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PROFESOR MADYA DR. ZAMRI BIN OMARTimbalan Dekan (Hal Ehwal Pelajar & Alumni) Fakulti Kejuruteraan Mekanikal & Pembuatan

Assoc. Professor at Aeronautical Eng. Dept.B.Eng(Mech-Aero), UTM

M.Eng (Mech), UTMPhD (Aerospace), RMIT University

Private Pilot License (DCA)

…Selamat Kembali Ke Parit Raja..BDA30703 Kejuruteraan Kawalan

Seksyen S5

Email : zamri@uthm.edu.myPhone : 4537618Room: A4-1st FloorMobile : 0127220907 (text only)

Semester I 2015/2016

BDA 30703 ~ Control Engineering

Section 5

Meeting: 3 hrs/weekVenue: G3-BKB 1 Day : Sunday (10am-11am)

Thursday (8am-10am)

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Important Reminder..

1. Class participation3. Communication4. E-Learning: Author5. Some rules; punctuality, dress code, don'ts..

Chapter 1 – Introduction & Block DiagramChapter 2 – Mathematical ModelingChapter 3 – Time Response AnalysisChapter 4 – Stability & Root Locus MethodChapter 5 – Frequency Response AnalysisChapter 6 – Control System Design

RPP ;a. Syllabusb. Assesmentc. References

BDA 30703 Control EngineeringSem I 15/16

Total lecture weeks : 141st Part : 7 Weeks2st Part : 7 WeeksMid-Sem Break :Study Week :Exam :

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Chap 1 : Intro & Block Diagram

How to control ?

• What is Control Engineering ? � deals with daily-life physical systems. � dynamic systems, contain several variables need to be controlled � control approach: develop math. model, time & frequency

response analysis, stability.

Chap 1 : Intro & Block Diagram

• Systems ?� an assemblage of inter-related components.� governed by physical laws.� also has diverse meaning.

• Engineering ? Engineer ??

U3

Slide 6

U3 stop here 100915.UTHM, 10/09/2015

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C1 : Block Diagram Representation

• Systems Representation � represented as block diagram

System

components

disturbances, n(t)

input, u(t) output, y(t)

� a block has input, output.� arrow represents signal (arrow in is i/p, arrow out is o/p)� Single input/output(SISO), multiple input/output (MIMO)� disturbance may occur.� input; controlled signal� output; dependent signal� disturbance; uncontrolled i/p signal

C1 : Block Diagram

• Example; Power Plant System

� input; fuel rate, f (m3/s)� output; electrical power, W (KW)� System components; represent by blocks� output of a block = input to another block� disturbance; system inefficiency, weather

Fuel rate , f

Boiler

Steampressure, p

Mechanicalrotationalpower, T

Electricalpower, W

TurbineElectrical

generator

disturbance disturbance disturbance

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• Control System � a device to control the power source � to cause the output is a depenndent of the input� it has objectives!!

� to design a startegy; the o/p is as desired.� 2 control strategies; open loop, closed loop

C1 : Control System & Open Loop

• Open Loop Control� o/p has no effect on the control action. � contains one signal path

1.Low (27o C )

2. Med (20o C )

3. High (16o C )

R1

R2

R3

Knob

setting

SwitchController

Process

Room

Aircond system

C1 : Open Loop Control

• Open Loop Control� room T is controlled by knob settings� each setting causes a diferrent electrical current (power)� syst. Performance; depends on the controller accuracy� user can’t control; ambient temperature, efficiency of cooling element� if any disturbance occurred; a/s system connnot correct itself

1.Low (27o C )

2. Med (20o C )

3. High (16o C )

R1

R2

R3

Knob

setting

SwitchController

Process

Room

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C 1 : Open Loop Block Diagram

� The aircond system can be represented by the following block diagram

Cooling

level ( switch )Controller

CurrentCoolingrate

RoomtemperatureCooling

elementRoom

� components; controller, system� a one way signals� Might not get the desired room temperature;

� controller inefficiency� ambient temperature

C1 : Closed Loop Control

• Closed Loop Control� the performance of a/c system can be improved by introducing;

� an operator (Ali) dedicated to control the knob settings� a room temperature sensor

� desired T = medium, set knob to 2� a hot day, T ≠ 20oC; change the knob setting to 3� after a while, T = 16oC (too cold); change knob setting to 2 please!!

� the T can be regulated/set at 20oC, but may be oscillated� needs a large effort from the operator� this system is known as a closed loop (feedback system);

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C1 : Closed Loop Block Diagram

• Closed Loop Control� extra components; actuator & sensor� if the operator is replaced by a mechancial/electrical device;

� an automatic feedback system

C1 : Block Diagram Elements

• Block Diaram Elements

System

component

input

signal, u

output

signal, v

V V

V

� a block / blocks

� summing point

� take-off point

V1

+

V2

V = V1 + V2

+ V

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C1 : Exercise; Block Diagram

• Exercise 1� a car driver uses a control system to maintain the speed of the car at a prescribed level. Sketch a block diagram to illustrate the feedback system.

C1 : Exercise; Block Diagram

• Exercise 2� an operator is to maintain the liquid level in the reservoir. The operator compares the actual level with the desired level and opens and closes the valve, adjusting the fluid flow out to maintain the desired level. Sketch the block diagram for this system.

