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DynamicSystems

 NyquistPlot
 plot frequency response in complex plane

 Calling Sequence NyquistPlot(sys, opts)

Parameters

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

Options

 • In addition to the following options, the NyquistPlot command takes many of the standard plot options; see plot,options.
 • frequencies = list or Vector of nonnegative values
 Specifies frequencies to be used to generate a frequency response. The list or Vector must be sorted, from smallest to largest. The units are determined by the hertz option.
 • hertz = truefalse
 Specifies the unit of frequency. If this value is set to true, the unit of frequency is Hertz; otherwise, it is radians per second. The default value is assigned by DynamicSystems[SystemOptions].
 • legend = list or element
 Specifies the legend for the plot. A list specifies a legend entry for each subsystem. The elements in the list correspond to the Matrix of subsystems taken in Fortran order. An element can be used for a one-by-one Matrix of subsystems. The default is no legend.
 • linearfreq = truefalse
 Specifies the frequency scale. If this value is set to $\mathrm{true}$, the scale is linear; otherwise, by default, the scale is logarithmic.
 • method = function or matrix
 Selects the method used to compute the frequency response. The function method generates the transfer functions of sys and evaluates them at the selected frequencies. The matrix method generates the state-space matrices of sys and evaluates the expression $C\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}.\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{\left(Iz-A\right)}^{\left(-1\right)}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}.\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}B+\mathrm{D}$ at specific values of $z$. The default is to use the function method for frequency-domain systems (TF, Coeff, and ZPK), and to use the matrix method for time-domain systems (DE and SS).
 • numpoints = nonnegative integer
 Specifies the number of points. The default is 100.
 • output = plot, data, or list of same
 Specifies the output of NyquistPlot. The name plot returns the plot structure. The name data returns the data. A list of those names returns a corresponding list of plots and data. The default is plot.
 The data is returned as a Matrix for a single selected subsystem and as a list of Matrices for multiple selected subsystems. Each Matrix has two columns: the first is the horizontal component and the second is the vertical component.
 • parameters = set(name = complexcons) or list(name = complexcons)
 Specifies numeric values for parameters in sys. These values override those specified by the parameters field of the system object, which in turn override the settings in in SystemOptions(parameters). The numeric value on the right-hand side of each equation is substituted for the name on the left-hand side in the expressions that define the model. No checking is done during the substitution to determine whether the substituted value is valid. For example, a complex value can be substituted for the coefficient of a polynomial. If the complex value had been originally assigned to the model at creation, a warning would be generated.
 • range = range( realcons )
 Specifies the frequency range to plot. The default setting is to compute an appropriate range based on the locations of the zeros and poles of the transfer functions of the selected subsystems. Similarly, if the right-hand side of range is infinity, a maximum is computed based on the zeros and poles. The units are specified by the hertz option.
 • subsystem = [ posint, posint ] or list of same
 Selects subsystems of a multi-input/multi-output system. Each selected subsystem is specified as a list of two indices: the first specifies the output and the second specifies the input. For example, $\left[1,2\right]$ specifies the subsystem from the second input to the first output. A list of lists selects multiple subsystems. The default setting is to select all subsystems, using Fortran ordering. That is, for an m x n system, the default list of subsystems is [ [1,1], ..., [m,1], ..., [1,n], ..., [m,n] ].

Description

 • The NyquistPlot command plots, in the complex plane, the frequency response of the transfer functions of the subsystems of sys, a system object.
 • If sys is a continuous system, its s-domain transfer function is computed and then converted to the real frequency domain using the transformation s -> I*omega, where omega is the angular frequency.
 • If sys is a discrete system, its z-domain transfer function is computed and then converted to the real frequency domain using the transformation z -> exp(I*omega*Ts), where omega is the angular frequency and Ts is the sample time.
 • The NyquistPlot command takes all standard plot,options.

Examples

 > $\mathrm{with}\left(\mathrm{DynamicSystems}\right):$
 > $\mathrm{sys}≔\mathrm{ZeroPoleGain}\left(\left[0,1\right],\left[2,4,6\right],1\right):$
 > $\mathrm{NyquistPlot}\left(\mathrm{sys}\right)$
 > $\mathrm{tx1}≔\frac{s}{\left(s+1+I\cdot 10\right)\left(s+1-I\cdot 10\right)}:$
 > $\mathrm{tx2}≔\frac{1}{s+1}:$
 > $\mathrm{tx3}≔\frac{1}{\left(s+1-I\cdot 10\right)\left(s+1+I\cdot 10\right)}:$
 > $\mathrm{tx4}≔\frac{1}{s-10}:$
 > $\mathrm{sys}≔\mathrm{TransferFunction}\left(⟨⟨\mathrm{tx1}|\mathrm{tx2}⟩,⟨\mathrm{tx3}|\mathrm{tx4}⟩⟩\right):$
 > $\mathrm{sys}:-\mathrm{tf}$
 $\left[\begin{array}{cc}\frac{{s}}{{{s}}^{{2}}{+}{2}{}{s}{+}{101}}& \frac{{1}}{{s}{+}{1}}\\ \frac{{1}}{{{s}}^{{2}}{+}{2}{}{s}{+}{101}}& \frac{{1}}{{s}{-}{10}}\end{array}\right]$ (1)

This is the command to create the 2-D plot from the Plotting Guide.

 > $\mathrm{NyquistPlot}\left(\mathrm{sys},\mathrm{color}=\left[\mathrm{red},\mathrm{green},\mathrm{blue},\mathrm{brown}\right],\mathrm{title}="Nyquist Plot"\right)$
 >