DCS Chapter1

7/30/2019 DCS Chapter1

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CHAPTER 1

DIGITAL CONTROL


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Introduction: Historical Development


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Introduction: Historical Development


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Contd


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Introduction (Contd)


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Introduction (contd)


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Practically all control systems that are implementedtoday are based on computer control. A computer

controlled system can be described schematically as:

COMPUTER/ DIGITAL CONTROL

SYSTEM


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A continuous time signal, y(t) is converted into digital

form by analog-to-digital converter (A-D) at sampling

times, tk.

The computer interprets the converted signal, {y(tk)} as

a sequence of numbers.

The computer processes the measurements using an

algorithm, resulting a new sequence of numbers, {u(tk)}.

This sequence is converted to analog signal by digital-

to-analog converter(D-A).


SYSTEM


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Sampled/ discrete-time

signal

Sampled-data system

Computer-controlled system

Discrete-time system


SYSTEM

Continuous-time signal


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DEVELOPMENT OF COMPUTER-

CONTROLLED SYSTEM

1955: Pioneering period

1962:Direct- digital-control period

1967:Minicomputer period

The computer systems were slow, expensive and unreliable.

Control process by printing instructions to the process operator.

More flexible and cheaper for large installations .

Computer controlled the process directly by basic control functions.

Efficient design of process control system was possible as computer

became smaller, faster, more reliable and cheaper.

Only restricted to large industrial system.

Practically all controllers are computer-based

1972: Microcomputer period


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1990: Distributed / Plantwide supervision

& control


CONTROLLED SYSTEM

1980:General use of digital controlPLC emerges as replacement for relays.

All computers and computer systems in industrial plants are

virtually integrated to achieve real-time exchange of data .


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Plantwide & supervision control in the industry


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By plantwide supervision & control there is datacommunication between all the computers.


CONTROLLED SYSTEM


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Data communication is the transfer of digital data

between computer systems by means of electrical

or optical transmission systems (called networks).

Data communication system is set of devices

(hosts) connected by a communication medium

that are able to share data through transmission

over the media.

Three common types of network are:

a) LAN: Local Area Network

b) MAN: Metropolitan Area Network

c) WAN: Wide Area Network


CONTROLLED SYSTEM


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LAN: Local Area Network


CONTROLLED SYSTEM


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LAN: Local Area Network

Provides interconnection of a variety of data

communication devices (computers, printers,

appliances) within a small area (< 1 mile), in an officebuilding or home.

There are two main benefits to using a local area

network: information sharing and resource sharing.

Examples of Information sharing include file sharing,

exchanging e-mail and using the Internet.

Examples of resource sharing include sharing hardware

and software, such as sharing an expensive printer.


CONTROLLED SYSTEM


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MAN: Metropolitan Area NetworkSimilar characteristics to LANs but larger distances:

about 10s of miles


CONTROLLED SYSTEM


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WAN: Wide Area Network


CONTROLLED SYSTEM

Networks that cover substantial distances and can evenbe worldwide

Examples:

- Public telephone networks

- Public packet switched networks (e.g., the Internet)


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CONTROLLED SYSTEM

FutureThere are 4 areas that are important for the development ofcomputer process control:

Process knowledge

Progress in system identification & data analysis; & installation

of process-control systems have provided valuable informationon process knowledge because it is easy to collect data,

perform experiment and analyse the result.

Measurement technology

Possibility of obtaining automatic calibration with a computer.

Computer technologyMicrocomputers are expected to have greater computing power.

Substantial improvement are expected in display techniques

and communications.

Control theory

Studies indicate significant improvements can be made.


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ANALOG CONTROL SYSTEM VS.

DIGITAL CONTROL SYSTEM

Block diagram of an analog feedback control

system configuration.


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The plant is the process to be controlled.

The feedback element/ sensor feeds the plant output

back to the input side of the system.

The controller is driven by the difference between the

input & feedback output.




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Block diagram of a digital feedback control system

configuration.




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The main difference between the twocontrol systems is, digital control systemhas analog to digital converter (ADC) anddigital to analog converter (DAC)




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Other differences:


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A digital control system offers many advantages

over its analog counterparts.

Although it has several disadvantages, its

advantages outweigh its disadvantages.

Since digital control systems are widely used

today, it is important to understand the underlyingtheories and concepts.


