Kendali on Off&PID

8/6/2019 Kendali on Off&PID

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Process Control 1Priyatmadi 2008

Pengendalian Proses

PriyatmadiJurusan teknik Elektro

FT UGM


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ARITHMETIC VERSUS LOGIC

CONTROL EXAMPLE OF ARITHMETIC CONTROL

PID control, fuzzy control, adaptive control etc

EXAMPLE OF LOGIC CONTROL Start-stop motor, sequential control, emergency

shut down system

COMBINATION OF ANALOG ANDLOGIC CONTROL


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Arithmetic Control

TT

TIC

I/P

4-20 mA4-20 mA

3-15psi

Set point

Cold water in

hot water outsteam in

PlantController

Sensor

+

-

Set point e(t) m(t) c(t)


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CONTROL ACTION

ON-OFF

PROPORTIONAL (P)

PROPORTIONAL + INTEGRAL (PI)

PROPORTIONAL + DIFFERENTIAL (PD)

PID AUCTIONEERING

RATIO CONTROL

MODERN CONTROL

How to compute m(t)

+

Controllere(t) m(t)


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ON-OFF CONTROL ACTION

m(t) = M1 if e(t)>0

m(t) = M2 if e(t)


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ON-OFF CONTROL ACTION WITH GAP

m(t) = M1 if e(t)>e1

m(t) = M2 if e(t)


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Example of ON-OFF action

h(t)

qi(t)

qo(t)

Level sensor


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example


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Proportional Control Action

m(t)=Kpe(t)

PlantController

Sensor

+

-

Set point

r(t)m(t)e(t) c(t)

c(t)

e(t)

m(t)

t


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Integral Control Action

m(t)=Kie(t)dt

e(t)

m(t)

t

PlantController

Sensor

+

-

Set point

r(t)m(t)e(t) c(t)

c(t)


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Derivative Control Action

m(t)=Kd(de(t)/dt)e(t)

m(t)

t

PlantController

Sensor

+

-

Set point

r(t)m(t)e(t) c(t)

c(t)


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Problem in control Stability

Sensitivity

Disturbance rejection

Steady state accuracy

Transient response

Noise


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STABILITYy A control loop will be stable if at the frequency of

oscillation that gives a total phase shift of 3600 around theloop, the gain around the loop is less then 1

PlantController

Sensor

+

-

Set point

r(t)m(t)e(t) c(t)

c(t)


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OUTPUT OF CONTROL SYSTEM WHEN SET POINT IS RISEN

[n t

c(t)

PlantController

Sensor

+

-

Set pointr(t)

m(t)e(t) c(t)

c(t)

UNSTABLE

r(t)


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SENSITIVITY

Sensitivity is a measure of changes in system characteristic

due to changes in parameters.Example:

Load change

Sensor characteristic change

Plant characteristic change etc.

Controller can be design to be insensitive to one parameterbut often it must be sensitive to the others.


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Disturbance rejectionThe input to the plant we manipulated is m(t). Plant also receives

disturbance input that we do not control. The plant then can bemodeled as follow

Methods to reduce Td(j[)1. make Gd(s) small2. increase loop gain by increasing Gc3. reducedD(s)4. use feed forward compensation

D(t)

M(t) + C(t)Gp(t)

Gd(s)

+

plant

Gc+

H

Gd(t)D(t)

R(r)


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Disturbance rejectionFeedforward compensation

Feedforward compensation can be applied if the disturbance can bemeasured.

C(s)

D(s)

M(s) +Gp(s)

Gd(s)

+

plant

Gc+

H

Gd

(s)D(s)Gcd(s)

R(s)


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5.5 Steady State Accuracy

C(t)M(t) Gp(t)Gc+

R(t)

E(t)

[n t

c(t)

R(t)

essC(t)

Used integrator to eliminate steady state error but be carefullsystem can be unstable

[n t

c(t)

r(t)


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Time Response of Control System

The typical of unit step response of a system is as

[nt

c(t)

Mpt

1.00.9

0.1

Tr Tp

1+ d

1 d

css

Ts


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Problem of

Noise

Random, meaningless signals can occur in many parts ofcontrol loops. These signals, often referred to as noise, caninterfere with the intelligence of the signal.

For example, heater control the cold water and heatedwater may not be completely intermixed by the time theyreach the thermometer bulb. Slugs of cold water mayalternate with hot water to give a rapidly fluctuating,wholly meaningless temperature signal at the bulb.

If such a noise bearing signal is allowed to reach thecontroller, it may result in wild and meaninglesscorrections to the process, which may cause fluctuating orcompletely unstable automatic control.


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Problem of

Noise

Similar noise problems can occur inconnection with most signals, e.g.,

random pulsations in pressure signals, waves in liquid-level signals,

turbulence in differential-measured flow

signals, and induced currents in circuits (electromagneticwave, lightning, groundloop, etc)


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Solutions to Noise Problem Derivative action produces difficulties where

noise exists and, therefore, it should generally notbe used in such instances.

Filtering or averaging the noise out of the signal.For example, in heater control the source of thethermal noise can be eliminated by better mixingof the hot and cold water in the tank or by using anaveraging-type thermometer bulb that measurestemperature over a considerable length instead ofat one point.


