Topic 4 Controller Actions And Tuning. In The Last Lecture… Controller Actions Proportional...
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Transcript of Topic 4 Controller Actions And Tuning. In The Last Lecture… Controller Actions Proportional...
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