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dynamics.py
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dynamics.py
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from __future__ import division
import numpy as np
from numpy import pi, sqrt, cos, sin, exp, tan
from solar import solarFlux
import state_setting as st
def uavDynamics(a1,a2,a3,h_0,v_0,config,mode):
'''
This function makes it possible to use the same model for root finding,
integration, power calculations and post processing
Integration
sol,output = odeint(uavDynamicsWrapper, SV0, t, args=(MV,h_0,[],smartsData,config,1))
Root Finding
eq = root(uavDynamicsWrapper,MV0,method='lm',args=([],[],h_0,v_0,smartsData,config,2))
Power Required
p_n = uavDynamicsWrapper(x_eq,[],[],h_0,v_0,smartsData,config,3)
Lift Coefficient
cl = uavDynamicsWrapper(x_eq,[],[],h_0,v_0,smartsData,config,4)
'''
# Initialize state machine if enabled
if config.sm_active:
state = st.state
## Process Inputs
if(mode==1):
# Integration
# Here we need to pass in the initial state variable conditions and
# the time to odeint. We also pass in a fixed set of MVs.
SV = a1
t = a2
MV = a3
# Load SVs
v,gamma,psi,h,x,y,e_batt = SV
# Load MVs
Tp_0, alpha_0, phi_0 = MV
# State Machine
if config.sm_active:
e_batt_max = config.aircraft.battery_max.value
# print('Stage 1')
# print(e_batt)
# print(e_batt_max)
# print(h)
# print(state)
#
# Determine state
if(e_batt>=e_batt_max and state==0):
state = 1
elif(state==1 and (h>=config.h.max or (h>config.h.min+100 and e_batt<=e_batt_max))):
state = 2
elif(state==2 and e_batt<=e_batt_max*0.99):
state = 3
elif(state==3 and h<=config.h.min):
state = 4
# Save state for next iteration
st.state = state
# Set gamma based on current state
if(state==1):
Tp_0 = np.interp(h,config.hlist_up,config.Tplist_up)
alpha_0 = np.interp(h,config.hlist_up,config.alphalist_up)
phi_0 = np.interp(h,config.hlist_up,config.philist_up)
elif(state==3):
Tp_0 = np.interp(h,config.hlist_down,config.Tplist_down)
alpha_0 = np.interp(h,config.hlist_down,config.alphalist_down)
phi_0 = np.interp(h,config.hlist_down,config.philist_down)
else:
Tp_0 = np.interp(h,config.hlist_level,config.Tplist_level)
alpha_0 = np.interp(h,config.hlist_level,config.alphalist_level)
phi_0 = np.interp(h,config.hlist_level,config.philist_level)
if(mode==2 or mode==3 or mode==4):
# Root Finding, Power
# In the root finding case, MV is the initial guesses. In the Power
# or cl case, it is a fixed set of MVs
MV = a1
t = 0 # time is arbitrary in this case
# Load MVs
Tp_0, alpha_0, phi_0 = MV
# Load SVs
v = v_0
h = h_0
psi = config.aircraft.psi.initial_value
initial_SOC = config.aircraft.battery_initial_SOC.value
E_d = config.aircraft.battery_energy_density.value # Battery energy density (W*hr/kg) (FB)
m_battery = config.aircraft.mass_battery.value # Battery mass
e_batt_max = m_battery*E_d*3.6/1000.0 # Max energy stored in battery (MJ)
e_batt = e_batt_max*initial_SOC # Initial Battery Charge
x = config.x.initial_value
y = config.y.initial_value
# State machine
if config.sm_active:
if config.aircraft.gamma.mode == 'level':
gamma = config.aircraft.gamma.level
elif config.aircraft.gamma.mode == 'up':
gamma = config.aircraft.gamma.up
elif config.aircraft.gamma.mode == 'down':
