# Getting input value from output data obtained from known transfer function in simulink

#### abdullah8391

Joined Sep 6, 2015
103
I am at beginner level of control system.
I want to:
1. Take a step signal and pass it through transfer function (lets say the TF is s/(s+1)).
2. After getting the result I want pass that signal from a block (IDK if using transfer function here would be suitable or not) and get back my step signal.
3. I want to do the implementation in simulink.
I do know the basic know how of simulink but I am weak in control systems, so kindly guide me how can I do it.

#### drc_567

Joined Dec 29, 2008
1,156
... a step signal is going to have the form '1/s' ... which forms a product with whatever transfer function that you choose, giving in the case above: a result of 1/(s+1). ... and 1/(s+1) is a decaying exponential function with time constant of -t. . So to get the original input function you would have to form a product that cancels the decaying exponential ... using a factor of (s+1) in the numerator and also (1/s) ... something like : (s+1)/s.
... might work ... report back if there is some sort of conflict.

#### abdullah8391

Joined Sep 6, 2015
103
... a step signal is going to have the form '1/s' ... which forms a product with whatever transfer function that you choose, giving in the case above: a result of 1/(s+1). ... and 1/(s+1) is a decaying exponential function with time constant of -t. . So to get the original input function you would have to form a product that cancels t he decaying exponential ... using a factor of (s+1) in the numerator and also (1/s) ... something like : (s+1)/s.
... might work ... report back if there is some sort of conflict.
Theoretically speaking, yes it works, but as shown in the attached screenshot it gives error in simulink. Also the type of TF I am dealing with is this type. 96.73/(s^2 + 3.067 s + 26.93), So is there any other other approach?

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#### drc_567

Joined Dec 29, 2008
1,156
... are you allowed to introduce a complex zero into the transfer function product? ... at least theoretically? ... If so, then multiply the numerator by (s^2 + 3.067s + 26.97) and also multiply by (1/96.73).
... Is there some reason for regenerating the original step function? Are you planning on constructing this scheme electronically ... with a circuit of some sort?

#### abdullah8391

Joined Sep 6, 2015
103
If so, then multiply the numerator by (s^2 + 3.067s + 26.97) and also multiply by (1/96.73).
Simulink gives error same as above screenshot.

Is there some reason for regenerating the original step function? Are you planning on constructing this scheme electronically ... with a circuit of some sort?
Nope, I had designed a state feedback controller for a system and that worked quite efficiently but then I was asked to add another instability to the system, when I do that the system doesn't remain controllable, same case for PID control. So at the end I concluded to use the approach that I asked in question.

#### drc_567

Joined Dec 29, 2008
1,156
re screenshot error ... It looks like in order to get it to work, it will be necessary to add a second order pole ... I.e. (s^2 + b*s + c) in the denominator of the transfer function, along with the complex zero mentioned above. However, that creates a function that is stable, but is not the step function that you started out with.
... Nevertheless, there may be a way to manipulate the resulting compatible (proper) transfer function if Simulink will allow access to a single transfer function sub-fraction that has been obtained by the method of Partial Fraction Expansion.
... The PFE method is simply a method of dividing up a complex fraction into its individual denominator components. See attachment below.
... So, to reiterate, you first develop a specific transfer function that is amenable to Simulink ... degree of N is equal to or less than degree of D. Then you take that transfer function and solve for the individual partial fraction expansion parts, one of which will be the original input function, or some multiple thereof. The big question, is whether Simulink will let you have any sort of useful access to the single partial fraction that is useful.

https://www.purplemath.com/modules/partfrac.htm

Last edited:

#### abdullah8391

Joined Sep 6, 2015
103
re screenshot error ... It looks like in order to get it to work, it will be necessary to add a second order pole ... I.e. (s^2 + b*s + c) in the denominator of the transfer function, along with the complex zero mentioned above. However, that creates a function that is stable, but is not the step function that you started out with.
... Nevertheless, there may be a way to manipulate the resulting compatible (proper) transfer function if Simulink will allow access to a single transfer function sub-fraction that has been obtained by the method of Partial Fraction Expansion.
... The PFE method is simply a method of dividing up a complex fraction into its individual denominator components. See attachment below.
... So, to reiterate, you first develop a specific transfer function that is amenable to Simulink ... degree of N is equal to or less than degree of D. Then you take that transfer function and solve for the individual partial fraction expansion parts, one of which will be the original input function, or some multiple thereof. The big question, is whether Simulink will let you have any sort of useful access to the single partial fraction that is useful.

https://www.purplemath.com/modules/partfrac.htm
Will check this solution after getting home, until then kindly guide me in another matter. This video link shows how to create a state space model. There is also a module name descriptor state space in simulink (details here). How can I implement it in Simulink?

I am doing this because in matlab (in coding form) when I used step(SS*res), I obtained step signal (i.e input and output are same) with negligible error.
where res is transfer function.
For SS, I converted transfer function to state space, took its inverse (the result is descriptor state space model) and stored it in SS.

#### abdullah8391

Joined Sep 6, 2015
103
re screenshot error ... It looks like in order to get it to work, it will be necessary to add a second order pole ... I.e. (s^2 + b*s + c) in the denominator of the transfer function, along with the complex zero mentioned above. However, that creates a function that is stable, but is not the step function that you started out with.
... Nevertheless, there may be a way to manipulate the resulting compatible (proper) transfer function if Simulink will allow access to a single transfer function sub-fraction that has been obtained by the method of Partial Fraction Expansion.
... The PFE method is simply a method of dividing up a complex fraction into its individual denominator components. See attachment below.
... So, to reiterate, you first develop a specific transfer function that is amenable to Simulink ... degree of N is equal to or less than degree of D. Then you take that transfer function and solve for the individual partial fraction expansion parts, one of which will be the original input function, or some multiple thereof. The big question, is whether Simulink will let you have any sort of useful access to the single partial fraction that is useful.

https://www.purplemath.com/modules/partfrac.htm
Thanks a lot for your help!
My approach of first system was a little rusty, after discussing with my instructor I came to know my mistake, thanks for the link though it didn't solve my stated problem but with its help I am assigned to design new model.