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Block Diagram Examples

Block Diagram Examples

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C1 : Transfer Function Concept

• Transfer Function (TF)� a ratio of output to input. Symbol/letter in the block represents TF, G(s)� ratio of Laplace transformation of o/p to Laplace transformation of i/p� for an open loop system

Transfer

function,

G(s)

Input ,

X(s)

Output,

Y(s)

)s(X

)s(Y)s(G =

� for a feedback system,

C1 : Closed Loop Transfer Function

)s(E

)s(C)s(G =� the forward path TF,

� the feedback path TF,

)s(C

)s(F)s(H =

)s(R

)s(F)s(H)s(G =� the open loop TF,

� the closed loop TF,)s(H)s(G1

)s(G

)s(R

)s(C

+=

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C1 : Block Diagram Reduction – To derive TF

)s(F)s(F 211

3 =θ

θ

• Transfer Function in Series� consider a system with 2 blocks in series,

F1(s) F

2(s)

1θ2θ 3θ

� It can be reduced/simplified to,

F1(s)F

2(s)

1θ3

θ

� TF in series is,

C1 : Blocks in Series – TF Derivation

(1) )s(F )s(F 11211

2 →=→= θθθ

θ

� θ1 and θ1 can be written as,

F1(s) F

2(s)

1θ2θ 3θ

(2) )s(F )s(F 22322

3 →=→= θθθ

θ

� eliminate θ2,

112223 )s(F)s(F )s(F θθθ ==

proved! seriesin TF )s(F)s(F 121

3⇒=∴

θ

θ

� For blocks in series, multply all individuals TF to obtain total TF

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C1 : Blocks in Series – Example

)s(R)s(M)s(Gf

W=

� The TF for this power plant system is,

C1 : Blocks in Parellel – TF Derivation

• Transfer Function in Parellel� parellel; arrows are in the same direction, not necessarily same signs � consider a system with 2 blocks in parellel,

F1(s)

1θ4

θ2

θ

3θF

2(s)

F1(s) + F

2(s)

1θ 4θ

� It can be reduced/simplifed to,

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C1 : Blocks in Parellel – TF Derivation

F1(s)

1θ

4θ

2θ

3θ

F2(s)

� Tf for each block can be written as,

(1) )s(F )s(F 1121

21 →=→= θθ

θ

θ(2) )s(F )s(F 123

1

32 →=→= θθ

θ

θ

� at the summing point; (3) 324 →+= θθθ

� thus the overall TF (θ4/θ1) is,

[ ])s(F)s(F)s(F)s(F 2111211324 +=+=+= θθθθθθ

! proved parellel in TF )s(F)s(F 211

4⇒+=∴

θ

θ

� For blocks in parellel, add up all individuals TF to obtain total TF

C1 : Blocks in Parellel – Example

F1(s)

1θ

4θ

2θ

3θ

F2(s)

� the TF is,

+

-

)s(F)s(F 211

4 −=θ

θ

Prove it !!

F1(s)

F2(s)

F3(s)

F4(s)

C(s) D(s)

� the TF is,

)s(F)s(F)s(F)s(F)s(C

)s(D 4321 +++=

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C1 : Feedback System (Closed Loop); TF Derivation

• Transfer Function for Feedback � feedback, positive feedback� consider a feedback systems,

� It can be reduced/simplifed to,

F1(s)

1θ 4θ2θ

3θ

F2(s)

+

-

1θ 4θ

)s(F)s(F1

)s(F

21

1

+ � carefully examine !!

C1 : FB Loop - TF Derivation

F1(s)

1θ 4θ2θ

3θ

F2(s)

+

-

� The overall TF (θ4/θ1) we can write the following,

(1) 312 →−= θθθ (2) )s(F)s(F 21412

4 →=→= θθθ

θ

� Eliminate θ2 and θ3

[ ]42114 )s(F)s(F θθθ −=

(3) )s(F 423 →= θθ

[ ]3114 )s(F θθθ −=

)s(F)s(F)s(F 214114 θθθ −=

)s(F)s(F)s(F 214411 θθθ +=

[ ])s(F)s(F1)s(F 21411 += θθ

)s(F)s(F1

)s(F

21

1

1

4

+=⇒

θ

θ

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C1 : FB Loop - TF Derivation

F1(s)

1θ 4θ2θ

3θ

F2(s)

+

-

� The overall TF for a FB loop,

Blocks OL1

Blocks ForwardTF

+=

Blocks Feedback X Blocks Forward1

Blocks ForwardTF

+=

� or,

C1 : Block Diagram (BD) Reduction Rules

� A summary of BD reduction rules is here.

� Assignment 1 is here.

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C1 : Block Diagram Reduction – Example 1

� obtain the TF for the following system,

G2(s)

+

-

G3(s)

H1(s)

H2(s)

+

-

R(s) C(s)

G1(s)

C1 : Block Diagram Reduction – Example 2

� obtain the TF for the following system,

G2(s) G

3(s)

H2(s) H

3(s)

+

-

X(s) Y(s)

G1(s)

H1(s)

++

--

+