MIMOtool Help Desk

Subsection ROOT LOCUS

In this subsection, the user can analyze the transfer functions of every channel of the current model.

The transfer matrix G of the model,

G = C inv( sI - A ) B +D ,

is a matrix with as many rows as the number of outputs and as many columns as the number of inputs, then its term in position ij represents the transfer function of the channel from the input j to the output i.

The function associated with the Root Locus command of the analysis menu or with the pushbuttons << and >>, in the window above, evaluates the transfer function of the selected channel, plots its root locus and computes its poles, transmission zeros and gain, which can be visualized pressing, respectively, the pushbuttons P, Z and K.

The root locus graphic is very useful to analyze the negative feedback loop

and shows the trajectories of the closed-loop poles of the channel when Gain varies from 0 to infinity.

Note: all the graphics are associated with a popup menu that can be activated pressing the right mouse button over them.