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pre-linear

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pulipakaa24
2026-02-11 17:33:18 -06:00
parent 48961ef0b8
commit 2d80505006
5 changed files with 5554 additions and 445 deletions
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4472
RL Testing/Ansys Results 12-9.csv Normal file
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RL Testing/Function Fitting.ipynb
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RL Testing/PWM_Circuit_Model.py
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@@ -2,46 +2,163 @@ import numpy as np
import matplotlib.pyplot as plt import matplotlib.pyplot as plt
from scipy.signal import TransferFunction, lsim from scipy.signal import TransferFunction, lsim
# ---- Parameters (edit these) ---- # ============================================================
R = 1.5 # ohms # Circuit Parameters
L = 0.0025 # henries # ============================================================
V = 12.0 # volts R = 1.5 # Resistance [Ω]
L = 0.0025 # Inductance [H] (2.5 mH)
V_SUPPLY = 12.0 # Supply rail [V]
tau = L / R # RL time constant ≈ 1.667 ms
# Time base # ============================================================
t_end = 0.2 # PWM Parameters
dt = 1e-4 # ============================================================
t = np.arange(0, t_end, dt) F_PWM = 16e3 # PWM frequency [Hz]
T_PWM = 1.0 / F_PWM # PWM period [s] (62.5 µs)
# ---- Define a duty command D(t) ---- # ============================================================
# Example: start at 0, step to 0.2 at 20 ms, then to 0.6 at 80 ms, then to 1.0 at 140 ms (DC full on) # Simulation Window
D = np.zeros_like(t) # ============================================================
D[t >= 0.020] = 0.2 T_END = 1e-3 # 1 ms → 16 full PWM cycles
D[t >= 0.080] = 0.6 DT = 1e-7 # 100 ns resolution (625 pts / PWM cycle)
D[t >= 0.140] = 1.0 # "straight DC" case (100% duty) t = np.arange(0, T_END + DT / 2, DT)
# Clamp just in case # ============================================================
D = np.clip(D, 0.0, 1.0) # Duty-Cycle Command D(t)
# ============================================================
# Ramp from 20 % → 80 % over the window so every PWM cycle
# has a visibly different pulse width.
def duty_command(t_val):
"""Continuous duty-cycle setpoint (from a controller)."""
return np.clip(0.2 + 0.6 * (np.asarray(t_val) / T_END), 0.0, 1.0)
# ---- Transfer function I(s)/D(s) = V / (L s + R) ---- D_continuous = duty_command(t)
# In scipy.signal.TransferFunction, numerator/denominator are polynomials in s
G = TransferFunction([V], [L, R])
# Simulate i(t) response to input D(t) # ============================================================
tout, i, _ = lsim(G, U=D, T=t) # MODEL 1 — Abstracted (Average-Voltage) Approximation
# ============================================================
# Treats the coil voltage as the smooth signal D(t)·V.
# Transfer function: I(s)/D(s) = V / (Ls + R)
G = TransferFunction([V_SUPPLY], [L, R])
_, i_avg, _ = lsim(G, U=D_continuous, T=t)
# ---- Print steady-state expectations ---- # ============================================================
# For constant duty D0, steady-state i_ss = (V/R)*D0 # MODEL 2 — True PWM Waveform (exact analytical solution)
print("Expected steady-state currents (V/R * D):") # ============================================================
for D0 in [0.0, 0.2, 0.6, 1.0]: # Between every switching edge the RL circuit obeys:
