%Discrete?Kalman?filter?for?PID?control
%Reference?kalman_2rank.m
%x=Ax+B（u+w（k））;
%y=Cx+D+v（k）
clear?all;
close?all;

ts=0.001;
%Continuous?Plant
a=25;b=133;
sys=tf（b[1a0]）;
dsys=c2d（systs‘z‘）;
[numden]=tfdata（dsys‘v‘）;

A1=[0?1;0?-a];
B1=[0;b];
C1=[1?0];
D1=[0];
[ABCD]=c2dm（A1B1C1D1ts‘z‘）;

Q=1;???????????????%Covariances?of?w
R=1;???????????????%Covariances?of?v

P=B*Q*B‘;??????????%Initial?error?covariance
x=zeros（21）;??????%Initial?condition?on?the?state

u_1=0;u_2=0;
y_1=0;y_2=0;
ei=0;
error_1=0;
for?k=1:1:1000
time（k）=k*ts;

rin（k）=1;
kp=8.0;ki=0.80;kd=0.20;

w（k）=0.002*rands（1）;???%Process?noise?on?u
v（k）=0.002*rands（1）;???%Measurement?noise?