# gamma = np.interp(h,config.hlist_down,config.gammalist_down)
gamma = config.aircraft.gamma.down
else:
gamma = config.aircraft.gamma.level
if(mode==5):
# Output all other variables
SV = a1
# t = a2
MV = a3
# Load SVs
v,gamma,psi,h,x,y,e_batt,t = SV
# Load MVs
Tp_0, alpha_0, phi_0 = MV
# State Machine
if config.sm_active:
e_batt_max = config.aircraft.battery_max.value
# print('Stage 2')
# print(e_batt)
# print(e_batt_max)
# print(h)
# print(state)
# Determine state
if(e_batt>=e_batt_max and state==0):
state = 1
elif(state==1 and (h>=config.h.max or (h>config.h.min+100 and e_batt<=e_batt_max))):
state = 2
elif(state==2 and e_batt<=e_batt_max*0.99):
state = 3
elif(state==3 and h<=config.h.min):
state = 4
# Save state for next iteration
st.state = state
# Set gamma based on current state
if(state==1):
Tp_0 = np.interp(h,config.hlist_up,config.Tplist_up)
alpha_0 = np.interp(h,config.hlist_up,config.alphalist_up)
phi_0 = np.interp(h,config.hlist_up,config.philist_up)
elif(state==3):
Tp_0 = np.interp(h,config.hlist_down,config.Tplist_down)
alpha_0 = np.interp(h,config.hlist_down,config.alphalist_down)
phi_0 = np.interp(h,config.hlist_down,config.philist_down)
else:
Tp_0 = np.interp(h,config.hlist_level,config.Tplist_level)
alpha_0 = np.interp(h,config.hlist_level,config.alphalist_level)
phi_0 = np.interp(h,config.hlist_level,config.philist_level)
## Run Model
m = model(t,v,gamma,psi,h,x,y,e_batt,Tp_0,alpha_0,phi_0,config,mode)
## Process Outputs
if(mode==1):
# Integration
output = [
m['dv_dt'],
m['dgamma_dt'],
m['dpsi_dt'],
m['dh_dt'],
m['dx_dt'],
m['dy_dt'],
m['de_batt_dt']
]
if(mode==2):
# Root Finding
output = [
m['dv_dt'],
m['dgamma_dt'],
m['radius_const']
]
output = np.ravel(output)
if(mode==3):
# Power
output = m['P_N']
if(mode==4):
# cl
output = m['cl']
if(mode==5):
# Output all other variables
if config.sm_active:
m['state'] = state
output = m
return output
def model(t,v,gamma,psi,h,x,y,e_batt,Tp_0,alpha_0,phi_0,config,mode):
'''
Inputs
'''
config = config
# Time
# Cycle back to beginning if past 24 hours
if(t>3600*24):
t = t-3600*24
# Atmospheric Effects
g = 9.80665 # Gravity (m/s**2)
R_air = 287.041 # Gas Constant for air (m**2/(s**2 K))
rho_11 = 0.364 # Standard air density at 11 km (kg/m**3)
T_11 = 216.66 # Standard air temp at 11 km (K)
# Masses and Densities
m = config.aircraft.mass_total.value # 425.0 # Total Mass (kg) (FB)
E_d = config.aircraft.battery_energy_density.value # 350.0 # Battery energy density (W*hr/kg) (FB)
m_battery = config.aircraft.mass_battery.value # 212.0 # (kg) (FB)
S = config.aircraft.wing_top_surface_area.value # 60.0 # Wing and solar panel area (m**2) (FB)
chord = config.aircraft.chord.value # Chord (m)
# Propeller Efficiency
R_prop = config.aircraft.propeller_radius.value # 2.0 # Propeller Radius (m) - Kevin
# Power
e_motor = config.aircraft.motor_efficiency.value # 0.95 # Efficiency of motor
P_payload = config.aircraft.power_for_payload.value # 250.0 # Power for payload (W)
e_batt_max = m_battery*E_d*3.6/1000.0 # Max energy stored in battery (MJ)
# Manipulated variables
Tp = Tp_0 #3.171 # 48.4 # Thrust (N) (function input)
alpha = alpha_0 # Angle of Attack (rad) (function input)
phi = phi_0 #0.038 #2.059E-03 # 0.0001 # Bank Angle (rad) (function input)
