def run_open_loop(ax, dt, method='time-stepping'):
''' Carry out an open-loop simulation of a DC motor with Coulomb friction
given an input signal obtained by the sum of a constant term, a linear
term (in time), and a sinusoidal term.
'''
from dc_motor import get_motor_parameters
T = 2 # simulation time
V_b = 0.0 # initial motor input
V_a = 0.0 # linear increase in motor input per second
V_w = .5 # frequency of the sinusoidal motor input
V_A = 1.1 # amplitude of the sinusoidal motor input
params = get_motor_parameters('Focchi2013')
params.tau_coulomb = 1
# simulate motor with linear+sinusoidal input torque
N = int(T / dt) # number of time steps
motor = MotorCoulomb(dt, params)
# motor.set_state(np.array([0.0, 1e-5]))
q = np.zeros(N + 1)
dq = np.zeros(N + 1)
tau_f = np.zeros(N + 1)
tau = np.zeros(N)
for i in range(N):
tau[i] = V_a * i * dt + V_b + V_A * np.sin(2 * np.pi * V_w * i * dt)
motor.simulate_torque(tau[i], method)
# motor.simulate(tau[i], method)
q[i + 1] = motor.q()
dq[i + 1] = motor.dq()
tau_f[i] = motor.tau_f / dt
tau[i] = motor.tau()
# plot motor angle, velocity and current
time = np.arange(0.0, T + dt, dt)
time = time[:N + 1]
alpha = 0.8
ax[0].plot(time, q, label='q ' + method, alpha=alpha)
ax[1].plot(time, dq, label='dq ' + method, alpha=alpha)
ax[2].plot(time[:-1], tau, label='tau ' + method, alpha=alpha)
ax[-1].plot(time, tau_f, '--', label='tau_f ' + method, alpha=alpha)
for i in range(len(ax)):
ax[i].legend()
plt.xlabel('Time [s]')
def run_open_loop(ax, dt, method='time-stepping'):
from dc_motor import get_motor_parameters
T = 2 # simulation time
V_b = 0.0 # initial motor voltage
V_a = 0.0 # linear increase in motor voltage per second
V_w = .5
V_A = 1.1
params = get_motor_parameters('Focchi2013')
params.tau_coulomb = 1
# simulate motor with linear+sinusoidal input torque
N = int(T/dt) # number of time steps
motor = MotorCoulomb(dt, params)
# motor.set_state(np.array([0.0, 1e-5]))
q = np.zeros(N+1)
dq = np.zeros(N+1)
tau_f = np.zeros(N+1)
tau = np.zeros(N)
for i in range(N):
tau[i] = V_a*i*dt + V_b + V_A*np.sin(2*np.pi*V_w*i*dt)
motor.simulate_torque(tau[i], method)
# motor.simulate(tau[i], method)
q[i+1] = motor.q()
dq[i+1] = motor.dq()
tau_f[i] = motor.tau_f/dt
tau[i] = motor.tau()
# plot motor angle, velocity and current
time = np.arange(0.0, T+dt, dt)
time = time[:N+1]
alpha = 0.8
ax[0].plot(time, q, label ='q '+method, alpha=alpha)
ax[1].plot(time, dq, label ='dq '+method, alpha=alpha)
ax[2].plot(time[:-1], tau, label ='tau '+method, alpha=alpha)
ax[-1].plot(time, tau_f, '--', label ='tau_f '+method, alpha=alpha)
for i in range(len(ax)): ax[i].legend()
plt.xlabel('Time [s]')
simulate_coulomb = 0 # flag to decide whether to simulate Coulomb friction
motor_name = 'Maxon148877'
if motor_name == 'Focchi2013':
# gains for motor Focchi2013
kp = 5000.0 # proportional gain
kd = 10.0 # derivative gain
elif motor_name == 'Maxon148877':
kp = .1 # proportional gain
kd = .01 # derivative gain
ki = 0.0 # integral gain
q_b = 1.0 # initial motor angle
q_a = 0.0 # linear increase in motor angle per second
q_w = 0.0 # frequency of sinusoidal reference motor angle
q_A = 0.0 # amplitude of sinusoidal reference motor angle
params = get_motor_parameters(motor_name)
# create motor and position controller
if simulate_coulomb:
motor = MotorCoulomb(dt, params)
else:
motor = Motor(dt, params)
controller = PositionControl(kp, kd, ki, dt)
# simulate motor with linear+sinusoidal reference motor angle
N = int(T / dt) # number of time steps
q = np.zeros(N)
dq = np.zeros(N)
current = np.zeros(N)
tau = np.zeros(N)
V = np.zeros(N)