print(f" D={D0:.1f} -> i_ss ~ {(V/R)*D0:.3f} A") #
# di/dt = (V_seg − R·i) / L (V_seg = V_SUPPLY or 0)
#
# Closed-form from initial condition i₀ at time t₀:
#
# i(t) = V_seg/R + (i₀ − V_seg/R) · exp(−R·(t − t₀) / L)
#
# We propagate i analytically from edge to edge — zero
# numerical-integration error. The only error source is
# IEEE-754 floating-point arithmetic (~1e-15 relative).
# --- Step 1: build segment table and propagate boundary currents ---
seg_t_start = [] # start time of each constant-V segment
seg_V = [] # voltage applied during segment
seg_i0 = [] # current at segment start
# ---- Plot ---- i_boundary = 0.0 # coil starts de-energised
plt.figure()
plt.plot(tout, D, label="Duty D(t)") cycle = 0
plt.plot(tout, i, label="Current i(t) [A]") while cycle * T_PWM < T_END:
plt.xlabel("Time [s]") t_cycle = cycle * T_PWM
plt.grid(True) D = float(duty_command(t_cycle))
plt.legend()
# ---- ON phase (V_SUPPLY applied) ----
t_on_start = t_cycle
t_on_end = min(t_cycle + D * T_PWM, T_END)
if t_on_end > t_on_start:
seg_t_start.append(t_on_start)
seg_V.append(V_SUPPLY)
seg_i0.append(i_boundary)
dt_on = t_on_end - t_on_start
i_boundary = (V_SUPPLY / R) + (i_boundary - V_SUPPLY / R) * np.exp(-R * dt_on / L)
# ---- OFF phase (0 V applied, free-wheeling through diode) ----
t_off_start = t_on_end
t_off_end = min((cycle + 1) * T_PWM, T_END)
if t_off_end > t_off_start:
seg_t_start.append(t_off_start)
seg_V.append(0.0)
seg_i0.append(i_boundary)
dt_off = t_off_end - t_off_start
i_boundary = i_boundary * np.exp(-R * dt_off / L)
cycle += 1
seg_t_start = np.array(seg_t_start)
seg_V = np.array(seg_V)
seg_i0 = np.array(seg_i0)
# --- Step 2: evaluate on the dense time array (vectorised) ---
idx = np.searchsorted(seg_t_start, t, side='right') - 1
idx = np.clip(idx, 0, len(seg_t_start) - 1)
dt_in_seg = t - seg_t_start[idx]
V_at_t = seg_V[idx]
i0_at_t = seg_i0[idx]
i_pwm = (V_at_t / R) + (i0_at_t - V_at_t / R) * np.exp(-R * dt_in_seg / L)
v_pwm = V_at_t # switching waveform for plotting
v_avg = D_continuous * V_SUPPLY # average-model voltage
# ============================================================
# Console Output — sanity-check steady-state values
# ============================================================
print(f"RL time constant τ = L/R = {tau*1e3:.3f} ms")
print(f"PWM period T = 1/f = {T_PWM*1e6:.1f} µs")
print(f"Sim resolution Δt = {DT*1e9:.0f} ns ({int(T_PWM/DT)} pts/cycle)")
print()
print("Expected steady-state currents i_ss = (V/R)·D :")
for d in [0.2, 0.4, 0.6, 0.8]:
print(f" D = {d:.1f} → i_ss = {V_SUPPLY / R * d:.3f} A")
# ============================================================
# Plotting — 4-panel comparison
# ============================================================
t_us = t * 1e6 # time axis in µs
fig, axes = plt.subplots(4, 1, figsize=(14, 10), sharex=True)
fig.suptitle("PWM RL-Circuit Model Comparison (16 kHz, 1 ms window)",
fontsize=13, fontweight='bold')
# --- 1. Duty-cycle command ---
ax = axes[0]
ax.plot(t_us, D_continuous * 100, color='tab:purple', linewidth=1.2)
ax.set_ylabel("Duty Cycle [%]")
ax.set_ylim(0, 100)
ax.grid(True, alpha=0.3)
# --- 2. Voltage waveforms ---
ax = axes[1]
ax.plot(t_us, v_pwm, color='tab:orange', linewidth=0.6, label="True PWM voltage")
ax.plot(t_us, v_avg, color='tab:blue', linewidth=1.4, label="Average voltage D·V",
linestyle='--')
ax.set_ylabel("Voltage [V]")
ax.set_ylim(-0.5, V_SUPPLY + 1)
ax.legend(loc='upper left', fontsize=9)
ax.grid(True, alpha=0.3)
# --- 3. Current comparison ---
ax = axes[2]
ax.plot(t_us, i_pwm, color='tab:red', linewidth=0.7, label="True PWM current (exact)")
ax.plot(t_us, i_avg, color='tab:blue', linewidth=1.4, label="Averaged-model current",
linestyle='--')
ax.set_ylabel("Current [A]")
ax.legend(loc='upper left', fontsize=9)
ax.grid(True, alpha=0.3)
# --- 4. Difference / ripple ---
ax = axes[3]
ax.plot(t_us, (i_pwm - i_avg) * 1e3, color='tab:green', linewidth=0.7)
