-
Notifications
You must be signed in to change notification settings - Fork 0
/
ILC_sim_v2.0.py
339 lines (300 loc) · 10.2 KB
/
ILC_sim_v2.0.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
import numpy as np
import scipy.signal
from common import *
from control_math import *
from numpy import pi
from scipy.signal import ss2tf, tf2ss, impulse, impulse2, step, butter, lsim, lsim2
from sympy import solve
from sympy.abc import a, b, c
from scipy.linalg import toeplitz
"""Plant"""
m = 0.03
k = 0
bb = 0
A = np.array([[0, 1], [-k / m, -bb / m]])
B = np.array([[0], [1 / m]])
C = np.array([1, 0])
D = np.array([0])
# rigid_plant_num, rigid_plant_den = ss2tf(A, B, C, D)
#
# res_freq = 200
# anti_res_freq = 150
# res_omega = res_freq * 2 * np.pi
# anti_res_omega = anti_res_freq * 2 * np.pi
#
# mass = 0.4
# beta1 = 0.1
# beta2 = 0.1
# res_num = (
# 1
# / mass
# * res_omega ** 2
# / anti_res_omega ** 2
# * np.array([1, 2 * beta1 * anti_res_omega, anti_res_omega ** 2])
# )
# res_den = np.array([1, 2 * beta2 * res_omega, res_omega ** 2, 0, 0])
# num = np.convolve(res_num, rigid_plant_num.flatten())
# den = np.convolve(res_den, rigid_plant_den.flatten())
# num = res_num
# den = res_den
# A, B, C, D = tf2ss(num, den)
sys_ss = StateSpaceModel(A, B, C, D, DT)
num = [1]
den = [m, 0, 0]
sys_tf = TransferFunc(num, den, DT)
"""Chirp信号初始化"""
start_freq = 10
end_freq = 2000
start_freq_ = 0.8 * start_freq
end_freq_ = 1.1 * end_freq
# 扫频时间
T4chirp = 1
T4chirp = (
int(((end_freq_ - start_freq_) / (end_freq - start_freq) * T4chirp) * SERVO_FREQ)
/ SERVO_FREQ
)
t4chirp = np.linspace(0, T4chirp, int(SERVO_FREQ * T4chirp) + 1)
u = np.sin(
2
* np.pi
* ((end_freq_ - start_freq_) / T4chirp * t4chirp ** 2 / 2 + start_freq_ * t4chirp)
)
# u = np.linspace(0, 1, len(t4dyn))
# u = np.sin(2 * pi * 500 * t4dyn)
"""计算Chirp响应"""
y = np.zeros_like(u)
for i in range(len(u)):
input_sig = u[i]
y_output, x_state = sys_ss.response(input_sig, method="zoh2")
y[i] = y_output
p = y
y = np.diff(y, 2) / DT / DT
y = np.pad(y, (2, 0), "constant", constant_values=(0, 0))
u_detrend = u - np.mean(u)
y_detrend = y - np.mean(y)
f_bode, fw_u = fft(hamm(u_detrend), DT)
f_y, fw_y = fft(hamm(y_detrend), DT)
resolution = 1 / DT / len(f_bode)
start_point = int(start_freq / resolution)
end_point = int(end_freq / resolution)
f_bode = f_bode[start_point:end_point]
fw = fw_y[start_point:end_point] / fw_u[start_point:end_point]
"""修正差分和离散化方法造成的伯德图误差"""
zoh_decay = (1 - np.e ** (-1j * 2 * pi * f_bode * DT)) / (1j * 2 * pi * f_bode * DT)
linear_decay = (
np.e ** (1j * 2 * pi * f_bode * DT)
* (1 - np.e ** (-1j * 2 * pi * f_bode * DT)) ** 2
/ (1j * 2 * pi * f_bode * DT) ** 2
)
fw = fw / zoh_decay / zoh_decay / zoh_decay
# 拟合传递函数
Bn, Am = fit2(f_bode, fw, 0, 0)
sys_fit = TransferFunc(Bn, Am, DT)
print("num:", num, "den:", den[:-2])
print("Bn:", Bn, "Am:", Am)
"""设计PID"""
num_a = np.array([1 / m])
den_a = np.array([1])
delay_num = np.array([-0.00005, 1])
delay_den = np.array([1])
num_a_delay = np.convolve(delay_num, num_a.flatten())
den_a_delay = np.convolve(delay_den, den_a.flatten())
sys_tf_delay = TransferFunc(num_a_delay, den_a_delay, DT) * TransferFunc(
[1], [1, 0, 0], DT
)
sys_tf = sys_tf_delay
f_fit4pid, fw_fit4pid = TransferFunc(num_a_delay, den_a_delay, DT).bode(
np.array(range(1, 500))
)
