def experiment(cfg):
control(cfg)
ts = 1.0
A = np.array([[0.89, 0.], [0., 0.45]])
B = np.array([[0.3], [2.5]])
C = np.array([[0.7, 1.]])
D = np.array([[0.0]])
tfin = 500
npts = int(old_div(tfin, ts)) + 1
Time = np.linspace(0, tfin, npts)
# Input sequence
U = np.zeros((1, npts))
U[0] = fset.GBN_seq(npts, 0.05)
##Output
x, yout = fsetSIM.SS_lsim_process_form(A, B, C, D, U)
# measurement noise
noise = fset.white_noise_var(npts, [0.05])
# Output with noise
y_tot = yout + noise
##System identification
method = 'PARSIM-S'
sys_id = system_identification(y_tot, U, method, SS_fixed_order=2)
from sippy import functionset as fset
import numpy as np
import control.matlab as cnt
import matplotlib.pyplot as plt
## TEST RECURSIVE IDENTIFICATION METHODS
# Define sampling time and Time vector
sampling_time = 1. # [s]
end_time = 400 # [s]
npts = int(old_div(end_time, sampling_time)) + 1
Time = np.linspace(0, end_time, npts)
# Define Generalize Binary Sequence as input signal
switch_probability = 0.08 # [0..1]
[Usim, _, _] = fset.GBN_seq(npts, switch_probability, Range=[-1, 1])
# Define white noise as noise signal
white_noise_variance = [0.01]
e_t = fset.white_noise_var(Usim.size, white_noise_variance)[0]
# ## Define the system (ARMAX model)
# ### Numerator of noise transfer function has two roots: nc = 2
NUM_H = [1., 0.3, 0.2, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]
# ### Common denominator between input and noise transfer functions has 4 roots: na = 4
DEN = [
1., -2.21, 1.7494, -0.584256, 0.0684029, 0., 0., 0., 0., 0., 0., 0., 0.,
fx = np.append(dx_0, dx_1)
return fx
# Build input sequences
U = np.zeros((m, npts))
# manipulated inputs as GBN
# Input Flow rate Fin = F = U[0] [m^3/min]
prob_switch_1 = 0.05
F_min = 0.4
F_max = 0.6
Range_GBN_1 = [F_min, F_max]
U[0, :] = fset.GBN_seq(npts, prob_switch_1, Range=Range_GBN_1)
# Steam Flow rate W = U[1] [kg/min]
prob_switch_2 = 0.05
W_min = 20
W_max = 40
Range_GBN_2 = [W_min, W_max]
U[1, :] = fset.GBN_seq(npts, prob_switch_2, Range=Range_GBN_2)
# disturbance inputs as RW (random-walk)
# Input Concentration Ca_in = U[2] [kg salt/m^3 solution]
Ca_0 = 10.0 # initial condition
sigma_Ca = 0.01 # variation
U[2, :] = fset.RW_seq(npts, Ca_0, sigma=sigma_Ca)
# Input Temperature T_in [°C]
Tin_0 = 25.0 # initial condition
# sample time
ts = 1.0
# SISO SS system (n = 2)
A = np.array([[0.89, 0.], [0., 0.45]])
B = np.array([[0.3], [2.5]])
C = np.array([[0.7, 1.]])
