def result_plots_mintime(pars: dict,
reftrack: np.ndarray,
s: np.ndarray,
t: np.ndarray,
x: np.ndarray,
u: np.ndarray,
ax: np.ndarray,
ay: np.ndarray,
atot: np.ndarray,
tf: np.ndarray,
ec: np.ndarray,
pwr: dict = None) -> None:
"""
Created by:
Fabian Christ
Extended by:
Thomas Herrmann ([email protected])
Documentation:
This function plots several figures containing relevant trajectory information after trajectory optimization.
Inputs:
pars: parameters dictionary
reftrack: contains the information of the reftrack -> [x, y, w_tr_right, w_tr_left]
s: contains the curvi-linear distance along the trajectory
t: contains the time along the trajectory
x: contains all state variables along the trajectory
u: contains all control variables along the trajectory
ax: contains the longitudinal acceleration along the trajectory
ay: contains the lateral acceleration along the trajectory
atot: contains the total acceleration along the trajectory
tf: contains all tire forces along the trajectory
ec: contains the used energy along the trajectory
"""
# ------------------------------------------------------------------------------------------------------------------
# PLOT OPTIONS -----------------------------------------------------------------------------------------------------
# ------------------------------------------------------------------------------------------------------------------
plt.rcParams['axes.labelsize'] = 10.0
plt.rcParams['axes.titlesize'] = 11.0
plt.rcParams['legend.fontsize'] = 10.0
plt.rcParams['figure.figsize'] = 25 / 2.54, 20 / 2.54
plot_opts = {"v_a_t": True,
"general": True,
"lateral_distance": True,
"power": True,
"kamm_circle": True,
"tire_forces": True,
"tire_forces_longitudinal": True,
"tire_forces_dynamic": True,
"energy_consumption": True,
"pwr_states": True,
"pwr_soc": True,
"pwr_losses": True}
# ------------------------------------------------------------------------------------------------------------------
# EXTRACT PLOT DATA ------------------------------------------------------------------------------------------------
# ------------------------------------------------------------------------------------------------------------------
# state variables
v = x[:, 0]
beta = x[:, 1]
omega_z = x[:, 2]
n = x[:, 3]
xi = x[:, 4]
if pars["pwr_params_mintime"]["pwr_behavior"]:
temp_mot = x[:, 5]
temp_batt = x[:, 6]
temp_inv = x[:, 7]
temp_radiators_cool_mi = x[:, 8]
temp_radiators_cool_b = x[:, 9]
soc_batt = x[:, 10]
# control variables
delta = np.append(u[:, 0], u[0, 0])
f_drive = np.append(u[:, 1], u[0, 1])
f_brake = np.append(u[:, 2], u[0, 2])
gamma_y = np.append(u[:, 3], u[0, 3])
# tire forces
tf_x_fl = tf[:, 0]
tf_y_fl = tf[:, 1]
tf_z_fl = tf[:, 2]
tf_x_fr = tf[:, 3]
tf_y_fr = tf[:, 4]
tf_z_fr = tf[:, 5]
tf_x_rl = tf[:, 6]
tf_y_rl = tf[:, 7]
tf_z_rl = tf[:, 8]
tf_x_rr = tf[:, 9]
tf_y_rr = tf[:, 10]
tf_z_rr = tf[:, 11]
# parameters
g = pars["veh_params"]["g"]
veh = pars["vehicle_params_mintime"]
tire = pars["tire_params_mintime"]
