Concept Building Through Block Diagram Using Matlab/Simulink

Journal ofThe Institution of

Electrical & ElectronicsEngineers Pakistan

Published by

Engr. Muhammad Anwar KhalidPresident

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The Institution ofElectrical and Electronics

Engineers Pakistan4-Lawrence Road, LahorePhone: (042) 3630 5289

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Editorial

PageNo

VOL # 66-67 Oct. -Mar. 2010

“New Horizons”

Email:[email protected]

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CONTENTS

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PresidentEngr. Muhammad Anwar Khalid

Vice PresidentEngr. Riaz Ahsan Baig (HQ)

Vice President (South)Engr. S. S. Jafri

Hony. Secretary GeneralEngr. M. Saleem Arif

Hony. TreasurerEngr. Shahid Aslam

Hony. Joint SecretaryEngr. Farrukh Javed Tariq

Hony EditorProf. Dr. Suhail Aftab QureshiElectrical Engg. Deptt.U.E.T. G.T. Road, Lahore - 54890Pakistan

Design of Underground Fire Detection System.Isaac Raso, Jamal Rizk, Mahmood NagrialSchool of Engineering, University of Western Sydney, Australia.

AMI Initiatives for Improvement in the Power Sector.Salman Akhtar.CO-CEO Techlogix, Pakistan.

Sustainable Energy Development & Linking Renewable Energy Resources.M. Usman Haider, M. Faheem Akhtar,U.E.T., Lahore

Lifetime & Energy Consumption Analysis for Cluster-based Wireless Sensor Networks with Topology Constraints.

1 2Abdul Sattar Malik , Suhail A. Qureshi , 2Muhammad kamran

1 Deptt. of Elect. Engg, UCET BZU Multan, Pakistan2 Deptt. of Elect. Engg., U.E.T. Lahore, Pakistan.

Introducing Single-Phase Distribution System.Riaz Ahsan Baig

Quality Improvement In Power Distribution Companies.Engr. Faisal Nafees Yousaf (GEPCO)M.Sc Engg. (UET)

WAPDA’s Annual Loss of Rs. 130 Billion Reasons And Remedies.Syed Tanzim Hussain NaqviEx-Member Power WAPDA and Chairman KESC

Concept Building Through Block Diagram Using Matlab/Simulink.

1 2 3Sajid Iqbal , Suhail Aftab Qureshi , Tahi Hussain Rizvi , 4 5Ghulam Abbas and Muhammad Majid Gulzar

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Abstract

n this paper, basic concepts of block diagrams have been discussed. Block diagrams have their own significance in every discipline of engineering. A block diagram is I

Fig. 1 Basic Block Diagramreduced to its canonical from using block diagram algebra.

Block diagram of a linear time-invariant (LTI) system We simulated the same problem in MATLAB and consists of four elements as shown in fig 2 [1]:SIMULINK. We applied the step input and observed the

1. Signalsbehavior of the system. 2. Systems

Index Terms - Transfer function, block diagram.3. Summing Junctions

I. Introduction 4. Pick off points

In different disciplines of engineering as Electrical, The three fundamental configurations in which blocks Chemical and Mechanical engineering, there are several can be connected are [1-3]:ways to represent a system or a process like block diagram, 1. Series formsignal-flow graph (SFG), schematic diagram and layout 2. Parallel formdiagram. 3. Feedback from

Block diagrams are used to represent a system or Any finite number of blocks in series may be process using blocks. Whereas schematic diagrams are algebraically combined by multiplication of transfer simplified representation of an electrical circuit. They functions [1-3] as shown in fig 3(a).represent the elements of a system using graphic symbols

Any finite number of blocks in parallel may be rather than realistic pictures [1-3].

algebraically combined by either addition or subtraction A signal-flow graph is a special type of block diagram according to the condition as shown in fig 3(b). Fig 3(c)

that shows the relations among the variables of a set with the shows feedback topology, which forms the basis of control help of nodes and arroes. Schematic diagram and layout systems engineering [1].diagram are used extensively in electrical engineering.

Block diagrams can also be simplified using the rules Layout diagram shows the width of each wire on the printed

of block diagram algebra. Summing/pickoff point(s) can be circuit board (PCB) [1-4]

easily relocated for the purpose of simplification by simply Initially key parameters of any physical system are following the shifting rules [1-3] as shown in fig 4.

defined for doing mathematical modeling. Then differential equations governing the system are developed. Then a transfer function for the whole system is determined and a block diagram is constructed [1].

II. Basics Of Block Diagram

A block diagram is a shorthand pictorial representation Fig. 2 Elements of Block Diagramof the cause and effect relationship between the input and

output of a physical system. Block diagrams are equally useful in management sciences, criminal justice and economics for the modeling and analysis of the system [1-4].

(a) Series ConfigurationWe can represent any complicated system and its

characteristics in a simple block diagram for our convenience, or we can represent a complete process by using block diagram representation.

Canonical form of a diagram contains only one block (b) Series Configurationwith single input and single output as shown in fig 1.

Concept Building Through Block Diagram Using Matlab/simulink1 2 3 4 5 Sajid Iqbal , Suhail Aftab Qureshi , Tahir Hussain Rizvi , Ghulam Abbas , and Muhammad Majid Gulzar

1 2Dept of Elect. Engg. Faculty of Engg. Univ. Gujrat, Dept. Of Elect. Engg. Univ. Of Engg. & Tech, Lahore13,5 4Faculty of Engg. Univ. Of Central Punjab, Dept. Of Chemical Engg. Faculty of Engg. Univ. Of Gujrat

The disadvantages of block diagrams are as follows [5-7]:

1. The differential equations that describe the system must be known.

(C). Feedback Configuration 2. The method is essentially a frequency-domain technique.

