Topic 4

Controller Actions And Tuning

In The Last Lecture…

Controller Actions

Proportional Control

Problems of Proportional-Only Control

What We Will Cover

Topic 1

Introduction To Process Control

Topic 2

Introduction To Process Dynamics

Topic 3

Plant Testing And Data Analysis

Topic 5Enhanced

Regulatory Control Strategies

Topic 6

Process Control Hardware Systems

Topic 4

Controller Actions And Tuning

Topic 7

Control Valves

Topic 8

Process Control Troubleshooting

In This Lecture…

Integral Control– Equation– How it works– Interaction with Proportional Action– Problems with Integral Action

Derivative Control– Equation– How it works– Problems with Derivative Action

P-Only Control ResponseFlow Rate

400

450

500

550

600

650

0 5 10 15 20 25 30

Time (Sec)

Flo

w (

BD

)

39.0%

44.0%

49.0%

54.0%

59.0%

SP

PV

OP

Integral Control Recap: The problem with P-only control is the offset.

– That’s why we have Integral Control (PI control)

I-control works as such:– If the error increases, the greater the OP change– The longer an error persists, e.g. constant error, the OP change

will increase– I-control “remembers” the past error– Related to the “Area” bounded between the SP and PV curves

P-control, in contrast:– If the error increases, the greater the OP change– If the error is constant, regardless of how long it persists, the OP

will not change– P-control only looks at the current error

An example

DeltaP fluctuates so flow fluctuates if loop is on MAN

Let’s say we now have a flow rate of PV=SP=500 BD, and at that flow rate, OP = 40% (i.e. valve is 40% open)– Bias = 40%

FC

Instrument range0~1000 BD

Pressure Drop,Delta P

SP = 500 BD(Barrels per Day)

An example

We now want to control the flow at 600 BD (Operator increase SP from 500 to 600)

Assume Kc = 0.5, so OP = 0.5(Error) + Bias

The controller detects an error of (600-500)/1000 = 10%

P-action OP = 0.5(10%)+40% = 45%

Because of the error, I-action also increases the OP further, say 0.5(10%) = 5%– PI-action = 45+5 = 50%

– Whether it’s actually 5% depends on both Kc and τI as you will see later. For now take it that it’s 5%

– New flow = PV = 625 BD

An example Next cycle 1

– Error = (600 – 625)/1000 = -2.5%– P-action = 0.5(-2.5%) + 40% = 38.75%– I-action = 5% + 0.5(-2.5%) = 3.75%– New OP = 38.75% + 3.75% = 42.5%– New flow = 531.3 BD

Next cycle 2– Error = (600 – 531.3)/1000 = 6.88%– P-action = 0.5(6.88%) + 40% = 43.44%– I-action = 3.75% + 0.5(6.88%) = 7.19%– New OP = 43.44% + 7.19% = 50.63%– New flow = 632.8 BD

From 1st to 3rd cycle, error decreased from 10% to 6.88%

If this cycle is repeated as in the case of a PI controller in AUTO, the PV will converge to SP at steady state

PI Control Response

PI Control

400

450

500

550

600

650

0 20 40 60 80 100 120

Time (Sec)

Flo

w (

BD

)

30.0%

40.0%

50.0%

60.0%

70.0%

80.0%

90.0%

SP

PV

OP

Essence Of I-Action

Take drastic action when you are far away from your goal

Increase the action even if you are NEARER to the goal now because of past error

(Some systems use )

I = Integral time– Error = SP-PV (depends on manufacturer)

dtError 1

IτOP

dtError K

I

c

τOP

Reset WindupA ir isin troduced toclose thecontro l va lve

A ir is s till be ingin troduced eventhough the contro lva lve is fu lly shut

A ir is be ing rem oved toopen the contro l va lve . B utenough a ir m ust berem oved for the spring toovercom e the pressure o fthe a ir be fore the va lveopens

Reset windup Consider an undersized valve

If the OP is fully saturated at 100%, e.g. valve is full open and the PV cannot reach SP, Error > 0 persists

I-action will increase indefinitely, i.e. Reset Windup

If suddenly the PV increases above the SP (or the SP is decreased), it will take time for the I-action to decrease such that the OP falls below 100% to begin closing the valve

Anti-reset windup: Most modern DCS freeze I-action when the OP saturates at its max (100%) or min (0%)

Also, I-action is generally limited to a max (eg 50%) and min (-50%) value

BiasErrorErrorKOPt

Ic

dt

10

Perspective On PI Control

90% of the loops in any plant is PI because it is good enough to do the job

Some argue that for level control, P alone is enough– Offset is ok so long as level does not exceed

high or low limits

Another viewpoint....