# ------------------------------------------------------------------------------------------------------------------
# PLOT: VELOCITY + LONGITUDINAL ACCELERATION + LATERAL ACCELERATION + TOTAL ACCELERATION + TIME --------------------
# ------------------------------------------------------------------------------------------------------------------
if plot_opts["v_a_t"]:
plt.figure(1)
plt.clf()
plt.plot(s, v)
plt.plot(s, ax)
plt.plot(s, ay)
plt.plot(s, atot)
plt.plot(s, t)
plt.grid()
plt.ylim(bottom=-15)
plt.xlabel('distance ' + r'$\it{s}$' + ' in ' + r'$\it{m}$')
plt.legend([r'$\it{v}$' + ' in ' + r'$\it{\frac{m}{s}}$',
r'$\it{a_x}$' + ' in ' + r'$\it{\frac{m}{s^2}}$',
r'$\it{a_y}$' + ' in ' + r'$\it{\frac{m}{s^2}}$',
r'$\it{a_{tot}}$' + ' in ' + r'$\it{\frac{m}{s^2}}$',
r'$\it{t}$' + ' in ' + r'$\it{s}$'])
plt.show()
# ------------------------------------------------------------------------------------------------------------------
# PLOT: SIDE SLIP ANGLE + YAW RATE + RELATIVE ANGLE TO TANGENT ON REFLINE + STEERING ANGLE -------------------------
# ------------------------------------------------------------------------------------------------------------------
if plot_opts["general"]:
plt.figure(2)
plt.clf()
plt.subplot(221)
plt.plot(s, beta * 180 / np.pi)
plt.xlabel('distance ' + r'$\it{s}$' + ' in ' + r'$\it{m}$')
plt.ylabel('side slip angle ' + r'$\beta$' + ' in ' + r'$\it{°}$')
plt.grid()
plt.subplot(222)
plt.plot(s, omega_z * 180 / np.pi)
plt.xlabel('distance ' + r'$\it{s}$' + ' in ' + r'$\it{m}$')
plt.ylabel('yaw rate ' + r'$\omega_{z}$' + ' in ' + r'$\it{\frac{°}{s}}$')
plt.grid()
plt.subplot(223)
plt.plot(s, xi * 180 / np.pi)
plt.xlabel('distance ' + r'$\it{s}$' + ' in ' + r'$\it{m}$')
plt.ylabel('relative angle to tangent on reference line ' + r'$\xi$' + ' in ' + r'$\it{°}$')
plt.grid()
plt.subplot(224)
plt.step(s, delta * 180 / np.pi, where='post')
plt.xlabel('distance ' + r'$\it{s}$' + ' in ' + r'$\it{m}$')
plt.ylabel('steering angle ' + r'$\delta$' + ' in ' + r'$\it{°}$')
plt.grid()
plt.show()
# ------------------------------------------------------------------------------------------------------------------
# PLOT: LATERAL DISTANCE TO REFERENCE LINE + ROAD BOUNDARIES -------------------------------------------------------
# ------------------------------------------------------------------------------------------------------------------
if plot_opts["lateral_distance"]:
plt.figure(3)
plt.clf()
plt.plot(s, n)
reftrack_cl = np.vstack((reftrack, reftrack[0, :]))
plt.plot(s, reftrack_cl[:, 3], color='black')
plt.plot(s, reftrack_cl[:, 3] - pars["optim_opts"]["width_opt"] / 2, color='grey')
plt.plot(s, -reftrack_cl[:, 2], color='black')
plt.plot(s, -reftrack_cl[:, 2] + pars["optim_opts"]["width_opt"] / 2, color='grey')
plt.xlabel('distance ' + r'$\it{s}$' + ' in ' + r'$\it{m}$')
plt.ylabel('lateral distance to reference line ' + r'$\it{n}$' + ' in ' + r'$\it{m}$')