D = np.array([[0.0]])
tfin = 500
npts = int(old_div(tfin, ts)) + 1
Time = np.linspace(0, tfin, npts)
# Input sequence
U = np.zeros((1, npts))
[U[0],_,_] = fset.GBN_seq(npts, 0.05)
##Output
x, yout = fsetSIM.SS_lsim_process_form(A, B, C, D, U)
# measurement noise
noise = fset.white_noise_var(npts, [0.15])
# Output with noise
y_tot = yout + noise
#
plt.close("all")
plt.figure(0)
plt.plot(Time, U[0])
plt.ylabel("input")
g_sample32 = cnt.tf(NUM32, DEN3, ts) g_sample33 = cnt.tf(NUM33, DEN3, ts) g_sample34 = cnt.tf(NUM34, DEN3, ts) H_sample1 = cnt.tf(H1, DEN1, ts) H_sample2 = cnt.tf(H2, DEN2, ts) H_sample3 = cnt.tf(H3, DEN3, ts) # tfin = 400 npts = int(old_div(tfin, ts)) + 1 Time = np.linspace(0, tfin, npts) # #INPUT# Usim = np.zeros((4, npts)) Usim_noise = np.zeros((4, npts)) Usim[0, :] = fset.GBN_seq(npts, 0.03, [-0.33, 0.1]) Usim[1, :] = fset.GBN_seq(npts, 0.03) Usim[2, :] = fset.GBN_seq(npts, 0.03, [2.3, 5.7]) Usim[3, :] = fset.GBN_seq(npts, 0.03, [8., 11.5]) # Adding noise err_inputH = np.zeros((4, npts)) err_inputH = fset.white_noise_var(npts, var_list) err_outputH = np.ones((3, npts)) err_outputH1, Time, Xsim = lsim(H_sample1, err_inputH[0, :], Time) err_outputH2, Time, Xsim = lsim(H_sample2, err_inputH[1, :], Time) err_outputH3, Time, Xsim = lsim(H_sample3, err_inputH[2, :], Time) Yout11, Time, Xsim = lsim(g_sample11, Usim[0, :], Time)
from sippy import functionsetSIM as fsetSIM
ts = 1.0
A = np.array([[0.89, 0.], [0., 0.45]])
B = np.array([[0.3], [2.5]])
C = np.array([[0.7, 1.]])
D = np.array([[0.0]])
tfin = 500000
npts = int(old_div(tfin, ts)) + 1
Time = np.linspace(0, tfin, npts)
# Input sequence
U = np.zeros((1, npts))
U[0] = fset.GBN_seq(npts, 0.05)
##Output
x, yout = fsetSIM.SS_lsim_process_form(A, B, C, D, U)
# measurement noise
noise = fset.white_noise_var(npts, [0.15])
# Output with noise
y_tot = yout + noise
##System identification
method = 'N4SID'
sys_id = system_identification(y_tot, U, method, SS_fixed_order=2)
xid, yid = fsetSIM.SS_lsim_process_form(sys_id.A, sys_id.B, sys_id.C, sys_id.D,
U, sys_id.x0)
dx_1 = (ro*cp*U[0]*U[3] - ro*cp*U[0]*X[1] + U[1]*Lam)/(V*ro*cp)
fx = np.append(dx_0,dx_1)
return fx
# Build input sequences
U = np.zeros((m,npts))
# manipulated inputs as GBN
# Input Flow rate Fin = F = U[0] [m^3/min]
prob_switch_1 = 0.05
F_min = 0.4
F_max = 0.6
Range_GBN_1 = [F_min,F_max]
[U[0,:],_,_] = fset.GBN_seq(npts, prob_switch_1, Range = Range_GBN_1)
# Steam Flow rate W = U[1] [kg/min]
prob_switch_2 = 0.05
W_min = 20
W_max = 40
Range_GBN_2 = [W_min,W_max]
[U[1,:],_,_] = fset.GBN_seq(npts, prob_switch_2, Range = Range_GBN_2)
# disturbance inputs as RW (random-walk)
# Input Concentration Ca_in = U[2] [kg salt/m^3 solution]
Ca_0 = 10.0 # initial condition
sigma_Ca = 0.01 # variation
U[2,:] = fset.RW_seq(npts, Ca_0, sigma = sigma_Ca)
# Input Temperature T_in [°C]
Tin_0 = 25.0 # initial condition
