1. CHE 185 – PROCESS CONTROL AND DYNAMICS
CASCADE AND RATIO CONTROL

2. METHODS TO IMPROVE BASIC PID CONTROL
APPLIED WHEN THE STANDARD PID DESIGN IS NOT DOES NOT PROVIDE ADEQUATE CONTROL
METHODOLOGY
ADDITIONAL MEASURES OF PROCESS OUTPUTS
ADDITIONAL MEASURES OF PROCESS INPUTS
EXPLICIT MODELS IN THE CONTROL CALCULATION
MODIFY THE PID ALGORITHM AND TUNING TO MEET CONTROL CRITERIA

3. Cascade, Ratio, and Feedforward Control
Each of these techniques offers advantages with respect to disturbance rejection:
Cascade reduces the effect of specific types of disturbances.
Ratio reduces the effect of feed flow rates changes
Feedforward control is a general methodology for compensating for measured disturbances.

4. METHODS TO IMPROVE BASIC PID CONTROL
CATEGORIES OF ENHANCEMENT
CASCADE CONTROL
FEEDFORWARD CONTROL
NONLINEAR FUNCTIONS - ADJUST CONTROL FOR VARYING PROCESS DYNAMICS
INFERENTIAL CONTROL - CHANGE THE MEASURED VARIABLES
LEVEL CONTROL - TO ADJUST INVENTORIES TO STABLE LEVELS
MODEL PREDICTIVE CONTROL - FOR COMPLEX PROCESS DYNAMICS

5. Compensating for Disturbances Reduces Deviations from Setpoint and Settling Time

6. CASCADE CONTROL CONDITIONS THAT SUPPORT APPLICATION
SINGLE LOOP CONTROL IS NOT SATISFACTORY
A MEASURED SECONDARY VARIABLE IS AVAILABLE
PROPERTIES OF THE SECONDARY VARIABLE
MUST BE AFFECTED BY SIGNIFICANT DISTURBANCES
MUST BE RELATED TO THE PRIMARY MANIPULATED VARIABLE
SECONDARY VARIABLE DYNAMICS MUST BE FASTER THAN THE PRIMARY VARIABLE DYNAMICS.

7. CASCADE CONTROL
CASCADE CONTROL GENERIC BLOCK FLOW DIAGRAM.

8. CASCADE CONTROL
THE CASCADE LOOP COMBINES TWO FEEDBACK CONTROLLERS WITH THE PRIMARY CONTROLLER OUTPUT SERVING AS THE SECONDARY CONTROLLER SETPOINT.
THE DISTURBANCE REJECTION CLOSED LOOP TRANSFER FUNCTION FOR THIS SYSTEM

9. CASCADE CONTROL
THE EFFECTIVE PROCESS TIME CONSTANT, τ`p, CAN BE SHORTER THAN THAT FOR THE PRIMARY PROCESS TIME CONSTANT
THE SECONDARY LOOP TIME CONSTANT IS SHORTER THAN THE PRIMARY LOOP
THE SECONDARY LOOP AND PRIMARY LOOP TIME CONSTANTS ARE COMBINED TO OBTAIN THE EFFECTIVE TIME CONSTANT (FOR FIRST ORDER Gpp(s) AND Gps(s) AND P-ONLY CONTROLLERS - A SECOND ORDER RESPONSE RESULTS)

10. CASCADE CONTROL
THE DISTURBANCE ENTERS THE SECONDARY CONTROL LOOP AND MAY BE EFFECTIVELY COUNTERACTED BY THE PRIMARY LOOP - SOMEWHAT LIKE A FILTER.
THE SECONDARY ERROR IS ADDED TO THE PRIMARY ERROR FOR EACH CYCLE.

