Controls Group Assignment

8/8/2019 Controls Group Assignment

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Contents

Introduction ................................ ................................ ................................ ................................ ...... 4

Introductory Exercise ................................ ................................ ................................ ......................... 5

Explanation of Interface ................................ ................................ ................................ ................. 5

Adjusting Parameters of the Graph ................................ ................................ ................................ 6

Introductory Exercise Transfer Function ................................ ................................ ......................... 6

Exercise A ................................ ................................ ................................ ................................ .......... 9

Exercise B ................................ ................................ ................................ ................................ ........ 14

Part I ................................ ................................ ................................ ................................ ............ 14

Part II ................................ ................................ ................................ ................................ ........... 17

Usefulness of the Exercise ................................ ................................ ................................ ............... 19


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Introduction

CODAS is a Controls System Design and Simulation Software.

Utilising the computers advanced processing capabilities to its advantage, it allows the simulation of controls

systems with complicated transfer functions and provides performance results within split seconds, in

comparison to the long time it would take to do the same calculations manually.

In this way, it also acts as a flexible controls systems design tool and learning tool, since it allows a

designer/student to easily change parameters of the system and view multiple possible performances without

too much trouble.

CODAS software can present data visually through four different graphs:

- Time Domain Graph- Frequency Domain Graph- Root Domain Graph- Non-Linear Domain Graph

The software allows for great flexibility in terms of changing the parameters of the graph the graph axes and

magnitudes can be easily changed. The accuracy of the simulation can also be adjusted with ease.

CODAS for Windows is a highly integrated software package for the design and simulation of control systems.

CODAS provides time-domain, frequency domain and s-plane environments for the study of linear continuous

time systems. Discrete time systems are handled too by defining transfer functions in terms of the z-operator.

Non-linearities can be defined interactively with the effects on the system time response being simulated and

its describing functions plotted in the frequency domain.

CODAS of Windows features: Automated lead/lag compensator design, Automated pole-placement and

optimisation, Wide range of mappings, rectangular rule, bi-linear transformers, z-transformers, Polynomial

simplification tools, Disturbance (load) inputs and measurement noise.

Transfer functions are entered using the built-in editor with systems described in pole-zero form or as

polynomials or as both. The transient response of the open or closed loop system can be drawn with both the

control effort and plant output displayed on-screen. Root loci are produced using an efficient branch following

method. The frequency responses of the open and closed loop system are available in Nyquist form, Nichols

plt or as bode gain and phase curves. Closed loop gain contours (M-Contours) are drawn.

Bytronic CODAS - http://www.bytronic.net/html/codas.html


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To input the transfer function into the Plant block, simply click the Plant block on the Systems Definition

Window and a new window will pop-up.

Enter the numerator of the Transfer function in the top textbox and the denominator in the bottom textbox.

Adjusting P g r g mh t h rs of th h Grg ph

First, type in the desired transfer function and the gain and then click on the Graph Scales button. The

following window will appear:

y Changing Axis Magnitudes:Input desired magnitudes of the graph axes in the top four boxes (Y-axis min, Y-axis max, X-axis min,

X-axis max).

y Simulation Step Sized Adjustment (to avoid numerical instability):This is adjusted by inputting a value into the Number of Points textbox. The higher the number of

points (i.e. points of calculations), the greater the accuracy of the simulation. The effect of this will be

illustrated in the next section.

y Adjusting Time of Simulation:This is done by inputting the desired duration of simulation to the Duration textbox.

Introductori

p xq rcis q Trr nsfq r Function

The introductory exercise uses the following transfer function (along with a gain of 5):

Activate the closed loop response by clicking the Closed Loop button (red clockwise circular button).


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Shown below is the system definition window for the above:

The first time-domain graph is plotted with the following settings:

We can now adjust the parameters of the graph. A point to be noted is the shape of the graph this is as aresult of simulation with just 20 points of calculations. In the next graph, this will be increased to 200 points, in

order to get a more accurate solution.


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The second time-domain graph is plotted with the following settings:


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Ex s rcis s A

Open loop transfer function

Determine Time Constant and Steady State Error of the Close Loop System Using CODAS

Step 1)

Input the Open Loop Transfer function to the Plant (Figure 2.1)

Figure 2.1

Step 2)

Draw the time domain response of the system (Graph 2.1)

Graph 2.1


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Determine Time Constant and Steady State Error of Close Loops System Using Analytical Method

Open loop transfer Function

NG = 1 DG = 1+0.5s Nk = 1 Dk = 1

General Form of Close Loop Transfer Function

Kss = Close Loop Steady State Gain d = Time ConstantBy comparing General form

Kss = 0.5 d = 0.25Output = steady state Gain Input = 0.5 1 = 0.5Steady State Error = 1-0.5 = 0.5

Therefore Analytical Values confirms the simulation values of the CODAS


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When Open Loop Gain = 0.5

Time Constant = 0.3333

Steady State error = 1- 0.3333 = 0.6667

When Open Loop Gain = 2

Time Constant = 0.5 / 3 = o.1667

Steady State Gain = 1 2/3 = o.3333

When Open Loop Gain = 5

Time Constant = 0.5/ 6 = 0.0833

Steady State Error = 1-5/6 = 0.16667


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Exe

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The following table shows the trial-and-error process by which the gain required to achieve 10 peak

overshoot was found. It involved changing the values in the gain box and obtaining values using the Plot-

Following Cursor.

GainO/P atpeak a

b(overshoot)

overshoot

1.0000 0.3694 0.3333 0.0361 10.8300

2.0000 0.5813 0.5000 0.0813 16.2600

0.5000 0.2154 0.2000 0.0154 7.7000

0.9000 0.3421 0.3103 0.0318 10.2480

0.8500 0.3278 0.2982 0.0296 9.9260

0.8750 0.3350 0.3043 0.0307 10.0887

0.8700 0.3336 0.3031 0.0305 10.0630

0.8600 0.3307 0.3007 0.0300 9.9767

0.8650 0.3321 0.3019 0.0302 10.0300

0.8625 0.3314 0.3013 0.0301 9.9900

0.8631 0.3316 0.3014 0.0302 10.0200

0.8638 0.3318 0.3016 0.0302 10.0100


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Steady StateE o (when gainis 0.8638) = 0.6984

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Part II

Us

P+I will re

cesteadystateerror of thesyste to zero:

Where I is the Inte

ral Action Time Constant.

At I=0.5s


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Ascan beseen in the graph above introducing P + I has reduced thesystemssteadystateerror to zero, but

has made it more oscillatory.

Increasing the I, increases the degree of damping on thesystem and makes thesystem less oscillatory.

I=0.5 I=0.7

I=0.9

I=1.1


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Usefulness of the Exercise

- The exercise gave us an opportunity to practice CODAS functions.- elped us improve and expand our knowledge of control systems, especially of high order systems.- elped us to see the accuracy of our analytical results, in comparison with the simulation.- Allowed us to see the effect of changing various parameters to the response of the system.

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Controls Group Assignment

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