plt.legend(['raceline', 'road boundaries', 'road boundaries - safety margin'], ncol=1, loc=4)
plt.grid()
plt.show()
# ------------------------------------------------------------------------------------------------------------------
# PLOT: KAMM's CIRCLE ----------------------------------------------------------------------------------------------
# ------------------------------------------------------------------------------------------------------------------
if plot_opts["kamm_circle"]:
plt.figure(5)
plt.clf()
plt.suptitle("Kamm's Circle")
plt.subplot(221)
circle1 = plt.Circle((0, 0), 1, fill=False)
fig = plt.gcf()
ax = fig.gca()
ax.add_artist(circle1)
plt.plot(tf_y_fl / (tf_z_fl * pars["optim_opts"]["mue"]),
tf_x_fl / (tf_z_fl * pars["optim_opts"]["mue"]), '^:')
plt.xlim(-1.2, 1.2)
plt.ylim(-1.2, 1.2)
plt.xlabel(r'$\it{\frac{F_{y}}{F_{ymax}}}$')
plt.ylabel(r'$\it{\frac{F_{x}}{F_{xmax}}}$')
plt.axis('equal')
plt.grid()
plt.subplot(222)
circle1 = plt.Circle((0, 0), 1, fill=False)
fig = plt.gcf()
ax = fig.gca()
ax.add_artist(circle1)
plt.plot(tf_y_fr / (tf_z_fr * pars["optim_opts"]["mue"]),
tf_x_fr / (tf_z_fr * pars["optim_opts"]["mue"]), '^:')
plt.xlim(-1.2, 1.2)
plt.ylim(-1.2, 1.2)
plt.xlabel(r'$\it{\frac{F_{y}}{F_{ymax}}}$')
plt.ylabel(r'$\it{\frac{F_{x}}{F_{xmax}}}$')
plt.axis('equal')
plt.grid()
plt.subplot(223)
circle1 = plt.Circle((0, 0), 1, fill=False)
fig = plt.gcf()
ax = fig.gca()
ax.add_artist(circle1)
plt.plot(tf_y_rl / (tf_z_rl * pars["optim_opts"]["mue"]),
tf_x_rl / (tf_z_rl * pars["optim_opts"]["mue"]), '^:')
plt.xlim(-1.2, 1.2)
plt.ylim(-1.2, 1.2)
plt.xlabel(r'$\it{\frac{F_{y}}{F_{ymax}}}$')
plt.ylabel(r'$\it{\frac{F_{x}}{F_{xmax}}}$')
plt.axis('equal')
plt.grid()
plt.subplot(224)
circle1 = plt.Circle((0, 0), 1, fill=False)
fig = plt.gcf()
ax = fig.gca()
ax.add_artist(circle1)
plt.plot(tf_y_rr / (tf_z_rr * pars["optim_opts"]["mue"]),
tf_x_rr / (tf_z_rr * pars["optim_opts"]["mue"]), '^:')
plt.xlim(-1.2, 1.2)
plt.ylim(-1.2, 1.2)
plt.xlabel(r'$\it{\frac{F_{y}}{F_{ymax}}}$')
plt.ylabel(r'$\it{\frac{F_{x}}{F_{xmax}}}$')
plt.axis('equal')
plt.grid()
plt.show()
# ------------------------------------------------------------------------------------------------------------------
# PLOT: TIRE FORCES (LONGITUDINAL + LATERAL + NORMAL) --------------------------------------------------------------
# ------------------------------------------------------------------------------------------------------------------
if plot_opts["tire_forces"]:
plt.figure(6)
plt.clf()
plt.suptitle("Tire Forces")
plt.subplot(221)
plt.plot(s, tf_x_fl)
plt.plot(s, tf_y_fl)
plt.plot(s, tf_z_fl)
plt.xlabel('distance ' + r'$\it{s}$' + ' in ' + r'$\it{m}$')
plt.ylabel(r'$\it{F_{i}}$' + ' in ' + r'$\it{N}$')
plt.legend([r'$\it{F_{x}}$', r'$\it{F_{y}}$', r'$\it{F_{z}}$'], ncol=3, loc=4)
plt.grid()
plt.subplot(222)
plt.plot(s, tf_x_fr)
plt.plot(s, tf_y_fr)
plt.plot(s, tf_z_fr)
plt.xlabel('distance ' + r'$\it{s}$' + ' in ' + r'$\it{m}$')
plt.ylabel(r'$\it{F_{i}}$' + ' in ' + r'$\it{N}$')
