CHE3162.Lecture8 Feedback PID

CHE3162 Lecture 8

Introduction To Feedback Control Loops

Chapter 7&8: Marlin Chapter 7: Seborg Chapter 6-1: Smith & Corripio

Learning Objectives

Introduce feedback control and important terms

Understand a feedback block diagram and relationship to real world

Intro to PID control

CHE3162: where are we up to?

So far, we have studied system responses A disturbance (step change,sine wave) enters

our process Shown how process responds, depending on

1st order, 2nd order, dead time, etc Ultimately, we want process control

Incoming disturbances have MINIMAL effect on process outputs Next step on to controlling the responses!

Plot

Time (sec)

0 1 2 3 4 5 6 7 8 9 10

-2.0

-1.5

-1.0

-.5

0

.5

1.0

1.5

2.0

Control benefits:Reducing variability

1 5 9

0

Plot

Time (sec)

0 2 3 4 6 7 8 10

-2.0

-1.5

-1.0

-.5

.5

1.0

1.5

2.0

Time Good

control

Control of Tank Level

Want to keep constant tank level

Flowrate of inlet stream is fluctuating

Denn. Chem Eng Intro

Control of Tank Level

Inlet flowrate initially steady at q*

Temporary step change in inlet flowrate occurs

Inlet flowrate increases by Q* then returns to original value

No Control: Tank level increases then plateaus

With Control: level increases but by less and returns to close to original level


Constant inlet fluctuations Inlet varying

constantly As a result, tank

level will also vary (without control)

Simple control (solid line) significantly reduces tank level changes

Inlet flowrate to tank

Tank level without and with control


A FEEDBACK Control System Temperature control of a heat exchanger

Cold fluid

Hot fluid

Steam Sensor & Transmitter

Steam or condensate

exhaust

Controller

Valve

Set point

Feedback loop

Temperature, flow changes are DISTURBANCES

Exercise: Find another disturbance variable

Cold fluid Steam or

condensate exhaust

Piping and Instrument Diagram (P&ID)

Heat exchanger temperature control

Field mounted instrument

Panel mounted controller

Hot fluid

Steam

TC 101

TT 101

SP

Computer control

PROCESS (Heat exchanger)

T F

Feedback Control System Block Diagram

VALVE Controller U

Measuring element (sensor)

Tm

DISTURBANCE D

+ + Ts E

+ -

All variables are functions of time. On the diagram we represent them as Laplace transforms of CHANGES

Error detector

Summing point

PROCESS (Heat exchanger)

T F

Feedback Control System Block Diagram

VALVE Controller U

Measuring element (sensor)

Tm

DISTURBANCE D

+ + Ts E

+ -

Each block is described mathematically by a TRANSFER FUNCTION

Error detector

U/E = Gc(s) Summing point

The Sensor and the Valve

A level measuring sensor usually has a fast response so its time constant is small and can be neglected (ie., = 0)

The sensor TF is just a gain: Km = Measurement Gain (or Ks)

A control valve is usually a pneumatic valve & can be represented by a 1st order TF

mm K

TT

=

sv1vK

UF

+= Typical V = 1 sec-1 min

(depends on valve size)

Closed Loop Block Diagram

TF of the

Process

Controller TF decides what to do

about the error

Error=SP-MC

TF of the final control element e.g. a 1st

order valve

Setpoint

SP

GM (s)

GD (s)

TF of the Measuring device

CV(s)

(or Y(s) T(s)etc)

D(s) TF of the disturbance

Closed loop feedback control

Marlin

Shortcut: CV = forward SP (1 + around the loop)

PROCESS Gp

CV F VALVE

Gv Controller

Gc

U

Measuring sensor Gs (or Gm)

Tm

DISTURBANCE Gd

D

+ + SP E

+ -

Controller

Process equipment

See Tute 4 Q5 for how to derive these two TF responses

Controllers

A controller calculates an output signal based on the measured error and a control algorithm Error = Setpoint Measured value

A simple controller: Proportional Control Output is proportional to the error u(t) = Kc*e(t) + u(0)