#### Atmospheric Effects
rho = rho_11 * exp(-(g/(R_air*T_11))*(h-11000)) # Air density (kg/m**3)
T_air = -56.46 + 273.15 # Air temperature (K)
mu = 1.458e-6*sqrt(T_air)/(1+110.4/T_air) # Dynamic viscosity of air (kg/(m s))
# Pitch from AoA
theta = gamma + alpha
# Alpha in degress for fitted functions
alpha_deg = np.degrees(alpha)
# Flat plate Reynolds number
Re = rho*v*chord/mu # Reynolds number
# CL from emperical fit
cl = config.aircraft.CL(alpha_deg,Re)
# CD from emperical fit
C_D = config.aircraft.CD(alpha_deg,Re)
#### Flight Dynamics
q = 1/2.0*rho*v**2 # Dynamic pressure (Pa)
L = q*cl*S # Lift (N) (simplified definition using q)
D = C_D*q*S # Corrected Drag (N)
nh = L*sin(phi)/(m*g) # Horizontal load factor
nv = L*cos(phi)/(m*g) # Vertical load factor
### Propeller Max Theoretical Efficiency
Adisk = pi * R_prop**2 # Area of disk
if v>0:
e_prop = 2.0 / (1.0 + ( Tp / (Adisk * v**2.0 * rho/2.0) + 1.0 )**0.5)
nu_prop = e_prop * e_motor
else:
e_prop = 0
nu_prop = 0
#### Power
if nu_prop > 0:
P_N = P_payload + v*Tp/nu_prop # Power Needed by Aircraft
else:
P_N = 999999999 # Big number
if(mode==1 or mode==5):
solar_data = solarFlux(config.solar.smartsData, t/3600.0, phi,theta, psi)
G_sol = solar_data[0][0]
zenith = solar_data[0][1]
azimuth = solar_data[0][2]
h_flux = solar_data[0][3]
mu_solar = solar_data[0][4]
sn1 = solar_data[0][5]
sn2 = solar_data[0][6]
sn3 = solar_data[0][7]
flux = solar_data[0][8]
else:
# These aren't required to find steady state flight or power needs
G_sol = 0
zenith = 0
azimuth = 0
h_flux = 0
mu_solar = 0
sn1 = 0
sn2 = 0
sn3 = 0
flux = 0
# Solar Efficiency
panel_efficiency = config.aircraft.panel_efficiency(G_sol)
P_solar = G_sol*S*panel_efficiency
# Flight Dynamics
dv_dt = ((Tp-D)/(m*g)-sin(gamma))*g
if v <= 0:
dpsi_dt = 99999999 # Just set this to a big number
dgamma_dt = 99999999
else:
dpsi_dt = g/v*(nh/cos(gamma))
dgamma_dt = g/v*(nv-cos(gamma))
dh_dt = v*sin(gamma)
dx_dt = v*cos(psi)*cos(gamma)
dy_dt = v*sin(psi)*cos(gamma)
dist = (sqrt(x**2+y**2))
if phi == 0:
radius = 99999999 # Just set this to a big number
else:
radius = v**2/(g*tan(phi))# Flight path radius
radius_max = config.x.max # 3000 (m)
# Power
P_bat = P_solar - P_N # Power used to charge or discharge battery (W)
de_batt_dt = P_bat*1e-6 # (Convert to MJ)
# Check for max battery and cut off
if(e_batt >= e_batt_max and de_batt_dt > 0):
de_batt_dt = 0
h_0 = config.h.initial_value
TE = e_batt + m*g*(h-h_0)*1e-6
# Clip d_e_batt at maximum battery
bat_switch = 1/(1+exp(-10*(e_batt_max - e_batt)))
if(de_batt_dt>0):
de_batt_dt = de_batt_dt * bat_switch
# Collect model outputs into dictionary
model_output = {"dv_dt":dv_dt,
"dgamma_dt":dgamma_dt,
"dpsi_dt":dpsi_dt,
"dh_dt":dh_dt,
"dx_dt":dx_dt,
"dy_dt":dy_dt,
"de_batt_dt":de_batt_dt,
"radius_const":radius-radius_max,
"P_N":P_N,
'cl':cl,
'mu_solar':mu_solar,
'flux':flux,
'sn1':sn1,
'sn2':sn2,
'sn3':sn3,
'azimuth':azimuth,
'zenith':zenith,
'sun_h':h_flux,
'g_sol':G_sol,
'panel_efficiency':panel_efficiency,
'p_solar':P_solar,
'p_n':P_N,
'p_bat':P_bat,
'd':D,
'cd':C_D,
'cl':cl,
'rho':rho,
'm':m,
'nh':nh,
'nv':nv,
'nu_prop':nu_prop,
'dist':dist,
'theta':theta,
'te':TE,
're':Re,
'mu':mu,
'tp':Tp,
'phi':phi,
'alpha':alpha}
return model_output