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Modify LQG speed control of DC motor example #418

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Jan 16, 2021
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Modify LQG speed control of DC motor example #418

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16 changes: 9 additions & 7 deletions example/dc_motor_lqg_design.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -4,7 +4,7 @@ Example for designing an LQG speed controller for an electrical DC motor.
"""

# Constants
Ke = 0.006156 # electromotive force constant in V/rpm
Ke = 0.006156 # electromotive force constant in V/rpm
Kt = 0.0728 # Torque constant (Nm/A)
J = 2.8*700e-6; # Inertia of motor plus load (kgm^2)
Rel = 0.11; # DC motor resistance (Ω)
Expand All @@ -29,8 +29,8 @@ function motor(Ke, Kt, L, R, J, b=1e-3)
end

p60 = motor(Ke, Kt, L, Rel, J)
stepplot(p60, 0.2, 0.001)
bodeplot(p60)
f1 = stepplot(p60)
f2 = bodeplot(p60)

# LQR control
Q = [1. 0;
Expand All @@ -39,7 +39,7 @@ Q = [1. 0;
R = 20.
K = lqr(p60.A, p60.B, Q, R)
# needs to be modified if Nbar is not a scalar
Nbar = 1. / (p60.D - (p60.C - p60.D*K) * inv(p60.A - p60.B*K) * p60.B)
Nbar = 1. ./ (p60.D - (p60.C - p60.D*K) * inv(p60.A - p60.B*K) * p60.B)

# Kalman filter based observer
Vd = [10. 0 # covariance of the speed estimation
Expand All @@ -49,6 +49,8 @@ G = LQG(p60, Q, mat(R), Vd, mat(Vn))
Gcl = G[:cl]
T = G[:T]
S = G[:S];
f1 = sigmaplot([S,T],logspace(-3,3,1000))
f2 = stepplot(Gcl, label=["Closed loop system using LQG"])
Plots.plot(f1,f2)

# 1000 logarithmically spaced values from -3 to 3
f3 = sigmaplot([S,T], exp10.(range(-3, stop=3, length=1000)))
f4 = stepplot(Gcl, label=["Closed loop system using LQG"])
Plots.plot(f1, f2, f3, f4, layout=(2,2), size=(800, 600))