Reduce Fast Dynamics

Fast dynamics can have a large impact on computation time. When the solver encounters rapidly occurring events such as stiff vibrations or water hammer, it must take smaller steps to compute each event. Reducing fast dynamics allows the solver to take larger steps, making your model more likely to be real-time capable. You can use frequency-response analysis and pole analysis to analyze the dynamics of the system.

Frequency-Response Analysis

Frequency response describes the steady-state response of a system to sinusoidal inputs. For a linear system, a sinusoidal input results in an output that is a sinusoid with the same frequency, ω, but with a different amplitude and phase, θ.

Frequency analysis shows how amplitude and phase change over a given range of frequencies. For a small change in frequency, a large magnitude or phase change indicates that a system has fast dynamics. The figure uses Bode plots, which allow you to see how the amplitude, in terms of magnitude in dB, and phase vary as a function of frequency.

Pole Analysis

Fast poles are also indicative of fast dynamics. Fast poles are poles that respond or oscillate rapidly. Poles that have real components that are far to the left of the imaginary axis on the complex plane have a fast response speed. Complex pole pairs that have imaginary components that are far from the real axis oscillate rapidly. For example, the real pole at -1500 has a faster response speed than the real pole at -1000 and the complex pole pair at -500 ± 1500i has a faster oscillation speed than the complex pole pair at -500 ± 500i.

For state-space models, the poles are the eigenvalues of the A-matrix. This example shows you how to examine pole speed by determining the state-space model and then, calculating and plotting the eigenvalues of the A-matrix values.