ax.set_ylabel("Δi (PWM − avg) [mA]")
ax.set_xlabel("Time [µs]")
ax.grid(True, alpha=0.3)
plt.tight_layout()
plt.show() plt.show()

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RL Testing/maglev_model.pkl
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RL Testing/polynomial_equations.txt Normal file
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@@ -0,0 +1,430 @@
Magnetic Levitation Force & Torque — Explicit Polynomial Equations
Polynomial Degree: 6
Variables:
currL [A] = Left coil current
currR [A] = Right coil current
rollDeg [deg] = Roll angle
invGap = 1 / GapHeight [1/mm]
================================================================================
FORCE [N] =
-1.3837763236e+01
+ (+3.4900958018e-01) * currL [A]
+ (+3.4444782070e-01) * currR [A]
+ (+1.3948921341e-07) * rollDeg [deg]
+ (+6.3404397040e+02) * invGap
+ (+2.0808153074e-02) * currL [A]^2
+ (-8.2940557511e-04) * currL [A] * currR [A]
+ (+2.2629904125e-02) * currL [A] * rollDeg [deg]
+ (-1.4941727622e+01) * currL [A] * invGap
+ (+2.1137560003e-02) * currR [A]^2
+ (-2.2629886279e-02) * currR [A] * rollDeg [deg]
+ (-1.4834895226e+01) * currR [A] * invGap
+ (-7.3648244412e-01) * rollDeg [deg]^2
+ (-7.6740357314e-06) * rollDeg [deg] * invGap
+ (+1.3767217831e+03) * invGap^2
+ (-1.1531758728e-04) * currL [A]^3
+ (+7.2971576377e-05) * currL [A]^2 * currR [A]
+ (+5.4868393021e-06) * currL [A]^2 * rollDeg [deg]
+ (-1.0521912466e+00) * currL [A]^2 * invGap
+ (+5.2348894922e-05) * currL [A] * currR [A]^2
+ (+2.1794350221e-09) * currL [A] * currR [A] * rollDeg [deg]
+ (+3.2678067078e-02) * currL [A] * currR [A] * invGap
+ (-6.3017520966e-03) * currL [A] * rollDeg [deg]^2
+ (-2.6462505434e-01) * currL [A] * rollDeg [deg] * invGap
+ (-2.9510804409e+01) * currL [A] * invGap^2
+ (-7.2152022082e-05) * currR [A]^3
+ (-5.4823932308e-06) * currR [A]^2 * rollDeg [deg]
+ (-1.0708822638e+00) * currR [A]^2 * invGap
+ (-6.3914882711e-03) * currR [A] * rollDeg [deg]^2
+ (+2.6462554272e-01) * currR [A] * rollDeg [deg] * invGap
+ (-3.0234998506e+01) * currR [A] * invGap^2
+ (+4.5881294085e-09) * rollDeg [deg]^3
+ (+2.5797308313e+01) * rollDeg [deg]^2 * invGap
+ (+4.6682794236e-05) * rollDeg [deg] * invGap^2
+ (-5.3401486713e+03) * invGap^3
+ (+1.3320765542e-06) * currL [A]^4
+ (+3.2152411427e-06) * currL [A]^3 * currR [A]
+ (+1.2629467079e-05) * currL [A]^3 * rollDeg [deg]
+ (+1.7892402808e-03) * currL [A]^3 * invGap
+ (+3.0619624267e-06) * currL [A]^2 * currR [A]^2
+ (-1.5568499556e-07) * currL [A]^2 * currR [A] * rollDeg [deg]
+ (-1.0714912904e-03) * currL [A]^2 * currR [A] * invGap
+ (+8.7713928261e-05) * currL [A]^2 * rollDeg [deg]^2
+ (+4.5854056157e-03) * currL [A]^2 * rollDeg [deg] * invGap
+ (+2.0746027602e+01) * currL [A]^2 * invGap^2
+ (+3.8655549044e-06) * currL [A] * currR [A]^3
+ (+1.5545726439e-07) * currL [A] * currR [A]^2 * rollDeg [deg]
+ (-7.0411774478e-04) * currL [A] * currR [A]^2 * invGap
+ (-3.8261231547e-05) * currL [A] * currR [A] * rollDeg [deg]^2
+ (-9.5017239129e-09) * currL [A] * currR [A] * rollDeg [deg] * invGap
+ (+7.0646804762e-01) * currL [A] * currR [A] * invGap^2
+ (-2.5574383917e-03) * currL [A] * rollDeg [deg]^3
+ (-3.3355499360e-02) * currL [A] * rollDeg [deg]^2 * invGap
+ (-2.1337761184e+01) * currL [A] * rollDeg [deg] * invGap^2
+ (+1.2343471808e+02) * currL [A] * invGap^3
+ (+7.7592074199e-07) * currR [A]^4
+ (-1.2629426979e-05) * currR [A]^3 * rollDeg [deg]
+ (+8.6147973530e-04) * currR [A]^3 * invGap
+ (+8.0130692138e-05) * currR [A]^2 * rollDeg [deg]^2
+ (-4.5854241649e-03) * currR [A]^2 * rollDeg [deg] * invGap
+ (+2.1139446060e+01) * currR [A]^2 * invGap^2
+ (+2.5574380197e-03) * currR [A] * rollDeg [deg]^3
+ (-2.9857453053e-02) * currR [A] * rollDeg [deg]^2 * invGap
+ (+2.1337762097e+01) * currR [A] * rollDeg [deg] * invGap^2
+ (+1.2514911864e+02) * currR [A] * invGap^3
