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add backward euler discretization #967

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Merged
merged 1 commit into from
Jan 31, 2025
Merged

add backward euler discretization #967

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14 changes: 13 additions & 1 deletion lib/ControlSystemsBase/src/discrete.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -67,6 +67,13 @@
elseif method === :fwdeuler
Ad, Bd, Cd, Dd = (I+Ts*A), Ts*B, C, D
x0map = I(nx)
elseif method === :bwdeuler
Ad = inv(I - Ts*A)
TsB = Ts*B
Bd = (Ad * TsB)
Cd = C*Ad
Dd = Cd * TsB + D
x0map = I(nx)
elseif method === :tustin
a = w_prewarp == 0 ? Ts/2 : tan(w_prewarp*Ts/2)/w_prewarp
a > 0 || throw(DomainError("A positive w_prewarp must be provided for method Tustin"))
Expand All @@ -77,7 +84,7 @@
Dd = a*Cd*B + D
x0map = Matrix{T}(I, nx, nx)
elseif method === :matched
error("NotImplemented: Only `:zoh`, `:foh`, :tustin and `:fwdeuler` implemented so far")
error("NotImplemented: Only `:zoh`, `:foh`, :tustin, `:fwdeuler` and `bwdeuler` implemented so far")

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else
error("Unsupported method: ", method)
end
Expand Down Expand Up @@ -111,6 +118,11 @@
Ac = (A-I)./sys.Ts
Bc = B./sys.Ts
Cc, Dc = C, D
elseif method === :bwdeuler
Ac = (I - inv(A))/sys.Ts
Bc = (A\B) ./ sys.Ts
Cc = C/A
Dc = D - sys.Ts*C*Bc
elseif method === :tustin
a = w_prewarp == 0 ? sys.Ts/2 : tan(w_prewarp*sys.Ts/2)/w_prewarp
a > 0 || throw(DomainError("A positive w_prewarp must be provided for method Tustin"))
Expand Down
4 changes: 2 additions & 2 deletions lib/ControlSystemsBase/test/test_discrete.jl
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Expand Up @@ -77,9 +77,9 @@ sysd = c2d(sys, 1)
@test d2c(sysd) ≈ sys


# forward euler / tustin
# forward euler / tustin / backward euler
@test c2d(C_111, 1, :fwdeuler).A == I + C_111.A
for method in (:fwdeuler, :tustin)
for method in (:fwdeuler, :tustin, :bwdeuler)
@test d2c(c2d(C_111, 0.01, method), method) ≈ C_111 atol = sqrt(eps())
@test d2c(c2d(C_212, 0.01, method), method) ≈ C_212 atol = sqrt(eps())
@test d2c(c2d(C_221, 0.01, method), method) ≈ C_221 atol = sqrt(eps())
Expand Down
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