Plotting functions

fig = bodeplot(sys, args...)
bodeplot(LTISystem[sys1, sys2...], args...; plotphase=true, balance = true, kwargs...)

Create a Bode plot of the LTISystem(s). A frequency vector w can be optionally provided. To change the Magnitude scale see setPlotScale. The default magnitude scale is "log10" (absolute scale).

• If hz=true, the plot x-axis will be displayed in Hertz, the input frequency vector is still treated as rad/s.
• balance: Call balance_statespace on the system before plotting.
• adjust_phase_start: If true, the phase will be adjusted so that it starts at -90*intexcess degrees, where intexcess is the integrator excess of the system.
• adaptive: If true, an adaptive frequency grid is used in order to keep the number of plotted points low, while resolving features in the frequency response well. If a manually provided frequency vector is used, this may be downsampled before plotting.

kwargs is sent as argument to RecipesBase.plot.

fig = gangoffourplot(P::LTISystem, C::LTISystem; minimal=true, plotphase=false, Ms_lines = [1.0, 1.25, 1.5], Mt_lines = [], sigma = true, kwargs...)

Gang-of-Four plot.

sigma determines whether a sigmaplot is used instead of a bodeplot for MIMO S and T. kwargs are sent as argument to RecipesBase.plot.

fig = marginplot(sys::LTISystem [,w::AbstractVector]; hz=false, balance=true, kwargs...)
marginplot(sys::Vector{LTISystem}, w::AbstractVector; hz=false, balance=true, kwargs...)

Plot all the amplitude and phase margins of the system(s) sys.

• A frequency vector w can be optionally provided.
• hz: If true, the plot x-axis will be displayed in Hertz, the input frequency vector is still treated as rad/s.
• balance: Call balance_statespace on the system before plotting.
• adjust_phase_start: If true, the phase will be adjusted so that it starts at -90*intexcess degrees, where intexcess is the integrator excess of the system.

kwargs is sent as argument to RecipesBase.plot.

fig = nicholsplot{T<:LTISystem}(systems::Vector{T}, w::AbstractVector; kwargs...)

Create a Nichols plot of the LTISystem(s). A frequency vector w can be optionally provided.

Keyword arguments:

text = true
Gains = [12, 6, 3, 1, 0.5, -0.5, -1, -3, -6, -10, -20, -40, -60]
pInc = 30
sat = 0.4
val = 0.85
fontsize = 10

pInc determines the increment in degrees between phase lines.

sat ∈ [0,1] determines the saturation of the gain lines

val ∈ [0,1] determines the brightness of the gain lines

Additional keyword arguments are sent to the function plotting the systems and can be used to specify colors, line styles etc. using regular RecipesBase.jl syntax

This function is based on code subject to the two-clause BSD licence Copyright 2011 Will Robertson Copyright 2011 Philipp Allgeuer

fig = nyquistplot(sys;                Ms_circles=Float64[], Mt_circles=Float64[], unit_circle=false, hz=false, critical_point=-1, kwargs...)
nyquistplot(LTISystem[sys1, sys2...]; Ms_circles=Float64[], Mt_circles=Float64[], unit_circle=false, hz=false, critical_point=-1, kwargs...)

Create a Nyquist plot of the LTISystem(s). A frequency vector w can be optionally provided.

• unit_circle: if the unit circle should be displayed. The Nyquist curve crosses the unit circle at the gain crossover frequency.
• Ms_circles: draw circles corresponding to given levels of sensitivity (circles around -1 with radii 1/Ms). Ms_circles can be supplied as a number or a vector of numbers. A design staying outside such a circle has a phase margin of at least 2asin(1/(2Ms)) rad and a gain margin of at least Ms/(Ms-1). See also margin_bounds, Ms_from_phase_margin and Ms_from_gain_margin.
• Mt_circles: draw circles corresponding to given levels of complementary sensitivity. Mt_circles can be supplied as a number or a vector of numbers.
• critical_point: point on real axis to mark as critical for encirclements
• If hz=true, the hover information will be displayed in Hertz, the input frequency vector is still treated as rad/s.
• balance: Call balance_statespace on the system before plotting.

kwargs is sent as argument to plot.

fig = pzmap(fig, system, args...; hz = false, kwargs...)

Create a pole-zero map of the LTISystem(s) in figure fig, args and kwargs will be sent to the scatter plot command.

To customize the unit-circle drawn for discrete systems, modify the line attributes, e.g., linecolor=:red.

If hz is true, all poles and zeros are scaled by 1/2π.

rgaplot(sys, args...; hz=false)
rgaplot(LTISystem[sys1, sys2...], args...; hz=false, balance=true)

Plot the relative-gain array entries of the LTISystem(s). A frequency vector w can be optionally provided.

• If hz=true, the plot x-axis will be displayed in Hertz, the input frequency vector is still treated as rad/s.
• balance: Call balance_statespace on the system before plotting.

kwargs is sent as argument to Plots.plot.

setPlotScale(str)

Set the default scale of magnitude in bodeplot and sigmaplot. str should be either "dB" or "log10". The default scale if none is chosen is "log10".

sigmaplot(sys, args...; hz=false balance=true, extrema)
sigmaplot(LTISystem[sys1, sys2...], args...; hz=false, balance=true, extrema)

Plot the singular values of the frequency response of the LTISystem(s). A frequency vector w can be optionally provided.

• If hz=true, the plot x-axis will be displayed in Hertz, the input frequency vector is still treated as rad/s.
• balance: Call balance_statespace on the system before plotting.
• extrema: Only plot the largest and smallest singular values.

kwargs is sent as argument to Plots.plot.

rlocusplot(siso_sys)
rlocusplot(sys::StateSpace, K::Matrix; output=false)

Plot the root locus of a system under feedback.

If a SISO system is passed, the feedback gain K is a scalar that ranges from 0 to K (if provided). If a StateSpace system is passed, K is a matrix that defines the feedback gain, and the poles are computed as K ranges from 0*K to 1*K. In this case, K is assumed to be a state-feedback matrix of dimension (nu, nx). To compute the poles for output feedback, pass output = true and K of dimension (nu, ny).