Pendahuluan Teori Kontrol Otomatik

SAEFUL BAHRI, ST, MT

DASAR SISTEM KONTROL

FILOSOFI SISTEM KONTROL

Program Studi Teknik ElektroFakultas Teknik

Universitas Muhammadiyah Jakarta

E&CE 380 Introduction

Course Objectives

To provide a general understanding of the characteristics of dynamic systems and feedback control.

To teach classical methods for analysing control system accuracy, stability and dynamic performance.

To teach classical control system design methods.

Control System Concepts

A system is a collection of components which are co-ordinated together to perform a function.

Systems interact with their environment across a separating boundary.

The interaction is defined in terms of variables.

system inputs

system outputs

environmental disturbances

Systems

Disturbance Inputs

Control Inputs

System Outputs

Engineering systems

Biological systems

Information systems

Subsystem

System Variables

The system’s boundary depends upon the defined objective function of the system.

The system’s function is expressed in terms of measured output variables.

The system’s operation is manipulated through the control input variables.

The system’s operation is also affected in an uncontrolled manner through the disturbance input variables.

Car and Driver Example

Objective function: to control the direction and speed of the car.

Outputs: actual direction and speed of the car

Control inputs: road markings and speed signs

Disturbances: road surface and grade, wind, obstacles.

Possible subsystems: the car alone, power steering system, braking system, . . .

Antenna Positioning Control System

Original system: the antenna withelectric motor drive systems.

Control objective: to point theantenna in a desired reference direction.

Control inputs: drive motor voltages.

Outputs: the elevation and azimuth of the antenna.

Disturbances: wind, rain, snow.

Antenna Control SystemFunctional Block Diagram

Physical VariablesInformation Variables

AntennaMotorPoweramp

Diff.amp

Ref.input

Anglesensor

volts volts

volts

+

_

power torque Angular

position

Antenna System

Wind force

Feedback

Path

Error

Control System Components

System or process (to be controlled)

Actuators (converts the control signal to a power signal)

Sensors (provides measurement of the system output)

Reference input (represents the desired output)

Error detection (forms the control error)

Controller (operates on the control error to form the

control signal, sometimes called compensators)

Feedback System Characteristics

Consider the following speed control system

Load

Kl

Motor

Km

Amp

Ka

Speed sensorKs

Reference

speed

u+

_

Disturbance

torque

wo

Open loop system

Feedback Path

wr

+

+

Td

Tm

Open Loop System Characteristics

Assume that each component may be represented by a simple gain, then

The accuracy of the open loop system depends upon the calibration of the gains and prior knowledge of the disturbance (choose the control u to give the desired wo ).

Problems:

nonlinear or time varying gains

unknown and varying disturbances

dllma

dmlo

TKuKKK

TTK

)(w

Closed Loop Characteristics

Now consider the case with feedback.

d

slma

lr

slma

lmao

dlosrlma

dmlo

TKKKK

K

KKKK

KKK

or

TKKKKK

TTK

11

)(

)(

ww

ww

w

Closed Loop Characteristics

If Ka is very large such that,

then,

Ks is the sensor gain in units of volts per rad/s.

The input/output relationship is not very Sensitive to disturbances or changes in the system gains

slmaslma KKKKKKKK 1

d

sma

r

s

o TKKKK

11 ww

rad/s volts 0

Closed Loop Characteristics System

Error

The control error is

Again, if the loop gain, Ka Km Kl Ks is large, then the error is small.

d

slma

slr

slma

d

slma

slr

slma

slma

osr

TKKKK

KK

KKKK

TKKKK

KK

KKKK

KKKK

Ke

11

1

111

)(

w

w

ww

Note: Gain Definitions

forward gain: Ka Km Kl

feedback gain: Ks

loop gain: Ka Km Kl Ks

closed loop gain: forward gain1 + loop gain

System Dynamics

Consider a sudden change in the speed reference, wr .

The output speed, wo will not respond instantaneously due to the inertial characteristics of the motor and load, i.e. their dynamic characteristics.

The motor and load need to be represented by dynamic equations rather than simple gains.

The output response will generally lag the input and may be oscillatory.

System Dynamics

Step Responses

0 2 4 6 8 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1Step Response, Ka=2

0 2 4 6 8 10-0.5

0

0.5

1

1.5

2Step Response, Ka=20

wowo

wr

wr

Tm

Tm

Ka = 2 Ka = 20

Assume Ks = 1.0

Control System Design Objectives

Primary Objectives:

1. Dynamic stability

2. Accuracy

3. Speed of response

Addition Considerations:

4. Robustness (insensitivity to parameter

variation)

5. Cost of control

6. System reliability

Control System Design Steps

Define the control system objectives.

Identify the system boundaries.

define the input, output and disturbance variables

Determine a mathematical model for the components and subsystems.

Combine the subsystems to form a model for the whole system.

Control System Design Steps

Apply analysis and design techniques to determine the control system structure and parameter values of the control components, to meet the design objectives.

Test the control design on a computer simulation of the system.

Implement and test the design on the actual process or plant.

Skema Sistem Kontrol

Prodi Teknik Elektro Fakultas Teknik UMJ

Target Proses Kontrol

Agar suatu proses itu berjalan sesuai dengan target-target yang ditentukan, maka proses itu harus dikontrol secara otomatis. Target-target proses yang tersebut antara lain adalah:

1. Terjaminnya keselamatan (safety) baik bagi buruh maupun peralatan yang ada.

2. Terjaganya kualitas produk, misalnya komposisi produk, warna, dll. pada keadaan yang kontinyu dan dengan biaya minimum.

3. Proses berlangsung sesuai dengan batasan lingkungan, maksudnya adalah limbah yang dihasilkan oleh proses tersebut tidak melebihi ambang batas lingkungan.


4. Proses berlangsung sesuai dengan batasan-batasan operasinya.

Sebagai contoh pada pabrik kimia dimana peralatan

yang digunakan dalam sebuah pabrik kimia memiliki batasan (constraint) yang inherent untuk operasi peralatan tersebut. Batasan-batasan itu seharusnya terpenuhi di seluruh operasi sebuah pabrik.

Misalnya :

pompa harus menjaga net positive suction head tertentu;

Tangki tidak overflow atau menjadi kering;

kolom distilasi tidak terjadi banjir (flood);

suhu pada sebuah reaktor katalitik tidak melebihi batas atasnya sehingga katalis menjadi rusak.


5. Ekonomis

Operasi sebuah industri harus sesuai dengan kondisi pasar, yakni ketersediaan bahan baku dan permintaan produk akhirnya. Oleh karena itu, harus seekonomis mungkin dalam konsumsi bahan baku, energi, modal, dan tenaga kerja.

Hal ini membutuhkan pengontrolan kondisi operasi pada tingkat yang optimum, sehingga terjadi biaya operasi yang minimum, keuntungan yang maksimum, dan sebagainya.


Hal yang perlu disiapkan

Agar studi proses berhasil dengan baik, maka perlu dilakukan pemodelan (modeling), yakni dengan membuat suatu persamaan differensial fungsi waktu (dinamik).

Untuk dapat melakukan pemodelan diperlukan penguasaan akan prinsip-prinsip rekayasa proses (prinsip-prinsip rangkaian listrik, prinsip-prinsip termodinamika, aliranfluida, perpindahan panas, proses separasi, proses reaksi, dll.) dan matematika.

Model yang sudah dibangun selanjutnya dibuat simulasimenggunakan komputer.


Documents

Pendahuluan Teori Kontrol Otomatik