1

Industrial controllers

Rferences

• U. Tietze, Ch.Schenk, Electronics Circuits – Handbook for Design and Applications, Springer,2008

• Advertisement materials and Application notes of:

– Linear Technology,

– Analog Device,

– Texas Instruments,

– National Semiconductors

– NEV Corporation

Electronic Controllers

The purpose of a controller is to bring a physical quantity to a predetermined value and hold it at this value

2

Underlying Principles

Where As is the gain of the controlled systemHence, the conytrolled variable is:

ZAA

AW

AAAA

Xsc

s

sc

sc

++

+=

11

)()( ZYAsXandXWAcY +=−=

P-controller

Bode plot of a system with a P-controller

Step response as a function of the

phase margin

Optimum controller

dBdBAporAs

ApAc dB 177lg20714.0

11 =⋅=====

771 =⋅== AsApg

%5.1271

1

1

1 =+

=+

=−gW

XW

The low-frequency limit value of the loop gain is therefore

This gives us a relative deviation of

3

PI-ControllerBode plot of a system

with a PI-Controller

PI-Controller

Block diagram of the PI-Controller Bode plot of the PI-Controller

PI-Controller

PI-Controller

211

2

2

1;

RCf

R

RAp I π

=−=

4

PI-Controller

Error signal for the P-controller sand the PI-controller with an optimum value of fI

PID-Controller

Block diagram of the PID-controllerBode plot of the PID-controller

PID-Controller

Bode plot of system and a PID-controller

−+=++=

ωω

ωω

ωτωτ I

DID jAp

jjApAc 1

1

WhereI

ID

D Apfand

Apf

τππτ 2

1==

5

PID-Controller

Comparison of the transient behavior of

a system with PI-controller and with a

PID-controllerPID-controller

1211

2

2

1;

2

1;

RCf

RCf

R

RAp

DDI ππ

==−=

The PID-Controller withAdjustable Parameters

PID-controller with decoupled parameters

DDDI

P

RCf

RCf

R

RAp

ππ 2

1;

2

1;

111

===

The PID-Controller withAdjustable Parameters

oscIoscDosc TTAcAp 10≈≈≈ ττ

6

Control of nonlinear systemStatic Nonlinearity

Linearization of a system that has static nonlinearity

Control of nonlinear systemDynamic Nonlinearity

Transient behavior of the

controlled variable for a

limited system slew rate Slew rate limiter for the

reference variable.RC

V

dt

dV max0 =

Phase-Locked Loop

Principle of the phase-locked loop (PLL)

7

PLL capture and hold frequency

Input Frequency

Ph.Det. signal

HOLD

CAPTURE

Phase-Locked Loop

ϕ

ϕαkkAc

ff

f

01 −=−

m

f

m

f

f jf

kk

j

kk

V

VAs ϕϕϕ

ωπ

===2

mjωωϕ 1=

∆

∫ ∫∫ ∆=−=t tt

tdtdtd0 0

1

0

2~~~ ωωωϕ

ϕαϕ

α −==k

V

tt mωωω cos)( ∆=∆

tt mm

ωω

ωϕ sin)(∆=

Phase-Locked LoopSample-and-Hold Circuit as a Phase Detector

A sample-and-hold circuit used

as a phase detector Voltage weveform in the phase detector

8

PLL – SH as Ph.Det. - dynamics

ϕϕ sin1̂VV = radVV /1̂ϕϕ ≈

radVd

dVk /1̂==

ϕϕ

ϕ

2221 /

1ffjTj mm eVekk πω

ϕϕ−⋅− ==

2/

1̂

ffjm

f

m

f

mejf

Vk

jf

kkAs π

ϕ ==

2

1

2

ˆ

f

fand

f

Vk

V

VAs m

mm

f

f

ππϕϕ −−===

PLL with a sample-and-hold circuit as phase detector

1;2

1;

2121

2 ==+

= II ARC

fRR

RAp

π

PLL – SH as Ph.Det. - parameters

Phase-Locked LoopSample-and-Hold Circuit as a Phase Detector

Mean absolute value of

the output voltage of a

multiplier for simusoidal

input voltages of

amplitude U

Application of a

synchronous demodulator

for the measurement of

noisy signalsOperation of a

synchronous demodulator

9

Phase-Locked LoopSynchronous Detector as a Phase Detector

PLL with a multiplier as

phase detector for

frequency demodulation

Transconductance multiplier as a switch

Transconductance multiplier as a switch

10

Transconductance multiplier as a switch

Transconductance multiplier as a switch

Multiplying circuit

φ

Gdy φ=0

VCC VCC

11

Synchronous AM detector

Gdy φ=0 To nie jest detekcja szczytowa,

a średnia

VCC VCC

AM synchronous detector

Det. fazy Filtr VCOfin

fout

VCC VCC

Phase-Locked LoopFrequency-Sensitive Phase Detector

Phase detector with

memory for sign of the

phase shift

Input and output signals

of the phase detector

Transfer characteristic of

the phase frequency

detector

12

Phase-Locked LoopPhase Detector with Extensive Range

Phase-Locked LoopPhase Detector with Extensive Range

Detection characteristic of

the phase detector

Frequency synthesis

n

f

k

f outin =

Phase Det. Filtr VCO:k

:n

fin

foutfin/k

fout/n

inout fk

nf =

13

Phase-Locked LoopSample-and-Hold Circuit as a Phase Detector

Phase-Locked LoopSample-and-Hold Circuit as a Phase Detector

PLL applications

• AM Demodulation

• Synchronous detection (LockIn Amp)

• FM, PM demodulation

• Frequency synthesis

• Synchronous telekommunication

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PLL IC - 4046

4046 phase detector I

4046 phase comparator II

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4046 features

Feature Detektor I (exor) Detektor II

Lack of input signal fwyj=f0 fwyj=fmin

Phase shift on output 90deg for f00 to 180 in the range of 2fT

0deg

Harmonic synchronization synchronize No synchronization

Immunity t noise high low

2fT (lock range) fmax - fmin

2fC (capture range) fC < fT (depends on filter) fC= fT

FM detector

ktuftf

ftmftf

ftmftf

out

out

in

⋅+=∆⋅+=

∆⋅+=

)()(

)()(

)()(

0

0

0

Det. fazy Filtr VCO

fin(t) fout(t)

)()( tmk

ftu

∆=

)()( tmk

ftu

∆=

4046 as FM demodulator

FM signal

10kHz

Follower

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4046 as AM demodulator

multiplier

PLL IC LM565 (up to 500kHz)

LM565

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NE564

NE564 (up to 50MHz)

NE567

18

NE567

ADF4360-7

(350-1800MHz)

ADF4360-7 (350-1800MHz)

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ADF4360-7

generator 500MHz

Summary

• P, PI, PID controllers

– parameters adjustment

• PLL

– Principle of operation

– examples of VCO, filters, phase detectors

– Applications – frequency synthesis, detectors

test questions• What is the practical algorithm for PID controller

parameters adjustment ?

• What is the principle of operation of PLL ?

• What is the principle of operation of PLL as FM

detector ?

• What is the principle of operation of PLL as AM

synchronous detector ?

• What is the principle of operation of PLL as

frequency synthesizer ?