Kc is called the (proportional) gain u(0) is the output when error = 0

cKEU

=

Cold fluid T change

Hot fluid

Steam

TC 101

TT 101

SP

Proportional Temperature Control using an FODT Model

Use steam flow Fs to control T at TSP

Incoming temp disturbance TD

Assume FODT models for: T/Fs T/TD

Start with a Proportional Controller for TC101

TSP

T

TD

Fs

U

Temperature Control of a Heat Exchanger Block Diagram

Gp T Fs

Gv Kc U

Km Tm

Gd TD

+ +

TSP E +

-

oC/oC

oC/(kg/min)

oC/oC (kg/min)/%

%/oC

Fast response

Exercise: Confirm that the product of all gains around the loop is dimensionless

Temperature Control of a Heat Exchanger Block Diagram

4e-2s 1 + 15s

T Fs 0.5 1 +0.5s Kc

U

Km = 1 Tm

1e-s 1+5s

TD

+ +

Ts E +

-

Time units: minutes oC/oC

oC/(kg/min)

oC/oC (kg/min)/%

%/oC

Fast response

Exercise: Confirm that the product of all gains around the loop is dimensionless

PID response matches common sense

If a big error occurs: You need a big response Proportional P

But there is still a remaining error: Adjust until you eliminate error Integral I

Rapid change rapid response required Derivative D

+++= u(0)]dtdee(t)dt

iT1[e(t)cKu(t) d

PID algorithm

PID algorithm considers the weighting of the following types of corrections: Proportional P - Corrections based on the present error

e(t) Integral I - Corrections based on the sum of the past

errors (integral of e(t)) Derivative D - Corrections based on future predictions of

errors, using the rate of change of errors over time (de/dt)


iT1[e(t)cKu(t) d

PID Transfer Function

++= s

sTK

EU

dI

c 11

Laplace transform


iT1[e(t)cKu(t) d

U is the controller output E is the difference between SP & the measured value

Kc = controller gain TI = Integral time d = derivative time

L

Typical responses

Seborg

Feedback control loop: CV and MV responses

Marlin

Error integrals

Smith & Corropio

Definition of Open Loop

Gp Y F

Gv U

Gm Ym

+ Gc

SP E +

-

Gd D

+

Open loop = no controller Controller is either off, disconnected, or in manual

Controller

Auto and Manual Control modes

Each controller can be set to auto (on) or manual which means off

Auto mode: Controller output depends on e(t), controller constants, and type of controller used. ( PI vs. PID etc.)

Manual Mode: Controller output is adjusted manually. Manual Mode is very useful when unusual conditions exist:

plant start-up plant shut-down emergencies

Percentage of controllers "on manual ?? (30% in 2001, Honeywell survey)

Seborg

Definition of Closed Loop

Gp Y F

Gv U

Gm Ym

+ Gc

SP E +

-

Gd D

+

This is CLOSED-LOOP

With control

Setpoint Change Closed Loop Servo Control

Gp CV Fs

Gv U

GS Tm

+ Gc

SP E +

-

Gd D

+

Make a SP change, triggers error between T & TSP, so loop adjusts valve to drive T towards TSP

Disturbance Change Closed Loop Regulatory Control

Gp CV Fs

Gv U

Gm Tm

+ Gc

SP E +

-

Gd D

+

Regulates any disturbances Disturbance upsets T Results in difference between T and TSP Controller sees error, adjusts valve to fix it

Proportional Control

Controller output signal is proportional to the error input signal

u(t) = Kc*e(t) + u(0) Kc is called the (proportional) gain u(0) is the output when error = 0 Called offset (or manual reset or bias)

cKEU

=

Controller Gain Kc

Controller gain Kc is a number that we can set Used by the controller during each control calculation

can be adjusted to make the controller output changes as sensitive as desired to deviations from the set point;

the sign of Kc can be chosen to make the controller output increase (or decrease) as the error signal increases.

Positive Kc = direct acting controller ie if temp is too high, valve open the opened.

Negative Kc = reverse acting controller. If temp is too high, then close the valve.

Typical responses after a disturbance step change

Seborg

CHE3162 Lecture 8Learning ObjectivesCHE3162: where are we up to?Slide Number 4Control of Tank LevelControl of Tank LevelConstant inlet fluctuationsA FEEDBACK Control SystemTemperature control of a heat exchangerPiping and Instrument Diagram (P&ID) Heat exchanger temperature controlFeedback Control SystemBlock DiagramFeedback Control SystemBlock DiagramThe Sensor and the ValveClosed Loop Block DiagramClosed loop feedback controlControllersProportional Temperature Control using an FODT ModelTemperature Control of aHeat Exchanger Block DiagramTemperature Control of aHeat Exchanger Block DiagramPID response matches common sensePID algorithmPID Transfer FunctionTypical responsesFeedback control loop:CV and MV responsesError integralsDefinition of Open LoopAuto and Manual Control modesDefinition of Closed LoopSetpoint Change Closed Loop Servo ControlDisturbance Change Closed Loop Regulatory ControlProportional ControlController Gain KcSlide Number 35Typical responses after a disturbance step change

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CHE3162.Lecture8 Feedback PID