(187f) Experimental Modeling of a Nonlinear Hybrid Dynamic System

An experimental multivariable pressure tank system was built inspired by previous experimental systems for liquid level modeling and control applications. The dynamic response of the pressure system exhibits significant nonlinear characteristics. A hybrid dynamic nonlinear model has been established to capture the switching behavior for flow through valves. The expression for flow through a valve can be modeled as either normal flow or choked flow when the pressure drop across the valve is high. Additionally, it was found that the control valve flow rate expression can be further refined by including additional hybrid switching behavior to implement an adjustable saturation behavior.

The valving of this experimental four-tank system can be operated to establish a number of possible SISO and MIMO configurations. The current work considers a relatively simple two-tanks in series configuration. The resulting nonlinear model includes expressions for flow across three different valves. Parameter estimation routines provide estimates for the various model parameters. Optimal switching conditions and model parameters have been determined from experimental data. A comparison of different types of models ranging from basic linear to full hybrid nonlinear will be presented.

Data from the system can be examined using phase plane analysis. The hybrid dynamic model presents transitions between different hybrid dynamic modes in the phase plane. For the experimental system, seven different discrete modes are reachable depending on operation of the system. Using the model, an input sequence may be developed so that numerous transitions between different hybrid states can be excited. This allows for improved empirical modeling of the experimental system by creating a data series for identification purposes which includes numerous hybrid mode transitions.