# How to model a multi input single output transfer function

#### dhevkumar

Joined Sep 11, 2015
21
hi sir..I have modeled the boost converter as circuit modelling and found the steady state and dynamic response. now i want to replace the boost converter by single block as transfer function.
so its similar to the first order system tf=k/(1+St)
t- time constant.
i found the gain from steady state response as 120
time constant to be 0.015s
so now my system is=120/1+S0.015
now my transfer function is vout/duty cyle=8000/s+66.66
so when is give the step input(duty cycle 0.5) my output is 60v

My clarification is the transfer function to be MISO(multi input single output), with duty cycle as one input and pv irradiation(that is boost converter input voltage) as disturbance and need to achieve the output voltage. that is finding transfer function vout/duty cyle(keeping input voltage =0) and finding vout/input voltage(keeping output voltage=0). how to do this process for boost converter with above mentioned response. please help

#### MikeML

Joined Oct 2, 2009
5,444
You can create arbitrarily complex transfer functions using LTSpice modelling, including Laplace...

#### MrAl

Joined Jun 17, 2014
8,502
Hi,

A single input single output transfer function might look something like this:
T(s)=Vin*N(s)/D(s)

and the only difference really is there will be two inputs for example:
T(s)=(Vin1*N1(s)+Vin2*N2(s))/D(s)

In matrix form you have one or more 2x2 matrixes and at least one 1x2 vector, one vector being made up of the individual inputs. So the simplified general form looks like this:
x'=A*x+B*u

For writing the equations you could use superposition for example if the whole network is linear, or just use nodal analysis having two inputs instead of one...it wont be that much different than with a single input.

For a simple example, a 2 input resistive voltage divider would look like:
Vout=Vin1*K1/D+Vin2*K2/D