What is scailing of the inputs of LS? Is it Linear Time Invariant System?

Ljubomir Jacic @: yes it is linear time invariant system

for example the output of sensor for feedback needs scaling to compare with the setpoint

how i must do that !!??

Hi

Please see this link

http://www.cns.nyu.edu/~david/handouts/linear-systems/linear-systems.html

So, we do not speak about scailing, but scaling. Your question is so general, bring the real problem to be discussed. What is the input, what is the type of control (PID...) and controller, sensor type, controlled object, output of the system... You have to be more precise!

In general, in feedback control, we use the method called normalization. First, you should create a math model (typically a set of linear or nonlinear differential equations). You define the parameter set, usually rated values of the system, which you are going to use as a reference for normalization. Next, you perform the normalization by dividing your sensed signals by corresponding references in your math model. This should bring all your physical signals (voltage, current, temperature, motor speed etc.) to the values close to or within zero to one (or -1 to +1) region. If you have analog or digital scaling by your equipment, typical for current and voltage sensing circuits, as well as A/D conversion, in place, you should include it in you calculations. Now, you can use these values for scaling of your other signals and component values, such as impedance normalization, power normalization, PWM signals etc. This way, you will have the entire system represented by p.u (per unit) non-dimensional math model, which you can apply to any other similar system, regardless of the power level. The only thing you need to do is to rescale it back using corresponding set of rated values. For more info, take a look at the following links: 

https://books.google.com/books?id=-MnG05siaG0C&pg=PA39&lpg=PA39&dq=power+system+normalization&source=bl&ots=JlmAolabyJ&sig=kNyvDd3zX7Fe8kQcTSteHbv81vY&hl=en&sa=X&ei=r9VtVeuqOsjPsAXc84GgAw&ved=0CCoQ6AEwAg#v=onepage&q=power%20system%20normalization&f=false

https://books.google.com/books?id=yR9KAAAAQBAJ&pg=PA12&lpg=PA12&dq=power+electronics+normalization&source=bl&ots=lU34WsD9aG&sig=iMaj0-3wxKH6KyqpLT22ZnNSJdM&hl=en&sa=X&ei=kNhtVbasEIrDsAWQrYPYDw&ved=0CCwQ6AEwAw#v=onepage&q=power%20electronics%20normalization&f=false

http://www.apicsllc.com/apics/Misc/PN.html

Dear Majid,

Can you specify the inputs you want to include.

The Properties of Linear System include Scaling of Inputs and Corresponding Scaling of Outputs. Refer the Following Excerpt from

Chapter 4

Linear Input/Output Systems

Theorem 2.

The solution to the homogeneous system of differential equation

        X dot x = Ax                                                       (4.4)

is given by

x(t) = (e ^  At} x(0)

:

Proof.: Substitute the solution into the differential equation.

The form of the solution immediately allows us to see that the solution is linear in

the initial condition. In  particular,if xh1 is the solution to equation (4.4) with initial

condition x(0) = x1 and xh2 with initial condition x2,then the solution with initial

condition x(0) = Alpha * x1 + Beta * x2 is given by

x(t) = (e^At)*( Alpha * x1 + Beta * x2 ) = (Alpha *  (e ^ At) * x1  + Beta * (e ^ At) * x2)

= Alpha * xh1(t) +Beta * xh2(t)

Similarly we see that the corresponding output is given by

y(t) = Cx(t) = Alpha * yh1(t) + Beta * yh2(t)

where y1 and y2 are the outputs corresponding to xh1(t) and xh2(t)

Link:   http://www.cds.caltech.edu/~murray/courses/cds101/fa03/caltech/am03_ch4-27oct03.pdf

P.S.

I watched the debate. We should always encourage the person who is interested in developments in science and asks questions. On the other hand, everyone must strive to ask questions about linear systems, input-output relations or other specific conditions. Then it will be achieved cooperation between question and answer.

http://www.cns.nyu.edu/~david/handouts/linear-systems/linear-systems.html