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Solutions to Noise Problem Reduction or elimination of the noise at itssource, for example

rotary instead of reciprocating pumps to avoid

pulsating pressures, larger mixing tanks or surge tanks, stirrers to obtain a uniform signal, longer pipe runs and straightening vanes in flow

measurement,

shielding of wires against stray voltages Use STP wires.


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Ratio Control

In ratio control, a predetermined ratio ismaintained between two or more variables.

Each controller has its own measured variable andoutput to a separate final control element. However, all set points are from a master primary

signal that is modified by individual ratio settings

A typical application of ratio control is the controlof the fuel flow/airflow ratio in a combustioncontrol system


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Auctioneering Control (Override

Control, Limiting Control) In suction and discharge pressure compressor

control, the discharge control valve is normally

regulated from the discharge pressure. However, if the suction pressure drops below itsset point, control is transferred to the suctionpressure controller.

This prevents excessive suction on the supply side,from demand exceeding supply, with resultantcompressor damage


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Auctioneering Control (Override

Control, Limiting Control)


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Modern Control Action Fuzzy control Optimal control

Sliding mode control Adaptive control (Self tuning control)


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Practical control system in

Process Industry

The system measures the process, compares it to a setpoint, and then manipulates the output in the directionwhich should move the process toward the set point.


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Valves are usually non-linear. That is, the flow

through the valve is not the same as the valveposition. Several types of valves exist: Linear

Same gain regardless of valve position

Equal Percentage Low gain when valve is nearly closed High gain when valve is nearly open

Quick Opening High gain when valve is nearly closed Low gain when valve is nearly open


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As we will see later, the gain of the process, including the valve, is very

important to the tuning of the loop.If the controller is tuned for one process gain, it may not work for otherprocess gains.


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At low flow, the head loss through the pipes is less,leaving a larger differential pressure across thevalve.

At high flow, the head loss through the pipe ismore, leaving a smaller differential pressure acrossthe valve.


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Valves are usually either: Fail

Closed, air to open or Fail Open, airto close


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The Process Response to the

Controller


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Process Dynamics:

Simple lag


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Process Dynamics: Dead time


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Measurement of dynamics


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Disturbances


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ThePI

D algorith

mPROCESS ACTION

Defines the relationship between changes in

the valve and changes in the measurement. DIRECT : Increase in valve position causes

an increase in the measurement.

REVERSE :Increase in valve positioncauses a decrease in the measurement.


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Th

ePI

D algorith

mCONTROLLER ACTIONDefines the relationship between changes in the measured

variable and changes in the controller output.

DIRECT Increase in measured variable causes anincrease in the output. REVERSE Increase in measured variable causes a

decrease in the output.

The controller action must be the opposite of the processaction.


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M

anualM

ode


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Automatic Mode:


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Key concepts

The PID control algorithm does not "know" the correctoutput to bring the process to the setpoint.

It merely continues to move the output in the direction whichshould move the process toward the setpoint.

The algorithm must have feedback (process measurement) toperform.

The PID algorithm must be "tuned" for the particularprocess loop. Without such tuning, it will not be able tofunction.

To be able to tune a PID loop, each of the terms of the PIDequation must be understood.

The tuning is based on the dynamics of the processresponse.


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PID Tuning Informal methods decay ration


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Minimum overshoot.PID Tuning Informal methods


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Maximum disturbance rejectionPID Tuning Informal methods


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IAE - Integral of absolute value of error ISE - Integral of error squared ITAE - Integral of time times absolute value of error

ITSE - Integral of time times error squared:

PID Tuning Mathematical criteria


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On-line trial tuning

The "by-guess-and-by-golly" method

1. Enter an initial set of tuning constants from

experience. A conservative setting wouldbe a gain of 1 or less and a reset of lessthan 0.1.

2. Put loop in automatic with process "linedout".

3. Make step changes (about 5%) in setpoint.

4. Compare response with diagrams and


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Ziegler Nichols tuning method:

open loop reaction rateAlso known as the "reaction curve"method.The process must be "lined out"

not changing.With the controller in manual, theoutput is changed by a smallamount.The process is monitored.

The following measurements are made from the reaction curve:X % Change of outputR %/min. Rate of change at the point of inflection (POI)D min. Time until the intercept of tangent line and original

process value


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open loop reaction rateGain Reset Derivative

P X/DR - -

PI 0.9X/DR 0.3/D -

PID 1.2X/DR 0.5/D 0.5D


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closed loop Place controller into automatic with low gain,

no reset or derivative. Gradually increase gain, making small changes

in the setpoint, until oscillations start. Adjust gain to make the oscillations continue

with a constant amplitude. Note the gain (Ultimate Gain, Gu,) and Period

(Ultimate Period, Pu.) The Ultimate Gain, Gu, is the gain at which the

oscillations continue with a constantamplitude.


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closed loop

Gain Reset Derivative

P 0.5 GU

PI 0.45 GU 1.2/Pu

PID 0.6 GU 2/Pu Pu/8


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