Merge pull request #700 from JuliaControl/Mt

add `Mt_circles` to `nyquistplot`

Author: baggepinnen

src/plotting.jl

@@ -292,22 +292,23 @@ end
 
 @userplot Nyquistplot
 """
-    fig = nyquistplot(sys; Ms_circles=Float64[], unit_circle=false, hz=false, critical_point=-1, kwargs...)
-    nyquistplot(LTISystem[sys1, sys2...]; Ms_circles=Float64[], unit_circle=false, hz=false, critical_point=-1, kwargs...)
+    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
+- `unit_circle`: if the unit circle should be displayed. The Nyquist curve crosses the unit circle at the gain corssover 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)`.
+- `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.
 
 `kwargs` is sent as argument to plot.
 """
 nyquistplot
-@recipe function nyquistplot(p::Nyquistplot; Ms_circles=Float64[], unit_circle=false, hz=false, critical_point=-1)
+@recipe function nyquistplot(p::Nyquistplot; Ms_circles=Float64[], Mt_circles=Float64[], unit_circle=false, hz=false, critical_point=-1)
     systems, w = _processfreqplot(Val{:nyquist}(), p.args...)
     ny, nu = size(systems[1])
     nw = length(w)
@@ -354,6 +355,21 @@ nyquistplot
                             label := "Ms = $(round(Ms, digits=2))"
                             (-1 .+ (1/Ms) * C, (1/Ms) * S)
                         end
+                    end 
+                    for Mt in Mt_circles
+                        @series begin
+                            subplot --> s2i(i,j)
+                            primary := false
+                            linestyle := :dash
+                            linecolor := :gray
+                            seriestype := :path
+                            markershape := :none
+                            label := "Mt = $(round(Mt, digits=2))"
+                            (-1 .+ (1/Mt) * C, (1/Mt) * S)
+                            ct = -Mt^2/(Mt^2-1) # Mt center
+                            rt = Mt/(Mt^2-1)    # Mt radius
+                            ct.+rt.*C, rt.*S
+                        end
                     end                
                     if unit_circle 
                         @series begin

test/test_plots.jl

@@ -15,7 +15,7 @@ function getexamples()
       setPlotScale("dB")
       bodeplot(sys,ws)
     end
-    nyquistgen() = nyquistplot(sysss,ws)
+    nyquistgen() = nyquistplot(sysss,ws, Ms_circles=1.2, Mt_circles=1.2)
     sigmagen() = sigmaplot(sysss,ws)
     #Only siso for now
     nicholsgen() = nicholsplot(tf1,ws)