g_sample32 = cnt.tf(NUM32, DEN3, ts) g_sample33 = cnt.tf(NUM33, DEN3, ts) g_sample34 = cnt.tf(NUM34, DEN3, ts) H_sample1 = cnt.tf(H1, DEN1, ts) H_sample2 = cnt.tf(H2, DEN2, ts) H_sample3 = cnt.tf(H3, DEN3, ts) # tfin = 400 npts = int(old_div(tfin, ts)) + 1 Time = np.linspace(0, tfin, npts) # #INPUT# Usim = np.zeros((4, npts)) Usim_noise = np.zeros((4, npts)) [Usim[0, :], _, _] = fset.GBN_seq(npts, 0.03, Range=[-0.33, 0.1]) [Usim[1, :], _, _] = fset.GBN_seq(npts, 0.03) [Usim[2, :], _, _] = fset.GBN_seq(npts, 0.03, Range=[2.3, 5.7]) [Usim[3, :], _, _] = fset.GBN_seq(npts, 0.03, Range=[8., 11.5]) # Adding noise err_inputH = np.zeros((4, npts)) err_inputH = fset.white_noise_var(npts, var_list) err_outputH1, Time, Xsim = cnt.lsim(H_sample1, err_inputH[0, :], Time) err_outputH2, Time, Xsim = cnt.lsim(H_sample2, err_inputH[1, :], Time) err_outputH3, Time, Xsim = cnt.lsim(H_sample3, err_inputH[2, :], Time) # OUTPUTS Yout = np.zeros((3, npts))
def control(cfg):
log.info("============= Configuration =============")
log.info(f"Config:\n{cfg.pretty()}")
log.info("=========================================")
dt = cfg.sys.params.dt
# System matrices
A = np.mat(cfg.sys.params.A)
B = np.mat(cfg.sys.params.B)
C = np.mat(cfg.sys.params.C)
D = np.mat(cfg.sys.params.D)
system = StateSpace(A, B, C, D, dt)
dx = np.shape(A)[0]
# Check controllability
Wc = ctrb(A, B)
print("Wc = ", Wc)
print(f"Rank of controllability matrix is {np.linalg.matrix_rank(Wc)}")
# Check Observability
Wo = obsv(A, C)
print("Wo = ", Wo)
print(f"Rank of observability matrix is {np.linalg.matrix_rank(Wo)}")
fdbk_poles = np.random.uniform(0, .1, size=(np.shape(A)[0]))
obs_poles = np.random.uniform(0, .01, size=(np.shape(A)[0]))
observer = full_obs(system, obs_poles)
K = place(system.A, system.B, fdbk_poles)
low = -np.ones((dx, 1))
high = np.ones((dx, 1))
x0 = np.random.uniform(low, high)
env = gym.make(cfg.sys.name)
env.setup(cfg)
y = env.reset()
x_obs = x0
# code for testing observers... they work!
# for t in range(100):
# action = controller(K).get_action(env._get_state())
# y, rew, done, _ = env.step(action)
# x_obs = np.matmul(observer.A, x_obs) + np.matmul(observer.B, np.concatenate((action, y)))
# print(f"Time {t}, mean sq state error is {np.mean(env._get_state()-x_obs)**2}")
log.info(f"Running rollouts on system {cfg.sys.name}")
n_random = 1000
# states_r, actions_r, reward_r = rollout(env, random_controller(env), n_random)
# log.info(f"Random rollout, reward {np.sum(reward_r)}")
states_r = []
actions_r = []
reward_r = []
# Input sequence
U = np.zeros((1, n_random))
U[0] = fset.GBN_seq(n_random, 0.05)
##Output
x, yout = fsetSIM.SS_lsim_process_form(A, B, C, D, U)
# measurement noise
noise = fset.white_noise_var(n_random, [0.15])
# Output with noise
y_tot = yout + noise
##System identification
method = 'N4SID'
system_initial = system_identification(
y_tot, U, method, SS_fixed_order=np.shape(A)[0]) #, tsample=dt)
system_initial.dt = dt
print(A)
print(np.round(system_initial.A, 2))
xid, yid = fsetSIM.SS_lsim_process_form(system_initial.A, system_initial.B,
system_initial.C, system_initial.D,
U, system_initial.x0)
# system_initial = sys_id(actions_r, states_r, dt, method='N4SID', order=dx, SS_fixed_order=np.shape(A)[0])
# system_initial.dt = dt
observer = full_obs(system_initial, obs_poles)
K = place(system_initial.A, system_initial.B, fdbk_poles)
# print(np.array(cfg.sys.params.A))
# TODO integrate observer so that we can use state feedback
log.info(
f"Running {cfg.experiment.num_trials} trials with SI and feedback control"
)
for i in range(cfg.experiment.num_trials):
# Rollout at this step
# states, actions, reward = rollout(env, controller(K), cfg.experiment.trial_timesteps)
states, actions, reward = rollout_observer(
