National Instruments 370753C-01 rlocus( )

Chapter 5 Classical Feedback Analysis

rlocus( )

rlroots=rlocus(sys,K,{xmin,xmax,ymin,ymax,pattern,graph})

rlocus(sys,{xmin,xmax,ymin,ymax,pattern})# (interactive)

The rlocus( ) function computes and draws root locus diagrams for

continuous-time and discrete-time SISO systems. The first syntax, in

which a vector of gain values is specified, generates a plot showing the

closed-loop pole locations for each gain. In the Graphics window, the

complete locus is drawn as a solid line, with os marking the location of

zeros and xs delineating open-loop pole locations. The second syntax

brings up a window through which you can interactively modify the

closed-loop gain and see the corresponding pole locations change on

the locus.

A grid showing pole stability range can be invoked with the pattern

keyword. The optional keywords specifying maximum and minimum x and

y values can be used to restrict the range of the selected s- or z-plane. These

can be changed interactively if the interactive syntax is used. Click

RECOMPUTE to activate rate changes.

Example 5-1 shows how to plot the rool locus created in Example2-9,

A Comparison of Several Discretization Methods.

Example 5-1 Plotting a Root Locus

H = system(0.5*polynomial([-0.36]),

makepoly([1,2.79,2.74,1.11,0.16]));

You can create and graph a root locus, scaling the range of the

real-imaginary plane as follows:

rlocus(H, {xmin=-2, xmax=0, ymax=0.5, ymin=-0.5})

These functions give the results shown in Figure 5-3. The large xs on the

plot correspond to the open-loop pole locations you found for this system

in Example 4-1, Using poles( ) with a System in Transfer Function Form,

and the zeros correspond to the single zero at –0.36.