plot zeros and poles of a linear system - Maple Help

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DynamicSystems[ZeroPolePlot] - plot zeros and poles of a linear system

 Calling Sequence ZeroPolePlot (sys, opts)

Parameters

 sys - System; system object to plot opts - (optional) equation(s) of the form option = value; specify options for the ZeroPolePlot command

Description

 • The ZeroPolePlot command plots the zeros and poles of a subsystem of sys, a System object. The zeros correspond to the roots of the numerator of the transfer-function of sys, the poles to the roots of the denominator.
 • The roots are plotted on the complex plane. The horizontal axis corresponds to the real part of the roots, the vertical axis to the imaginary part.
 • Zeros are plotted as circles, poles are plotted as crosses.
 • The default plot-option axes is set to boxed; this permits viewing a pole (cross) that would otherwise lie on an axis.
 • For a multi-input/multi-output system, some or all of the subsystems can be selected. The option subsystem selects the subsystems.
 • The ZeroPolePlot command takes all standard plot,options. For the special syntax that ZeroPolePlot uses with the color option, see below.

Examples

 > $\mathrm{with}\left(\mathrm{DynamicSystems}\right):$

Create a system with two inputs and two outputs:

 > $\mathrm{sys}:=\mathrm{TransferFunction}\left(⟨⟨\frac{s}{\left(s+1+I\cdot 10\right)\left(s+1-I\cdot 10\right)}|\frac{1}{s+1}⟩,⟨\frac{1}{\left(s+3-I\cdot 7\right)\left(s+3+I\cdot 7\right)}|\frac{1}{\left(s+3\right)\left(s+5\right)}⟩⟩\right):$
 > $\mathrm{sys}:-\mathrm{tf}$
 $\left[\begin{array}{cc}\frac{{s}}{{{s}}^{{2}}{+}{2}{}{s}{+}{101}}& \frac{{1}}{{s}{+}{1}}\\ \frac{{1}}{{{s}}^{{2}}{+}{6}{}{s}{+}{58}}& \frac{{1}}{{{s}}^{{2}}{+}{8}{}{s}{+}{15}}\end{array}\right]$ (1)
 > $\mathrm{ZeroPolePlot}\left(\mathrm{sys},\mathrm{color}=\left[\mathrm{red},\mathrm{green},\mathrm{blue},\mathrm{brown}\right],\mathrm{title}="Zeros and Poles"\right)$
 > $\mathrm{ZeroPolePlot}\left(\mathrm{sys},\mathrm{subsystem}=\left[1,1\right],\mathrm{color}=\mathrm{red},\mathrm{title}="System \left[1,1\right]"\right)$
 > $\mathrm{ZeroPolePlot}\left(\mathrm{sys},\mathrm{subsystem}=\left[\left[1,2\right],\left[2,1\right]\right],\mathrm{color}=\left[\mathrm{red},\mathrm{blue}\right],\mathrm{title}="Systems \left[1,2\right] and \left[2,1\right]"\right)$
 > $\mathrm{dx}:=\mathrm{ZeroPolePlot}\left(\mathrm{sys},\mathrm{output}=\mathrm{data}\right)$
 ${\mathrm{dx}}{:=}\left[\left[\left[{0.}\right]{,}\left[{-}{1.000000000}{-}{10.00000000}{}{I}{,}{-}{1.}{+}{10.00}{}{I}\right]\right]{,}\left[\left[{}\right]{,}\left[{-}{3.000000000}{-}{7.000000000}{}{I}{,}{-}{3.}{+}{7.000000000}{}{I}\right]\right]{,}\left[\left[{}\right]{,}\left[{-}{1.}\right]\right]{,}\left[\left[{}\right]{,}\left[{-}{5.}{,}{-}{3.000000000}\right]\right]\right]$ (2)

The commands to create the plot from the Plotting Guide are

 > $\mathrm{sys_z}:=\mathrm{TransferFunction}\left(\frac{40\left(3z-4\right)}{200{z}^{3}-420{z}^{2}+300z-70},\mathrm{discrete},\mathrm{sampletime}=0.1\right):$
 > $\mathrm{ZeroPolePlot}\left(\mathrm{sys_z},\mathrm{color}=\mathrm{red},\mathrm{title}="Discrete System"\right)$