Fig. 3 Basic Topologies of Block Diagrams3. Block diagrams rely heavily upon the concepts of

linear system theory (e.g., Transfer functions, feedback.

4. Since a block diagram involves high-level view of the system, it does not offer the details information required for comprehensive planning and analysis.

IV. Manual Solution

We will solve an example of block diagram to find its canonical form. The step by step solution is given below in fig 5

Fig. 4 Basic Block Diagram Transformations

III. Advantages and Disadvantages Of Block Diagrams

Block diagram representation of any system offers the following educational advantages [5-7]:

1. A block diagram is a direct, graphical illustration of a set of coupled, linear differential equations.

2. Each block describes a specific process within the system in terms of a transfer function. Dimensionally, transfer functions can be ratios of interdisciplinary quantities. Figure 5(a)

3. The interactive coupling among all processes in the system is clearly shown and provided by the block interconnections.

4. Any input/output relationship is determined from a straight forward rearrangement of the block diagram. These simple graphical manipulations may provide additional insight into the behavior of the system. Thus it effectively portrays the interrelationship of distinct parts of the system.

5. Generally the number of operations required to carry out a complete block diagrams reduction are fewer and more direct than would be necessary to eliminate variables in the original equations. Also, the reduction process gives graphical significance to algebraic operations and is less susceptible to error.

6. The block diagram representation readily lends itself to the study of specific problems involving synthesis

Figure 5(b)and system optimization.

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V. System Simulation With the help ofMatlab and Simulink

Now for analyzing the behavior of the system shown in fig. 6, we used MATLAB and SIMULINK.

Figure 5(c)

Fig 6

A. MATLAB Simulation

We defined the transfer function by using MATLAB’s command “tf (num, den)” where num and den are user defined variables. Then, we used different commands to

Figure 5(d)solve series, parallel and feedback configurations.

Figure 5(e)

Figure 5(f)

Figure 5(g)

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Fig. 7 shows all the MATLAB commands. After reducing B. SIMULINKthe block diagram using block diagram algebra to its

Now we implement the same block diagram in canonical form, we applied the step input to observe the

SIMULINK and applied step input as shown in fig. 9, and behavior of the given system as shown in fig 8.

observed its output as shown in fig 10.

Fig 9. SIMULINK ImplementationFig 8 MATLAB output

Fig 7 MATLAB Commands & Their Outputs

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Fig. 10 SIMULINK Output

VI. Conclusion

We have revisited the basic concepts of block diagram as these are being employed for designing new systems or processes and improving present ones. Firstly, we solved a block diagram manually. Secondly, we simulated the same system in MATLAB and SIMULINK. The output waveforms showed similar results. This approach makes teaching of block diagrams a much easier task. It is concluded that block diagrams are a valuable source of concept building, and are educationally beneficial in various engineering and non-engineering disciplines.

Acknowledgment

The authors wish to thank Dr. Muhammad Jamil, Director Faculty of Engineering, University of Gujrat for his guidance and encouragement.

References

[1] Norman S. Nise, Control Systems Engineering. New York, Springer-Verlag, 1985, ch. 4. Pp.123-135.

[2] Joseph J. DiStefano, Allen R. Stubberud & Ivan J. Williams. Feedback and Control Systems. 2nd ed. Ch. 7

[3] Katsuhiko Ogata, Modern Control Engineering Person Education. 4th ed. Pp. 70-74

[4] Mei C., “On Teaching the Simplification of Block Diagrams”, Int. Journal of Engg. Vol. 18, 2002, pp. 697-703.

[5] Preis D., “Block Diagrams: A Tutorial Alternative to Dynamical Analogies: IEEE Trans. Vol. E-19, No 4 Nov. 1976. Pp. 143-148.

[6] Pierre, D.A. “Supplementary MATLAB tools for systems and control education,” in Proc. 26th Annu. Frontiers in Education Conf. 1996. FIE 96. Nov 1996. Vol. 3, pp. 1215-1218

[7] Hideg, L.M, “Block diagram in undergraduate engineering courses other than control systems,” in Proc. 28th Annu. Frontiers in Educational Conf. 1998. FIE 98. 1998. Vol. 2, pp. 958-962

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Quotation

*. Courage is grace under pressure-- Ernest Hemingway

* A timid person is frightened before a danger, a coward during the time and a courageous person afterwards.

-- Jean Paul Friendrich

* Fear always springs from ignorance.-- Ralph Waldo Emerson

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-- Joseph Conrad

* The man who knows when not to act is wise. To my mind, bravery is forethought.

-- Euripides

* Our greatest glory is not in ever falling but in rising every time we fall.

-- Confucius

* To generalize is to be an idiot.-- William Blake

* The human heart refuses to believe in a universe without a purpose.

-- Immanuel Kant

* Great works are performed not by strength but by Preserverance.

-- Samuel Johnson

* There is nothing like dream to create the future.-- Victor Hugo

* I am an idealist. I don’t know where I am going but I’m on my way.

-- Carl Sandburg

* It is very bad thing to become accustomed to good luck.

-- Publilius Syrus

* Fame is proof that the people are gullible.-- Ralph Waldo Emerson