ME 534 - 01 Introduction (Rev. 2.1)

8/13/2019 ME 534 - 01 Introduction (Rev. 2.1)

1/13

Outline Introduction

Classification of Control S stems

Analog Controllers

Op-amp circuits

Comparison

Signals in Control Engineering

I/O interfaces

Control computer

on ro a gor m

Example: Water Level Control

P control law Hysteresis control

Chapter 1 ME 534 2

Classification of Control S stems

-

Mostly referred to as Analog Control Controller takes corrective action continuously in time.

Analog circuit elements are used to implement such controllers.

Discrete-time Control

Also known as Digital- or Numerical Control

Corrections take place at particular instances in time. Controllers output stays constant between these instances.

Microprocessors are generally employed to realize thesecontrollers.

A blend of both control systems (and strategies).

Chapter 1 ME 534 3

Discrete-time Control A lications

Home a liances Millitar a lications Dishwasher

Washing machine

Advanced weapons systems

Radar systems

Robotics Mobile robots

Electric Motor Drivers

Consumer goods

n us r a ro o s

Automations systems Factory automation

TV sets

CD / DVD players / recorders

Aerospace applications Aircraft control / guidance

Mobile phones

Personal Computing

Rocket / missile guidance

ar s r ves

CD-RW drives

Chapter 1 ME 534 4

Di ital A lications Contd

Several computers are onboard.

by these computers (calledelectronic control units orECUs

Fuel injection / Ignitioncontrol

Anti-lock Break Systems

Stability and tractioncontrol (anti-skid)

Climate control Automatic transmission

system

Chapter 1 ME 534 5


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Typical Digital Control SystemPower Disturbance

Control

Element

m(t) u(t) y(t)

Computer

Sensorb(t)

Computation of correction signal

Decision making

Chapter 1 ME 534 6

.

Typical Analog Control System

Function of analog computer:

Analog filtering of the measurement noise in the input signals Comparison of the measurement (b) and the command (r)

Generation of correction signal (m) on a continuous basis.

Chapter 1 ME 534 7

Analog Control using Op-amps

Analog controllers are frequently

implemented via operational amplifiers

(or simply op-amps).

One can implement almost any desired

function.+

_2

1

7

8

+V

Of f s e t n u l l N o c o nne c t io n

I n v e r t i n g i n p u t

Op-amps are very versatile amplifiers: Precise

Error tolerant / Robust

4 5-V O f f s e t n u l l

o n- n v e r n g n p u

Low-cost

There exists a wide variety of

-

-

applications:

Radio/video

onar ra ar

Automation

Automotive

Chapter 1 ME 534 8

ns rumen a on, e c.

Inverting Amplifier

A number of different functions can be implemented by employing op-amps with various

passive circuit elements.

Integrator:

ZA= R

ZB= 1/(Cs)

Transfer function of this circuit is s

1

RC

1

)s(E

)s(E

i

o

=

Differentiator:( )

( ) ( )o B

i

i A

G sE s Z s

= =

ZA= 1/(Cs)ZB= Rwhere ZA, ZB refer to the generalized

s)RC()s(E)s(E

i

o =

impedances [] of the components.Note that the bipolar voltage supply(+V, -V) of the circuit is customari ly

ME 534 9

.

Chapter 1


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Common O -am CircuitsSumming Amplifier (Mixer): Buffer (Voltage Follower):

=

Rf

o i

R1Rn

_

+

+

e1

+

en

RL eoLow-pass Filter:

n 1E s

1

f

i

R

o iRi

e e=

= ( ) ( ) 1iE s RC s=

+

Chapter 1 ME 534 10

Differential Am lifier

Differential am lifier is used to

amplify small signals buried in

much larger signals.

R resistances alon with R s

ek)vv(v 12RR

o1

2 ==

must be equalized to reduce the

effect of common mode voltage on

the out ut v .

Chapter 1 ME 534 11

Voltage Limiter

Output of op-amps cannot exceed a certain voltage level Vsat:

sa s .

