Robust control design for a proportional valve with backlash compensation
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[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] In this work, a linear technique is used to study the stability of a nonlinear system. Most of dynamic systems in industrial and fluid power systems are nonlinear and include uncertainties. Thus, unexpected changes in the stability can be exhibited and can lead these systems to become unstable exhibit oscillatory behavior. Engineers have been trying to develop nonlinear mathematical models to be able to predict whether or not a designed system will be exposed to such an oscillation before considering building and implementing the system. The focus of this study is to predict the existence of nonlinear oscillation in a dynamic system. A nonlinear model validation of a solenoid operated proportional control valve was performed using open loop testes. The model consists of linear and nonlinear parts. The linear part was developed by linearizing the nonlinear equations governing the operations of the valve at nominal conditions. The nonlinear parts constructed by analyzing open loop tests showed that two major nonlinearities found in the system; saturation effect of the current input and backlash hysteresis behavior of the valve; were considered to be the cause of instability. Each one of these nonlinearities was represented by its linear model and several limit cycles were predicted using the describing function analysis method. In order to control limit cycle behavior, a control system was designed in order to ensure robust stability and performance. Two aspects of the valve system were considered in the design. First, the uncertainty model of the valve operation due to the uncertainty found for the 30 replications of the first stage spool valve was considered. Second, the nonlinearities embedded in the system were considered which can cause stability issues if they have not been considered in the design. Thus, two different controllers were designed and implemented for the system, anti-backlash and H-infinity controllers. Designing both of the controllers in a way that robust stability and performance are to be achieved proved to be the main challenge. A technique was developed to extract the best stability and performance characteristics for each type of controller. Finally, the control system was tested experimentally for all the replications of the valve system. Results showed a significant amount of hysteresis reduction as well as robust stability and performance objectives were me by all the system uncertain replications using the designed controllers.
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