# Question:Time delay in transfer function

## Question:Time delay in transfer function

Maple
Hi. I have a transfer function like this one: y:=(2.5)/((8*s^2+6*s+1)*s); and I can make inverse Laplace transformation in time and plot it by: y1:=invlaplace(y,s,t); plot(y1,t=0..25); I try it also with time delay in transfer function but it doesn`t work. y:=(2.5*exp(-1.5*s))/((8*s^2+6*s+1)*s); > y1:=invlaplace(y,s,t); > plot(y1,t=0..25); So i find a solution in differential equation and make an algorithm to convert transfer function to differential equation. ode := 8*(diff(x(t), t, t))+6*(diff(x(t), t))+x(t) = 2.5*Heaviside(t-1.5); ics := x(0) = 0, (D(x))(0) = 0; sol := dsolve({ics, ode}, x(t), numeric, stiff = true, range = 0 .. 25); odeplot(sol); And my problem is: I do know how to integrate time delay into the differential equation.It is all about industrial automation and PID controllers.Maybe it is really simple, but it is a problem for me.I would be gratefull for any suggestion and help. thanks
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