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%基于 BP 神经网络的 PID 控制
9 w9 p% S# I) l/ wclear all;/ x- }& j, @# }5 [9 Z/ z3 `
x1=0.3;a1=0.07;# d$ A2 I. W: y! I9 M, W; O# j
S=1; %信号类型4 _' D4 v3 H) i; g4 x3 ~" Y' ?7 F& i
In=4;h=5;Out=3; %神经网络结构
* x A2 l( j' Tif S==1, %阶跃信号8 ?: g. `- `! d& [! E7 ^7 e o+ D% n
wi=[-0.6394 -0.2696 -0.3756 -0.7023;7 |' |" q# u; @/ I% a' ?
-0.8603 -0.2013 -0.05024 -0.2596;
& h3 j# v- W' X* B$ F9 s) I-1.0749 0.5543 -1.6820 -0.5437;
, X, U l6 s3 l; d3 K# W4 J-0.3625 -0.0724 -0.6463 -0.2859;
+ k4 g: v/ E- }0.1425 0.0279 -0.5406 -0.7660];& X- }8 |/ ~; v$ \
%wi=0.50*rands(h,In);
! m, f6 ]$ e: V! D$ Wwi1=wi;wi2=wi;wi3=wi;
0 x% W8 `( c. y9 b/ Bwo=[0.7576 0.2616 0.5820 -0.1416 -0.1325;
% U5 @# F* `6 ^6 l-0.1146 0.2949 0.8352 0.2205 0.4508;
. E* k6 p1 f* N0.7201 0.4566 0.7672 0.4962 0.3632];
' o8 M; R- |5 E, S; q, G%wo=0.50*rands(Out,h);# }; W- x a, H. }4 M4 W9 X& [# S
wo1=wo;wo2=wo;wo3=wo;' M$ i1 c! s2 I ^8 d
end- v, o) q1 h7 o3 Y2 V" z; a" [! ^
if S==2 %正弦信号" A* c/ x" v5 e8 [/ M
wi=[-0.2846 0.2193 -0.5097 -1.0668;
5 v5 i; v& a3 u% j& v$ v-0.7484 -0.1210 -0.4708 0.0988;0 M+ g% `6 b$ C/ L: [
-0.7176 0.8297 -1.6000 0.2049;- r( n, I) ^' l0 }
-0.0858 0.1925 -0.6346 0.0347;
, O1 C* F' B [/ r0.4358 0.2369 -0.4564 -0.1324];5 i) W5 N. z" Y
%wi=0.50*rands(h,In);
2 b$ l2 w$ N& j- Iwi1=wi;wi2=wi;wi3=wi;
& x7 I X2 A1 K1 `wo=[1.0438 0.5478 0.8682 0.1446 0.1537;
& C4 K! I$ C, c' Z! W7 Z R* O- [0.1716 0.5811 1.1214 0.5067 0.7370;# X; W' N5 f% N0 e5 ?1 _
1.0063 0.7428 1.0534 0.7824 0.6494];% V) I; z2 W5 c& V
%wo=0.50*rands(Out,h);
: Y2 }) N- x) B! }0 N, mwo1=wo;wo2=wo;wo3=wo;; l% I' q& o: j' J- ?* ~
end
& E! A! `3 I6 \/ H; vx=[0,0,0];- |+ x: v$ r0 p
u1=0;u2=0;u3=0;u4=0;u5=0;
" Z5 l) E) v" w g3 Oy1=0;y2=0;y3=0;
) ]9 G& ?! z0 N voh=zeros(h,1); %神经网络中间层输出1 G. y9 T; g1 g) Z* y7 T- r: | @) j
I=oh;%神经网络中间层输入$ H; a+ s" V p7 Z
error1=0;
u- C; P* E+ ierror2=0;
5 F8 E! {/ ~) C1 Y, f! E3 C$ uts=0.003;
6 c# R( a' U( _ y; L- dfor k=1:1:1000,6 I9 {2 v5 J4 S3 u) w, q# l$ ]
time(k)=k*ts;
+ k: N- _; q/ D4 w' Yif S==1,8 x8 ^6 m% I% ^+ U1 w1 ^( E5 ?' |& w
rin(k)=1.0;
7 L8 c2 p( P9 R9 b" k2 }9 I. delseif S==2,5 @& @2 j8 T& o
rin(k)=sin(1*2*pi*k*ts);" g6 g( r' Q% U _% @. {
end( P# P* n# v' O$ s
%非线性模型3 `- m1 p9 _% [, U# N
a(k)=1+0.15*sin(k*pi*ts/25);
" [/ n# o+ n1 C3 ly(k)=(a(k)*y1+u1)/(1+y1^2)+u1;: b' D5 ^# v+ i( v
error(k)=rin(k)-y(k);( W1 |: A9 l: j( l7 n
xi=[rin(k),y(k),error(k),1];
, O6 V `6 U8 S bx(1)=error(k)-error1;
1 t8 J5 T+ f% B$ D. Dx(2)=error(k);
$ ]0 \- Y, Y u1 b4 r8 I. _0 ^) yx(3)=error(k)-2*error1+error2;( K" B& J L, F- @% b2 ^
ed=[x(1);x(2);x(3)];
7 r2 L, u7 U- H. q1 wI=xi*wi';1 w2 [4 Y. d2 s5 V8 ]
for j=1:1:h
# C+ ], n0 H3 i8 r( y' g2 W3 H# coh(j)=(exp(I(j))-exp(-I(j)))/(exp(I(j))+exp(-I(j)));2 |+ [. s9 B7 m6 _% ^
end9 C1 o7 M1 ^8 q7 g( Y2 Q! b- ]
