make feedback handle numbers in signal spec.

lib/ControlSystemsBase/src/connections.jl

@@ -331,6 +331,14 @@ function feedback(sys1::AbstractStateSpace, sys2::AbstractStateSpace;
     if !(isa(Y2, Colon) || allunique(Y2)); @warn "Connecting single output to multiple inputs Y2=$Y2"; end
     if !(isa(U1, Colon) || allunique(U1)); @warn "Connecting multiple outputs to a single input U1=$U1"; end
     if !(isa(U2, Colon) || allunique(U2)); @warn "Connecting a single output to multiple inputs U2=$U2"; end
+    U1 isa Number && (U1 = [U1])
+    Y1 isa Number && (Y1 = [Y1])
+    U2 isa Number && (U2 = [U2])
+    Y2 isa Number && (Y2 = [Y2])
+    W1 isa Number && (W1 = [W1])
+    Z1 isa Number && (Z1 = [Z1])
+    W2 isa Number && (W2 = [W2])
+    Z2 isa Number && (Z2 = [Z2])
 
     if (U1 isa Colon ? size(sys1, 2) : length(U1)) != (Y2 isa Colon ? size(sys2, 1) : length(Y2))
         error("Lengths of U1 ($U1) and Y2 ($Y2) must be equal")
@@ -394,13 +402,13 @@ function feedback(sys1::AbstractStateSpace, sys2::AbstractStateSpace;
         R1 = try
             inv(α*I - s2_D22*s1_D22) # slightly faster than α*inv(I - α*s2_D22*s1_D22)
         catch
-            error("Ill-posed feedback interconnection,  I - α*s2_D22*s1_D22 or I - α*s2_D22*s1_D22 not invertible")
+            error("Ill-posed feedback interconnection,  I - α*s2_D22*s1_D22 not invertible")
         end
 
         R2 = try
             inv(I - α*s1_D22*s2_D22)
         catch
-            error("Ill-posed feedback interconnection,  I - α*s2_D22*s1_D22 or I - α*s2_D22*s1_D22 not invertible")
+            error("Ill-posed feedback interconnection,  I - α*s1_D22*s2_D22 not invertible")
         end
 
         s2_B2R2 = s2_B2*R2
@@ -463,7 +471,7 @@ r  |  -  |       |    |    |       |    y
 ```
 """
 function feedback2dof(P::TransferFunction{TE}, C::TransferFunction{TE}, F::TransferFunction{TE}) where TE
-    !issiso(P) || return tf(feedback2dof(ss(P), ss(C), ss(F)))
+    issiso(P) || return tf(feedback2dof(ss(P), ss(C), ss(F)))
     timeevol = common_timeevol(P, C, F)
 
     Pn,Pd = numpoly(P)[], denpoly(P)[]

lib/ControlSystemsBase/src/pid_design.jl

@@ -131,8 +131,9 @@ The `form` can be chosen as one of the following (determines how the arguments `
 This controller has negative feedback built in, and the closed-loop system from `r` to `y` is thus formed as
 ```
 Cr, Cy = C[1, 1], C[1, 2]
-feedback(P, Cy, pos_feedback=true)*Cr # Alternative 1
-feedback(P, -Cy)*Cr                   # Alternative 2
+feedback(P, Cy, pos_feedback=true)*Cr                    # Alternative 1
+feedback(P, -Cy)*Cr                                      # Alternative 2
+feedback(P, C, U2=2, W2=1, W1=[], pos_feedback=true) # Alternative 3, less pretty but more efficient, returns smaller realization
 ```
 """
 function pid_2dof(args...; state_space = true, Ts = nothing, disc = :tustin, kwargs...)

lib/ControlSystemsBase/src/sensitivity_functions.jl

@@ -156,7 +156,7 @@ T  = G[P.ny+1:end, P.ny+1:end] # Input complimentary sensitivity function
 The gang of four can be plotted like so
 ```julia
 Gcl = extended_gangoffour(G, C) # Form closed-loop system
-bodeplot(Gcl, lab=["S" "CS" "PS" "T"], plotphase=false) |> display # Plot gang of four
+bodeplot(Gcl, lab=["S" "PS" "CS" "T"], plotphase=false) |> display # Plot gang of four
 ```
 Note, the last input of Gcl is the negative of the `PS` and `T` transfer functions from `gangoffour2`. To get a transfer matrix with the same sign as [`G_PS`](@ref) and [`input_comp_sensitivity`](@ref), call `extended_gangoffour(P, C, pos=false)`.
 See `glover_mcfarlane` from RobustAndOptimalControl.jl for an extended example. See also `ncfmargin` and `feedback_control` from RobustAndOptimalControl.jl.