def run_simulation():
"""Run a simulation of the controller."""
# Define system parameters
p_atm = 14.0 # psi
t_step = 0.01 # simulation time step, seconds
t_step_ctrl = 0.1 # controller update rate, seconds
K = 0.1 # static pressure sensor gain, V/psi (?)
offset = 1.0 # static pressure sensor offset, V (?)
K_mfcs = [99.21, 7.968, 8.007] # MFC gains: [air, pilot, outer], SLPM/V
zeta_mfcs = [0.7054, 0.6, 0.6] # MFC damping ratios: [air, pilot, outer]
wn_mfcs = [1.3501, 1, 1] # MFC natural frequencies: [air, pilot, outer], rad/sec
td_mfcs = [1.8, 0.139, 0.306] # MFC time delays: [air, pilot, outer], sec
K_mid = 7.964 # middle fuel MFC static gain, SLPM/V
tau_mid = 0.516 # middle fuel MFC time constant, sec (first-order)
td_mid = 0.194 # middle fuel MFC time delay, sec
y0 = [0.0, 0.0, 0.0, 0.0] # initial value, 2nd order sys with 3,2 order Pade approximation of time delay
mfc_list = []
control_law_list = []
Q = np.ndarray([[100, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0] [0, 0, 0, 1]])
R = np.ndarray([[1]])
sensor_locations = [43.81, 76.2, 236.728, 609.6] # dynamic P sensor locations from base, mm
# Initialize sensor list
sensor_list = [lab_hardware.StaticSensor(model=lambda y: sim_functions.static_model(y, K, offset),
location=0.0)]
for loc in sensor_locations:
sensor_list.append(lab_hardware.DynamicSensor(model=tf1, location=loc))
# TODO figure out sensor transfer functions or models!
# Initialize mass flow controller (MFC) list and control law list
for K, zeta, wn, td in zip(K_mfcs, zeta_mfcs, wn_mfcs, td_mfcs):
A, B, C = sim_functions.get_second_ord_matrices(K, zeta, wn, td)
K_lqr = sim_functions.make_lqr_law(A, B, Q, R)
mfc_list.append(lab_hardware.MFC(lambda t, y, u: sim_functions.system_state_update(t, y, u, A, B),
lambda y: sim_functions.system_output(y, C),
y0))
control_law_list.append(lambda e:-K_lqr.dot(e))
# Insert our first-order-modeled middle fuel MFC
A, B, C = sim_functions.get_state_matrices(K_mid, tau_mid, td_mid)
K_lqr = sim_functions.make_lqr_law(A, B, Q[:2, :2], R) # smaller Q matrix, only 3 states
mfc_list.insert(2, lab_hardware.MFC(lambda t, y, u: sim_functions.system_state_update(t, y, u, A, B),
lambda y: sim_functions.system_output(y, C),
y0[:2])) # shorter y0, only 3 states
control_law_list.insert(2, lambda e:-K_lqr.dot(e))
# mfc and control law list should be in order: [air, pilot, middle, outer]
# Initialize the combustor object
combustor = lab_hardware.Combustor(p_atm, t_step, t_step_ctrl, sensor_list,
mfc_list, control_law_list)
def test_make_lqr_law(self):
"""Tests for make_lqr_law function."""
# Define constants
tau_list = [0.3, 1, 3]
delay_list = [0.1, 0.3]
param_list = set(itertools.chain(*[zip(tau_list, x) for x in
itertools.permutations(delay_list, len(tau_list))]))
Q = np.array([[100, 0, 0], [0, 1, 0], [0, 0, 1]]) # state error weight
R = np.array([[1]]) # control effort weight
for tau, delay in param_list:
den = tau * delay ** 2
A = np.array([[0, 1, 0], [0, 0, 1], [-12 / den, -(6 * delay + 12 * tau) / den, -(6 * tau + delay) / tau / delay]])
B = np.array([[0], [0], [12 / den]])
# Create control law
K_lqr, _, eig_vals = sim_functions.make_lqr_law(A, B, Q, R)
print(eig_vals)
# Test return type
self.assertIsInstance(K_lqr, np.ndarray,
"LQR law not returned as ndarray.")
# Test return dimensions
self.assertTupleEqual(K_lqr.shape, (1, 3),
"LQR law not the correct shape: {}, expected (1, 3).".format(K_lqr.shape))
# Test that controlled system is stable
self.assertTrue(all([np.real(item) < 0 for item in eig_vals]),
"All LQR-controlled poles not in left-half plane.")
