1. Topic 4 Controller Actions And Tuning

2. In The Last Lecture…  Controller Actions  Proportional Control  Problems of Proportional-Only Control

3. What We Will Cover Topic 1 Introduction To Process Control Topic 2 Introduction To Process Dynamics Topic 3 Plant Testing And Data Analysis Topic 5 Enhanced Regulatory Control Strategies Topic 6 Process Control Hardware Systems Topic 4 Controller Actions And Tuning Topic 7 Control Valves Topic 8 Process Control Troubleshooting

4. 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

5. P-Only Control Response

6. 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

7. 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%

8. An example  We now want to control the flow at 600 BD (Operator increase SP from 500 to 600)  Assume K c = 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 τ I as you will see later. For now take it that it’s 5% –New flow = PV = 625 BD

9. 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

10. PI Control Response

11. 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)

12. Reset Windup

13. 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

14. 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....

15. Level Control  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?

16. 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.

17. Feedback control loop cycle

18. Recap: P-only and PI-control  P-only control introduces an offset at the final steady state –This offset is reduced by increasing K c –Increasing K c introduces fluctuations –Too large a K c results in PV cycling and instability  PI control eliminates the offset completely –The time to steady state decreases with decreasing τ I, i.e. loop becomes faster –Decreasing τ I introduces fluctuations –Too small a τ I results in PV cycling and instability

19. 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

20. 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

21. 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!

22. 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

23. 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

24. 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

25. 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

26. PID Controller Equation

27. 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

28. In The Next Lecture…  Controller tuning methods –Cycling method –Step change method –Trial and error method –Lambda method for integrating processes