# f_fit4pid, fw_fit4pid = TransferFunc(num_a_delay, den_a_delay, DT).bode(
# np.array(range(1, 500))
# )
# f_fit4pid, fw_fit4pid = sys_fit.bode(np.array(range(1, 500)))
plant_gain = np.mean(20 * np.log10(np.abs(fw_fit4pid)))
kp, ki, kd = pole_placement(plant_gain, 100, 0, SERVO_FREQ)
# kp = 1000
# ki = 0.1
# kd = 1000
print(kp, ki, kd)
pid_controller = PID(kp, ki, kd, SERVO_FREQ)
pid_tf = TransferFunc([kd, kp, ki], [1, 0], DT)
# SPG
T4dyn = 0.03
T4settling = 0.03
T4move = T4dyn + T4settling
y1 = 0.005
sol = solve(
[
a * T4dyn ** 5 + b * T4dyn ** 4 + c * T4dyn ** 3 - y1,
5 * a * T4dyn ** 4 + 4 * b * T4dyn ** 3 + 3 * c * T4dyn ** 2,
20 * a * T4dyn ** 3 + 12 * b * T4dyn ** 2 + 6 * c * T4dyn,
],
[a, b, c],
)
t4dyn = np.arange(0, T4dyn, DT)
set_p = sol[a] * t4dyn ** 5 + sol[b] * t4dyn ** 4 + sol[c] * t4dyn ** 3
set_v = 5 * sol[a] * t4dyn ** 4 + 4 * sol[b] * t4dyn ** 3 + sol[c] * 3 * t4dyn ** 2
set_a = 20 * sol[a] * t4dyn ** 3 + 12 * sol[b] * t4dyn ** 2 + sol[c] * 6 * t4dyn ** 1
t4move = np.arange(0, T4move, DT)
T4move = round(t4move[-1] + DT, 10)
set_p = np.append(set_p, y1 * np.ones(len(t4move) - len(t4dyn)))
set_v = np.append(set_v, np.zeros(len(t4move) - len(t4dyn)))
set_a = np.append(set_a, np.zeros(len(t4move) - len(t4dyn)))
"""计算PS响应"""
identity_tf = TransferFunc([1], [1], DT)
closed_loop_tf = pid_tf * sys_tf / (identity_tf + pid_tf * sys_tf)
ps_tf = sys_tf / (identity_tf + pid_tf * sys_tf)
# ps_inv_tf = pid_tf + identity_tf / sys_tf
# ps_inv_tf_scipy = scipy.signal.TransferFunction(ps_inv_tf.num, ps_inv_tf.den)
T4ir = T4move
t4ir = np.arange(DT, T4ir + DT, DT)
# t4ir = np.arange(0, T4ir, DT)
t4ir, process_sensitivity_ir = impulse(
(ps_tf.num, ps_tf.den),
T=t4ir,
)
# process_sensitivity_ir = process_sensitivity_ir
# for i in range(len(process_sensitivity_ir)):
# if process_sensitivity_ir[i] <= 0:
# process_sensitivity_ir[i] = 0
# else:
# break
process_sensitivity_ir = np.roll(process_sensitivity_ir, 1)
process_sensitivity_ir[0] = 0
ps_response_mat = np.mat(
toeplitz(process_sensitivity_ir, np.zeros_like(process_sensitivity_ir)), dtype=float
)
ps_pinv_mat = np.linalg.pinv(ps_response_mat)
plt.figure()
plt.plot(t4ir, process_sensitivity_ir)
# Filter
# Q_num, Q_den = butter(3, 1000, "low", analog=True)
Q_num, Q_den = ([1], [1])
butter_filter = scipy.signal.TransferFunction(Q_num, Q_den)
# iteration
f_kp1 = np.zeros_like(set_p)
datalog = dict()
datalog["p_fbk"] = np.zeros_like(set_p, dtype=float)
datalog["err"] = np.zeros_like(set_p, dtype=float)
datalog["pid_output"] = np.zeros_like(set_p, dtype=float)
datalog["f_k"] = np.zeros_like(set_p, dtype=float)
datalog["plant_input"] = np.zeros_like(set_p, dtype=float)
print("Total Samples:", len(set_p))
for k in range(10):
p_fbk = 0
sys_ss.reset()
pid_controller.reset()
f_k = f_kp1
for i in range(len(set_p)):
if i % 1000 == 0:
print(k + 1, i)
p_cmd = set_p[i]
a_cmd = set_a[i]
err = p_cmd - p_fbk
pid_output = pid_controller.response(err)
plant_input = pid_output + f_k[i]
p_fbk, x_state = sys_ss.response(
plant_input, method="zoh2"
) # +random.normal()/4/5
p_fbk = p_fbk[0, 0]
datalog["p_fbk"][i] = p_fbk
datalog["err"][i] = err
datalog["pid_output"][i] = pid_output
datalog["plant_input"][i] = plant_input
datalog["f_k"] = f_k
plant_input_list = datalog["plant_input"]