+ (+2.9443521553e-02) * rollDeg [deg]^4
+ (-7.9265644452e-09) * rollDeg [deg]^3 * invGap
+ (-2.3563990269e+02) * rollDeg [deg]^2 * invGap^2
+ (+1.6353835994e-04) * rollDeg [deg] * invGap^3
+ (-2.2354105572e+03) * invGap^4
+ (+3.1117360777e-07) * currL [A]^5
+ (-1.8750259301e-07) * currL [A]^4 * currR [A]
+ (-8.5198564648e-08) * currL [A]^4 * rollDeg [deg]
+ (-6.3869937977e-05) * currL [A]^4 * invGap
+ (-1.4911217505e-07) * currL [A]^3 * currR [A]^2
+ (+1.7061909929e-07) * currL [A]^3 * currR [A] * rollDeg [deg]
+ (-7.4262537249e-06) * currL [A]^3 * currR [A] * invGap
+ (+7.2402232831e-07) * currL [A]^3 * rollDeg [deg]^2
+ (+2.1841125430e-05) * currL [A]^3 * rollDeg [deg] * invGap
+ (-3.4357925518e-03) * currL [A]^3 * invGap^2
+ (-1.6416880300e-07) * currL [A]^2 * currR [A]^3
+ (+3.6385798723e-05) * currL [A]^2 * currR [A]^2 * invGap
+ (+5.2924336558e-07) * currL [A]^2 * currR [A] * rollDeg [deg]^2
+ (+8.5467922645e-05) * currL [A]^2 * currR [A] * rollDeg [deg] * invGap
+ (+4.5573594510e-03) * currL [A]^2 * currR [A] * invGap^2
+ (-2.9680843072e-05) * currL [A]^2 * rollDeg [deg]^3
+ (-3.7951808035e-03) * currL [A]^2 * rollDeg [deg]^2 * invGap
+ (+4.7717250306e-02) * currL [A]^2 * rollDeg [deg] * invGap^2
+ (-1.4608679078e+02) * currL [A]^2 * invGap^3
+ (-1.2370955460e-07) * currL [A] * currR [A]^4
+ (-1.7060417434e-07) * currL [A] * currR [A]^3 * rollDeg [deg]
+ (-1.3936700967e-05) * currL [A] * currR [A]^3 * invGap
+ (+4.5908154078e-07) * currL [A] * currR [A]^2 * rollDeg [deg]^2
+ (-8.5469212391e-05) * currL [A] * currR [A]^2 * rollDeg [deg] * invGap
+ (+1.6991917750e-03) * currL [A] * currR [A]^2 * invGap^2
+ (-3.7373312737e-04) * currL [A] * currR [A] * rollDeg [deg]^2 * invGap
+ (+1.5086926031e-07) * currL [A] * currR [A] * rollDeg [deg] * invGap^2
+ (-7.5987537316e+00) * currL [A] * currR [A] * invGap^3
+ (+6.6508849418e-04) * currL [A] * rollDeg [deg]^4
+ (+9.6378055653e-02) * currL [A] * rollDeg [deg]^3 * invGap
+ (+2.4435308561e+00) * currL [A] * rollDeg [deg]^2 * invGap^2
+ (+1.2664933542e+02) * currL [A] * rollDeg [deg] * invGap^3
+ (+5.1887450366e+01) * currL [A] * invGap^4
+ (+2.3180087538e-07) * currR [A]^5
+ (+8.5217195078e-08) * currR [A]^4 * rollDeg [deg]
+ (-6.9233585420e-05) * currR [A]^4 * invGap
+ (+7.5608402383e-07) * currR [A]^3 * rollDeg [deg]^2
+ (-2.1841873013e-05) * currR [A]^3 * rollDeg [deg] * invGap
+ (+3.1131797033e-03) * currR [A]^3 * invGap^2
+ (+2.9680840171e-05) * currR [A]^2 * rollDeg [deg]^3
+ (-3.7292231655e-03) * currR [A]^2 * rollDeg [deg]^2 * invGap
+ (-4.7717023731e-02) * currR [A]^2 * rollDeg [deg] * invGap^2
+ (-1.4923564858e+02) * currR [A]^2 * invGap^3
+ (+6.6540367362e-04) * currR [A] * rollDeg [deg]^4
+ (-9.6378069105e-02) * currR [A] * rollDeg [deg]^3 * invGap
+ (+2.3836959223e+00) * currR [A] * rollDeg [deg]^2 * invGap^2
+ (-1.2664937015e+02) * currR [A] * rollDeg [deg] * invGap^3
+ (+5.2627468646e+01) * currR [A] * invGap^4
+ (+1.4646059365e-10) * rollDeg [deg]^5
+ (-1.0417153181e+00) * rollDeg [deg]^4 * invGap
+ (+1.1431957446e-06) * rollDeg [deg]^3 * invGap^2
+ (+9.2056028147e+02) * rollDeg [deg]^2 * invGap^3
+ (-3.1228040188e-04) * rollDeg [deg] * invGap^4
+ (-5.9623186232e+02) * invGap^5
+ (+2.9763214116e-09) * currL [A]^6
+ (-6.2261733547e-09) * currL [A]^5 * currR [A]
+ (-3.7175269085e-08) * currL [A]^5 * rollDeg [deg]
+ (-3.1125615720e-06) * currL [A]^5 * invGap
+ (-9.9876729109e-09) * currL [A]^4 * currR [A]^2
+ (-1.3294041423e-08) * currL [A]^4 * currR [A] * rollDeg [deg]
+ (+2.2610334440e-06) * currL [A]^4 * currR [A] * invGap
+ (+2.4101829865e-08) * currL [A]^4 * rollDeg [deg]^2
+ (+2.5320289563e-06) * currL [A]^4 * rollDeg [deg] * invGap
+ (+2.0532678993e-04) * currL [A]^4 * invGap^2
+ (-7.0411871889e-09) * currL [A]^3 * currR [A]^3
+ (+1.1956544199e-08) * currL [A]^3 * currR [A]^2 * rollDeg [deg]
+ (+1.9188820701e-06) * currL [A]^3 * currR [A]^2 * invGap
