systems with parametric uncertainty. Within any mass-manufactured dynamic system, parameters such as masses, springs or geometrical attributes can vary from one system to the next. Overall performance or stability of the system can therefore be a function of the extent of uncertainty within the physical parameters. In typical robust control designs, uncertainty models work to account for all possible error within the system. The error modeling approach presented here is unique in that only a fraction of possible error is represented by the model. Validation of the uncertainty modeling technique was completed on a pilot operated proportional control valve. Thirty replications of the pilot stage of the proportional control valve were obtained and tested with one main stage. An uncertainty model which takes into account only a fraction of error is formed based on simulated frequency response data from an analytical model. A comparison is presented of two different control designs, a mixed sensitivity H-infinity and a proportional controller. The controllers are implemented in a closed-loop experimental setup in which all 30 pilot valves were retested. This study is shown to verify the ability of the robustness analysis utilizing the uncertainty model to approximate the probability of a system obtaining performance or stability specifications given parametric uncertainty within the system.