plt.legend([r'$\it{F_{x}}$', r'$\it{F_{y}}$', r'$\it{F_{z}}$'], ncol=3, loc=4)
plt.grid()
plt.subplot(223)
plt.plot(s, tf_x_rl)
plt.plot(s, tf_y_rl)
plt.plot(s, tf_z_rl)
plt.xlabel('distance ' + r'$\it{s}$' + ' in ' + r'$\it{m}$')
plt.ylabel(r'$\it{F_{i}}$' + ' in ' + r'$\it{N}$')
plt.legend([r'$\it{F_{x}}$', r'$\it{F_{y}}$', r'$\it{F_{z}}$'], ncol=3, loc=4)
plt.grid()
plt.subplot(224)
plt.plot(s, tf_x_rr)
plt.plot(s, tf_y_rr)
plt.plot(s, tf_z_rr)
plt.xlabel('distance ' + r'$\it{s}$' + ' in ' + r'$\it{m}$')
plt.ylabel(r'$\it{F_{i}}$' + ' in ' + r'$\it{N}$')
plt.legend([r'$\it{F_{x}}$', r'$\it{F_{y}}$', r'$\it{F_{z}}$'], ncol=3, loc=4)
plt.grid()
plt.show()
# ------------------------------------------------------------------------------------------------------------------
# PLOT: TIRE FORCES (LONGITUDINAL) ---------------------------------------------------------------------------------
# ------------------------------------------------------------------------------------------------------------------
if plot_opts["tire_forces_longitudinal"]:
plt.figure(7)
plt.step(s, f_drive / 1000, where="post")
plt.step(s, f_brake / 1000, where='post')
plt.step(s, (f_drive + f_brake) / 1000, where='post')
plt.plot(s, veh["power_max"] / (v * 1000), linewidth=0.5)
plt.xlabel('distance ' + r'$\it{s}$' + ' in ' + r'$\it{m}$')
plt.ylabel(r'$\it{F}$' + ' in ' + r'$\it{kN}$')
plt.legend([r'$\it{F_{drive}}$', r'$\it{F_{brake}}$',
r'$\it{F_{drive}}$' + " + " + r'$\it{F_{brake}}$',
r'$\it{F_{P_{max}}}$'], ncol=1, loc=4)
plt.grid()
plt.show()
# ------------------------------------------------------------------------------------------------------------------
# PLOT: DYNAMIC WHEEL LOAD TRANSFER --------------------------------------------------------------------------------
# ------------------------------------------------------------------------------------------------------------------
if plot_opts["tire_forces_dynamic"]:
f_xroll = tire["c_roll"] * pars["veh_params"]["mass"] * g
f_xdrag = pars["veh_params"]["dragcoeff"] * v ** 2
f_zlift_fl = 0.5 * veh["liftcoeff_front"] * v ** 2
f_zlift_fr = 0.5 * veh["liftcoeff_front"] * v ** 2
f_zlift_rl = 0.5 * veh["liftcoeff_rear"] * v ** 2
f_zlift_rr = 0.5 * veh["liftcoeff_rear"] * v ** 2
f_zlong_fl = -0.5 * veh["cog_z"] / veh["wheelbase"] * (f_drive + f_brake - f_xroll - f_xdrag)
f_zlong_fr = -0.5 * veh["cog_z"] / veh["wheelbase"] * (f_drive + f_brake - f_xroll - f_xdrag)
f_zlong_rl = 0.5 * veh["cog_z"] / veh["wheelbase"] * (f_drive + f_drive - f_xroll - f_xdrag)
f_zlong_rr = 0.5 * veh["cog_z"] / veh["wheelbase"] * (f_drive + f_drive - f_xroll - f_xdrag)
f_zlat_fl = - veh["k_roll"] * gamma_y
f_zlat_fr = veh["k_roll"] * gamma_y
f_zlat_rl = - (1 - veh["k_roll"]) * gamma_y
f_zlat_rr = (1 - veh["k_roll"]) * gamma_y
plt.figure(8)
plt.suptitle("Dynamic Wheel Load")
plt.subplot(221)
plt.plot(s, f_zlift_fl)
plt.plot(s, f_zlong_fl)
plt.plot(s, f_zlat_fl)
plt.plot(s, f_zlift_fl + f_zlong_fl + f_zlat_fl, color='black')