One can built a voltage limiterusing this important property. To accomplish

that, two cascaded op-amp circuits are designed: i

some desired level.

o The following circuit (Attenuator) , which has a reciprocal of the amplifiers gain, reverts the

amplified voltage back.

As an illustration, assume that

we would like to limit ei such that

- i

Let Vs = 15[V] and Vsat = 13[V].

In this case, the gain of the

amplifier is calculated as

= =sat i, max .

Hence, we choose R1

= 10 kand R2 = 26 k.

Chapter 1 ME 534 12

Analog PID Controller

Kdd

D-control Analog computations involved in PID: Integration (dt)

Ki dt+r(t) m(t)

+

I-control

eren a on

Amplification (by a gain)

Summation (addition, subtraction)

Kp

_P-control 2

1 2( 1)( 1)( ) d p ii

K s K s K s sM sK

+ + + += =

Transfer Function:

b(t) ( ) ( ) ( )E s R s B s=

1 1 1R C =

=

2 2 2

4

1 3 2

iRK

R R C=

Chapter 1 ME 534 13


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Another PID Controller A more versatile version of the PID

controller can be built by simply

im lementin each control law via a

separate circuit.

Controller gains can be conveniently

adjusted via R1, R2, and R3.

3

4

p

RK

R=

1 1

1i

KR C

=

= 2 2d

Chapter 1 ME 534 14

A Multi- ur ose PID Controller

Chapter 1 ME 534 15

Com arison

Analog Control Digital Control

Control computations (such as dt, d/dt,, , , etc.) are continuous in time.

All computations are performed in

distinct time intervals.

Op-amps are used as computingelements.

Ps, DSPs, Cs, PLCs are commonlyutilized.

ar w re o su a e or

reconfiguration.

ex e eas y programme .

Very sensitive to measurement- and Somewhat sensitive to signal

process noise. conversion errors, quantization noise,

and round-off / truncation errors.

Inex ensive for sim le control s stems Hardware is inex ensive but control

but can be quite costly for complexsystems.

software development tools can be

expensive.

Chapter 1 ME 534 16

. -2. Discrete-time signal

3. Amplitude-quantized discrete-time signal

- -.signal

Chapter 1 ME 534 17


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T e 1: Continuous-time

,

The signal ranges between a lower bound (fmin)

max min, max By definition, f(t) = 0 when t < 0.

Chapter 1 ME 534 18

-

f(t) f*(t)

TTtt ,...2,,0,*

=

elset

,0)(

tT 2T 3T0

Time: t {0, T, 2T, ... , kT, ...}

The si nal ran es between a lower bound f and an upper bound (fmax):f [fmin, fmax ]

Chapter 1 ME 534 19

Type 3: Amplitude Quantized

Discrete-time

nm

fff

+

= minmax

f

*~( )

, {0, ,...}f t

f floor t Tt

= 3 f

0, elseT 2T 3T0

f

Time: t {0, T, 2T, ... , kT, ...}

e range o e unc on ecomes

},,2,,0,,)1(,{~

* fmfffnfnf

Chapter 1 ME 534 20

T e 4: uantized Continuous-time

Time: t 0 +

The range of the

],[ maxmin~

fff =

Since the transitions of

the function at T, 2T, 3T,

... are extremely fast, the

function values

predominantly reside atthe quantized levels.

Chapter 1 ME 534 21


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Properties of Digital Control

Systems

All physical quantites are represented by

length.

All computations are synchronized and are

carried out eriodicall .

The period in which all these computations

(T).

Chapter 1 ME 534 22

Properties (Contd)

All uantites in discrete-time domain could be

expressed as

X t = kT X k where k 0 1 2 ... k is called time index.

expression (difference equation) which

also that of the manipulation):

==

+=j

j

i

i jkebikmakm01

)()()(

Chapter 1 ME 534 23

A General Digital Control SystemPower Disturbance

m(kT) m(t)~

u(t) y(t)e(kT)r(kT) OutputInterface

DifferenceEquation

t t t tt Control

Alg ori thm

Latch &

D/AErrorCommand Manipulation OutputManipulated

Input

Control

Element Plant+

_

Clock

b(t)

t

b(kT)

t

~

Measurement

A/D Sensor

Control Computer

and Software InputInterface

Digital Domain Analog Domain

Control elements:

o or r ver + ec r c o or

Servo-valve + Hydraulic Cylinder / Motor

+

Chapter 1 ME 534 24

Elements of I/O Interfaces

.

