In this work, the describing function technique is used to study the stability of a nonlinear system. All of dynamic systems in industrial and fluid power systems are nonlinear and include uncertainties to some degree. Thus, unexpected changes in the stability can be exhibited and can lead these systems to become unstable or exhibit oscillatory behavior. Engineers have developed 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 behavior in a dynamic system using a simplified approach. A nonlinear model validation of a solenoid operated proportional control valve was performed using open loop testes. The type of two-stage hydraulic valve considered in this research is used to control the velocity of hydraulic cylinders. The pilot valve, which is the focus of this research, is a pressure control 3-way valve. A number of 30 replications of this pilot spool valve were studied and tested experimentally along with a single main stage valve. The model consists of linear and nonlinear parts. The linear part of the model was developed by linearizing the nonlinear governing equations at nominal conditions. The nonlinear part was constructed by analyzing open loop experimental test data. The data showed that two major nonlinearities are found that are key to describing the behavior of the system: saturation of the current input and backlash hysteresis behavior. These nonlinearities were considered to be the cause of limit cycle behavior. Each one of these nonlinearities was represented by its describing function and limit cycles were predicted using the describing function analysis method. In using the describing function method, the complexities of working with the nonlinear physics based model to determine limit cycle behavior were avoided.