# Is this function realizable for every yes/no why should be provided?

1. Sep 24, 2011

### Arslan

Is this function realizable for every yes/no "why" should be provided???

(s^2+1)/(s+1)

2. Sep 24, 2011

### Arslan

Re: Is this function realizable for every yes/no "why" should be provided???

its the laplace transform , give me intution based answer

3. Oct 5, 2011

Re: Is this function realizable for every yes/no "why" should be provided???

I thought about this for a bit while sitting in Sensors & Controls class, using a ton of Laplace transforms. I think this is right, but here goes:

The determining factor concerns the highest power of s in both the numerator and denominator, so let's call them m and n, respectively. Mathematically, real systems correspond to transforms where n >= m, so the highest power in the denominator has to be greater than the highest power in the numerator. As you can see in your example, the numerator power is higher, so this is not a realizable system. Also, try doing an inverse laplace transform on it.

Intuitively, though, the frequency response of such systems tend towards infinity, with nothing damping it. This never happens in reality because no quantity ever "reaches" infinity -- there's always something damping it. Things like air resistance, friction, heat transfer, and viscocity all stop systems from racing off towards infinity; even subatomic particles are (ostensibly) limited by the speed of light. Any physically relizable system needs to have damping factors like these included in the system's model.

Plot this system in MATLAB to see the frequency response:
bode(tf([1 0 1], [1 1])).

Anyways, that's my interpretation... can anyone confirm this?

4. Oct 6, 2011

### Arslan

Re: Is this function realizable for every yes/no "why" should be provided???

i was doing the modeling of inverted pendulum attached to cart and pulley and also a servo motor attached with it.I divided transfer function in 3 parts i.e
1.Voltage and angular frequency of pulley
2.angular frequency of pulley and force on cart
3.Force on cart and angle of pendulum

. and there i get a transfer function between force applied on cart and angular frequency as
Jw'=(F-Bw)*r

F(s)/w(s)=(J/r)s+B

and it is a realizable and practicle system.
But theries are saying it is not realizable????

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5. Oct 6, 2011

### Arslan

Re: Is this function realizable for every yes/no "why" should be provided???

and also its simulink results are showing an impulse as output to step response.
And it is intuitively correct that the applied torque will only apply force on cart in form of pulse. i.e body can experience constant force if it is accelerating. if it is moving with contant velcity applied force will be zero.