continuous control systems -...

Continuous Control Systems

California State University,

Fullerton

Certificate Award

Industrial Controls Technology

Instructor: Victor Wegelin

PMA ConceptsPhone: (562) 434-6728

E-Mail: [email protected]

Web: http://www.pmaconcepts.com

Continuous Control Systems Agenda

• Week 1

Sec. 1 Introduction to Industrial Controls

Sec. 2 Block Diagrams, Transfer

Functions

Sec. 3 Properties of Physical Systems

Lab #1 Process Dynamics: Sections 1-3


• Week 2

Sec. 4 Control Strategies

On-Off Control

Open Loop, Feed Forward,

Feedback

Modes of Control

Sec. 5 Proportional Control


• Week 3

Sec. 6 Two Mode Control

Sec. 7 Three Mode Control

Modifications to PID Control

• Week 4

Sec. 8 Controller Tuning Methods


• Week 5

Lab #9 Open Loop Tuning

Lab #10 Closed Loop Tuning


• Week 6

Sec. 9 Advanced Regulatory Control

Sec. 10 Ratio Control

Sec. 11 Cascade Control

Sec. 12 Feed Forward Control


• Week 7

Sec. 13 Override Control

Sec. 14 Multiple Input-Multiple Output

Processes

Sec. 15 Summary of All Methods


• Week 8

Lab #16 Feedforward Control

Extra Credit

Lab #1 Process Dynamics: Sections 4, 5

Lab #15 Cascade Control

Overview

• This course will explore the cause and

effect relationship of properties of physical

systems and their control.

• Topics include modeling of physical

systems, feedback control characteristics,

stability, digital control, tuning of control

loops, and basics of proportional, integral,

and derivative (PID) control.

At the end of this course you should be

able to:

• Describe process characteristics relevant to

analysis and design of selected industrial

applications

• Relate to mathematical fundamentals

• Describe the behavior of the three modes of

control of a classical PID controller

• Identify several methods for tuning feedback

control loops

• Understand the use of advanced control strategies

Section 1

INTRODUCTION TO

INDUSTRIAL CONTROLS

TECHNOLOGY

What is Automatic Control?

• Application of feedback theory to the

control of various physical processes

• Expressed and applied through the language

of mathematics

• Involved with transient or dynamic

behavior, rather than static or equilibrium

state

Examples of Automatic Control

Aviation

Power Generation

Communication

Building

Energy Management

Space

Automotive

Factory Automation

History of Automatic Control

EARLY: Add more or less wood to keep the water boiling

FERTILE

CRESCENT: Measurement of water to irrigate fields

SAMURAI: Product Quality introduced - Sword Making

1788: James Watt - Flywheel Governor

1866: Whitehead - Torpedo Control

1880: Fisher - Pressure Activated Pump Governor

1920’s: Petrochemicals - Pneumatic Feedback Control

1930’s: Formal Feedback Theory developed - Electronics,

Communications, Servomechanisms

History of Automatic Control

1940’s: Autopilots, Radar Control Rooms emerge

1950’s: Aircraft, Power Generation Electronic Controllers,

Supervisory and Digitally Directed Analog Control

1960’s: Direct Digital Control (DDC)

1970’s: LSI Technology improves reliability, Distributed

Control Systems (DCS)

1980’s: Plant-Wide Control, Networks, Global Standards

1990’s: Integration of Plant Information Systems, Quality

Control as a Mechanism, Vision Recognition

1990’s: Internet Access and Integration

What is an Industrial Control System?

• Distributed Process Control System?

(e.g. Honeywell TDC 3000)

• PLC Network?

• Personal Computers, connected to a Local

Network, with Process I/O?

• Any Control System that comes in two or

more pieces?

• Any or all of the above?