env, controller(K), observer, cfg.experiment.trial_timesteps)
[states_r.append(s) for s in states]
[actions_r.append(a) for a in actions]
[reward_r.append(r) for r in reward]
# Run system ID on the dataset
# system = sys_id(actions, states, order=dx) # partial
system = sys_id(actions_r, states_r, dt, order=dx) # full
system.dt = dt
observer = full_obs(system, obs_poles)
print(system.A.round(2))
# Create controller
K = place(system.A, system.B, fdbk_poles)
log.info(f"Rollout {i}: reward {np.sum(reward)}")
plot_rollout(states_r, actions_r)
g_sample33 = cnt.tf(NUM33, DEN3, ts) g_sample34 = cnt.tf(NUM34, DEN3, ts) H_sample1 = cnt.tf(H1, DEN1, ts) H_sample2 = cnt.tf(H2, DEN2, ts) H_sample3 = cnt.tf(H3, DEN3, ts) # time tfin = 400 npts = int(old_div(tfin, ts)) + 1 Time = np.linspace(0, tfin, npts) #INPUT# Usim = np.zeros((4, npts)) Usim_noise = np.zeros((4, npts)) [Usim[0, :], _, _] = fset.GBN_seq(npts, 0.03, Range=[-0.33, 0.1]) [Usim[1, :], _, _] = fset.GBN_seq(npts, 0.03) [Usim[2, :], _, _] = fset.GBN_seq(npts, 0.03, Range=[2.3, 5.7]) [Usim[3, :], _, _] = fset.GBN_seq(npts, 0.03, Range=[8., 11.5]) # Adding noise err_inputH = np.zeros((4, npts)) err_inputH = fset.white_noise_var(npts, var_list) err_outputH = np.ones((3, npts)) err_outputH1, Time, Xsim = cnt.lsim(H_sample1, err_inputH[0, :], Time) err_outputH2, Time, Xsim = cnt.lsim(H_sample2, err_inputH[1, :], Time) err_outputH3, Time, Xsim = cnt.lsim(H_sample3, err_inputH[2, :], Time) # Noise-free output Yout11, Time, Xsim = cnt.lsim(g_sample11, Usim[0, :], Time)
from sippy import *
import numpy as np
import control.matlab as cnt
import matplotlib.pyplot as plt
# ## Define sampling time and Time vector
sampling_time = 1. # [s]
end_time = 400 # [s]
npts = int(old_div(end_time, sampling_time)) + 1
Time = np.linspace(0, end_time, npts)
# ## Define pseudo random binary sequence as input signal and white noise as noise signal
switch_probability = 0.08 # [0..1]
Usim = fset.GBN_seq(npts, switch_probability)
white_noise_variance = [0.005]
e_t = fset.white_noise_var(Usim.size, white_noise_variance)[0]
# ## Define the system
# ### Numerator of noise transfer function has only one root: nc = 1
NUM_H = [1., 0.3, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]
# ### Common denominator between input and noise transfer functions has 4 roots: na = 4
DEN = [
1., -2.21, 1.7494, -0.584256, 0.0684029, 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0.
]
g_sample32 = cnt.tf(NUM32, DEN3, ts) g_sample33 = cnt.tf(NUM33, DEN3, ts) g_sample34 = cnt.tf(NUM34, DEN3, ts) H_sample1 = cnt.tf(H1, DEN1, ts) H_sample2 = cnt.tf(H2, DEN2, ts) H_sample3 = cnt.tf(H3, DEN3, ts) # tfin = 400 npts = int(old_div(tfin, ts)) + 1 Time = np.linspace(0, tfin, npts) # #INPUT# Usim = np.zeros((4, npts)) Usim_noise = np.zeros((4, npts)) Usim[0, :] = fset.GBN_seq(npts, 0.03, [-0.33, 0.1]) Usim[1, :] = fset.GBN_seq(npts, 0.03) Usim[2, :] = fset.GBN_seq(npts, 0.03, [2.3, 5.7]) Usim[3, :] = fset.GBN_seq(npts, 0.03, [8., 11.5]) # Adding noise err_inputH = np.zeros((4, npts)) err_inputH = fset.white_noise_var(npts, var_list) err_outputH1, Time, Xsim = cnt.lsim(H_sample1, err_inputH[0, :], Time) err_outputH2, Time, Xsim = cnt.lsim(H_sample2, err_inputH[1, :], Time) err_outputH3, Time, Xsim = cnt.lsim(H_sample3, err_inputH[2, :], Time) # OUTPUTS Yout = np.zeros((3, npts))