149184839 control-lab-experiment-5-docx

EE491 – Ex5; Second-order control system properties Wednesday group أنس مفتاح محمد17639 – القعود

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Objective:

To study second order control system and the effect of the open-loop gain (Kp) on the system stability.

Required apparatus:

1- Process simulator B3510-D

2-Process controller B3510-E

3-DC power supply

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4- OSC

Introduction:

The block diagram shows the closed-loop system understudy with unity negative-feedback arm. The direct arm amplifier (Kp), an integrator and a derivator. In the second order system the denominator of its transfer function has two roots. The position of the roots depends on te open-loop gain. By sufficiently rising the gain the system can be turned from a stable operation to permanent oscillations.

-Why Study Second Order Systems?

Second order systems are important for a number of reasons. They are the simplest systems that exhibit oscillations and overshoot.

Many important systems exhibit second order system behavior.

Second order behavior is part of the behavior of higher order systems and understanding second order systems helps you to understand higher order systems.

-Note On System Responses

Knowing how to compute impulse and step response is not an end in itself. Let's face it, any system you build will not have many impulses or steps as inputs. However, it is important that these responses are important for several reasons.

*Step response is an important response. Step inputs are often used as test inputs to determine how well a system is performing. The shape of the step response - how fast it occurs, how much it oscillates, etc. help the designer predict how well the system will respond to other inputs.

*How the damping ratio influences the response is important. We have seen how the step response changes when the damping ratio is varied.

*Pole location is a function of damping ratio. A change in damping ratio means that the

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pole location has changed. Pole location is important for predicting responses to all kinds of inputs.

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From the experiment we have cases like these;

1- Overdamped system

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2- Underdamped system

3- Undamped system

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In the following: depiction of separate step responses for systems through a simulation software

A) Overdamped

B) Underdamped

C) Undamped

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In each and everyone of those we should note how the response is related to the unit step. Where there is OS (underdamped) and where there are permanent oscillations. (last figure)

Now, to sum things up: this figure shows how a system would be stable, or critically stable or unstable

The location of the poles is very important in this determination. Whether it was on the LHP or the RHP, whether they’re real or imaginary, distinct or repeated

We tried the values in the laboratory and got similar results.

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149184839 control-lab-experiment-5-docx

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