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julia 0.7 | ||
Plots | ||
Polynomials | ||
LaTeXStrings | ||
DelayDiffEq | ||
OrdinaryDiffEq | ||
IterTools | ||
Colors | ||
DSP | ||
Interpolations |
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using Plots | ||
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# Frequency domain analysis of a simple system with time delays | ||
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s = tf("s") | ||
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P = delay(0.2) * ss(1/(s+1)) | ||
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K = 3; Ti = 0.3; | ||
C = DelayLtiSystem(ss(K*(1 + 1/s))) | ||
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ω = exp10.(LinRange(-2,2,500)) | ||
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L_fr = freqresp(C*P, ω)[:] | ||
plot(real(L_fr), imag(L_fr), xlim=[-2,1], ylim=[-2,2], title="Nyquist curve") | ||
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G_yd = feedback(P, C) | ||
plot(ω, abs.(freqresp(G_yd, ω)[:]), xscale=:log, yscale=:log, | ||
title="Transfer function from load disturbances to output.") |
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using ControlSystems, Plots | ||
gr() | ||
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sys = feedback(1.0, ss(-1.0, 2, 1, 0) * (delay(2.0) + delay(3.0) + delay(2.5))) | ||
sys = feedback(ss(-1.0, 1, 1, 0), delay(1.0)) | ||
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t = 0:0.02:8 | ||
@time y, t, x = lsim(sys, t-> [t>=0 ? 1.0 : 0.0], t) | ||
@time y, t, x = lsim(sys, [1.0], t) | ||
@time y, t, x = lsim(sys, (out, t) -> (out .= (t>=0 ? 1.0 : 0.0)), t) | ||
@time y, t, x = lsim(sys, (out, t) -> (out[1] = (t>=0 ? 1.0 : 0.0)), t) | ||
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function u0(out,t) | ||
if t > 0 | ||
out[1] = 1 | ||
else | ||
out[1] = 0 | ||
end | ||
return | ||
end | ||
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@time y, t, x = lsim(sys, u0, t) | ||
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plot(t, y') | ||
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s = tf("s") | ||
P = delay(2.6)*ss((s+3.0)/(s^2+0.3*s+1)) | ||
C = 0.06 * ss(1.0 + 1/s); | ||
P*C | ||
T = feedback(P*C,1.0) | ||
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t = 0:0.1:70 | ||
y, t, x = lsim(T, t -> (t<0 ? 0 : 1 ), t) | ||
plot(t, y, c = :blue) | ||
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w = 10 .^ (-2:0.01:2) | ||
marginplot(P*C, w) | ||
marginplot(P*C) | ||
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notch = ss(tf([1, 0.2, 1],[1, .8, 1])); | ||
C = ss(0.05 * (1 + 1/s)); | ||
Tnotch = feedback(P*C*notch, 1.0) | ||
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stepplot(Tnotch) | ||
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y, t, x = step(C, method=:zoh) | ||
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y2, t2, x2 = step(Tnotch) | ||
stepplot(Tnotch) | ||
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stepplot(Tnotch, 40, 0.1) | ||
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stepplot(T, 100) | ||
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G = delay(5)/(s+1) | ||
T = feedback(G, 0.5) | ||
w = 10 .^ (-2:0.01:3) | ||
bodeplot(T, w, plotphase=false) | ||
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# Test conversion, promotion | ||
delay(1,Int64) + 3.5 | ||
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G = 1 + 0.5 * delay(3) | ||
w = 10 .^(-2:0.001:2) | ||
bodeplot(G, w, plotphase=false) | ||
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G = delay(1) * ((0.8*s^2+s+2)/(s^2+s)) | ||
T = feedback(G,1) | ||
# Not possible with direct term | ||
stepplot(T) | ||
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bodeplot(T) | ||
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G = 1/(s+1) + delay(4) | ||
T = feedback(1,G) | ||
# Not possible to lsim with direct term | ||
stepplot(T) | ||
bodeplot(T) | ||
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s = tf("s") |
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