def cost_derivative(prob, obj):
jac = Condition(prob.number_of_variables)
index_m0 = prob.index_states(4, 0, 0)
index_mf = prob.index_states(4, 0, -1)
m = prob.states_all_section(4)
# jac.change_value(index_m0, - m[-1] / m[0]**2)
# jac.change_value(index_mf, - 1.0 / m[0])
jac.change_value(index_mf, -1.0)
return jac()
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 equality(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()
# event condition
result.equal(h[0], obj.H0)
result.equal(v[0], obj.V0)
result.equal(m[0], obj.M0)
result.equal(v[-1], 0.0)
result.equal(m[-1], obj.Mf)
return result()
def equality(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()
# event condition
result.equal(x[0], 0.0)
result.equal(y[0], 0.0)
result.equal(v[0], 0.0)
result.equal(x[-1], obj.l)
result.equal(y[-1], 0.0)
# result.equal(v[-1], 0.0)
return result()
def equality(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()
# event condition
result.equal(u[0], 0.0)
result.equal(v[0], 0.0)
result.equal(x[0], 0.0)
result.equal(y[0], 0.0)
result.equal(u[-1], 1.0)
result.equal(v[-1], 0.0)
result.equal(y[-1], 1.0)
return result()
def equality(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()
# event condition
result.equal(r[0], obj.r0)
result.equal(vr[0], obj.vr0)
result.equal(vt[0], obj.vt0)
result.equal(r[-1], obj.rf)
result.equal(vr[-1], obj.vrf)
result.equal(vt[-1], obj.vtf)
return result()
def _og_equality(self, prob, obj):
""" define the equality conditions to be met. in theory the user should be able to provide/modify this"""
result = Condition()
for i in range(5):
result.equal(prob.states_all_section(i)[0], obj.s_0[i]), #r, v, m = [r,v,m](0)
for i in range(4):
result.equal(prob.states_all_section(i)[-1], 0.) #r, v = 0
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(tf, 0.1)
result.lower_bound(y, 0)
result.lower_bound(theta, 0)
# upper bounds
# result.upper_bound(theta, np.pi/2)
# result.upper_bound(y, x * np.tan(obj.theta0) + obj.h)
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):
R = prob.states_all_section(0)
v = prob.states_all_section(1)
m = prob.states_all_section(2)
T = prob.controls_all_section(0)
ts0 = prob.time_final(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_2nd * obj.Mc)
result.lower_bound(T, 0.0)
result.lower_bound(ts0, 50)
result.lower_bound(tf, 50)
# upper bounds
result.upper_bound(m, obj.M0)
result.upper_bound(T, obj.max_thrust * obj.M0 * obj.g0)
return result()
def equality(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()
# event condition
result.equal(R[0], obj.Re)
result.equal(v[0], 0.0)
result.equal(m[0], obj.M0)
result.equal(v[-1], 0.0)
result.equal(m[-1], obj.M0_2nd * obj.Mc)
# knotting condition
R1 = prob.states(0, 0)
v1 = prob.states(1, 0)
m1 = prob.states(2, 0)
R2 = prob.states(0, 1)
v2 = prob.states(1, 1)
m2 = prob.states(2, 1)
result.equal(R1[-1], R2[0])
result.equal(v1[-1], v2[0])
result.equal(m1[-1], m2[0] - 1200)
return result()
def cost_derivative(prob, obj):
jac = Condition(prob.number_of_variables)
index_R_end = prob.index_states(0, 0, -1)
jac.change_value(index_R_end, -1)
return jac()
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()
def equality(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)
unit_R = prob.unit_states[0][0]
unit_V = prob.unit_states[0][2]
unit_m = prob.unit_states[0][4]
result = Condition()
# event condition
result.equal(R0[0], obj.Re + obj.H0, unit=unit_R) # 初期地表
result.equal(theta0[0], 0.0)
result.equal(Vr0[0], 0.0, unit=unit_V)
result.equal(Vt0[0], obj.V0, unit=unit_V)
result.equal(m0[0], obj.Minit,
unit=unit_m) # (1st stage and 2nd stage and Payload) initial
# knotting condition
result.equal(m1[0], obj.M0[1],
unit=unit_m) # (2nd stage + Payload) initial
result.equal(R1[0], R0[-1], unit=unit_R)
result.equal(theta1[0], theta0[-1])
result.equal(Vr1[0], Vr0[-1], unit=unit_V)
result.equal(Vt1[0], Vt0[-1], unit=unit_V)
# Target Condition
result.equal(R1[-1], obj.Rtarget, unit=unit_R) # Radius
result.equal(Vr[-1], 0.0, unit=unit_V) # Radius Velocity
result.equal(Vt[-1], obj.Vtarget, unit=unit_V)
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 equality(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)
result = Condition()
# event condition
result.equal(R[0], obj.Re, unit=prob.unit_states[0][0])
result.equal(theta[0], 0.0, unit=prob.unit_states[0][1])
result.equal(Vr[0], 0.0, unit=prob.unit_states[0][2])
result.equal(Vt[0], 0.0, unit=prob.unit_states[0][3])
result.equal(m[0], obj.M0, unit=prob.unit_states[0][4])
result.equal(R[-1], obj.Rtarget, unit=prob.unit_states[0][1])
result.equal(Vr[-1], 0.0, unit=prob.unit_states[0][2])
result.equal(Vt[-1], obj.Vtarget, unit=prob.unit_states[0][3])
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 cost_derivative(prob, obj):
jac = Condition(prob.number_of_variables)
# index_tf = prob.index_time_final(0)
index_tf = prob.index_time_final(-1)
jac.change_value(index_tf, 1)
return jac()
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)
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()