# Linear system which is time independent

1. Mar 12, 2009

### gegitur

hi guys,

can a time independent system model be controlled via a controller?
I am assuming that we can obtain a solution for the model at each sample time, just assume that the model is of c= a*u type, i.e u is input which varing with the time. I am confsed....

2. Mar 12, 2009

### HallsofIvy

It would help if you would say what you mean by "controlled" and "a controller".

3. Mar 13, 2009

### gegitur

let say, a an algebraic equation representing a boiler model, what you give is voltage and the output is temperature. Is it possible to control the temperature by just knowing its algebraic form of equation, which is not differential equation but its approximation to an algebraic form.

more clearly,

Q=m.c.delta(T) --> the equation in diff. form would be dQ/dT=m.c.dT/dt,

what I have is something like Q=m.c.delta(T),for this eq. the heater input for example, u, is varying with the time. (I am supposing that I have many many approximated formulas, not their differential forms and I cant have differential form of them)

thank you for your help..

4. Mar 13, 2009

### gegitur

hi guys,

I have sorted out the problem, and this solution has led to a new question. We have had a buch of equations in excel form where there were only time dependent. They were in fact a solution to a differential equation. for exmp:(1)..> dx/dt =x_{2dot}+ a*x_{dot}+c*x and what we have had in excel docs were the solution to above diff. eqns, i.e.(2)..> x(t)=exp(-a*t)+ blah blah..., are the second eq. controllable using a discrete PID or any type of controller? the input to the 2nd equation is time only and the output is let say position.

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