def test_get_state_matrices(self):
"""Tests the get_state_matrices function."""
# Define constants
K_list = [1, 3, 10]
tau_list = [0.1, 0.3, 1]
delay_list = [0.01, 0.1, 0.3, 1]
param_list = set(itertools.chain(*[zip(K_list, x, y) for x in
itertools.permutations(tau_list, len(K_list))
for y in
itertools.permutations(delay_list, len(K_list))]))
for K, tau, td in param_list:
den = tau * td ** 2
A_exp = np.array([[0, 1, 0], [0, 0, 1], [-12 / den, -(6 * td + 12 * tau) / den, -(6 * tau + td) / tau / td]])
B_exp = np.array([[0], [0], [12 / den]])
C_exp = np.array([[K, -K * td / 2, K * td ** 2 / 12]])
A, B, C = sim_functions.get_state_matrices(K, tau, td)
self.assertListEqual(A.tolist(), A_exp.tolist(),
"A matrix does not match expected.")
self.assertListEqual(B.tolist(), B_exp.tolist(),
"B matrix does not match expected.")
self.assertListEqual(C.tolist(), C_exp.tolist(),
"C matrix does not match expected")
def test_get_second_ord_matrices(self):
"""Tests the sim_functions.get_second_ord_matrices method."""
pass
def setUp(self):
"""Run repeated setup code once."""
# Define class and local parameters
unittest.TestCase.setUp(self)
self.K_list = [3, 10, 99.21]
self.tau_list = [0.3, 1]
self.delay_list = [0.03, 0.1, 0.3]
self.t_step = 0.01
self.stop_time = 20.0
self.input_val = 1.0
self.t_step_ctrl = 0.1
self.zeta = 0.7054 # air MFC damping ratio
self.wn = 1.3501 # air MFC natural frequency, rad/s
self.td = 1.8 # air MFC time delay, sec
self.y0_1 = [0]
self.y0_2 = [0] * 3 # for first-order model
self.y0_3 = [0] * 4 # for second-order model
A, B, self.C = sim_functions.get_state_matrices(
self.K_list[1], self.tau_list[-1], self.delay_list[0])
A2, B2, self.C2 = sim_functions.get_second_ord_matrices(
self.K_list[-1], self.zeta, self.wn, self.td)
self.Kp_list = [4.0, 5.0]
self.mass_flow_des = [4.0, 2.0]
self.std = 1.0
self.Ks = 2.0 # filter static gain (?)
Q = 1e-5 * np.identity(A2.shape[0]) # process noise covariance
R = self.std # measurement noise covariance
self.P = Q # initial estimate of error covariance
self.offset = 0.0
mean = 0.0
# Define objects
self.test_mfc1 = lab_hardware.MFC(
lambda t, y, u: test_ode(t, y, u, self.K_list[1], self.tau_list[-1]
), lambda x: x[0], self.y0_1)
self.test_mfc2 = lab_hardware.MFC(
lambda t, y, u: sim_functions.system_state_update(t, y, u, A, B),
lambda y: sim_functions.system_output(y, self.C), self.y0_2)
self.test_mfc3 = lab_hardware.MFC(
lambda t, y, u: sim_functions.system_state_update(t, y, u, A2, B2),
lambda y: sim_functions.system_output(y, self.C2), self.y0_3)
self.mfc_list = [
lab_hardware.MFC(lambda t, y, u: test_ode(t, y, u, K, tau),
lambda x: x[0], self.y0_1)
for K, tau in zip(self.K_list, self.tau_list)
]
self.test_KF = lab_hardware.KalmanFilter(A2, B2, self.Ks * self.C2, Q,
R, self.P)
self.test_sensor = lab_hardware.StaticSensor(
lambda y: sim_functions.static_model(y, self.Ks, self.offset, mean,
self.std), 1.0)
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 setUp(self):
"""Run repeated setup code once."""
# Define class and local parameters
unittest.TestCase.setUp(self)
self.K_list = [3, 10, 99.21]
self.tau_list = [0.3, 1]
self.delay_list = [0.03, 0.1, 0.3]
self.t_step = 0.01
self.stop_time = 20.0
self.input_val = 1.0
self.t_step_ctrl = 0.1
self.zeta = 0.7054 # air MFC damping ratio
self.wn = 1.3501 # air MFC natural frequency, rad/s
self.td = 1.8 # air MFC time delay, sec
self.y0_1 = [0]
self.y0_2 = [0] * 3 # for first-order model
self.y0_3 = [0] * 4 # for second-order model
A, B, self.C = sim_functions.get_state_matrices(self.K_list[1],
self.tau_list[-1],
self.delay_list[0])
A2, B2, self.C2 = sim_functions.get_second_ord_matrices(self.K_list[-1],
self.zeta, self.wn,
self.td)
self.Kp_list = [4.0, 5.0]
self.mass_flow_des = [4.0, 2.0]
self.std = 1.0
self.Ks = 2.0 # filter static gain (?)
Q = 1e-5 * np.identity(A2.shape[0]) # process noise covariance
R = self.std # measurement noise covariance
self.P = Q # initial estimate of error covariance
self.offset = 0.0
mean = 0.0
# Define objects
self.test_mfc1 = lab_hardware.MFC(lambda t, y, u: test_ode(t, y, u, self.K_list[1], self.tau_list[-1]),
lambda x: x[0], self.y0_1)
self.test_mfc2 = lab_hardware.MFC(lambda t, y, u: sim_functions.system_state_update(t, y, u, A, B),
lambda y: sim_functions.system_output(y, self.C),
self.y0_2)
self.test_mfc3 = lab_hardware.MFC(lambda t, y, u: sim_functions.system_state_update(t, y, u, A2, B2),
lambda y: sim_functions.system_output(y, self.C2),
self.y0_3)
self.mfc_list = [lab_hardware.MFC(lambda t, y, u: test_ode(t, y, u, K, tau),
lambda x: x[0], self.y0_1)
for K, tau in zip(self.K_list, self.tau_list)]
self.test_KF = lab_hardware.KalmanFilter(A2, B2, self.Ks * self.C2, Q, R, self.P)
self.test_sensor = lab_hardware.StaticSensor(lambda y: sim_functions.static_model(y, self.Ks, self.offset, mean, self.std),
1.0)
