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Update DC motor example to use @mtkmodel #249

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Update DC motor example to use @mtkmodel #249

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111 changes: 46 additions & 65 deletions docs/src/tutorials/dc_motor_pi.md
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Original file line number Diff line number Diff line change
Expand Up @@ -20,82 +20,63 @@ using ModelingToolkitStandardLibrary.Blocks
using OrdinaryDiffEq
using Plots

@parameters t

R = 0.5 # [Ohm] armature resistance
L = 4.5e-3 # [H] armature inductance
k = 0.5 # [N.m/A] motor constant
J = 0.02 # [kg.m²] inertia
f = 0.01 # [N.m.s/rad] friction factor
tau_L_step = -0.3 # [N.m] amplitude of the load torque step
nothing # hide
```

The actual model can now be composed.

```@example dc_motor_pi
@named ground = Ground()
@named source = Voltage()
@named ref = Blocks.Step(height = 1, start_time = 0)
@named pi_controller = Blocks.LimPI(k = 1.1, T = 0.035, u_max = 10, Ta = 0.035)
@named feedback = Blocks.Feedback()
@named R1 = Resistor(R = R)
@named L1 = Inductor(L = L)
@named emf = EMF(k = k)
@named fixed = Fixed()
@named load = Torque()
@named load_step = Blocks.Step(height = tau_L_step, start_time = 3)
@named inertia = Inertia(J = J)
@named friction = Damper(d = f)
@named speed_sensor = SpeedSensor()

connections = [connect(fixed.flange, emf.support, friction.flange_b)
connect(emf.flange, friction.flange_a, inertia.flange_a)
connect(inertia.flange_b, load.flange)
connect(inertia.flange_b, speed_sensor.flange)
connect(load_step.output, load.tau)
connect(ref.output, feedback.input1)
connect(speed_sensor.w, :y, feedback.input2)
connect(feedback.output, pi_controller.err_input)
connect(pi_controller.ctr_output, :u, source.V)
connect(source.p, R1.p)
connect(R1.n, L1.p)
connect(L1.n, emf.p)
connect(emf.n, source.n, ground.g)]

@named model = ODESystem(connections, t,
systems = [
ground,
ref,
pi_controller,
feedback,
source,
R1,
L1,
emf,
fixed,
load,
load_step,
inertia,
friction,
speed_sensor,
])
nothing # hide
@mtkmodel dcmotor begin
@parameters begin
R = 0.5 # [Ohm] armature resistance
L = 4.5e-3 # [H] armature inductance
k = 0.5 # [N.m/A] motor constant
J = 0.02 # [kg.m²] inertia
f = 0.01 # [N.m.s/rad] friction factor
tau_L_step = -0.3 # [N.m] amplitude of the load torque step
end
@components begin
ground = Ground()
source = Voltage()
ref = Blocks.Step(height = 1, start_time = 0)
pi_controller = Blocks.LimPI(k = 1.1, T = 0.035, u_max = 10, Ta = 0.035)
feedback = Blocks.Feedback()
R1 = Resistor(R = R)
L1 = Inductor(L = L)
emf = EMF(k = k)
fixed = Fixed()
load = Torque()
load_step = Blocks.Step(height = tau_L_step, start_time = 3)
inertia = Inertia(J = J)
friction = Damper(d = f)
speed_sensor = SpeedSensor()
end
@equations begin
connect(fixed.flange, emf.support, friction.flange_b)
connect(emf.flange, friction.flange_a, inertia.flange_a)
connect(inertia.flange_b, load.flange)
connect(inertia.flange_b, speed_sensor.flange)
connect(load_step.output, load.tau)
connect(ref.output, feedback.input1)
connect(speed_sensor.w, :y, feedback.input2)
connect(feedback.output, pi_controller.err_input)
connect(pi_controller.ctr_output, :u, source.V)
connect(source.p, R1.p)
connect(R1.n, L1.p)
connect(L1.n, emf.p)
connect(emf.n, source.n, ground.g)
end
end
nothing #hide
```

Now the model can be simulated. Typical rotational mechanical systems are described via `DAE`
(differential algebraic equations), however in this case, ModelingToolkit can simplify the model enough
so that it can be represented as a system of `ODEs` (ordinary differential equations).

```@example dc_motor_pi
sys = structural_simplify(model)
@mtkbuild sys = dcmotor()
prob = ODEProblem(sys, [], (0, 6.0))
sol = solve(prob, Rodas4())

p1 = Plots.plot(sol.t, sol[inertia.w], ylabel = "Angular Vel. in rad/s",
p1 = Plots.plot(sol.t, sol[sys.inertia.w], ylabel = "Angular Vel. in rad/s",
label = "Measurement", title = "DC Motor with Speed Controller")
Plots.plot!(sol.t, sol[ref.output.u], label = "Reference")
p2 = Plots.plot(sol.t, sol[load.tau.u], ylabel = "Disturbance in Nm", label = "")
Plots.plot!(sol.t, sol[sys.ref.output.u], label = "Reference")
p2 = Plots.plot(sol.t, sol[sys.load.tau.u], ylabel = "Disturbance in Nm", label = "")
Plots.plot(p1, p2, layout = (2, 1))
```

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