11. CASCADE CONTROL THE SECONDARY LOOP RESPONDS TO SHORT TERM DISTURBANCES
THE PRIMARY LOOP RESPONDS TO LONGER TERM TRENDS
THERE CAN BE MULTIPLE LEVELS OF CASCADE CONTROL
HAVING ADDITIONAL CONTROL COMPONENTS CAN REDUCE THE OVERALL CONTROL SYSTEM RELIABILITY

12. CASCADE CONTROL
CSTR COOLING EXAMPLE

13. CASCADE CONTROL CRITERIA FOR ADDING CASCADE CONTROL
SINGLE LOOP DOES NOT EXHIBIT SATISFACTORY RESPONSES
TO FEED CHANGES
TO COOLING WATER TEMPERATURE CHANGES
LAG TIME IS EXCESSIVE

14. CASCADE CONTROL
CSTR COOLING EXAMPLE
Modified control system

15. CASCADE CONTROL CSTR COOLING EXAMPLE
SECONDARY LOOP VARIABLE CAN BE MEASURED = DISCHARGE COOLING WATER TEMPERATURE
SECONDARY LOOP VARIABLE IS RELATED TO PRIMARY CONTROL VARIABLE - HEAT TRANSFER TO REACTOR IS REFLECTED IN DISCHARGE COOLING WATER TEMPERATURE

16. CASCADE CONTROL CSTR COOLING EXAMPLE
SECONDARY LOOP CAN BE INFLUENCED BY THE MEASURED VARIABLE - CHANGE IN PRODUCT EXIT TEMPERATURE WILL CHANGE SETPOINT TO SECONDARY CONTROLLER
SECONDARY LOOP HAS SHORTER TIME CONSTANT - TEMPERATURE CHANGE IN COOLING WATER SHOULD BE QUICKER IN RESPONSE TO A DISTURBANCE BECAUSE THERE IS LESS CAPACITANCE ON THE COOLING WATER SIDE.

17. CASCADE CONTROL CSTR COOLING EXAMPLE
WHY NOT USE COOLING WATER FLOW AS THE SECONDARY VARIABLE?
CAN IT HANDLE CHANGES IN FEED RATES?
HOW WILL IT RESPOND TO CHANGES IN EITHER FEED OR COOLING WATER TEMPERATURE?

18. Level Controller on a Tank With and Without Cascade Control

19. Analysis of Cascade Example
Without a cascade level controller, changes in downstream pressure will disturb the tank level.
With cascade level controller, changes in downstream pressure will be absorbed by the flow controller before they can significantly affect tank level because the flow controller responds faster to this disturbance than the tank level process.

20. Features for Cascade Control to be Successful
Secondary loop should reduce the effect of one or more disturbances.
Secondary loop must be at least 3 times faster than master loop.
The CV for the secondary loop should have a direct effect on the CV for the primary loop.
The secondary loop should be tuned tightly

21. Multiple Cascade Example
This approach works because the flow control loop is much faster than the temperature control loop which is much faster than the composition control loop.

22. Quick check
Draw schematic: A temperature controller on the outlet stream is cascaded to a pressure controller on the steam which is cascaded to a control valve on the condensate.

23. Quick check solution

24. RATIO CONTROL THIS IS A VARIATION OF CASCADE CONTROL
THE RATIO CONTROLLER RESPONDS A DISTURBANCE IN A MASTER VARIABLE, BY SENDING A RATIO SETPOINT TO THE CONTROLLER FOR A SLAVE VARIABLE.
THE PRIMARY CONTROLLER SENDS A RATIO SETPOINT TO THE RATIO CONTROLLER

25. RATIO CONTROL Typical applications Mixing streams
Maintaining stochiometric flows to a reaction system
Maintaining reflux rates on distillation columns
Maintaining fuel/air ratios to combustion systems

26. RATIO CONTROL
CONSIDER THE TOP OF A DISTILLATION COLUMN

27. RATIO CONTROL
THE TARGET IS TO MAINTAIN THE COMPOSITION AT A CERTAIN VALUE
THE PRIMARY METHOD IS TO ADJUST THE REFLUX RATIO
A SECOND OBJECTIVE IS TO HAVE THE SYSTEM RESPOND TO CHANGES IN BOILUP RATES
NOTE THIS SKETCH DOES NOT SHOW THE PRESSURE CONTROL, WHICH IS ASSUMED TO HAVE A VERY SHORT LAG TIME AND BE LINEAR

28. RATIO CONTROL
THE PRIMARY MEASURE OF ANALYSIS IS EITHER AN ON-LINE SAMPLER OR AN OFF-LINE ANALYSIS - EITHER ONE WITH A RELATIVELY LONG LAG TIME
THE SIGNAL FROM THIS LOOP BECOMES THE SETPOINT FOR THE TRAY TEMPERATURE CONTROLLER
THE OUTPUT FROM THE TRAY TEMPERATURE CONTROLLER IS THE RATIO SIGNAL TO THE FFRC.