+ (+6.3643952330e-08) * currL [A]^3 * currR [A] * rollDeg [deg]^2
+ (-3.3660324359e-06) * currL [A]^3 * currR [A] * rollDeg [deg] * invGap
+ (+1.0594658745e-05) * currL [A]^3 * currR [A] * invGap^2
+ (-2.5937761805e-07) * currL [A]^3 * rollDeg [deg]^3
+ (-7.2227672945e-06) * currL [A]^3 * rollDeg [deg]^2 * invGap
+ (+9.6876113423e-05) * currL [A]^3 * rollDeg [deg] * invGap^2
+ (+8.5422144858e-03) * currL [A]^3 * invGap^3
+ (-1.0519386251e-08) * currL [A]^2 * currR [A]^4
+ (-1.1957411061e-08) * currL [A]^2 * currR [A]^3 * rollDeg [deg]
+ (+2.1222821118e-06) * currL [A]^2 * currR [A]^3 * invGap
+ (+4.4935102750e-08) * currL [A]^2 * currR [A]^2 * rollDeg [deg]^2
+ (-1.2807847845e-04) * currL [A]^2 * currR [A]^2 * invGap^2
+ (+5.7679319987e-08) * currL [A]^2 * currR [A] * rollDeg [deg]^3
+ (-1.4777475671e-05) * currL [A]^2 * currR [A] * rollDeg [deg]^2 * invGap
+ (-2.5449360510e-04) * currL [A]^2 * currR [A] * rollDeg [deg] * invGap^2
+ (-1.2272562713e-02) * currL [A]^2 * currR [A] * invGap^3
+ (+8.8287809685e-07) * currL [A]^2 * rollDeg [deg]^4
+ (+4.4586018461e-04) * currL [A]^2 * rollDeg [deg]^3 * invGap
+ (+3.8576999819e-02) * currL [A]^2 * rollDeg [deg]^2 * invGap^2
+ (+3.4044411238e-01) * currL [A]^2 * rollDeg [deg] * invGap^3
+ (+3.5950095140e+02) * currL [A]^2 * invGap^4
+ (-8.4967268776e-09) * currL [A] * currR [A]^5
+ (+1.3295050394e-08) * currL [A] * currR [A]^4 * rollDeg [deg]
+ (+1.7032328259e-06) * currL [A] * currR [A]^4 * invGap
+ (+7.0043846279e-08) * currL [A] * currR [A]^3 * rollDeg [deg]^2
+ (+3.3657944138e-06) * currL [A] * currR [A]^3 * rollDeg [deg] * invGap
+ (+6.8900834879e-05) * currL [A] * currR [A]^3 * invGap^2
+ (-5.7674824028e-08) * currL [A] * currR [A]^2 * rollDeg [deg]^3
+ (-1.4623729019e-05) * currL [A] * currR [A]^2 * rollDeg [deg]^2 * invGap
+ (+2.5450219980e-04) * currL [A] * currR [A]^2 * rollDeg [deg] * invGap^2
+ (-1.0593500843e-03) * currL [A] * currR [A]^2 * invGap^3
+ (+1.0484950490e-06) * currL [A] * currR [A] * rollDeg [deg]^4
+ (-3.0932389983e-10) * currL [A] * currR [A] * rollDeg [deg]^3 * invGap
+ (+5.6370243409e-03) * currL [A] * currR [A] * rollDeg [deg]^2 * invGap^2
+ (-6.1682354633e-07) * currL [A] * currR [A] * rollDeg [deg] * invGap^3
+ (+2.2923219836e+01) * currL [A] * currR [A] * invGap^4
+ (-2.3420164800e-05) * currL [A] * rollDeg [deg]^5
+ (-9.2739975478e-03) * currL [A] * rollDeg [deg]^4 * invGap
+ (-7.4080422659e-01) * currL [A] * rollDeg [deg]^3 * invGap^2
+ (-2.1756879968e+01) * currL [A] * rollDeg [deg]^2 * invGap^3
+ (-3.5929041347e+02) * currL [A] * rollDeg [deg] * invGap^4
+ (+1.3909390562e+01) * currL [A] * invGap^5
+ (+6.1617129177e-09) * currR [A]^6
+ (+3.7175730938e-08) * currR [A]^5 * rollDeg [deg]
+ (-2.1826492898e-06) * currR [A]^5 * invGap
+ (+3.0887363778e-08) * currR [A]^4 * rollDeg [deg]^2
+ (-2.5321109476e-06) * currR [A]^4 * rollDeg [deg] * invGap
+ (+2.0057675659e-04) * currR [A]^4 * invGap^2
+ (+2.5936417813e-07) * currR [A]^3 * rollDeg [deg]^3
+ (-7.9156716870e-06) * currR [A]^3 * rollDeg [deg]^2 * invGap
+ (-9.6870862064e-05) * currR [A]^3 * rollDeg [deg] * invGap^2
+ (-1.1576514633e-02) * currR [A]^3 * invGap^3
+ (+1.0210733379e-06) * currR [A]^2 * rollDeg [deg]^4
+ (-4.4586066717e-04) * currR [A]^2 * rollDeg [deg]^3 * invGap
+ (+3.8287512141e-02) * currR [A]^2 * rollDeg [deg]^2 * invGap^2
+ (-3.4044501906e-01) * currR [A]^2 * rollDeg [deg] * invGap^3
+ (+3.6814992351e+02) * currR [A]^2 * invGap^4
+ (+2.3420159192e-05) * currR [A] * rollDeg [deg]^5
+ (-9.2337309491e-03) * currR [A] * rollDeg [deg]^4 * invGap
+ (+7.4080431520e-01) * currR [A] * rollDeg [deg]^3 * invGap^2
+ (-2.1520950367e+01) * currR [A] * rollDeg [deg]^2 * invGap^3
+ (+3.5929051935e+02) * currR [A] * rollDeg [deg] * invGap^4
+ (+1.4109361400e+01) * currR [A] * invGap^5
+ (+1.7232857807e-04) * rollDeg [deg]^6
+ (-1.5228368774e-09) * rollDeg [deg]^5 * invGap
+ (+7.4229949571e+00) * rollDeg [deg]^4 * invGap^2