K=wo*oh; %输出层
; O% I5 _- U3 D4 n. hfor j=1:1:Out
" ~& I: U# B# V8 L# X5 H% Z- a4 R5 KK(j)=exp(K(j))/(exp(K(j))+exp(-K(j))); %求 kp,ti,td% \# Y# r7 r3 X* }( A, S& @2 y% T+ B
end
- p5 r6 K: c ]$ Qkp(k)=K(1);ti(k)=K(2);td(k)=K(3);
( S# H' C& p( K8 a' A- `- QKd=[kp(k),ti(k),td(k)];
% F& D. E' I$ K8 g `du(k)=Kd*ed;
t" W$ `5 W% K U) `' C: Vu(k)=u1+du(k); I. A$ D8 |! V# W$ k' D
if u(k)>=10, %限制控制器输出# G& e1 T+ w: ?4 C- ?8 J
u(k)=10;
' \1 @4 [! j, A5 C% O/ J2 C iend
* V* g7 `7 m& l7 G- X8 {if u(k)<=-10,
" _0 ?; c4 g8 R9 Nu(k)=-10;
# S: L# {: j- l. G; u) n' `: Aend
8 E4 v. W8 r6 {/ wdyu(k)=sign((y(k)-y1)/(u(k)-u1+0.0000001));2 C: X- J: d$ O0 V. S2 D
for j=1:1:Out,
" C: @% _4 @+ x$ DdK(j)=2/(exp(K(j))+exp(-K(j)))^2;" ? F' s7 q( R% t. I. W* h
end/ y% u6 A+ x. y* y2 m# R
for i=1:1:Out,8 |% `- ^4 M* _3 b8 E
de3(i)=error(k)*dyu(k)*ed(i)*dK(i);9 U" n$ d& R! j! Y4 w. s
end
- v* h( V" T s0 g$ d ]' W( Nfor j=1:1:Out,
* `8 ~! S$ \) B. Afor i=1:1:h,# U# D* ?! f4 O# I/ J1 m- r
dwo=x1*de3(j)*oh(i)+a1*(wo1-wo2);
. Q* G! D- v9 P% {* Z& e* [; rend: |' [- U% ^6 O, R' R5 o
end
; ]% E: M% _3 h* V g: Hwo=wo1+dwo+a1*(wo1-wo2);
! |; f( Q$ n. h8 j- X; f% J6 [. ]# Q+ _%隐含层4 q T% d% m# E* ^, b
for i=1:1:h," B+ B: I& t1 _6 P: v( a* U! `+ d
dO(i)=4/(exp(I(i))+exp(-I(i)))^2;. W& Z1 s+ |/ A8 u- z/ h
end
$ U4 q9 a) B N8 \seg=de3*wo;
5 _& S2 y3 S; R4 `" V! gfor i=1:1:h
- ]8 e% b) e# [' t- Z1 Jde2(i)=dO(i)*seg(i);
) V7 T8 h- V* @( s1 zend
' N( z# R8 F& ?0 r# Fdwi=x1*de2'*xi;) Q2 L) p6 l! O: U; |
wi=wi1+dwi+a1*(wi1-wi2);* {' j1 r6 V$ j7 L: {# f0 j
%参数更新& A% \( O$ @% d3 k
u5=u4;u4=u3;u3=u2;u2=u1;u1=u(k);9 b. ]4 K( J. E7 a. ]! f, A
y2=y1;y1=y(k);! o a5 E4 `/ a8 x
wo3=wo2;wo2=wo1;wo1=wo;4 }8 o m. j/ o1 ?2 H
wi3=wi2;wi2=wi1;wi1=wi;, M @8 f3 Z) c# v
error2=error1;
& f0 F6 F5 W: Q. ^+ R8 ^error1=error(k);5 \! }( G: ~, s% D8 \) b( l
end
% _1 ~5 b/ ~) H: e5 I/ Gfigure(1);
( u6 ~, s2 H( ~. f. l4 w) w! `plot(time,rin,'r',time,y,'c');% e, Z9 o, h% W; A
xlabel('时间(秒)');ylabel('输出跟踪输入的响应曲线');% a5 T4 l# m! e8 L. r+ O/ V
figure(2);, z' ^% m+ z- S3 Q" r0 S$ u# G1 j" ^
plot(time,u,'r');
. U. S1 w2 @- C* E6 m z% axlabel('时间(秒)');ylabel('控制信号 u(k)的变化曲线');: u2 d1 x5 c. {6 u7 [
figure(3);2 Z2 l% s3 C" |$ p4 N
subplot(311);
+ f/ F; n% s# \% bplot(time,kp,'r');
7 [' n; P2 B7 j; Y. nxlabel('时间(秒)');ylabel('参数 kp');. e3 Q0 u: j F/ l4 r! O( F+ ^
subplot(312);/ _) {- C4 e5 {- W" v
plot(time,ti,'r');
% p, [- i3 k& `# {! m( j! hxlabel('时间(秒)');ylabel('参数 ki');- S6 X+ X/ A1 w% ?! S
subplot(313);2 T% L1 j3 R/ w: g7 H
plot(time,td,'r');$ V1 z+ r( U$ w
xlabel('时间(秒)');ylabel('参数 kd');+ x5 F K' d$ b; A# h8 _
, }( A8 b$ }) x4 k
6 s) ]0 a4 t' j6 O& X( A目标值不能过大怎么解决
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