29. RATIO CONTROL
THE MASTER SIGNAL FOR THE FFRC IS THE PRODUCT FLOW RATE AND THE SLAVE IS THE REFLUX FLOW RATE
THE PRODUCT FLOW RATE IS BASED ON THE OUTPUT FROM THE LEVEL CONTROL IN THE DISTILLATE ACCUMULATOR

30. RATIO CONTROL FOR THIS SYSTEM TO WORK AS SHOWN:
THE TRAY TEMPERATURE NEEDS TO BE LINEAR WITH COMPOSITION
THE LEVEL CONTROL SHOULD HAVE A SHORTER LAG TIME THAN CHANGES IN BOIL-UP RATES

31. RATIO CONTROL example
Ratio Control for Wastewater Neutralization

32. RATIO CONTROL example Analysis
The flow rate of base scales directly with the flow rate of the acidic wastewater.
The output of the pH controller is the ratio of NaOH flow rate to acid wastewater flow rate; therefore, the product of the controller output and the measured acid wastewater flow rate become the setpoint for the flow controller on the NaOH addition.

33. FEEDFORWARD CONTROL CHARACTERISTICS
THIS TECHNIQUE DOES NOT USE FEEDBACK CONTROL
IT IS EFFECTIVE IN REDUCING DISTURBANCES, THOUGH NOT AS EFFECTIVELY AS FEEDBACK CONTROL
IT IS TYPICALLY USED MOST EFFECTIVELY IN COMBINATION WITH FEEDBACK CONTROL

34. FEEDFORWARD CONTROL Consider feedback control Positive factors
Disturbance source does not prevent corrective action
PID control works in a wide range of processes
Control design needs limited process information
Negative factors
Does not respond to disturbance variables
Based on measured value for cv
No corrective action until there is a setpoint deviation
Long delays or large time constants may limit effectiveness

35. FEEDFORWARD CONTROL
GENERIC BLOCK FLOW DIAGRAM

36. FEEDFORWARD CONTROL Compare with feedback control Positive factors
Changes can be made based on Disturbance source instead of waiting for process change
Provides potentially better
Negative factors
Based on measured value for control disturbance
No corrective action based on other disturbances
Typically requires a more detailed process model to set control parameters

37. FEEDFORWARD CONTROL
GENERAL FORM FOR THE FEEDFORWARD TRANSFER FUNCTION IS
COMBINING THE TERMS IN THE DENOMINATOR INTO A SINGLE PROCESS FUNCTION:

38. FEEDFORWARD CONTROL
ASSUMING THE PROCESS AND DISTURBANCE TRANSFER FUNCTIONS HAVE FOPDT FORMS

39. FEEDFORWARD CONTROL
Summary of parameters

40. FEEDFORWARD CONTROL STATIC FEEDFORWARD CONTROL
FEEDFORWARD LOOP THAT DOES NOT PROVIDE DYNAMIC COMPENSATION
CAN BE USED WHEN THE PROCESS HAS SIMILAR DYNAMIC RESPONSE TO DISTURBANCE CHANGES AND THE CHANGES IN THE MANIPULATED VARIABLE, WHERE THE LEAD/LAG RATIO ≈ 1

41. FEEDFORWARD CONTROL Static Feedforward Controller
A static feedforward controller make a correction that is directly proportional to the disturbance change.
A static feedforward controller is used when the process responds in a similar fashion to a change in the disturbance and the manipulated variable.

