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Minor formatting #9

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Apr 19, 2024
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Minor formatting #9

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33 changes: 17 additions & 16 deletions src/glider.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -27,32 +27,33 @@ function glider_model(nh)

model = Model()

@variable(model, step >= 0.0, start=1/nh)
# State variables
@variable(model, 0.0 <= x[k=0:nh], start=x_0 + vx_0*(k/nh))
@variable(model, y[k=0:nh], start=y_0 + (k/nh)*(y_f - y_0))
@variable(model, 0.0 <= vx[k=0:nh], start=vx_0)
@variable(model, vy[k=0:nh], start=vy_0)
# Control variables
@variable(model, cL_min <= cL[k=0:nh] <= cL_max, start=cL_max/2.0)
@variables(model, begin
0 <= t_f, (start=1.0)
0.0 <= x[k=0:nh], (start=x_0 + vx_0*(k/nh))
y[k=0:nh], (start=y_0 + (k/nh)*(y_f - y_0))
0.0 <= vx[k=0:nh], (start=vx_0)
vy[k=0:nh], (start=vy_0)
cL_min <= cL[k=0:nh] <= cL_max, (start=cL_max/2.0)
end)

@objective(model, Max, x[nh])

@expressions(model, begin
r[i=0:nh], (x[i]/r_0 - 2.5)^2
u[i=0:nh], u_c*(1 - r[i])*exp(-r[i])
w[i=0:nh], vy[i] - u[i]
v[i=0:nh], sqrt(vx[i]^2 + w[i]^2)
D[i=0:nh], 0.5*(c0+c1*cL[i]^2)*rho*S*v[i]^2
L[i=0:nh], 0.5*cL[i]*rho*S*v[i]^2
step, t_f / nh
r[i=0:nh], (x[i]/r_0 - 2.5)^2
u[i=0:nh], u_c*(1 - r[i])*exp(-r[i])
w[i=0:nh], vy[i] - u[i]
v[i=0:nh], sqrt(vx[i]^2 + w[i]^2)
D[i=0:nh], 0.5*(c0+c1*cL[i]^2)*rho*S*v[i]^2
L[i=0:nh], 0.5*cL[i]*rho*S*v[i]^2
vx_dot[i=0:nh], (-L[i]*(w[i]/v[i]) - D[i]*(vx[i]/v[i]))/m
vy_dot[i=0:nh], (L[i]*(vx[i]/v[i]) - D[i]*(w[i]/v[i]))/m - g
end)

# Dynamics
@constraints(model, begin
x_eqn[j=1:nh], x[j] == x[j-1] + 0.5 * step * (vx[j] + vx[j-1])
y_eqn[j=1:nh], y[j] == y[j-1] + 0.5 * step * (vy[j] + vy[j-1])
x_eqn[j=1:nh], x[j] == x[j-1] + 0.5 * step * (vx[j] + vx[j-1])
y_eqn[j=1:nh], y[j] == y[j-1] + 0.5 * step * (vy[j] + vy[j-1])
vx_eqn[j=1:nh], vx[j] == vx[j-1] + 0.5 * step * (vx_dot[j] + vx_dot[j-1])
vy_eqn[j=1:nh], vy[j] == vy[j-1] + 0.5 * step * (vy_dot[j] + vy_dot[j-1])
end)
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84 changes: 27 additions & 57 deletions src/robot.jl
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Expand Up @@ -19,68 +19,38 @@ function robot_model(nh)

model = Model()

@variable(model, 0 <= rho[k=1:nh+1] <= L, start=rho0)
@variable(model, -pi <= the[k=1:nh+1] <= pi, start=2*pi/3*(k/nh)^2)
@variable(model, 0 <= phi[k=1:nh+1] <= pi, start=phi0)
# Derivatives
@variable(model, rho_dot[k=1:nh+1], start=0.0)
@variable(model, the_dot[k=1:nh+1], start=4*pi/3*(k/nh))
@variable(model, phi_dot[k=1:nh+1], start=0.0)
# Control
@variable(model, -max_u_rho <= u_rho[1:nh+1] <= max_u_rho, start=0.0)
@variable(model, -max_u_the <= u_the[1:nh+1] <= max_u_the, start=0.0)
@variable(model, -max_u_phi <= u_phi[1:nh+1] <= max_u_phi, start=0.0)
# Steps and final time
@variable(model, step >= 0.0)
# The moments of inertia
@variable(model, I_the[1:nh+1], start=((L-rho0)^3+rho0^3)*(sin(phi0))^2/3.0)
@variable(model, I_phi[1:nh+1], start=((L-rho0)^3+rho0^3)/3.0)
@variables(model, begin
0 <= rho[k=1:nh+1] <= L, (start=rho0)
-pi <= the[k=1:nh+1] <= pi, (start=2*pi/3*(k/nh)^2)
0 <= phi[k=1:nh+1] <= pi, (start=phi0)
rho_dot[k=1:nh+1], (start=0.0)
the_dot[k=1:nh+1], (start=4*pi/3*(k/nh))
phi_dot[k=1:nh+1], (start=0.0)
-max_u_rho <= u_rho[1:nh+1] <= max_u_rho, (start=0.0)
-max_u_the <= u_the[1:nh+1] <= max_u_the, (start=0.0)
-max_u_phi <= u_phi[1:nh+1] <= max_u_phi, (start=0.0)
tf >= 0.0, (start=1.0)
end)

