def inequality(prob, obj):
r = prob.states_all_section(0)
vr = prob.states_all_section(1)
vt = prob.states_all_section(2)
ur1 = prob.controls_all_section(0)
ur2 = prob.controls_all_section(1)
ut1 = prob.controls_all_section(2)
ut2 = prob.controls_all_section(3)
tf = prob.time_final(-1)
result = Condition()
# lower bounds
result.lower_bound(r, obj.r0)
result.lower_bound(ur1, 0.0)
result.lower_bound(ut1, 0.0)
result.lower_bound(ur2, 0.0)
result.lower_bound(ut2, 0.0)
result.lower_bound(tf, 0.0)
# upper bounds
result.upper_bound(r, obj.rf)
result.upper_bound(ur1, obj.u_max)
result.upper_bound(ut1, obj.u_max)
result.upper_bound(ur2, obj.u_max)
result.upper_bound(ut2, obj.u_max)
result.upper_bound(tf, obj.tf_max)
return result()
def inequality(prob, obj):
u = prob.states_all_section(0)
v = prob.states_all_section(1)
x = prob.states_all_section(2)
y = prob.states_all_section(3)
beta = prob.controls_all_section(0)
tf = prob.time_final(-1)
result = Condition()
# lower bounds
result.lower_bound(beta, -np.pi / 2)
# upper bounds
result.upper_bound(beta, np.pi / 2)
return result()
def inequality(prob, obj):
x = prob.states_all_section(0)
y = prob.states_all_section(1)
v = prob.states_all_section(2)
theta = prob.controls_all_section(0)
tf = prob.time_final(-1)
result = Condition()
# lower bounds
result.lower_bound(x, 0)
result.lower_bound(y, 0)
result.lower_bound(theta, 0)
# upper bounds
result.upper_bound(theta, np.pi)
result.upper_bound(x, obj.l)
return result()
def inequality(prob, obj):
h = prob.states_all_section(0)
v = prob.states_all_section(1)
m = prob.states_all_section(2)
T = prob.controls_all_section(0)
tf = prob.time_final(-1)
result = Condition()
# lower bounds
result.lower_bound(h, obj.H0)
result.lower_bound(v, 0.0)
result.lower_bound(m, obj.Mf)
result.lower_bound(T, 0.0)
result.lower_bound(tf, 0.1)
# upper bounds
result.upper_bound(m, obj.M0)
result.upper_bound(T, obj.T_max)
return result()
def inequality(prob, obj):
R = prob.states_all_section(0)
v = prob.states_all_section(1)
m = prob.states_all_section(2)
T = prob.controls_all_section(0)
tf = prob.time_final(-1)
result = Condition()
# lower bounds
result.lower_bound(R, obj.Re)
result.lower_bound(v, 0.0)
result.lower_bound(m, obj.M0 * obj.Mc)
result.lower_bound(T, 0.0)
result.lower_bound(tf, 10)
# upper bounds
result.upper_bound(m, obj.M0)
result.upper_bound(T, obj.max_thrust * obj.M0 * obj.g0)
return result()
def _og_inequality(self, prob, obj):
""" define inequality conditions """
s = [prob.states_all_section(i) for i in range(5)]
result = Condition()
u_m = prob.controls(0, 0)
u_a = prob.controls(1, 0)
result.lower_bound(u_m, 0)
result.upper_bound(u_m, 1)
result.lower_bound(u_a, (-np.pi/2)) #thrust force to the left
result.upper_bound(u_a, (+np.pi/2)) #thrust force to the right
#bound states
for i in range(5):
result.lower_bound(s[i], obj.ranges[i][0])
result.upper_bound(s[i], obj.ranges[i][1])
#cone constraint
result.lower_bound(s[1], 1.*s[0]) # z > (1/tan(th)) * x
return result()
def inequality(prob, obj):
R = prob.states_all_section(0)
theta = prob.states_all_section(1)
Vr = prob.states_all_section(2)
Vt = prob.states_all_section(3)
m = prob.states_all_section(4)
Tr = prob.controls_all_section(0)
Tt = prob.controls_all_section(1)
tf = prob.time_final(-1)
rho = obj.air_density(R - obj.Re)
Dr = 0.5 * rho * Vr * np.sqrt(Vr**2 + Vt**2) \
* obj.Cd * obj.A # [N]
Dt = 0.5 * rho * Vt * np.sqrt(Vr**2 + Vt**2) \
* obj.Cd * obj.A # [N]
g = obj.g0 * (obj.Re / R)**2 # [m/s2]
# dynamic pressure
q = 0.5 * rho * (Vr**2 + Vt**2) # [Pa]
# accelaration
a_r = (Tr - Dr) / m
a_t = (Tt - Dt) / m
a_mag = np.sqrt(a_r**2 + a_t**2) # [m/s2]