+ (-4.7116044996e-06) * rollDeg [deg]^3 * invGap^3
+ (+4.0058823232e+02) * rollDeg [deg]^2 * invGap^4
+ (+7.4032294285e-04) * rollDeg [deg] * invGap^5
+ (-1.3151563792e+02) * invGap^6
================================================================================
TORQUE [mN*m] =
-2.5609643910e+00
+ (+1.2736755974e+01) * currL [A]
+ (-1.3082527996e+01) * currR [A]
+ (-1.3305641735e+01) * rollDeg [deg]
+ (+4.4151637366e+01) * invGap
+ (-6.3923649292e-02) * currL [A]^2
+ (-1.1560951475e-02) * currL [A] * currR [A]
+ (+1.8386370689e+00) * currL [A] * rollDeg [deg]
+ (-4.5922645259e+02) * currL [A] * invGap
+ (+9.8233200925e-02) * currR [A]^2
+ (+1.8386371393e+00) * currR [A] * rollDeg [deg]
+ (+4.7236896866e+02) * currR [A] * invGap
+ (+9.1214755261e-01) * rollDeg [deg]^2
+ (-1.0749540976e+03) * rollDeg [deg] * invGap
+ (-1.7435331556e+02) * invGap^2
+ (+1.3682740756e-03) * currL [A]^3
+ (+1.9533070101e-03) * currL [A]^2 * currR [A]
+ (+1.9657240805e-02) * currL [A]^2 * rollDeg [deg]
+ (+2.0525258396e+00) * currL [A]^2 * invGap
+ (-2.0087168696e-03) * currL [A] * currR [A]^2
+ (-7.7704180912e-03) * currL [A] * currR [A] * rollDeg [deg]
+ (+4.6783332660e-01) * currL [A] * currR [A] * invGap
+ (-1.5697787523e-01) * currL [A] * rollDeg [deg]^2
+ (-2.5279026405e+01) * currL [A] * rollDeg [deg] * invGap
+ (-2.6796288784e+03) * currL [A] * invGap^2
+ (-6.9397567186e-04) * currR [A]^3
+ (+1.9657238531e-02) * currR [A]^2 * rollDeg [deg]
+ (-3.1136966908e+00) * currR [A]^2 * invGap
+ (+1.8298169417e-01) * currR [A] * rollDeg [deg]^2
+ (-2.5279027176e+01) * currR [A] * rollDeg [deg] * invGap
+ (+2.5386184669e+03) * currR [A] * invGap^2
+ (+6.2974733858e-01) * rollDeg [deg]^3
+ (-1.3210284466e+01) * rollDeg [deg]^2 * invGap
+ (+4.7007171607e+04) * rollDeg [deg] * invGap^2
+ (-3.3555302551e+02) * invGap^3
+ (-1.4305035722e-04) * currL [A]^4
+ (-1.6602474226e-05) * currL [A]^3 * currR [A]
+ (-1.2886823540e-04) * currL [A]^3 * rollDeg [deg]
+ (+6.0143039665e-03) * currL [A]^3 * invGap
+ (+1.2951511025e-05) * currL [A]^2 * currR [A]^2
+ (-5.1776437670e-04) * currL [A]^2 * currR [A] * rollDeg [deg]
+ (-3.8569371878e-02) * currL [A]^2 * currR [A] * invGap
+ (+5.2166822420e-03) * currL [A]^2 * rollDeg [deg]^2
+ (-6.2117182881e-01) * currL [A]^2 * rollDeg [deg] * invGap
+ (+9.0620919904e+01) * currL [A]^2 * invGap^2
+ (+1.3270592660e-06) * currL [A] * currR [A]^3
+ (-5.1776417343e-04) * currL [A] * currR [A]^2 * rollDeg [deg]
+ (+4.2265553856e-02) * currL [A] * currR [A]^2 * invGap
+ (-2.2041148798e-04) * currL [A] * currR [A] * rollDeg [deg]^2
+ (+2.4509139646e-01) * currL [A] * currR [A] * rollDeg [deg] * invGap
+ (-4.9160159525e+00) * currL [A] * currR [A] * invGap^2
+ (-1.7295894521e-01) * currL [A] * rollDeg [deg]^3
+ (-6.7494817486e+00) * currL [A] * rollDeg [deg]^2 * invGap
+ (-8.6427297569e+02) * currL [A] * rollDeg [deg] * invGap^2
+ (+8.5965909925e+03) * currL [A] * invGap^3
+ (-1.6550913550e-05) * currR [A]^4
+ (-1.2886821877e-04) * currR [A]^3 * rollDeg [deg]
+ (-3.0326211668e-02) * currR [A]^3 * invGap
+ (-5.1175783571e-03) * currR [A]^2 * rollDeg [deg]^2
+ (-6.2117181767e-01) * currR [A]^2 * rollDeg [deg] * invGap
+ (-7.5004948389e+01) * currR [A]^2 * invGap^2
+ (-1.7295894543e-01) * currR [A] * rollDeg [deg]^3
+ (+5.7289182157e+00) * currR [A] * rollDeg [deg]^2 * invGap
+ (-8.6427297453e+02) * currR [A] * rollDeg [deg] * invGap^2
+ (-8.1554262787e+03) * currR [A] * invGap^3
+ (-8.0890042154e-02) * rollDeg [deg]^4
+ (+1.7462417614e+02) * rollDeg [deg]^3 * invGap
+ (+5.9548102453e+01) * rollDeg [deg]^2 * invGap^2
+ (-9.1016550502e+04) * rollDeg [deg] * invGap^3
+ (-1.2462037728e+02) * invGap^4
+ (-1.2219304153e-05) * currL [A]^5
+ (-6.3133366268e-06) * currL [A]^4 * currR [A]
+ (+5.1514166444e-07) * currL [A]^4 * rollDeg [deg]
+ (+1.1879557083e-03) * currL [A]^4 * invGap
+ (-1.0954778098e-06) * currL [A]^3 * currR [A]^2