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Multi axis motion controller board on which isimplemented a microcontroller used to control dc

brush, dc brushless, ac induction, stepper andvariable reluctance motor.


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DESIGN PROCESS OF A DIGITAL

CONTROL SYSTEM

System specification specifies the

design parameter

Mathematical modeling of physical system

Analysis of the model of a system

Detailed design

Verification by simulation packages:

MATLAB, CAE,etc

Implementation & the implemented design

enters the world as new product

From the world the need/ desire todesign a control system arises


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EXAMPLES OF DIGITALCONTROL SYSTEMS


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Example 1.1 Digital Filter

A digital filter is a simple example of a computer/ digitalcontrol system.


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The block diagram of a digital filter

The response of the system on external

stimulus depends on how it is synchronized

with the internal clock of the computer system.

Sampled system is not time-invariant


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The step responses of a digital computerimplementations for 4 different delays in the input step

(dashed) compared with the first sampling instant.



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Example 1.2 Controlling the Arm of Disk Drive

The purpose of the control system is to control the

position of the arm so that the head follows a given

track and rapidly moves to a different track. Benefits of

improved control: better trackkeeping allows narrower

tracks and higher packing density.

The block diagram of the system:


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Let be the moment of inertia of the arm assembly.

The dynamics relating the position of the arm, y to

the voltage of the drive amplifier, u is approximately

described by

(1.1)

Where is a constant

Let uc

be the command signal.

A simple servo controller can be described by

(1.2)

2)( JsksG

J

k

)()()( sYas

bsKsU

a

bKsU c


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If the controller parameters are chosen as

A system with the characteristic polynomial

is obtained.

To obtain an algorithm for a computer-controlled

system, the control law given by (1.2) is first written as

k

Jk

b

a

2

0

0

0

2

2/

2

3

0

2

0

2

0

322)( ssssP

)()()()()()()( sXsYsU

a

bKsY

as

baKsKYsU

a

bksU cc


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This control law can be written as

(1.3)

To obtain an algorithm for a control computer, the

derivative is approximated with a difference. This gives

ybaaxdt

dx

txtytua

bKtu c

)(

)()(()(

)()()()()(

tybataxh

txhtx


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The following approximation of the continuous

algorithm (1.3) is then obtained:

kkkk

kkkck

taxtybahtxhtx

txtytua

bKtu

)()(

)()()()(


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The simulation of the disk arm servo with analog(dashed) and computer/digital control (solid).



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Example 1.3 Simplified Single Axis Autopilot Control System

The figure shows the block diagram of a simplifiedsingle axis analog control of an aircraft or missile. This

is a typical analog control system. The signal can all

be represented as functions of continuous time

variable, t. The objective of the control is that the

attitude of the airframe follow the command signal.


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Instead of using analog controller, a digital controller withADC and DAC can be used for the same objective, as

shown in the figure . Since all components other than the

digital controller are still analog, ADC and DAC are

necessary for signal conversions.



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The figure shows the digital autopilot control systemin which the position and rate information are

obtained by digital transducers, and the operations

are represented by sample and hold devices.



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The sampler samples the analog signal at some

uniform sampling rate, and the hold device holds the

value of the pulse signal until the next samplecomes along. This system is called multirate

sampled-data system since the two samplers have

different sampling periods T1 and T2.


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The figure shows the basic element of a rolling mills

regulating system in industrial process. It can be seen

that the computer controls the drive speed, tension and

thickness.

Example 1.4 Digital Computer-Controlled Rolling MillRegulating System


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Example 1.4 Digital Computer-Controlled Rolling MillRegulating System

Figure 1. shows a block diagram of the thickness

control portion of the system.

Figure 1. Thickness control in a rolling mill regulating system


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The figure shows the block diagram and the essentialelements of a minicomputer system used for speed and

voltage control, and data acquisition of a turbine-generator

unit. The DAC forms interface between the digital computer

and the speed and voltage controls. The data-acquisition

system measures variables such as the generator speed, rotor

angle, terminal voltage, field and armature current, and real

and reactive power.

Example 1.5 Digital Controller for a Turbine and Generator


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The figure shows an all-digital data system. It contains

all digital elements so that ADC and DAC for signalmatching are unnecessary. It is used to control the read-

write head of a computer memory disk. The prime mover

used in this system is a step motor driven by pulse

commands. The step motor moves one fixed

displacement increment in response to each pulse input.