Integrated Control SystemBlock Diagram

(SGS)

Safety Shutdown

System PLC’s

FIE

LD

DE

VIC

ES

Dedicated PLC’s

Process Analyzer

Systems

Tank Gauging

System

Blending System

SCADA Systems

MIS COMPUTERS

DISTRIBUTED

CONTROL SYSTEM

Process Control

Computers

Engineering

Workstations

Lab Analysis

Computers

Machinery

Monitoring

HC/H2S/GAS

Monitoring

FIE

LD

DE

VIC

ES

Hierarchical Control

MARKET DEMAND

DELIVERY DATES

RAW MATERIALS

MFG. RESOURCES

MIS

PROCESS / MFG

CONTROL

MANAGEMENT

INFO

SYSTEM

PLANNING/

SCHEDULING

UNIT/PLANT

OPTIMIZATION

MES

EXPERT SYSTEMS

CONTINUOUSFEED FORWARD

INTERACTING

BATCHSEQUENCE

RECIPES

BANG/BANG CONTROL

ADVANCED CONTROL

BASIC CONTROL

DATA FOR

EXECUTIVE

MANAGEMENT

DATA FOR

PLANT

MANAGEMENT

MAXIMIZE PROFIT

EFFICIENT

OPERATION

PROCESS

Why Automatic Control?

Direct Benefits:

• Increase Productivity

– Throughput, Yield

• Reduce Costs

– Materials, Manpower, Energy

• Environmental Compliance

– Waste Minimization

Why Automatic Control?

Indirect Benefits:

• Improve Safety

– Plant, Personnel

• Better Information

– Production, Management, Engineering

– Predictive Maintenance

• Improve Customer Response

– Order Scheduling, JIT (Just In Time)

The Purpose of Automation is to

Eliminate Product Variation

Normal Control

90

92

94

96

98

100

Product Quality Spec

Average Quality



Improved Control

90

92

94

96

98

100



92

94

96

98

100

Reduction in Quality Giveaway

90

Old Target

New Target

Section 2

BLOCK DIAGRAMS,

TRANSFER FUNCTIONS

Piping & Instrumentation Diagram

(P&ID)

LT

Supply

Outlet

X sp

SetpointDESIRED VALUE

LC

ControlValve

LevelController

LevelTransmitter Demand

MANIPULATED

VARIABLE

PROCESS

VARIABLE(LOAD)

PROCESS

CONTROLLINGSYSTEM

CONTROLLEDSYSTEM

X

Block Diagram

(MEASURED)

Xsp

X

++

+

eX

m

_

SETPOINTERROR

CONTROLLER

MANIPULATED

VARIABLE

PROCESS

PROCESS

VARIABLE

PROCESS(MEASURED)

VARIABLE

FEEDBACKELEMENTS

CONTROLLINGSYSTEM

CONTROLLEDSYSTEM

BIAS

LOAD (DEMAND)

DISTURBANCES

Σ ΣGC GP

GF

Some Definitions

• Process Variable (PV):

– Measured Variable: such as Pressure, Level Temperature, Flow, Concentration, Time

– Controlled Variable (C)

• Setpoint (SP):

– Desired setting of the Process Variable (PV)

• Error (E):

– Difference between SP and PV (E=SP-PV)

» Relationship indicates a negative feedback control system

Some Definitions

• Controlled Output (CO):

– Manipulated Variable (MV)

– Result of the mathematical relationship which

causes the PV to move toward the SP.

– Direct Action: An increase in process

measurement causes the controlled output to

increase (e.g. open gas valve to increase

temperature).

– Reverse Action: An increase in process

measurement causes the controlled output to

decrease (e.g. increase fan speed to decrease

temperature).

Controller Action

ReverseNoIncrease-CloseReverse

DirectNoIncrease-CloseDirect

DirectYesIncrease-CloseReverse

ReverseYesIncrease-CloseDirect

DirectNoIncrease-OpenReverse

ReverseNoIncrease-OpenDirect

Controller

Action

Signal ReversalActuator

(Valve) Action

Process Action

Types of Disturbances

• Change in Setpoint

• Change in Supply

• Change in Demand

• Change in Environment

Typical Heat Exchanger

T

TIC

TT

Steam

Supply

Insulation

Cold Waterin, Qw

Hot Water toProcess

Condensate

to Trap

Shell

Tube

sP

uP

Tout

Tin

m1

X

X 1

m

TE

sp

(e)