# current plant in as next ffc
# Le = np.zeros_like(set_p)
# Le_after_Q = np.zeros_like(set_p)
# current_ILC_after_Q = np.zeros_like(set_p)
# next_ILC = current_ILC + pid_output
# inverse plant
# Le = np.array(plant_pinv_mat * err.reshape(-1, 1)).reshape(-1)
# Le_after_Q = np.zeros_like(set_p)
# current_ILC_after_Q = np.zeros_like(set_p)
# next_ILC = current_ILC + pid_output + Le
# inverse ps (paper method)
# 矩阵计算方法
Le = np.array(ps_pinv_mat * datalog["err"].reshape(-1, 1)).reshape(-1)
# scipy库计算，行不通，因为非因果系统。Le = L * e = ps_inv * e
# t4move, Le, x_out = lsim2(ps_inv_tf_scipy, datalog["err"], t4move)
# without Q
plant_input_list_after_Q = plant_input_list
# with Q
# t4move, f_k_after_Q, x_out = lsim(butter_filter, plant_input_list, t4move)
f_kp1 = plant_input_list_after_Q + Le
fig, axs = plt.subplots(4, 2, figsize=(12, 12))
fig.suptitle("Iteration " + str(k + 1))
axs[0, 0].plot(t4move, set_p, label="cmd")
axs[0, 0].plot(t4move, datalog["p_fbk"], label="p_fbk")
axs[0, 0].legend(loc="upper left")
axs[0, 1].plot(t4move, datalog["err"], label="err")
axs[0, 1].legend(loc="upper left")
axs[1, 0].plot(t4move, datalog["pid_output"], label="pid out")
axs[1, 0].legend(loc="upper left")
axs[1, 1].plot(t4move, datalog["f_k"], label="f_k")
axs[1, 1].legend(loc="upper left")
axs[2, 0].plot(t4move, Le, label="Le")
axs[2, 0].legend(loc="upper left")
axs[2, 1].plot(t4move, plant_input_list_after_Q, label="plant_input_list aft Q")
axs[2, 1].legend(loc="upper left")
axs[3, 0].plot(t4move, plant_input_list, label="plant_input_list")
axs[3, 0].legend(loc="upper left")
axs[3, 1].plot(t4move, f_kp1, label="f_k+1 (aft Q)")
axs[3, 1].legend(loc="upper left")
# plt.show()
# # 输入和加速度时域响应
# fig, axes = plt.subplots(1, 2, figsize=(14, 5))
#
# axes[0].set_xlabel("t4chirp/[s]")
# axes[0].set_ylabel("u/[N]")
# axes[0].plot(t4chirp, u, label="u")
#
# axes[1].set_xlabel("t4chirp/[s]")
# axes[1].set_ylabel("acc/[m/s**2]")
# axes[1].plot(t4chirp, y, label="acc")
# plt.suptitle("Input and Acc")
# # plt.legend()
#
# fig, axes = plt.subplots(1, 2, figsize=(14, 5))
#
# axes[0].set_xlabel("t4chirp/[s]")
# axes[0].set_ylabel("u/[N]")
# axes[0].plot(t4chirp, u, label="u")
#
# axes[1].set_xlabel("t4chirp/[s]")
# axes[1].set_ylabel("pos/[m]")
# axes[1].plot(t4chirp, p, label="pos")
#
# plt.suptitle("Chirp Response")
# # plt.legend()
#
# # 修正后和拟合的伯德图
# f_fit, fw_fit = sys_fit.bode(np.array(range(start_freq, end_freq)))
# fig, axes = plt.subplots(1, 2, figsize=(14, 5))
#
# axes[0].set_xlabel("f/[Hz]")
# axes[0].set_ylabel("Gain/[dB]")
# axes[0].semilogx(f_bode, 20 * np.log10(np.abs(fw)), label="Gain")
# axes[0].semilogx(f_fit, 20 * np.log10(np.abs(fw_fit)), label="Fit Gain")
#
# axes[1].set_xlabel("f/[Hz]")
# axes[1].set_ylabel("Phase/[deg]")
# axes[1].semilogx(f_bode, np.angle(fw, deg=True), label="Phase")
# axes[1].semilogx(f_fit, np.angle(fw_fit, deg=True), label="Fit Phase")
# plt.suptitle("sys id bode plot")
# plt.legend()
# #
# f_pid, fw_fit4pid = closed_loop_tf.bode(np.array(range(1, 2000)))
# fig, axes = plt.subplots(1, 2, figsize=(14, 5))
#
# axes[0].set_xlabel("f/[Hz]")
# axes[0].set_ylabel("Gain/[dB]")
# axes[0].semilogx(f_pid, 20 * np.log10(np.abs(fw_fit4pid)), label="Gain")
#
# axes[1].set_xlabel("f/[Hz]")
# axes[1].set_ylabel("Phase/[deg]")
# axes[1].semilogx(f_pid, np.angle(fw_fit4pid, deg=True), label="Phase")
# plt.suptitle("PID bode plot")
# plt.legend()
plt.show()