-
Notifications
You must be signed in to change notification settings - Fork 1
/
fuzzy_PID.py
262 lines (232 loc) · 6.08 KB
/
fuzzy_PID.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
from __future__ import division
import PID
import time
import matplotlib.pyplot as plt
import numpy as np
import simulator
import random
from scipy.interpolate import BSpline, make_interp_spline
# fuzzy set
NB = 0 # negative big
NM = 1 # negative mid
NS = 2 # negative small
ZE = 3 # zero
PS = 4 # positive small
PM = 5 # positive mid
PB = 6 # positive big
# scale of P, I, D, err, d_err
scale_P = 2 / 3
scale_I = 2 / 3
scale_D = 1 / 3
scale_err = 1
scale_d_err = 1 / 3
# rules, 7x7 matrix, err and d_err -> P, I, D
# row: err [NB, NM, NS, ZE, PS, PM, PB]T
# col: d_err [NB, NM, NS, ZE, PS, PM, PB]
rules_P = [
[PB, PB, PM, PM, PS, ZE, ZE],
[PB, PB, PM, PS, PS, ZE, ZE],
[PM, PM, PM, PS, ZE, NS, NS],
[PM, PM, PS, ZE, NS, NM, NM],
[PS, PS, ZE, NS, NS, NM, NM],
[PS, ZE, NS, NM, NM, NM, NB],
[ZE, ZE, NM, NM, NM, NB, NB]
]
rules_I = [
[PS, NS, NB, NB, NB, NM, PS],
[PS, NS, NB, NM, NM, NS, ZE],
[ZE, NS, NM, NM, NS, NS, ZE],
[ZE, NS, NS, NS, NS, NS, ZE],
[ZE, ZE, ZE, ZE, ZE, ZE, ZE],
[PB, NS, PS, PS, PS, PS, PB],
[PB, PM, PM, PM, PS, PS, PB]
]
rules_D = [
[NB, NB, NM, NM, NS, ZE, ZE],
[NB, NB, NM, NS, NS, ZE, ZE],
[NB, NM, NS, NS, ZE, PS, PS],
[NM, NM, NS, ZE, PS, PM, PM],
[NM, NS, ZE, PS, PS, PM, PB],
[ZE, ZE, PS, PS, PM, PB, PB],
[ZE, ZE, PS, PM, PM, PB, PB]
]
#membership function 1
def fuzzy1(x):
# input must be rescaled
# output is a list of membership
# [NB, NM, NS, ZE, PS, PM, PB]
membership = [0, 0, 0, 0, 0, 0, 0]
# NB
if x <= -3:
membership[0] = 1
elif -3 < x and x <= -1:
membership[0] = (-1 - x) / 2
# NM
if -3 <= x and x <= -2:
membership[1] = x + 3
elif -2 < x and x<= 0:
membership[1] = (0 - x) / 2
# NS
if -3 <= x and x <= -1:
membership[2] = (x + 3) / 2
elif -1 < x and x <= 1:
membership[2] = (1 - x) / 2
# ZE
if -2 <= x and x <= 0:
membership[3] = (x + 2) / 2
elif 0 < x and x <= 2:
membership[3] = (2 - x) / 2
# PS
if -1 <= x and x <= 1:
membership[4] = (x + 1) / 2
elif 1 < x and x <= 3:
membership[4] = (3 - x) / 2
# PM
if 0 <= x and x <= 2:
membership[5] = (x - 0) / 2
elif 2 < x and x <= 3:
membership[5] = 3 - x
# PB
if 1 <= x and x < 3:
membership[6] = (x - 1) / 2
elif 3 <= x:
membership[6] = 1
return membership
# membership function 2
def fuzzy2(x):
# input must be rescaled
# output is a list of membership
# [NB, NM, NS, ZE, PS, PM, PB]
membership = [0, 0, 0, 0, 0, 0, 0]
# NB
if x <= -3:
membership[0] = 1
elif -3 < x and x <= -2:
membership[0] = (-2 - x) / 1
# NM
if -3 <= x and x <= -2:
membership[1] = x + 3
elif -2 < x and x<= -1:
membership[1] = (-1 - x) / 1
# NS
if -2 <= x and x <= -1:
membership[2] = (x + 2) / 1
elif -1 < x and x <= 0:
membership[2] = (0 - x) / 1
# ZE
if -1 <= x and x <= 0:
membership[3] = (x + 1) / 1
elif 0 < x and x <= 1:
membership[3] = (1 - x) / 1
# PS
if 0 <= x and x <= 1:
membership[4] = (x - 0) / 1
elif 1 < x and x <= 2:
membership[4] = (2 - x) / 1
# PM
if 1 <= x and x <= 2:
membership[5] = (x - 1) / 1
elif 2 < x and x <= 3:
membership[5] = 3 - x
# PB
if 2 <= x and x < 3:
membership[6] = (x - 2) / 1
elif 3 <= x:
membership[6] = 1
return membership
def inv_fuzzy(membership):
# Sugeno-style
# input is a list of membership
# [NB, NM, NS, ZE, PS, PM, PB]
# output must be rescaled
numerator = 0
denominator = 0
if sum(membership) == 0:
return 0
for i in range(7):
numerator += membership[i] * (i - 3)
denominator += membership[i]
return numerator / denominator
def fuzzy_and(typ, x, y):
# two types
if typ == 0:
return min(x, y)
else:
return x * y
def fuzzy_or(typ, x, y):
if typ == 0:
return max(x, y)
else:
return x + y - x * y
if __name__ == "__main__":
pid = PID.PID(1, 1, 0.5, 10)
pid.point = 1
pid.sample_time = 0.01
pid.windup = 5
feedback = 0
feedback_list = []
time_list = []
setpoint_list = []
fuzzy_P = [0, 0, 0, 0, 0, 0, 0]
fuzzy_I = [0, 0, 0, 0, 0, 0, 0]
fuzzy_D = [0, 0, 0, 0, 0, 0, 0]
L = 100
output = 0
for i in range(1, L):
output += pid.update(feedback)
feedback = simulator.func1(output + 1 / i)
err = pid.point - feedback
d_err = err - pid.last_error
print 'output of PID contoller is: ', output
print 'error is: ', err
print 'delta error is: ', d_err
fuzzy_err = fuzzy2(err / scale_err) # get membership vector
fuzzy_d_err = fuzzy2(d_err / scale_d_err) # get membership vector
feedback_list.append(feedback)
setpoint_list.append(pid.point)
time_list.append(i)
time.sleep(0.01)
# rule-based reasoning
fuzzy_P = [0, 0, 0, 0, 0, 0, 0]
fuzzy_I = [0, 0, 0, 0, 0, 0, 0]
fuzzy_D = [0, 0, 0, 0, 0, 0, 0]
typ = 0
for i in range(7):
for j in range(7):
fuzzy_P[rules_P[i][j]] = max(fuzzy_and(typ, fuzzy_err[i], fuzzy_d_err[j]), fuzzy_P[rules_P[i][j]])
fuzzy_I[rules_I[i][j]] = max(fuzzy_and(typ, fuzzy_err[i], fuzzy_d_err[j]), fuzzy_I[rules_I[i][j]])
fuzzy_D[rules_D[i][j]] = max(fuzzy_and(typ, fuzzy_err[i], fuzzy_d_err[j]), fuzzy_I[rules_I[i][j]])
dP = inv_fuzzy(fuzzy_P) * scale_P
dI = inv_fuzzy(fuzzy_I) * scale_I
dD = inv_fuzzy(fuzzy_D) * scale_D
print 'membership vector of error is: ', fuzzy_err
print 'membership vector of delta error is: ', fuzzy_d_err
print 'membership vector of Kp is: ', fuzzy_P
print 'membership vector of Ki is: ', fuzzy_I
print 'membership vector of Kd is: ', fuzzy_D
# make sure Kp/i/d are in the domain
pid.Kp = min(max(0, pid.Kp + dP), 3 * scale_P)
pid.Ki = min(max(0, pid.Ki + dI), 3 * scale_I)
pid.Kd = min(max(0, pid.Kd + dD), 3 * scale_D)
print 'delta Kp is: ', dP
print 'delta Ki is: ', dI
print 'delta Kd is: ', dD
print 'Kp is: ', pid.Kp
print 'Ki is: ', pid.Ki
print 'Kd is: ', pid.Kd
print '\n'
time_sm = np.array(time_list)
time_smooth = np.linspace(time_sm.min(), time_sm.max(), 300)
helper_x3 = make_interp_spline(time_list, feedback_list)
feedback_smooth = helper_x3(time_smooth)
# draw the response curve
plt.plot(time_smooth, feedback_smooth)
plt.plot(time_list, setpoint_list)
plt.xlim((0, L))
plt.ylim((min(feedback_list)-0.5, max(feedback_list)+0.5))
plt.xlabel('time (s)')
plt.ylabel('PID (PV)')
plt.title('FUZZY PID')
plt.ylim((1-0.5, 1+0.5))
plt.grid(True)
plt.show()