plt.xlabel('distance ' + r'$\it{s}$' + ' in ' + r'$\it{m}$')
plt.ylabel(r'$\it{F_{i}}$' + ' in ' + r'$\it{N}$')
plt.grid()
plt.subplot(222)
plt.plot(s, f_zlift_fr)
plt.plot(s, f_zlong_fr)
plt.plot(s, f_zlat_fr)
plt.plot(s, f_zlift_fr + f_zlong_fr + f_zlat_fr, color='black')
plt.xlabel(r'$\it{s}$' + ' in ' + r'$\it{m}$')
plt.ylabel(r'$\it{F_{i}}$' + ' in ' + r'$\it{N}$')
plt.grid()
plt.subplot(223)
plt.plot(s, f_zlift_rl)
plt.plot(s, f_zlong_rl)
plt.plot(s, f_zlat_rl)
plt.plot(s, f_zlift_rl + f_zlong_rl + f_zlat_rl, color='black')
plt.xlabel('distance ' + r'$\it{s}$' + ' in ' + r'$\it{m}$')
plt.ylabel(r'$\it{F_{i}}$' + ' in ' + r'$\it{N}$')
plt.grid()
plt.subplot(224)
plt.plot(s, f_zlift_rr)
plt.plot(s, f_zlong_rr)
plt.plot(s, f_zlat_rr)
plt.plot(s, f_zlift_rr + f_zlong_rr + f_zlat_rr, color='black')
plt.xlabel('distance ' + r'$\it{s}$' + ' in ' + r'$\it{m}$')
plt.ylabel(r'$\it{F_{i}}$' + ' in ' + r'$\it{N}$')
plt.legend([r'$\it{F_{lift}}$', r'$\it{F_{dyn,long}}$', r'$\it{F_{dyn,lat}}$',
r'$\it{F_{lift}}$' + ' + ' + r'$\it{F_{dyn,long}}$' + ' + ' + r'$\it{F_{dyn,lat}}$'], ncol=2, loc=4)
plt.grid()
plt.show()
# ------------------------------------------------------------------------------------------------------------------
# PLOT: ENERGY CONSUMPTION -----------------------------------------------------------------------------------------
# ------------------------------------------------------------------------------------------------------------------
if plot_opts["energy_consumption"]:
plt.figure(9)
plt.clf()
plt.plot(s, ec)
plt.xlabel('distance ' + r'$\it{s}$' + ' in ' + r'$\it{m}$')
plt.ylabel('energy consumption ' + r'$\it{ec}$' + ' in ' + r'$\it{Wh}$')
plt.grid()
plt.show()
# ------------------------------------------------------------------------------------------------------------------
# PLOT: POWER ------------------------------------------------------------------------------------------------------
# ------------------------------------------------------------------------------------------------------------------
if plot_opts["power"]:
plt.figure(4)
plt.clf()
plt.plot(s, v * (f_drive + f_brake) / 1000.0)
plt.xlabel('distance ' + r'$\it{s}$' + ' in ' + r'$m$')
plt.ylabel('power ' + r'$\it{P}$' + ' in ' + r'$kW$')
plt.grid()
plt.legend(r'$\it{P_{wheel}}$')
if pwr is not None:
plt.plot(s[:-1], pwr["batt"].p_loss_total + pwr["batt"].p_out_batt)
plt.legend([r'$\it{P_{wheel}}$', r'$\it{P_{system}}$'])
plt.show()
# ------------------------------------------------------------------------------------------------------------------
# PLOT: POWERTRAIN TEMPERATURES ------------------------------------------------------------------------------------
# ------------------------------------------------------------------------------------------------------------------
if pars["pwr_params_mintime"]["pwr_behavior"] and plot_opts["pwr_states"]:
plt.figure(10)
plt.plot(s, temp_mot)
plt.plot(s, temp_batt)
plt.plot(s, temp_inv)
plt.plot(s, temp_radiators_cool_mi)