+ (-5.8420851161e-06) * currL [A]^3 * currR [A] * rollDeg [deg]
+ (+2.5831185234e-03) * currL [A]^3 * currR [A] * invGap
+ (+7.9254089698e-05) * currL [A]^3 * rollDeg [deg]^2
+ (-1.7220995748e-03) * currL [A]^3 * rollDeg [deg] * invGap
+ (-4.0028155701e-01) * currL [A]^3 * invGap^2
+ (+1.7079834365e-06) * currL [A]^2 * currR [A]^3
+ (-7.8935650691e-06) * currL [A]^2 * currR [A]^2 * rollDeg [deg]
+ (-3.2330488590e-04) * currL [A]^2 * currR [A]^2 * invGap
+ (+9.9753661971e-05) * currL [A]^2 * currR [A] * rollDeg [deg]^2
+ (+7.2169993632e-03) * currL [A]^2 * currR [A] * rollDeg [deg] * invGap
+ (+5.4494940800e-01) * currL [A]^2 * currR [A] * invGap^2
+ (-1.5381149512e-03) * currL [A]^2 * rollDeg [deg]^3
+ (-1.9907607357e-01) * currL [A]^2 * rollDeg [deg]^2 * invGap
+ (+1.0517964842e+01) * currL [A]^2 * rollDeg [deg] * invGap^2
+ (-5.9716223372e+02) * currL [A]^2 * invGap^3
+ (+5.7682329953e-06) * currL [A] * currR [A]^4
+ (-5.8420830129e-06) * currL [A] * currR [A]^3 * rollDeg [deg]
+ (-3.1387669824e-03) * currL [A] * currR [A]^3 * invGap
+ (-9.2627696858e-05) * currL [A] * currR [A]^2 * rollDeg [deg]^2
+ (+7.2169983158e-03) * currL [A] * currR [A]^2 * rollDeg [deg] * invGap
+ (-5.4112374537e-01) * currL [A] * currR [A]^2 * invGap^2
+ (-3.1504005406e-05) * currL [A] * currR [A] * rollDeg [deg]^3
+ (-1.7005015703e-04) * currL [A] * currR [A] * rollDeg [deg]^2 * invGap
+ (-2.3976914010e+00) * currL [A] * currR [A] * rollDeg [deg] * invGap^2
+ (+2.0162876449e+01) * currL [A] * currR [A] * invGap^3
+ (+3.0541236561e-02) * currL [A] * rollDeg [deg]^4
+ (+6.0909890705e+00) * currL [A] * rollDeg [deg]^3 * invGap
+ (+1.8686476537e+02) * currL [A] * rollDeg [deg]^2 * invGap^2
+ (+5.4569961037e+03) * currL [A] * rollDeg [deg] * invGap^3
+ (+3.6521334233e+03) * currL [A] * invGap^4
+ (+1.2356741024e-05) * currR [A]^5
+ (+5.1514541610e-07) * currR [A]^4 * rollDeg [deg]
+ (-3.2093123475e-04) * currR [A]^4 * invGap
+ (-9.5040930219e-05) * currR [A]^3 * rollDeg [deg]^2
+ (-1.7221002130e-03) * currR [A]^3 * rollDeg [deg] * invGap
+ (+6.5615872016e-01) * currR [A]^3 * invGap^2
+ (-1.5381149487e-03) * currR [A]^2 * rollDeg [deg]^3
+ (+2.0395948760e-01) * currR [A]^2 * rollDeg [deg]^2 * invGap
+ (+1.0517964822e+01) * currR [A]^2 * rollDeg [deg] * invGap^2
+ (+4.9837046412e+02) * currR [A]^2 * invGap^3
+ (-3.0694304201e-02) * currR [A] * rollDeg [deg]^4
+ (+6.0909890702e+00) * currR [A] * rollDeg [deg]^3 * invGap
+ (-1.7712281328e+02) * currR [A] * rollDeg [deg]^2 * invGap^2
+ (+5.4569961045e+03) * currR [A] * rollDeg [deg] * invGap^3
+ (-3.4643372364e+03) * currR [A] * invGap^4
+ (-3.1967283950e-01) * rollDeg [deg]^5
+ (+7.2465373581e-01) * rollDeg [deg]^4 * invGap
+ (-3.7694440105e+03) * rollDeg [deg]^3 * invGap^2
+ (+4.4429019352e+01) * rollDeg [deg]^2 * invGap^3
+ (-3.9730669147e+04) * rollDeg [deg] * invGap^4
+ (-3.1813627757e+01) * invGap^5
+ (+2.0551811986e-07) * currL [A]^6
+ (-2.2810121436e-07) * currL [A]^5 * currR [A]
+ (-1.3383146324e-07) * currL [A]^5 * rollDeg [deg]
+ (+1.6049756900e-04) * currL [A]^5 * invGap
+ (-5.6453359321e-07) * currL [A]^4 * currR [A]^2
+ (+2.6031671041e-07) * currL [A]^4 * currR [A] * rollDeg [deg]
+ (+1.2744387021e-05) * currL [A]^4 * currR [A] * invGap
+ (+2.8978174669e-06) * currL [A]^4 * rollDeg [deg]^2
+ (-9.3438872511e-05) * currL [A]^4 * rollDeg [deg] * invGap
+ (-3.2491823205e-03) * currL [A]^4 * invGap^2
+ (+3.7946676912e-09) * currL [A]^3 * currR [A]^3
+ (+1.7599444391e-07) * currL [A]^3 * currR [A]^2 * rollDeg [deg]
+ (+2.4965108992e-05) * currL [A]^3 * currR [A]^2 * invGap
+ (+1.1286476678e-06) * currL [A]^3 * currR [A] * rollDeg [deg]^2
+ (+4.5300600434e-05) * currL [A]^3 * currR [A] * rollDeg [deg] * invGap
+ (-1.5200582693e-02) * currL [A]^3 * currR [A] * invGap^2
+ (+2.7490628440e-06) * currL [A]^3 * rollDeg [deg]^3
+ (-8.2493098857e-04) * currL [A]^3 * rollDeg [deg]^2 * invGap
