# control system, poles and stability response

1. ## control system, poles and stability response

Can you help me compare these results? They're the simulations of a closed loop system . When we change the poles, (in this case, there are 4 poles), the response system also changes. The 4 poles involves 2 complex numbers and 2 integers, but I don't see the relationship between the poles and the response. I don't see an exact description. I mean, a description like:
if the real number is increased, then the response would be more oscillatory or if the imaginary part is smaller, then the faster the convergence to 0.

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2. ## Re: control system, poles and stability response

Can you help me compare these results? They're the simulations of a closed loop system . When we change the poles, (in this case, there are 4 poles), the response system also changes. The 4 poles involves 2 complex numbers and 2 integers, but I don't see the relationship between the poles and the response. I don't see an exact description. I mean, a description like:
if the real number is increased, then the response would be more oscillatory or if the imaginary part is smaller, then the faster the convergence to 0.

Hi MissP.25_5

I don't see anything surprising ! when you change location of poles of a circuit response of a circuit will be involved by some changes which depends on where are the poles exactly .

A suitable Article from MIT can lead you through a good understanding :

Best Wishes
Goldsmith

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3. ## Re: control system, poles and stability response

Originally Posted by goldsmith
Hi MissP.25_5

I don't see anything surprising ! when you change location of poles of a circuit response of a circuit will be involved by some changes which depends on where are the poles exactly .

A suitable Article from MIT can lead you through a good understanding :

Best Wishes
Goldsmith
Yes, that's what I said. The response depends on the poles. But I need to compare these 3 results. They're the results of 3 different poles. I also need to write the relationship between the complex numbers and the response. Can you help?

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4. ## Re: control system, poles and stability response

MissP - it is not easy to answer your question because it is not clear which parameters of the closed-loop sysytem are shown.
Watching the first line I see something like a step response, correct?
In this context, I am confused about the last line showing an input. Which input?

As a general (and preliminary) answer:
A complex pole pair causes overshoot in the step response. When the (negative) real part of these poles come closer to the origin (imag. parts constant) the overshoot increases.
Moreover, a negative real pole (at s=-sigma) causes a damping of the step response corresponding to exp(-sigma*t). Thus, the duration of the step response is inverse proportional to sigma.
I think, the time response (first line) can confirm these statements.

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5. ## Re: control system, poles and stability response

Originally Posted by LvW
MissP - it is not easy to answer your question because it is not clear which parameters of the closed-loop sysytem are shown.
Watching the first line I see something like a step response, correct?
In this context, I am confused about the last line showing an input. Which input?

As a general (and preliminary) answer:
A complex pole pair causes overshoot in the step response. When the (negative) real part of these poles come closer to the origin (imag. parts constant) the overshoot increases.
Moreover, a negative real pole (at s=-sigma) causes a damping of the step response corresponding to exp(-sigma*t). Thus, the duration of the step response is inverse proportional to sigma.
I think, the time response (first line) can confirm these statements.
The input is the voltage input used to produce the torque for the pendulum arm to oscillate. The poles consist of 2 pair of real numbers and 2 pairs of conjugate numbers. What do the real numbers say about the response?

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6. ## Re: control system, poles and stability response

Originally Posted by MissP.25_5
The input is the voltage input used to produce the torque for the pendulum arm to oscillate. The poles consist of 2 pair of real numbers and 2 pairs of conjugate numbers. What do the real numbers say about the response?