@objective(model, Min, step * nh)
@objective(model, Min, tf)

# Physical equations
@constraint(
model,
[i=1:nh+1],
I_the[i] == ((L-rho[i])^3+rho[i]^3)*(sin(phi[i]))^2/3.0
)
@constraint(
model,
[i=1:nh+1],
I_phi[i] == ((L-rho[i])^3+rho[i]^3)/3.0
)
@expressions(model, begin
step, tf /nh
I_the[i=1:nh+1], ((L-rho[i])^3+rho[i]^3)*(sin(phi[i]))^2/3.0
I_phi[i=1:nh+1], ((L-rho[i])^3+rho[i]^3)/3.0
end)

# Dynamics
@constraint(
model,
[j=2:nh+1],
rho[j] == rho[j-1] + 0.5 * step * (rho_dot[j] + rho_dot[j-1]),
)
@constraint(
model,
[j=2:nh+1],
phi[j] == phi[j-1] + 0.5 * step * (phi_dot[j] + phi_dot[j-1]),
)
@constraint(
model,
[j=2:nh+1],
the[j] == the[j-1] + 0.5 * step * (the_dot[j] + the_dot[j-1]),
)
@constraints(model, begin
[j=2:nh+1], rho[j] == rho[j-1] + 0.5 * step * (rho_dot[j] + rho_dot[j-1])
[j=2:nh+1], phi[j] == phi[j-1] + 0.5 * step * (phi_dot[j] + phi_dot[j-1])
[j=2:nh+1], the[j] == the[j-1] + 0.5 * step * (the_dot[j] + the_dot[j-1])
[j=2:nh+1], rho_dot[j] == rho_dot[j-1] + 0.5 * step * (u_rho[j] + u_rho[j-1]) / L
[j=2:nh+1], the_dot[j] == the_dot[j-1] + 0.5 * step * (u_the[j] / I_the[j] + u_the[j-1] / I_the[j-1])
[j=2:nh+1], phi_dot[j] == phi_dot[j-1] + 0.5 * step * (u_phi[j] / I_phi[j] + u_phi[j-1] / I_phi[j-1])
end)

@constraint(
model,
[j=2:nh+1],
rho_dot[j] == rho_dot[j-1] + 0.5 * step * (u_rho[j] + u_rho[j-1]) / L
)
@constraint(
model,
[j=2:nh+1],
the_dot[j] == the_dot[j-1] + 0.5 * step * (u_the[j] / I_the[j] + u_the[j-1] / I_the[j-1])
)
@constraint(
model,
[j=2:nh+1],
phi_dot[j] == phi_dot[j-1] + 0.5 * step * (u_phi[j] / I_phi[j] + u_phi[j-1] / I_phi[j-1])
)
# Boundary condition
@constraints(
model, begin
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12 changes: 6 additions & 6 deletions src/rocket.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -22,16 +22,16 @@ function rocket_model(nh)
model = Model()

@variables(model, begin
0.0 <= h[i=0:nh], (start=1.0)
0.0 <= v[i=0:nh], (start=i/nh*(1.0 - i/nh))
m_f <= m[i=0:nh] <= m_0, (start=(m_f - m_0)*(i/nh) + m_0)
1.0 <= h[i=0:nh], (start=1.0)
0.0 <= v[i=0:nh], (start=i/nh*(1.0 - i/nh))
m_f <= m[i=0:nh] <= m_0, (start=(m_f - m_0)*(i/nh) + m_0)
0.0 <= T[i=0:nh] <= T_max, (start=T_max/2.0)
0.0 <= step, (start=1/nh)
0.0 <= step, (start=1/nh)
end)

@expressions(model, begin
D[i=0:nh], D_c*v[i]^2*exp(-h_c*(h[i] - h_0))/h_0
g[i=0:nh], g_0 * (h_0 / h[i])^2
D[i=0:nh], D_c*v[i]^2*exp(-h_c*(h[i] - h_0))/h_0
g[i=0:nh], g_0 * (h_0 / h[i])^2
dh[i=0:nh], v[i]
dv[i=0:nh], (T[i] - D[i] - m[i]*g[i]) / m[i]
dm[i=0:nh], -T[i]/c
Expand Down
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