how to find settling time of an arbitrary signal

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Ali Esmaeilpour 2019-10-1

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https://ww2.mathworks.cn/matlabcentral/answers/483055-how-to-find-settling-time-of-an-arbitrary-signal

编辑： Ali Esmaeilpour 2019-10-1

I got a code which results a "y" signal as output and I wanted to find its settling time. I gave an arbitrary input signal "W" as shown in my code

my code is as follows:

clc;
clear;
close all;
%% Initialization
T0=0 ;
Tf=20 ;
Ts=0.1 ;
t=T0:Ts:Tf ;
system=tf([1 1],[1 1 2]); % system=(s+1)/(s^2+s+2)
system_dis=c2d(system,Ts) ;
system_dis_ss=ss(system_dis) ;
Am=system_dis_ss.a;
Bm=system_dis_ss.b;
Cm=system_dis_ss.c;
n=size(Am,1); % Number of state variables
Om=zeros(1,n);
A=[Am,Om';Cm*Am,1];
B=[Bm ;Cm*Bm];
C=[Om 1];
p=10; % Prediction horizon
m=5; % Control horizon
Q=1;
R=1;
F=zeros(p,n+1);
for i=1:p
    F(i,:)=C*A^i;
end
PHI=zeros(p,m);
for i=1:p
    for j=1:i
        PHI(i,j)=C*A^(i-j)*B;
    end
end
PHI=PHI(:,1:m);
%% Main Loop
Nt=numel(t);
%W=ones(Nt,1); % Reference signal
W=[ones(floor(Nt/4),1);2*ones(floor(Nt/4),1);-ones(floor(Nt/4),1);zeros(floor(Nt/4+1),1)];
y=zeros(Nt,1);
du=zeros(Nt,1);
x=zeros(n+1,Nt); % (System state)+integral ===> n+1
Fval=zeros(Nt,1);
for i=1:Nt-1
    FreeResponse=F*x(:,i);
    dU=(PHI'*Q*PHI+R)\(PHI'*Q*(W(i)-FreeResponse)) ;
    du(i)=dU(1); % Receding horizon
    x(:,i+1)=A*x(:,i)+B*du(i); % State variable update
    y(i+1)=C*x(:,i+1); % Output update
end
%%
ynew=y(21:101);
Wnew=W(21:101);
Mp=100*(max(ynew)/ynew(81,1))
figure(1)
plot(t(21:101),y(21:101),'linewidth',2)