-
Notifications
You must be signed in to change notification settings - Fork 0
/
PIFANVC.m
212 lines (180 loc) · 6.58 KB
/
PIFANVC.m
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
% PIFANVC
%
% Paulo Alexandre Crisóstomo Lopes, 21/4/2022
% Instituto de Engenharia de Sistemas e Computadores - Investigação e Desenvolvimento
% Instituto Superior Técnico
% Universidade de Lisboa
% simulation parameters
Nsim = 100; % number of simulations
fs = 2000; % sampling frequency
simulation_time = 20000; % simulation samples
change_at = 2.5*fs; % 2.5 s
change_time = fs; % 1s fast
qn_steady = 1/400/fs; % state noise
qn_change = 1/change_time; % state noise at change
stability_margin = 0.1; % distance of model poles and zeros from the unit circle
f = 200*(1:3)'; % primary noise sinusoids frequencies
amplitudes = [0.5, 1.2, 0.3]'; % primary noise sinusoids amplitudes
phases = [56, 170, -23]'*pi/180; % primary noise sinusoids phases
frequency_noise = 1; % rms Hz
Nx = 6; % model order (size-1)
on_id = 100; % system identification start
on = 1000; % ANC start
qv0 = 0.01; % background noise power
% algorithm parameters
N = 16; % model order (size-1)
L = 64; % length of the filtering horizon
lambda = 0.999; % forgetting factor of the RLS algorithm
alpha = 1.01;
Lu = 10; % saturation of the antinoise signal
% LOGS
log_e = zeros(simulation_time,Nsim);
log_u = zeros(simulation_time,Nsim);
log_z = zeros(simulation_time,Nsim);
warning('off', 'MATLAB:singularMatrix');
warning('off', 'MATLAB:nearlySingularMatrix');
for n_sim = 1:Nsim
tic
rng(3439489+n_sim);
% simulation intializations
frequency = f'+frequency_noise*randn(simulation_time+L, length(f));
phase = 2*pi*cumsum(frequency)/fs + phases';
d0 = sin(phase)*amplitudes;
d = d0 + sqrt(qv0)*randn(simulation_time+L, 1); % primary noise signal
[a,b] = generate_plant(Nx, stability_margin);
uv = zeros(L,1); % anti-noise buffer
e1v = zeros(Nx+1,1); % residual noise minus background noise buffer
% algorithm initialization
u = 0; % anti-noise signal
ev = zeros(N+1,1); % residual noise buffer
ah = zeros(N+1,1); ah(1) = 1; % \hat{a}: a estimate
bh = zeros(N+1,1); bh(1) = 1; % \hat{b}: b estimate
theta = [ah(2:end); bh];
Pm = eye(2*N+1); % RLS algorithm covariance matrix
z = nan; % RLS algorithm error
e0v = zeros(L,1); % predicted error signal when u becomes 0
for k = 1:simulation_time
% simulation
qn = qn_steady + qn_change*(abs(k-change_at)<=change_time/2);
a = a + sqrt(qn)*randn(Nx+1,1);
b = b + sqrt(qn)*randn(Nx+1,1);
if qn > 0
[a,b] = adjust_plant(a,b,stability_margin);
end
log_u(k,n_sim) = u; % logs u(n) and not u(n+1)
uv = [u; uv(1:end-1)]; % simulation and algorithm
e1v = [0; e1v(1:end-1)];
e1 = b'*uv(1:Nx+1) - a'*e1v;
e1v(1) = e1;
e = e1 + d(k);
% algorithm
ev = [e; ev(1:end-1)];
if k >= on_id
% id
% RLS to calculate the parameters
phi = [-ev(2:N+1); uv(1:N+1)]';
Lm = Pm/lambda;
Pm = Lm - Lm*phi'*(1+phi*Lm*phi')^-1*phi*Lm;
z = e-phi*theta;
theta = theta + Pm*phi'*z;
ah(2:end) = theta(1:N);
bh = theta(N+1:end);
if k>=on
% prediction
evx = ev(1:N);
uvx = uv(1:N+1);
for n=1:L
uvx = [0; uvx(1:end-1)];
ex = bh'*uvx - ah(2:end)'*evx;
evx = [ex; evx(1:end-1)];
e0v(n) = ex;
end
e_signal = [zeros(L,1); e0v];
% inverse filter
u_signal = non_causal_filter_v3(...
ah, ...
bh, ...
e_signal,...
alpha...
);
u = - u_signal(L+1);
u = min(Lu, max(-Lu,u));
else
u = randn;
end
else
u = 0;
end
log_e(k,n_sim) = e;
log_z(k,n_sim) = z;
end
qe = mean(log_e(end-simulation_time/10:end,n_sim).^2);
fprintf(1, 'sim: %d, residual noise power: %f\n', n_sim, qe);
toc
end
warning('on', 'MATLAB:singularMatrix');
warning('on', 'MATLAB:nearlySingularMatrix');
% save PIFANVC
figure(1)
plot_xy_p2((0:size(log_e,1)-1)/fs, 10*log10(smooth(log_e.^2,min(round(simulation_time/200),200))));
set(gca, 'YLim', [-20,30]);
xlabel('time (s)');
ylabel('Noise (dB)');
grid on;
title('Residual noise versus time percentile plot');
i = 21:23;
figure(2)
plot((0:size(log_e,1)-1)/fs, 10*log10(smooth(log_e(:,i).^2,min(round(simulation_time/200),200))));
set(gca, 'YLim', [-20,30]);
xlabel('time (s)');
ylabel('Noise (dB)');
grid on;
legend('simulation 1', 'simulation 2', 'simulation 3');
title('Residual noise versus time plot of 3 simulations');
figure(3);
histogram(10*log10(mean(log_e(end-simulation_time/10:end,:).^2)),[-25:0.5:0,inf]);
xlabel('Noise Power (dB)');
ylabel('Frequency');
grid on;
title('Final residual noise power histogram');
figure(4);
plot(roots(a),'x'); hold on;
plot(roots(b),'o');
plot(exp((0:0.1:2.1*pi)*1i));
%set(gca,'XLim',[-2,2]);
line([0,cos(2*pi*f(1)/fs)], [0,sin(2*pi*f(1)/fs)]);
hold off;
title('Actual model pole zero plot');
figure(5);
plot(roots(ah),'x'); hold on;
plot(roots(bh),'o');
plot(exp((0:0.1:2.1*pi)*1i));
% set(gca,'XLim',[-2,2]);
line([0,cos(2*pi*f(1)/fs)], [0,sin(2*pi*f(1)/fs)]);
hold off;
title('Estimated model pole zero plot');
figure(6);
[h, ~] = freqz(b, a, 1024, fs);
[hh, fx] = freqz(bh, ah, 1024, fs);
subplot(2,1,1);
plot(fx, 20*log10(abs(h))); hold on;
plot(fx, 20*log10(abs(hh))); hold off;
xlabel('frequency (Hz)');
ylabel('amplitude (dB)');
grid on;
title('Actual and estimated model frequency response');
subplot(2,1,2);
plot(fx, unwrap(angle(h))/pi*180); hold on;
plot(fx, unwrap(angle(hh))/pi*180); hold off;
xlabel('frequency (Hz)');
ylabel('phase (deg)');
grid on;
figure(7);
plot_xy_p2((0:size(log_e,1)-1)/fs, 10*log10(smooth(log_z.^2,100)));
grid on;
title('Model identification error signal');
figure(8);
plot(e0v); hold on;
plot(d(k+1:end)); hold off;
legend('predicted', 'actual');
title('Predicted and actual primary noise');