The first group of interactive tools are devoted to analyzing open-loop dynamical systems. The analytical models for most engineering systems are nonlinear, these tools focus on how to obtain dynamic linear models from nonlinear physical models through linearization using a Taylor series expansion about a nominal steady- state operating point, to make clear that the linearized models are only valid in the vicinity of the selected operating point.
The tank level system
In this interactive tool it is possible to compare, through simulation, the time re- sponses (transient and steady-state responses) obtained using both the nonlinear and linear models of the tank level process. A step signal is used as a test input for the simulation. The tool also allows for analysis at different operating points and using different tank geometries (different areas of the tank and the discharge hole), providing quantitative and qualitative information on the validity range of the linear approximations. System parameters can be changed by interacting with the visual geometric representation of the tank.
Variable section tank level system
In this interactive tool it is possible to compare, through a simulation, the step responses obtained using the nonlinear and linear models of a spherical tank level system. The tool is useful to visualize the degree of nonlinearity of the system and how it changes depending on the selected operating point, thus influencing the validity of the linearized model.