II. Analog-to-Digital (A/D) Converter

III. Latch

- -.

Chapter 1 ME 534 25


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I Sam ler

f*(t)

Sampler

f(t)

Type 2Type 1

t

T 3T0

Tf(t) f*(t)

t

-

instances.

into a discrete-time one (Type 2).

Chapter 1 ME 534 26

II A/D Converter

It converts a voltage level into a corresponding

instant of time.

Chapter 1 ME 534 27

Pro erties of A/D Converters Input Voltage Range:

n po ar:

5V Bipolar: -5V +5V

10V Bipolar: -10V +10V

Denotes quantization level

-

Conversion time:

an N-bit binary number

Chapter 1 ME 534 28

A/D Converters Contd

designed specifically to do this

conversion:

in min, max Vout0, ..., VoutN {0, 5 V} (TTL)

For convenience, out ut volta e states

are represented as binary numbers:

0 Volt 0 (low logic level)

For A/D converter chips, prices go up as

Resolution (and accuracy) increases

Conversion time decreases

Chapter 1 ME 534 29


8/13

Uni olar A/D Converter

- ,

we have the following ADC output code:

Output Voltage at Pins [V] Binary

Number

Unsigned

IntegerDB7 DB6 DB5 DB4 DB3 DB2 DB1 DB0

0 0 0 0 0 0 0 5 00000001 1

0 0 0 0 0 0 5 0 00000010 2

0 0 0 0 0 0 5 5 00000011 3

... ... ...

Chapter 1 ME 534 30

Uni olar ADC Out ut 8-bitOutput of ADC

11111111

00000010

00000011

00000001

00000000 Input Voltage0 V V V V

(Vmin)

Chapter 1 ME 534 31

Bipolar ADC Output (8-bit)Note that the ADC output format in bipolar operation is

device-dependent: Device manufacturers commonly

em lo direct strai ht binar - and/or twos com lement

representations.

8

V

max

)

7

V

6

V

8

V

7

V

6

Vmin)

Chapter 1 ME 534 32

1 (11-12

-12

-12(

Exam le A/D Converter

Consider a 10V unipolar A/D converter with

- = reso u on.a) Determine the voltage resolution of this

device.

b Find the out ut re resentation as unsi ned

integer) when an input voltage of 3.27 V is

a lied.

Chapter 1 ME 534 33


9/13

Solution Part a

Voltage resolution (i.e. quantization level) can be given as

max min| |

2NV V

V

=

Hence,

8

|10 0 | 1039.0625[ ]V mV

= = =

Chapter 1 ME 534 34

Solution Part bThe corresponding number representation can be simply

33.27 83inVoutput floor floor = = =

.

where flooris a function rounding its argument to the

.

Input Voltage Range [V] Binary # Rep. Unsigned Int. Rep.

[0, 0.0391) 00000000 0

[3.2422, 3.2813) 01010011 83[9.9219,9.9609) 11111110 254

9.9609,10 11111111 255

Chapter 1 ME 534 35

Quantization Error (or Accuracy)

A/D conversion

mentioned here leads to

a quantization error of

significant bit: LSB) at

maximum.

Such an quantization

error mi ht be

unacceptable for certain

applications.

Chapter 1 ME 534 36

Quantization Error (Contd)

To reduce this error, a

better A/D conversion

method is adapted by ADC

A bias of V/2 is internallyadded to Vin.

Quantization error now ranges

between -V/2 and V/2 (or.

Output (code) of the ADC

can be ex ressed as

output = floor(Vin/V + )

Chapter 1 ME 534 37


10/13

In ut Interface

f*(t)~

*~ Type 3f t

f(t)

Type 1

amp er

& ADCt

T 3T0

3 f

ft

In ractice, sam ler & ADC are considered to be

a single unit:

In ut to the unit is an analo volta e var in in time, Output is binary number sequence with finite word

length.