Level ControlFin

LC

OP

SP = 50%

If you want SP = 50% and now you are at 52% because of offset

What if inflow increases?

Outflow will also increase but now the PV may be 54%

What if inflow increases again, and again and again?

Derivative Control

‘Derivative is your friend.’

Dr. Robert V. Bartman, Procontrol Inc.

 

‘If you do not use enough derivative there is no benefit at all, and there could be some harm.’

David W. St. Clair, Straight-Line Control Co. Inc.

Feedback control loop cycle

1. Obtain new PV fromtransmitter

2. Calculate newError = (SP - PV)based oncurrent SP

3. Calculate new OP usingPID algorithm

4. Send new OP down tofinal control element

5. Process responds to newOP

Process Dynamics:SS Gain, Deadtime, Lag timeProcess Gain (Integrate), Deadtime

Bias

dt

ErrordErrorErrorKOP

t

DI

c

0 dt

1

Recap: P-only and PI-control

P-only control introduces an offset at the final steady state– This offset is reduced by increasing Kc

– Increasing Kc introduces fluctuations

– Too large a Kc results in PV cycling and instability

PI control eliminates the offset completely– The time to steady state decreases with decreasing τI,

i.e. loop becomes faster

– Decreasing τI introduces fluctuations

– Too small a τI results in PV cycling and instability

Derivative Control

Before we talk about what is bad about derivative control, let’s talk about what’s good about it

In a way I-action addresses the problem of P-action but it brings about its own problems

I-action only cares about bringing PV to SP, it does not care if it is so fast that it will overshoot the SP

Derivative Control

Derivative action can look at the trajectory of the PV and try and see if it is going too fast

If it is, D-action will restrain the OP

Take a temperature controller that adjusts a FG flow valve– If PV increases quickly, Error decreases quickly– d(Error)/dt is very negative– D-action reduces OP to reduce FG flow

D-action looks at how fast the PV is changing and adjusts the OP accordingly

dt

ErrordKOP Dc

Derivative Control

Let us imagine we are trying to control a process with a long deadtime

When the controller changes the MV, initially nothing happens

The controller thinks that it is not doing enough and so does something very drastic

But once the deadtime period is over we find that the action taken has been too strong!

Derivative Action

I-action won’t care as long as it has not reached the SP

Only after it overshoots the SP then it try to reverse direction

If you have D-action, it will look at the way the PV is shooting and decide that it has to reverse direction even though it is not at the SP

Derivative Action

Derivative action acts to prevent over eager response by I-action

A good place to use D-action is therefore when we want to control processes with long deadtime

This usually occurs in temperature processes, but not always!– Some analyzers, e.g. viscosity analyzers, have

significant deadtimes (a couple of minutes)

Don’t get suckered by people telling you D-action must be and can only be used on temperature processes

Problem With D-Action

What happens when you change a SP and press “enter”?

What will the OP be?

Modern control systems have ways of dealing with this problem– Derivative on PV instead of error

– Apply a lag filter to the derivative action

dt

ErrordKOP Dc

dt

PVdKOP Dc

PID Controller We have now covered the PID controller

The PID controller is modelled after how we would behave if we are the controller

Process control books or lecturers like to say– P-action results in offset– I-action removes offset– D-action reduces overshoot

Now you know why

PID Controller Equation

Bias

dt

dEdt E

1EKOP D

Ic

In This Lecture…

Integral Control– Equation– How it works– Interaction with Proportional Action– Problems with Integral Action

Derivative Control– Equation– How it works– Problems with Derivative Action

In The Next Lecture…

Controller tuning methods– Cycling method– Step change method– Trial and error method– Lambda method for integrating processes