# Thrust
T = np.sqrt(Tr**2 + Tt**2)
result = Condition()
# lower bounds
result.lower_bound(R, obj.Re, unit=prob.unit_states[0][0])
# result.lower_bound(Vr, 0.0, unit=prob.unit_states[0][2])
# result.lower_bound(Vt, 0.0, unit=prob.unit_states[0][3])
result.lower_bound(m[1:], (obj.M0 - obj.Mp), unit=prob.unit_states[0][4])
result.lower_bound(Tr, 0.0, unit=prob.unit_controls[0][0])
# result.lower_bound(Tt, obj.Tmax / obj.unit_T, unit=prob.unit_controls[0][0])
result.lower_bound(Tt, 0.0, unit=prob.unit_controls[0][0])
# upper bounds
result.upper_bound(m, obj.M0, unit=prob.unit_states[0][4])
result.upper_bound(Tr, obj.Tmax, unit=prob.unit_controls[0][0])
result.upper_bound(Tt, obj.Tmax, unit=prob.unit_controls[0][0])
result.upper_bound(T, obj.Tmax, unit=prob.unit_controls[0][0])
# result.upper_bound(q, obj.MaxQ, unit = prob.unit_states[0][0])
result.upper_bound(a_mag, obj.MaxG * obj.g0)
return result()
def inequality(prob, obj):
R = prob.states_all_section(0)
theta = prob.states_all_section(1)
Vr = prob.states_all_section(2)
Vt = prob.states_all_section(3)
m = prob.states_all_section(4)
Tr = prob.controls_all_section(0)
Tt = prob.controls_all_section(1)
tf = prob.time_final(-1)
R0 = prob.states(0, 0)
R1 = prob.states(0, 1)
theta0 = prob.states(1, 0)
theta1 = prob.states(1, 1)
Vr0 = prob.states(2, 0)
Vr1 = prob.states(2, 1)
Vt0 = prob.states(3, 0)
Vt1 = prob.states(3, 1)
m0 = prob.states(4, 0)
m1 = prob.states(4, 1)
Tr0 = prob.controls(0, 0)
Tr1 = prob.controls(0, 1)
Tt0 = prob.controls(1, 0)
Tt1 = prob.controls(1, 1)
rho = obj.airDensity(R - obj.Re)
Mach = np.sqrt(Vr**2 + Vt**2) / obj.airSound(R - obj.Re)
Cd = obj.Cd(Mach)
Dr0 = 0.5 * rho * Vr * np.sqrt(Vr**2 + Vt**2) * Cd * obj.A[0] # [N]
Dt0 = 0.5 * rho * Vt * np.sqrt(Vr**2 + Vt**2) * Cd * obj.A[0] # [N]
Dr1 = 0.5 * rho * Vr * np.sqrt(Vr**2 + Vt**2) * Cd * obj.A[1] # [N]
Dt1 = 0.5 * rho * Vt * np.sqrt(Vr**2 + Vt**2) * Cd * obj.A[1] # [N]
g = obj.g0 * (obj.Re / R)**2 # [m/s2]
# dynamic pressure
q = 0.5 * rho * (Vr**2 + Vt**2) # [Pa]
# accelaration
a_r0 = (Tr - Dr0) / m
a_t0 = (Tt - Dt0) / m
a_mag0 = np.sqrt(a_r0**2 + a_t0**2) # [m/s2]
a_r1 = (Tr - Dr1) / m
a_t1 = (Tt - Dt1) / m
a_mag1 = np.sqrt(a_r1**2 + a_t1**2) # [m/s2]
# Thrust
T0 = np.sqrt(Tr0**2 + Tt0**2)
T1 = np.sqrt(Tr1**2 + Tt1**2)
dThrust0 = (obj.airPressure(obj.H0) -
obj.airPressure(R0 - obj.Re)) * obj.Ae[0]
dThrust1 = obj.airPressure(R1 - obj.Re) * obj.Ae[1]
result = Condition()
# lower bounds
result.lower_bound(R, obj.Re, unit=prob.unit_states[0][0]) # 地表以下
result.lower_bound(m0,
obj.Mdry[0] + obj.M0[1],
unit=prob.unit_states[0][4]) # 乾燥質量以下
result.lower_bound(m1, obj.Mdry[1], unit=prob.unit_states[0][4])
result.lower_bound(Tr, -obj.ThrustMax[1], unit=prob.unit_controls[0][0])
result.lower_bound(Tt, -obj.ThrustMax[1], unit=prob.unit_controls[0][0])
# upper bounds
result.upper_bound(m0, obj.Minit, unit=prob.unit_states[0][4]) # 初期質量以上
result.upper_bound(m1, obj.M0[1], unit=prob.unit_states[0][4])
result.upper_bound(Tr0,
obj.ThrustMax[0] + dThrust0,
unit=prob.unit_controls[0][0])
result.upper_bound(Tt0,
obj.ThrustMax[0] + dThrust0,
unit=prob.unit_controls[0][0])
result.upper_bound(T0,
obj.ThrustMax[0] + dThrust0,
unit=prob.unit_controls[0][0])
result.upper_bound(Tr1,
obj.ThrustMax[1] + dThrust1,
unit=prob.unit_controls[0][0])
result.upper_bound(Tt1,
obj.ThrustMax[1] + dThrust1,
unit=prob.unit_controls[0][0])
result.upper_bound(T1,
obj.ThrustMax[1] + dThrust1,
unit=prob.unit_controls[0][0])
result.upper_bound(q, obj.MaxQ, unit=prob.unit_states[0][0])
result.upper_bound(a_mag0, obj.MaxG * obj.g0)
result.upper_bound(a_mag1, obj.MaxG * obj.g0)
return result()