Merge pull request #952 from JuliaControl/fb2dof

make `feedback2dof` work for any system type

Author: baggepinnen

docs/src/man/creating_systems.md

@@ -34,7 +34,7 @@ Continuous-time transfer function model
 ```
 
 The transfer functions created using this method will be of type `TransferFunction{SisoRational}`.
-For more general expressions, it is often more convenient to define `s = tf("s")`:
+For more general expressions, it is sometimes more convenient to define `s = tf("s")` (only use this approach for low-order systems).:
 #### Example:
 ```julia
 julia> s = tf("s")
@@ -295,10 +295,10 @@ The returned closed-loop system will have a state vector comprised of the state
 ---
 Closed-loop system from reference to output
 ```
-r   ┌─────┐     ┌─────┐
-───►│     │  u  │     │ y
-    │  C  ├────►│  P  ├─┬─►
- -┌►│     │     │     │ │
+    ┌─────┐     ┌─────┐
+r   │     │  u  │     │ y
+──+►│  C  ├────►│  P  ├─┬─►
+ -▲ │     │     │     │ │
   │ └─────┘     └─────┘ │
   │                     │
   └─────────────────────┘
@@ -396,6 +396,32 @@ Here, we have reversed the order of `P` and `C` to get the correct sign of the c
 
 ---
 
+Two degree of freedom control system with feedforward ``F`` and feedback controller ``C``
+
+```
+         +-------+
+         |       |
+   +----->   F   +----+
+   |     |       |    |
+   |     +-------+    |
+   |     +-------+    |    +-------+
+r  |  -  |       |    |    |       |    y
++--+----->   C   +----+---->   P   +---+-->
+      |  |       |         |       |   |
+      |  +-------+         +-------+   |
+      |                                |
+      +--------------------------------+
+```
+
+```math
+Y = (F+C)\dfrac{P}{I + PC}R
+```
+
+Code: `feedback(P,C)*(F+C)` or `feedback2dof(P, C, F)`
+- [`feedback2dof`](@ref)
+
+---
+
 Linear fractional transformation
 
 ```
@@ -445,9 +471,9 @@ I & P
 w_1 \\ w_2
 \end{bmatrix}
 ```
-Code: This function requires the package [RobustAndOptimalControl.jl](https://juliacontrol.github.io/RobustAndOptimalControl.jl/dev/).
+Code: 
 ```julia
-RobustAndOptimalControl.extended_gangoffour(P, C, pos=true)
+extended_gangoffour(P, C, pos=true)
 # For SISO P
 S  = G[1, 1]
 PS = G[1, 2]

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
@@ -442,7 +450,7 @@ end
 feedback2dof(B,A,R,S,T) = tf(conv(B,T),zpconv(A,R,B,S))
 
 """
-    feedback2dof(P::TransferFunction, C::TransferFunction, F::TransferFunction)
+    feedback2dof(P, C, F)
 
 Return the transfer function
 `P(F+C)/(1+PC)`
@@ -463,7 +471,7 @@ r  |  -  |       |    |    |       |    y
 ```
 """
 function feedback2dof(P::TransferFunction{TE}, C::TransferFunction{TE}, F::TransferFunction{TE}) where TE
-    !issiso(P) && error("Feedback not implemented for MIMO systems")
+    issiso(P) || return tf(feedback2dof(ss(P), ss(C), ss(F)))
     timeevol = common_timeevol(P, C, F)
 
     Pn,Pd = numpoly(P)[], denpoly(P)[]
@@ -473,6 +481,10 @@ function feedback2dof(P::TransferFunction{TE}, C::TransferFunction{TE}, F::Trans
     tf(Cd*Pn*Fn + Pn*Cn*Fd, den, timeevol)
 end
 
+function feedback2dof(P,C,F)
+    feedback(P,C)*(F+C)
+end
+
 """
     lft(G, Δ, type=:l)
 

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.

lib/ControlSystemsBase/test/test_connections.jl

@@ -294,6 +294,8 @@ F = tf(1.0, [1,1])
 @test feedback2dof(P0, C, 0*F) == feedback(P0*C)
 @test_nowarn feedback2dof(P0, C, F)
 
+C = pid(1, 0, 1, form=:parallel)
+hinfnorm(minreal(feedback2dof(ss(P0), ss(C*F), ss(F)) - feedback2dof(P0, C*F, F)))[1] < 1e-8
 
 
 G1 = tf([1, 0],[1, 2, 2])