42. FEEDFORWARD CONTROL DYNAMIC COMPENSATION
THIS EXAMINES HOW THE PROCESS RESPONDS RELATIVE TO THE SIGNAL FROM A FEEDFORWARD CONTROLLER

43. FEEDFORWARD CONTROL
WHEN THE LEAD/LAG RATIO IS > 1, THEN AN INITIAL OVERCOMPENSATION IS NECESSARY
WHEN THE LEAD/LAG IS < 1 THEN AN UNDERCOMPENSATION PROVIDES A BETTER CONTROL

44. FEEDFORWARD CONTROL
TAKEN AT EXTREMES, WHEN THE LEAD ≈ 0, THEN THE FUNCTION BECOMES AN FOPDT RESPONSE
WHEN THE VALUE OF THE LAG ≈ 0, THEN THE FUNCTION APPROACHES A PROPORTIONAL/DERIVATIVE FORM:

45. FEEDFORWARD CONTROL
Feedforward When τp « τd

46. FEEDFORWARD CONTROL
Example of Feedforward Control for τd<τp

47. FEEDFORWARD CONTROL Static Feedforward Results
When the inlet temperature drops by 20ºC, Q is immediately increased by 20 kW.
Deviations from setpoint result from dynamic mismatch

48. FEEDFORWARD CONTROL
CONSIDER THE DISTILLATION COLUMN PREVIOUSLY PROVIDED WITH A CASCADE CONTROL
WHAT FEED FORWARD ELEMENTS COULD BE ADDED
TO ALLOW FOR CHANGES IN COLUMN FEED RATE?
TO ALLOW FOR CHANGES IN FEED COMPOSITION?
WOULD THESE DUPLICATE OR SUPPLEMENT THE FUNCTIONS OF EXISTING LOOPS?

49. FEEDFORWARD CONTROL TUNING FACTORS
FEEDFORWARD CAN AMPLIFY NOISE WHICH CAN CAUSE OVERSHOOT.
BASED ON THE PROCESS APPROXIMATING AN FOPDT MODEL, THEN LEAD/LAG RATIOS < 2.0 ARE RECOMMENDED

50. FEEDFORWARD CONTROL Perfect Feedforward Control
FF correction is mirror image of disturbance effect.
Net effect is no change in controlled variable.

51. FEEDFORWARD CONTROL
INITIAL TUNING SEQUENCE – see figures on next slide
ESTIMATE Kff, τld, τlg, AND θff FOR PROCESS
Under open loop conditions, ADJUST ONLY Kff WHILE HOLDING OTHER PARAMETERS CONSTANT, TO ELIMINATE OFFSET
ADJUST θff TO ELIMINATE DYNAMIC MISMATCH

52. FEEDFORWARD CONTROL
ADJUST τld - τlg AND UNTIL THERE ARE EQUAL AREAS ABOVE AND BELOW THE SETPOINT

53. FEEDFORWARD CONTROL COMBINING FEEDFORWARD AND FEEDBACK CONTROL
FEEDBACK AND FEEDFORWARD CONTROL HAVE COMPLEMENTARY CHARACTERISTICS
MOST EFFECTIVE LOOPS MIGHT COMBINE BOTH TECHNIQUES

54. Feedforward and Feedback Level Control
Reference figure

55. Feedforward and Feedback Level Control analysis
Feedback-only must absorb the variations in steam usage by feedback action only.
Feedforward-only handle variation in steam usage but small errors in metering will eventually empty or fill the tank.
Combined feedforward and feedback has best features of both controllers

56. Feedforward and Feedback
COMBINING FEEDFORWARD AND feedback
AN EXAMPLE OF THE COMBINATION IS SHOWN GRAPHICALLY

57. Feedforward and Feedback
Combined FF and FB for the CSTR

58. Feedforward and Feedback
Comparative Results for CSTR

59. FEEDFORWARD CONTROL
FEEDBACK ONLY PRODUCES OVERSHOOT BECAUSE OF THE DELAY DUE TO THE INVENTORY OF THE SYSTEM
FEEDFORWARD ONLY, EVEN WITH DYNAMIC COMPENSATION, RESULTED IN LESS OVERSHOOT BECAUSE THE HEATING FLOW WAS INCREASED RELATIVE TO THE FEED, BUT THE SYSTEMS HAD AN EXTENDED SETTLING TIME
COMBINING THE TWO METHODS ELIMINATES EXCESSIVE OVERSHOOT AND REDUCES SETTLING TIME