Example 1.6 Step Motor Control System


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Example 1.7 Motor Position Control System

The digital controller of the motor position controlsystem is a microcontroller.


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The figure shows the block diagram of a dc motorcontrol system that uses special purpose

microprocessor; GALIL GL-1200 that provides closed

loop position and velocity control of a dc motor. GALIL

GL-1200 is designed with proportional and derivative

(PD) control.

Example 1.8 Microprocessor-Controlled Systems


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The figure illustrates the same dc motor controlsystem but uses National Semiconductor LM 628

controller, designed with PID controls.


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The microprocessors in this example can bereplaced by a DSP, which may result in greaterimprovement in the system performance.



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Social and economic systems can also be modeled bya discrete-data system model.

Assume that:

Example 1.10 Discrete-Data Model of an Interest-Payment Problem

p(0) : amount of capital borrowed initially

R : percent of unpaid balance per period

U : principal & interest to be paid in N equal payments

p(k) : the amount owned after the kth period.

Then, the difference equation can be written for the problem:

p(k+1) = (1+R) p(k) - U


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The block diagram of the discrete-data system model is

described as

Example 1.10 Discrete-Data Model of an Interest-Payment Problem

Where:

p(k+1) : amount still owed at the end of the (k+1)th

periodThe given p(0) and p(N)=0 are the boundary conditions


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An antenna pointing system is illustrated in Figure

1.1. The yaw angle, (t), is controlled by the electric

motor and the gear system.The voltage v0(t) is directly

proportional to the yaw angle (t) of the antenna, andthe voltage vi(t) is directly proportional to the desired

yaw angle. If the yaw angle and the desired yaw

angle are different, the error voltage e(t) is nonzero.

This voltage is amplified and applied to the motor to

cause rotation of the motor shaft in the direction thatreduces the error voltage. The block diagram of this

analog control system is described in Figure 1.2.

Assignment 1


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Assignment 1

Figure 1.1 Antenna pointing system


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Assignment 1

Figure 1.2 Block diagram of antenna pointing system


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1. Simulate the analog control system of the antennapointing system by using MATLAB, providing theresponse behaviour of the system to a unit-stepinput.

2. Convert the analog control system block diagramto its corresponding digital control system blockdiagram, highlighting all the elements of the digitalcontrol system.

3. Explain (and provide the necessary diagram), howthis system can be implemented by using digitalsignal processor (DSP) based on Example 1.9.

Assignment 1


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General Conversion System Organisation for Control


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Integrated ADC and DAC in DCS

C t I t f S t


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Computer Interface System

Measurement in Digital Control systems


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Measurement in Digital Control systems

Real Time Computer Control


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Real-Time Computer Control


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Real-Time Computer Control

Real-time implies the ability of the computer to respond to stimuli from the

system in a timely fashion, that is, it must respond sufficiently fast in order to

accommodate the needs of the process. For example, the computer mustbe capable of reacting to any emergency conditions in the plant.

The challenge of real-time responses becomes more critical for processes

operating on short time scales, hence careful attention must be given to the

selection of computer, its structure and the designing of the overall system.

Several trends are emerging:

Rapid development of inexpensive, fast computer hardware

Introduction of standard high-level languages (with necessary extensions of

real-time applications)

Wider availability of sophisticated executive systems for monitoring computer

operations

All of the above are reducing the requirement of specialized knowledge.


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Example 1

Direct Digital Control Systems


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g y DDC control consists of microprocessor-based controllers with the

control logic performed by software. Analog-to-Digital (A/D)converters transform analog values into digital signals that amicroprocessor can use. Analog sensors can be resistance, voltage

or current generators. Most systems distribute the software toremote controllers to eliminate the need for continuouscommunication capability (stand-alone). The computer is primarilyused to monitor the status of system, store back-up copies of theprograms and record alarming and trending functions. The centraldiagnostic capabilities are a significant asset. Software andprogramming are constantly improving, becoming increasingly user-friendly with each update.

Benefits of DDCThe benefits of direct digital control over past control technologies(pneumatic or distributed electronic) is that it improves the controleffectiveness and increases the control efficiency. The three maindirect benefits of DDC are improved effectiveness, improved

operation efficiency and increased energy efficiency.


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DCS Chapter1