Block Diagram of Heat Exchanger

and Transmitter

Controller Valve top and

PositionerProcess

Sensing Element

Load Changes

Inlet Water

TemperatureSteam Supply

Pressure

Water Flow

RateQ

w

m1

x2

Pu

m

Tin

ToutX sp e

x 1

2

+ _Σ

Dynamic Systems

• Dynamic System Representation

– Dynamic systems are represented as a function

of time by differential equations - f(t)

– f(t) consists of terms in integral and differential

calculus (differential equations)

– Represents systems in the time domain

– Continuous functions with no discontinuities

– Difficult to solve

LaPlace Transforms

• The LaPlace Transform Method:

– Used to simplify the problem to an algebraic

representation in the frequency domain

– Should be unique

– Function must exist over the whole region of

interest in either domain

– Continuous and no discontinuities

F(s) = ,f(t)

F(s) = 4kf(t)e-st dtI

0

Z Transforms

• The Z Transform Method:

– All computers used today are digital (sampled data)

– The Z Transform is the digital equivalent of the LaPlace Transform

– z-n is the delay operator of n samples

– Time series generating current output value

• Current input value xn

• Previous input values xn-1, xn-2, … xn-i

• Previous output values yn-1, yn-2, … yn-i

– Transfer function

• g(z) = y(z) / x(z) = a0 + (1 + a1z-1)

– Time series

• yn = a0xn + a1yn-1

Section 3

PROPERTIES OF PHYSICAL

SYSTEMS

4 Characteristics

• If you wish to control the process, you must first understand

the process

• All Processes exhibit these 4 Characteristics:• Gain

• Direction

• Deadtime

• Time Constant

Static Gain

Input Change

Output Change

Static Gain

Case A B C

10%

10%

10%

20%

10%

5%

1010

2010

510= = =1 2 2

1

Input Output

GAIN =% inputªªªªªªªª% output

Dynamic Gain

Input Output

Amplifier

Output Output

InputInput

1 sec.

0.5AA

= 1 Hz

Frequency (Log Scale)

Gain

,

am

plit

ude

ratio

0.75

1.00

0.50

0.00

0.25

Bode Plot

GAIN of temperature control loop is product of the

gains of the individual elements in the loop

∆

HEATED PRODUCT OUT

Loop gain =

Loop gain =

Gain transmitter Gain controller Gain valve operator Gain valve plug Gain process

psi out

mA inTemp. of Product, F

mA

opsi

Inches Travel Steam Pressure, psi

Valve-plug Travel, in

Temperature, Fo

Steam Pressure, psi

x

x

x

x

x

x

x

x∆

∆

∆∆

∆

∆∆

∆ ∆

∆

Temperature of Product, F

COLD PRODUCT IN

PROCESS

CONTROLLER

PRIMARYELEMENT

TEMPERATURETRANSMITTER

mAo

psi

Temperature, Fo

Steam Pressure. psiin. Travel

Steam Pressure, psi

Valve Plug Travel, in

STEAM

∆

∆

∆

∆

∆∆

∆mA out

mA in

∆

∆

I/Ppsi out

mA in∆∆

Time Constants

• Deadtime - td:

– The time that elapses from the moment a

change is introduced into an element of the

control loop and the moment the output begins

to change

» Also called transport lag or distance/velocity lag

DEADTIME occurs in a weight-belt system

Hopper

Point A Point B

WeightTransmitter

GateAdjustment

Pro

cess

Time

Input,

(Poin

t A

)

Pro

cess

Outp

ut,

(Poin

t B

)

td

td

Time Constants

• RC Time Constant - τ:

– Capacitance: Response dominated by system

capacity.