plt.plot(s, temp_radiators_cool_b)
plt.xlabel('distance ' + r'$\it{s}$' + ' in ' + r'$\it{m}$')
plt.ylabel('component temperatures ' + r'$\it{T}$' + ' in ' + r'°C')
plt.legend([r'$\it{T_\mathrm{Machine}}$', r'$\it{T_\mathrm{Battery}}$', r'$\it{T_\mathrm{Inverter}}$',
r'$\it{T_\mathrm{Fluid_{MI}}}$', r'$\it{T_\mathrm{Fluid_B}}$'])
plt.grid()
plt.show()
# ------------------------------------------------------------------------------------------------------------------
# PLOT: SOC BATTERY ------------------------------------------------------------------------------------------------
# ------------------------------------------------------------------------------------------------------------------
if pars["pwr_params_mintime"]["pwr_behavior"] and plot_opts["pwr_soc"]:
plt.figure(11)
plt.plot(s, soc_batt)
plt.xlabel('distance ' + r'$\it{s}$' + ' in ' + r'$\it{m}$')
plt.ylabel('SOC battery [1 - 0]')
plt.grid()
plt.show()
# ------------------------------------------------------------------------------------------------------------------
# PLOT: POWER LOSSES -----------------------------------------------------------------------------------------------
# ------------------------------------------------------------------------------------------------------------------
if pars["pwr_params_mintime"]["pwr_behavior"] and plot_opts["pwr_losses"]:
if pars["pwr_params_mintime"]["simple_loss"]:
plt.figure(12)
plt.plot(s[:-1], pwr["machine"].p_loss_total)
plt.plot(s[:-1], pwr["inverter"].p_loss_total)
plt.plot(s[:-1], pwr["batt"].p_loss_total)
plt.legend([r'$\it{P_\mathrm{loss,machine}}$', r'$\it{P_\mathrm{loss,inverter}}$',
r'$\it{P_\mathrm{loss,battery}}$'])
plt.ylabel('Power loss ' + r'$\it{P_\mathrm{loss}}$' + ' in ' + r'kW')
else:
plt.figure(12)
plt.subplot(311)
plt.plot(s[:-1], pwr["machine"].p_loss_total)
plt.plot(s[:-1], pwr["machine"].p_loss_copper)
plt.plot(s[:-1], pwr["machine"].p_loss_stator_iron)
plt.plot(s[:-1], pwr["machine"].p_loss_rotor)
plt.ylabel('Power loss single machine\n' + r'$\it{P_\mathrm{loss}}$' + ' in ' + r'kW')
plt.legend([r'$\it{P_\mathrm{loss,total}}$', r'$\it{P_\mathrm{loss,copper}}$',
r'$\it{P_\mathrm{loss,statorIron}}$', r'$\it{P_\mathrm{loss,rotor}}$'])
plt.grid()
plt.subplot(312)
plt.plot(s[:-1], pwr["inverter"].p_loss_total)
plt.plot(s[:-1], pwr["inverter"].p_loss_switch)
plt.plot(s[:-1], pwr["inverter"].p_loss_cond)
plt.legend([r'$\it{P_\mathrm{loss,total}}$', r'$\it{P_\mathrm{loss,switching}}$',
r'$\it{P_\mathrm{loss,conducting}}$'])
plt.ylabel('Power loss single inverter\n' + r'$\it{P_\mathrm{loss}}$' + ' in ' + r'kW')
plt.grid()
plt.subplot(313)
plt.plot(s[:-1], pwr["batt"].p_loss_total)
plt.ylabel('Power loss battery\n' + r'$\it{P_\mathrm{loss}}$' + ' in ' + r'kW')
plt.xlabel('distance ' + r'$\it{s}$' + ' in ' + r'$\it{m}$')
plt.grid()
plt.show()
# testing --------------------------------------------------------------------------------------------------------------
if __name__ == "__main__":
pass