Chapter 1 ME 534 38

III Latch

Latch holds a binary number during onesamp ng per o .

It is an inte rated circuit which holds the

input (N-bit digital) signal throughout one

.

The output of the device remains the same

ur ng s per o .

Chapter 1 ME 534 39

IV D/A Converter

Converts an N-bit digital signal into a

corres ondin volta e level:

Complementary operation of A/D converter.

Output Voltage Range:

5V unipolar, 5V bipolar, 10V unipolar, 10V bipolar

Resolution and Accurac

Conversion Time

Chapter 1 ME 534 40

Out ut Interface

single unit (output interface).

Sample and Hold (S/H) Unit.

Chapter 1 ME 534 41


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Errors in Di ital Control S stems

Chapter 1 ME 534 42

Control Com uter

As control com uters there exist a wide

variety of choices in practice:

PC + Motion Control Card

Microcontroller: Single Control IC

Pro rammable Lo ic Controller PLC

Chapter 1 ME 534 43

A Simple Control Algorithm

.

2. Fetch (or generate) command r(k)

3. Compute error e(k) = r(k) - b(k)

.

5. Output m(k)

6. Wait till end of sampling period

. o o ep

Chapter 1 ME 534 44

Illustrative Exam le

Consider the waterlevel control system.

Servo-valve or Pro .ensor

Flow Control Valve): m(t) is control voltage:L

evel

S

0 V qi = 0 lt/s

5 V qi = 100 lt/s

ensor: b(t) is sensor output

0 V h = 0 m 5 V h = 5 m

Chapter 1 ME 534 45


12/13

Control System

Controlr(k) + Latch &m(t) qi(t)

qo(t)

Servo- Waterh(t)m(k)

8-bit / 5V

unipolar

_

ClockT

Data AcquisitionBoard

Sampler

& A/D

b(t) Level

Sensor

b(k)

Program

8-bit / 5V

unipolar

- Desired water level: -

Control Law: Proportional Control

Sampling Time: T = 0.1 sec. D/A Converter: 8-bit / 5V unipolar

A/D Converter: 8-bit / 5V unipolar

Chapter 1 ME 534 46

C Librar Functions

drivers along with high-level language support. . .

For this example, let us assume that the

read_ADC(): returns water-level as unsigned integer.

write DAC(m): enerates out ut volta e de endin_on the input argument m. Here, m < 256 is anunsigned integer.

pause(n): e ays e execu on y n m secon s.

init(): initializes the units on the DAQ board.

Chapter 1 ME 534 47

Control Program 1 (ANSI C)#include

#include

#include control.h

#define K 1.2

voidmain() {

float r,dr,e,b,qi; unsigned intm;

r = 0; dr = 3/3000;init(); /* Initialize */

while(1){ /* Infinite loop */

b = 5*read_ADC()/255; /* Read sensor */

r += dr; if (r>3) r = 3; /* Calculate cmd */

e = r b; qi = K*e; /* P-control law */

if (qi < 0) qi = 0; /* 0


13/13

H steresis Control

hysteresis (a.k.a. bang-bang or on/off)

.

The power control element (PCE) is either

magnitude of error:

.

If error < -threshold then PCE is switched off.

res o s o en mes re erre o as error-

band, deadband, or tolerance.

Chapter 1 ME 534 50

H steresis Control Contd

Chapter 1 ME 534 51

Control Program 2 (ANSI C)#include

#include

#include control.h

#define dh 0.1 /* Define deadband */

voidmain() {

float r,dr,e,b; unsigned intm;

r = 0; dr = 3/3000;init(); /* Initialize */

write_DAC(255); /* Turn on valve */

while(1) { /* Infinite loop */

b = 5*read_ADC()/255; /* Read sensor */

r += dr; if (r>3) r = 3; /* Calculate cmd */

e = r b;

if (e > dh) m = 255; /* Hit lower bound? */

if (e

Documents

ME 534 - 01 Introduction (Rev. 2.1)