– Resistance: Response dominated by system

resistance

First order system: g(t) = e-t/τ, τ = RC

The time it takes for the controlled variable to

reach 63.2% of its final value (First Order).R

C

Time Constants

Time e-t/ττττ 1st Order 2nd Order 3rd Order

5.000 5.000 5.000

0.0 1.000 0.000 0.000 0.000

0.1 0.980 0.020 0.000 0.000

0.2 0.961 0.039 0.002 0.000

0.5 0.905 0.095 0.009 0.001

1.0 0.819 0.181 0.033 0.006

2.0 0.670 0.330 0.109 0.036

3.0 0.549 0.451 0.204 0.092

4.0 0.449 0.551 0.303 0.167

5.0 0.368 0.632 0.400 0.253

6.0 0.301 0.699 0.488 0.341

7.0 0.247 0.753 0.568 0.428

8.0 0.202 0.798 0.637 0.508

9.0 0.165 0.835 0.697 0.582

10.0 0.135 0.865 0.748 0.646

11.0 0.111 0.889 0.791 0.703

12.0 0.091 0.909 0.827 0.752

13.0 0.074 0.926 0.857 0.793

14.0 0.061 0.939 0.882 0.828

15.0 0.050 0.950 0.903 0.858

16.0 0.041 0.959 0.920 0.883

17.0 0.033 0.967 0.934 0.903

18.0 0.027 0.973 0.946 0.920

19.0 0.022 0.978 0.956 0.934

20.0 0.018 0.982 0.964 0.946

21.0 0.015 0.985 0.970 0.956

22.0 0.012 0.988 0.976 0.964

23.0 0.010 0.990 0.980 0.970

24.0 0.008 0.992 0.984 0.976

25.0 0.007 0.993 0.987 0.980

Cascaded Lags - Step Response

0.0

0.2

0.4

0.6

0.8

1.0

0 5 10 15 20 25

Time (sec)

un

its

1st Order 2nd Order 3rd Order

CAPACITANCE dominates level control in

tank

F

Pro

cess

Time

Outp

ut,

Le

vel

Pro

cess

Input, F

i

i

LT FO

DisplacementPositive

Pump

Most Processes have both resistance (R) and

capacitance (C)

TI

Heat Input

Thermowell

TemperatureElement

Agitator

Total Time Constant of temperature control loop is

sum of the Time Constants and Deadtimes of the

individual elements in the loop

Temperature of Product, F.

HEATED PRODUCT OUTCOLD PRODUCT IN

PROCESS

CONTROLLER

PRIMARYELEMENT

TEMPERATURETRANSMITTER

mA0

psi

Temperature, F0

Steam Pressure. psiin. Travel

Steam Pressure, psi

Valve Plug Travel, in

STEAM

I/Ppsi out

mA in

mA out

mA in

∆

∆

∆

∆

∆

∆

∆

∆

∆

∆

∆

∆

Effect of time lag on input and output

ProcessInput, A Output, B

45o

Input, A

360o

Output, B

Output, B

Input, A

Frequency (Log Scale)

-270

-180

-90

0

Phase A

ng

le,

Deg.

Bode Plot

Relation of Input and Output Sine Waves

SINE

INPUT

SINE

OUTPUT

360 DEGREESPERIOD - ONE CYCLE

INPUTAMPLITUDE

TIMEINPUTMAGNITUDE

PHASE ANGLEOR LAG

OUTPUTAMPLITUDE

TIME

OUTPUT MAGNITUDE

INPUT MAGNITUDE= MAGNITUDE RATIO OR GAIN

Ai

Ao

Mo OUTPUT

MAGNITUDE

P

Mi

Open Loop Step Response Graph

OUT

Pseudo

Dead Time

Pseudo

Time

Constant

Time

PVΔ

Δ

Kp =ΔPV

ΔOUT

63.2%

Td Tp

T0 T2T1

(Δout)

Kp =ΔOUT

(Δin)

Δout

Δin=

Open Loop Response Testing

Lag 1: First order system (1 lag)

Lag 2: Second order system (2 lags)

FOL+DT: First order lag + dead time approximation of second order system

Lab Exercise 1

How to determine the 4 Characteristics of Process Behavior:

• Gain

• Direction

• Deadtime

• Time Constant

continuous control systems -...

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