Merge pull request #41 from baggepinnen/rel

prepare for release

Author: baggepinnen

Project.toml

@@ -16,13 +16,13 @@ Symbolics = "0c5d862f-8b57-4792-8d23-62f2024744c7"
 UnPack = "3a884ed6-31ef-47d7-9d2a-63182c4928ed"
 
 [compat]
-ControlSystemIdentification = "2"
-ControlSystemsBase = "1"
+ControlSystemIdentification = "2.4.1"
+ControlSystemsBase = "1.0.1"
 ModelingToolkit = "8.18"
 ModelingToolkitStandardLibrary = "1.5"
 Optim = "1"
 OrdinaryDiffEq = "6"
-RobustAndOptimalControl = "0.4.13"
+RobustAndOptimalControl = "0.4.14"
 SymbolicControlSystems = "0.1.3"
 Symbolics = "4.10"
 UnPack = "1"

README.md

@@ -100,4 +100,26 @@ ModelingToolkit tends to give weird names to states etc., to access variables ea
 julia> P02_named.x
 1-element Vector{Symbol}:
  Symbol("x[1](t)")
-```
+```
+
+
+### Internals: Transformation of non-proper models to proper statespace form
+For some models, ModelingToolkit will fail to produce a proper statespace model (a non-proper model is differentiating the inputs, i.e., it has a numerator degree higher than the denominator degree if represented as a transfer function) when calling `linearize`. For such models, given on the form
+$$\dot x = Ax + Bu + \bar B \dot u$$
+we create the following augmented descriptor model
+```math
+\begin{aligned}
+sX &= Ax + BU + s\bar B U \\
+[X_u &= U]\\
+s(X - \bar B X_u) &= AX + BU \\
+s \begin{bmatrix}I & -\bar B \\ 0 & 0 \end{bmatrix} &= 
+\begin{bmatrix} A & 0 \\ 0 & -I\end{bmatrix}
+\begin{bmatrix}X \\ X_u \end{bmatrix} + 
+\begin{bmatrix} B \\ I_u\end{bmatrix} U \\
+sE &= A_e x_e + B_e u
+\end{aligned}
+```
+where $X_u$ is a new algebraic state variable and $I_u$ is a selector matrix that picks out the differentiated inputs appearing in $\dot u$ (if all inputs appear, $I_u = I$).
+
+This model may be converted to a proper statespace model (if the system is indeed proper) using `DescriptorSystems.dss2ss`.
+All of this is handled automatically by `named_ss(sys)`.

src/ode_system.jl

@@ -206,12 +206,31 @@ function RobustAndOptimalControl.named_ss(
     matrices, ssys = ModelingToolkit.linearize(sys, inputs, outputs; kwargs...)
     symstr(x) = Symbol(string(x))
     unames = symstr.(inputs)
-    if size(matrices.B, 2) == 2length(inputs)
+    nu = length(inputs)
+    ny = length(outputs)
+    if size(matrices.B, 2) == 2nu
+        nx = size(matrices.A, 1)
          # This indicates that input derivatives are present
-         unames = [unames; Symbol.("der_" .* string.(unames))]
+        duinds = findall(any(!iszero, eachcol(matrices.B[:, nu+1:end])))
+        B̄ = matrices.B[:, duinds .+ nu]
+        ndu = length(duinds)
+        B = matrices.B[:, 1:nu]
+        Iu = duinds .== (1:nu)'
+        E = [I(nx) -B̄; zeros(ndu, nx+ndu)]
+
+        Ae = cat(matrices.A, -I(ndu), dims=(1,2))
+        Be = [B; Iu]
+        Ce = [matrices.C zeros(ny, ndu)]
+        De = matrices.D[:, 1:nu]
+        dsys = dss(Ae, E, Be, Ce, De)
+        sys = ss(RobustAndOptimalControl.DescriptorSystems.dss2ss(dsys)[1])
+        # unames = [unames; Symbol.("der_" .* string.(unames))]
+        # sys = ss(matrices...)
+    else
+        sys = ss(matrices...)
     end
     named_ss(
-        ss(matrices...);
+        sys;
         x = symstr.(states(ssys)),
         u = unames,
         y = symstr.(outputs),