+ (+2.3944496913e-02) * currL [A]^3 * rollDeg [deg] * invGap^2
+ (+1.2946953968e+00) * currL [A]^3 * invGap^3
+ (+5.9211265580e-07) * currL [A]^2 * currR [A]^4
+ (+1.7599464286e-07) * currL [A]^2 * currR [A]^3 * rollDeg [deg]
+ (-3.7773169680e-05) * currL [A]^2 * currR [A]^3 * invGap
+ (-7.7324017411e-08) * currL [A]^2 * currR [A]^2 * rollDeg [deg]^2
+ (+1.6224376321e-04) * currL [A]^2 * currR [A]^2 * rollDeg [deg] * invGap
+ (+1.1125393841e-03) * currL [A]^2 * currR [A]^2 * invGap^2
+ (-1.8213825115e-08) * currL [A]^2 * currR [A] * rollDeg [deg]^3
+ (-1.1582951117e-03) * currL [A]^2 * currR [A] * rollDeg [deg]^2 * invGap
+ (-2.7423615740e-02) * currL [A]^2 * currR [A] * rollDeg [deg] * invGap^2
+ (-1.8375761343e+00) * currL [A]^2 * currR [A] * invGap^3
+ (+1.8148082155e-05) * currL [A]^2 * rollDeg [deg]^4
+ (+2.5582361106e-02) * currL [A]^2 * rollDeg [deg]^3 * invGap
+ (+1.8719567169e+00) * currL [A]^2 * rollDeg [deg]^2 * invGap^2
+ (-7.9375540256e+00) * currL [A]^2 * rollDeg [deg] * invGap^3
+ (+1.3851610060e+03) * currL [A]^2 * invGap^4
+ (+3.6572413364e-07) * currL [A] * currR [A]^5
+ (+2.6031864309e-07) * currL [A] * currR [A]^4 * rollDeg [deg]
+ (-1.3740560576e-05) * currL [A] * currR [A]^4 * invGap
+ (-1.1634704791e-06) * currL [A] * currR [A]^3 * rollDeg [deg]^2
+ (+4.5300591111e-05) * currL [A] * currR [A]^3 * rollDeg [deg] * invGap
+ (+1.7827349035e-02) * currL [A] * currR [A]^3 * invGap^2
+ (-1.8220930542e-08) * currL [A] * currR [A]^2 * rollDeg [deg]^3
+ (+1.0311063391e-03) * currL [A] * currR [A]^2 * rollDeg [deg]^2 * invGap
+ (-2.7423615867e-02) * currL [A] * currR [A]^2 * rollDeg [deg] * invGap^2
+ (+1.8202040056e+00) * currL [A] * currR [A]^2 * invGap^3
+ (+1.4693588980e-05) * currL [A] * currR [A] * rollDeg [deg]^4
+ (+2.0391970869e-03) * currL [A] * currR [A] * rollDeg [deg]^3 * invGap
+ (-5.1289752136e-03) * currL [A] * currR [A] * rollDeg [deg]^2 * invGap^2
+ (+1.3585046026e+01) * currL [A] * currR [A] * rollDeg [deg] * invGap^3
+ (-2.5312909994e+01) * currL [A] * currR [A] * invGap^4
+ (-1.2892918352e-03) * currL [A] * rollDeg [deg]^5
+ (-4.2744856185e-01) * currL [A] * rollDeg [deg]^4 * invGap
+ (-4.5230140146e+01) * currL [A] * rollDeg [deg]^3 * invGap^2
+ (-1.2691925261e+03) * currL [A] * rollDeg [deg]^2 * invGap^3
+ (-1.7946912044e+04) * currL [A] * rollDeg [deg] * invGap^4
+ (+9.8200368161e+02) * currL [A] * invGap^5
+ (+1.4402604620e-07) * currR [A]^6
+ (-1.3383078112e-07) * currR [A]^5 * rollDeg [deg]
+ (-1.5877721700e-04) * currR [A]^5 * invGap
+ (-1.8463799734e-06) * currR [A]^4 * rollDeg [deg]^2
+ (-9.3438911534e-05) * currR [A]^4 * rollDeg [deg] * invGap
+ (-2.0062450751e-03) * currR [A]^4 * invGap^2
+ (+2.7490636967e-06) * currR [A]^3 * rollDeg [deg]^3
+ (+1.0293575893e-03) * currR [A]^3 * rollDeg [deg]^2 * invGap
+ (+2.3944496992e-02) * currR [A]^3 * rollDeg [deg] * invGap^2
+ (-2.1505766179e+00) * currR [A]^3 * invGap^3
+ (-4.8050087258e-05) * currR [A]^2 * rollDeg [deg]^4
+ (+2.5582361094e-02) * currR [A]^2 * rollDeg [deg]^3 * invGap
+ (-1.8925775930e+00) * currR [A]^2 * rollDeg [deg]^2 * invGap^2
+ (-7.9375540232e+00) * currR [A]^2 * rollDeg [deg] * invGap^3
+ (-1.1457282555e+03) * currR [A]^2 * invGap^4
+ (-1.2892918417e-03) * currR [A] * rollDeg [deg]^5
+ (+4.3570132351e-01) * currR [A] * rollDeg [deg]^4 * invGap
+ (-4.5230140146e+01) * currR [A] * rollDeg [deg]^3 * invGap^2
+ (+1.2356182202e+03) * currR [A] * rollDeg [deg]^2 * invGap^3
+ (-1.7946912045e+04) * currR [A] * rollDeg [deg] * invGap^4
+ (-9.3157391357e+02) * currR [A] * invGap^5
+ (+1.9887971069e-03) * rollDeg [deg]^6
+ (+4.1532416818e+00) * rollDeg [deg]^5 * invGap
+ (-3.7128109697e+00) * rollDeg [deg]^4 * invGap^2
+ (+1.9150570779e+04) * rollDeg [deg]^3 * invGap^3
+ (+1.9562107621e+01) * rollDeg [deg]^2 * invGap^4
+ (-1.0765823661e+04) * rollDeg [deg] * invGap^5
+ (-6.8540115783e+00) * invGap^6