Non-linear loads

I want to implement these loads as nonlinear and harmonic by using codes or Simulink to deal with this problem in control system?

Answer 1

[Dr. Pemendra Kumar Pardhi]

Hello Mohammed Yakoob,

For above you need to use MATLAB Simulink, in Simulink you can devoloped model as atteched picture file.

Thanks

Pemendra Pardhi

Answer 2

[Mohammed Yakoob]

Hello dear and thanks so much for your answer!! I agree with your answer but I want the way that implemented this loads as a model to deal with them in control system not as the simscap electrical!!

[Dr. Pemendra Kumar Pardhi]

In simscape electrical, control can also be implements,

For what you want, can you share paper (if it is possible)?

Answer 3

[Mohammed Yakoob]

Yes dear friend I attached the article that I want to simulate

[Mohammed Yakoob]

But my problem with the disturbance term as implents in this article as different loads

Answer 4

[Mohammed Yakoob]

Hello Dear

I tray to implement these disturebance loads if I deal correct as shown bellow but the last one is the nonlinear signal I can't get it so please if you have any information let me knw??

My codes :

clc

close all

clear

%% Plant Paramiters

f= 60;

Ts= 1/f; %% one period

Th=Ts/2; %%half period

Wo= 2*pi*f;

Vdc= 300;

C_st=15*10^-6;

L_t=2*10^-3;

R_l= 40; %resistance load

R_li=3; %resistance of the line

%% Implement a Single Phase Microgrid in a contious time form

% x_dot= AX+BU+dW ; Y= CX+DU+0W.

% X=[il Vg]' ; U=[Vsw] ; d= [ig]; Y=[Vg].

% for i= 1:1000

Aop=[0 1/L_t; 1/C_st 0];

Bop= [1/L_t; 0];

d=[0; -1/C_st];

Cop=[0 1];

Dop= [0];

B= [Bop d];

%% Imlement the system

sys=ss(Aop,B, Cop, Dop);

sys_d= c2d(sys,0.0001);

[Ad,Bd,Cd,Dd]=ssdata(sys_d);

%% Performance of The Open Loop System

t = 0.000:0.0001:Th;

V_r =Vdc*sin(Wo* t);

%% Cotrollability of the system

Co= ctrb(sys);

rank(Co);

%% LQR_LMI

Ac=Aop;

Bc= Bop;

C= Cop;

nx = size(Ac,2);

nu = size(Bc,2);

% closed loop

% LQR weights

Q = diag([1 1e-5]);

R = 1;

Klqr = lqr(Ac,Bop,Q,R,[]);

% % % LMI

% % A=Ac;

% % B1 = eye(nx);

% % B2=Bc;

% %

% % C1 = eye(nx);

% % D11 = zeros(nx,nx);

% % D12 = zeros(nx,nu);

% %

% % C2 = [sqrt(Q);

% % zeros(nu,nx)];

% % D21 = zeros(nx+nu,nx);

% % D22 = [zeros(nx,nu);

% % sqrt(R)];

% %

% % Pp = ltisys(A, [B1 B2], [C1; C2], [D11 D12; D21 D22]);

% %

% % siz = size(D22);

% % gamma0 = 0;

% % obj = [gamma0 0 0 1];

% %

% % [gopt,h2opt,Klmi,Pcl,X] = msfsyn(Pp,siz,obj);

% %

% % Klqr

% % Klmi

%% Closed loop system

Acl= [Aop-(Bop*Klqr)];

Bcl= [B];

Ccl= [0 1];

Dcl= [0 0];

states = {'i_L' 'V_g'};

inputs1 = {'V_r' 'dis'};

outputs1 = {'V_g'};

poles= eig(Acl);

sys_cl = ss(Acl,Bcl,Ccl,Dcl,'statename',states,'inputname',inputs1,'outputname',outputs1);

%% At the disturebance eqaul to zero

input1 = [V_r; zeros(size(t))]; %%assume tha the disturebance =0.

[y1,t,x]=lsim(sys_cl,input1,t);

figure()

plot(t,y1)

ylabel('V_out')

xlabel('time')

title('LQR controller Without the Disterbance Term')

grid on

%% LQR when the system has a load term at R=40 Ohm

dis = (V_r/R_l+R_li);

input2 = [V_r' dis'.*0.01];

[y2,t,x]=lsim(sys_cl,input2,t);

figure()

plot(t,y2)

ylabel('V_out')

xlabel('time')

title('LQR controller With the Disterbance Term at R=40Ohm')

grid on

%% 1) PERFORMANCE AGAINST UNKNOWN LOAD

z1=complex(0,-Wo*62.86e-6);

z2= complex(0.35,Wo*223.8e-3);

z3= complex(228);

z4=complex(76,-Wo*10e-6);

z5=complex(152,Wo*111.9e-3);

Z11= (1/z1)+ (1/z2) +(1/z3);

Z22=(1/z4)+(1/z5);

n= numel(t);

% % for m= 1:n

% %

% % if m<= 36

% % dis11= (y1(m,1)/R_li+Z11)';

% % dis11(1,m)=dis11;

% % elseif m<=n-36

% %

% % dis12= (y1(36+m,1)/R_li+Z11+Z22)';

% % dis12(1,m)=dis12;

% %

% % end

% %

% % end

% dis1=[dis11 dis12];

for m= 1:n

if m<= 36

dis11= 1e-1*[cos(5*2*pi*m')+cos(1*2*pi*m')+cos(.1*2*pi*m')];

dis11(1,m)=dis11;

elseif m<=n-36

dis12= 1*[cos(4*2*pi*m')+cos(2*2*pi*m')+cos(.2*2*pi*m')];

dis12(1,m)=dis12;

end

end

dis1=[dis11 dis12];

input3 = [V_r' dis1'];

[y3,t,x]=lsim(sys_cl,input3,t);

figure()

plot(t,y3)

ylabel('V_out')

xlabel('time')

title('PERFORMANCE AGAINST UNKNOWN LOAD')

grid on

%% (2) PERFORMANCE AGAINST HARMONIC LOAD

dis = ((V_r/R_l+R_li)+7*sin(Wo*t'));

input3 = [V_r' dis'.*0.001];

[y3,t,x]=lsim(sys_cl,input3,t);

figure()

plot(t,y3)

ylabel('V_out')

xlabel('time')

title('PERFORMANCE AGAINST HARMONIC LOAD')

grid on

Answer 5

[Mohammed Yakoob]

if you ask me, why dont use the simscape electrical, because I dont know the why how to connect these loads to my control simulink with the output of my system (Y) or as reterun disturebance as input??