MATLAB: How do i find a difference equation difference I have this first order differential equation given: i need to find a difference equation using MATLAB. I would appreciate if someone could help me with that. Thanks Best Answer Choose your sample time TeTe=0.1 % Your sample timeN=1.5D=[1 -0.5]Modelc=tf(N,D) % Your continue transfer functionModeld=c2d(Modelc,Te) % Your discrete transfer function[Nd,Dd]=tfdata(Modeld,'v');% From Y(z)/U(z)=Nd(z)/Dd(z) you can find the relation between y{n] and u[n] Related SolutionsMATLAB: Discrete transfer fcn 1/z-1 (Z-transform) How it Works If the input of your system is u[n] and its output is Y[n] then% H(z)=Y(z)/U(z) % 1/(z-1)=Y(z)/U(z)% which gives Y(z)(z-1)=U(z)% zY(z)-Y(z)=U(z)% In the temporal domain% y[n+1]-y[n]=u[n]% y[n+1]=y[n]+u[n]% finaly: y[n]=y[n-1]+u[n-1]% In your example% y[1]=y[0]+u[0]= 0+1% y[2]=y[1]+u[1]=1+1=2% y[3]=y[2]+u[2]=2+1=3% and so on MATLAB: Discrete system solving with MATLAB you will need initials condition y(0) and y(-1); because Matlab don't allow negative index we 'll consider y(2) and y(1) as initials conditions y(1)=0; y(2)=0 k=0:20; x=exp(-2*k); %your input system; for n=3:numel(k) y(n)=-(1/4)*y(n-1)+(1/8)*y(n-2)+x(n-2) end hold on stem(k(1:end-2),y(3:end),'r');Or you can use lsim commandN=[1 0 0];D=[1 1/4 -1/8];te=1 % Sample timemodel=tf(N,D,te);lsim(model,x,k,[0 0]) Related QuestionSolving non linear delay differential equations with dde23How to get z transfer function from difference equationC2d with ‘impulse’ methodHow to find out the cordinates of the intersection point of a line and a surfacePossibility of implementing transfer function in arduino.
Best Answer