Control System - Position Control system

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EE491 Ex1; Position Control System, Wednesday group 93671

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Introduction:

The primary concept of this experiment is to study position control techniques, using linear

transducers (potentiometers) in a live application. Demonstrating the effect of different values ofloop gains on the entire system response. We used the B3510-J position control board,connected with a DC power supply and an Oscilloscope to measure the final position error for thereference change made at different values ofloop gain.

Design and analysis:

First I should summarize orders of systems and their step responses to familiarize with thepurpose of the experiment:

1) First order systems:

The transfer function of such a system is in the form G(s) = C(s) / R(s) = 1 / (s + 1); where isthe time-constant.

Then we have the output can be expressed as: C(s) = (1 / (s + 1) * R(s)Concluding the unit-step response in the time-domain is the Laplace inverse of the output; we

then have c(t) = 1e ^ (-t / ) where is the time constant of the given control system. We canplot the result of the response in this figure:

2) Second order systems

Although true second-order control systems are rare in practice, their analysis generally helps toform a basis for understanding of design and analysis techniques. The transfer function of aclassical second-order system can be represented as

Where the damping ratio zeta follows the conditions to determine the response and the dynamic

behavior of thesecond-order system

: overdamped : underdamped : critically damped

: is the undamped natural frequency

When : and a unit-step injected into the system gives a time-response of

c(t) =

where

,


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The different types of responses

Effect of the damping ratio on underdamped response

Effect of the damping ratio on overdamped response

0

0.5

1

1.5

2

0 4 8 12t/t p

y(t)/AKp

z=1.0

z=0.1

0.4

0.7

0

0.2

0.4

0.6

0.8

1

0 4 8 12

y(t)/AK

p

t/tp

z=1

z=3

z=2


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The procedure of the experiment:

Starting with 1 cm and increasing as we measure the following parameters: 1)The referencesignal indicated as TP2. 2)The feedback signal TP1, and more importantly 3)The error signalTP3 (TP3 equals the difference between reference and feedback signals)

At each indicated recording we increased the gain gradually to observe closely the consequenceof adjusting the gain on the performance, especially on the error signal.

Increasing the gain ( from low to Max value) we managed to minimize the error signal TP3 tovalues as small as 2.3 mV at P1/cm. (check table). Although there will be a tradeoff with theovershoot and undershoot of the signals when observed in MATLAB/Simulink. What we gain

by decreasing the error signal we would probably lose in other parameters such as OS, and US(for instance the underdamped signal had the most Overshoot value from the simulation, more

on this in a few)Table of the recordingsP1/cm Reference Signal (TP2) Feedback Signal (TP1) Error Signal (TP3)

Level

of gainMin Med Max Min Mid Max Min Med Max

1 cm 9.3 9.45 9.24 9.30 9.42 9.16 86.6mV 57.4mV 2.3mV2 cm 7.11 7.39 7.22 7.63 7.38 7.16 0.59 69.3mV 6.4mV3 cm 5.18 5.13 5.33 5.7 5.09 5.28 0.57 7.5mV 4.9mV4 cm 3.12 3.01 3.02 3.63 2.98 2.991 0.534 2.7mV 3.9mV

* only indicated values have a unit of millivolt, otherwise its just volt.

Important remarks:1- We observed from the movement of the motor that the effect of gain is decisive in determining

the response of the system as a whole; meaning we managed to stumble upon the undampedresponse where the system was oscillating back and forth around the value of the position (indicating the response is a sinusoidal without an element of decay as en exponential).

Demonstrating in fact a very important response. As demonstrated in the indicated figure.

2 - Its worth mentioning that the main concept of using thepotentiometeris that we associate

each centimeter with an amount of resistance and a given voltage. For instance a one-centimeter

of position with one ohm of resistance and one unit of voltage. Thus we managed to see the

position control in practice.

In the computer simulation, we managed to try different values for the damping ratio and the

natural frequency in the general formula to figure out the difference between different types of

responses and their responses plot. (e.g. Entering values [0 1 1] in the denominator resulted in

underdamped response that is equivalent to the one in page2, entering [1 0 1] instead gave

undamped response oscillating back and forth, also [1 1 1] gave overdamped response for

example)


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* One important final point to conclude is that even though the error signal was becoming

smaller and smaller by increasing the gain of the system we still had found a trade-off between

the error signal and other characteristics such as the overshoot and the time response of each

signal.

We can easily observe the changes in parameters such as the OS and US from trying different

parameters values for the zeta and omega as designated in the MATLAB/Simulink simulation.

For example we can easily determine the values from the plots designated for every separate

response for example

Figure to demonstrate various performance criteria such as rise time, peak timeand over/undershoot for overdamped response

Control System - Position Control system

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