Isa saint-louis-exceptional-opportunities-short-course-day-1
1. ISA Saint Louis Short Course Dec 6-8, 2010 Exceptional Process Control Opportunities - An Interactive Exploration of Process Control Improvements - Day 1
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8. (4) - Resonance Top Ten Concepts For all of you frequency response and Bode Plot Fans 1 Ultimate Period 1 1 Faster Tuning Log of Ratio of closed loop amplitude to open loop amplitude Log of ratio of disturbance period to ultimate period no attenuation of disturbances resonance (amplification) of disturbances amplitude ratio is proportional to ratio of break frequency lag to disturbance period 1 no better than manual worse than manual improving control
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10. The attenuation of oscillations can be estimated from the expression of the Bode plot equation for the attenuation of oscillations slower than the break frequency where ( f ) is the filter time constant, electrode or thermowell lag, or a mixed volume residence time Equation is also useful for estimating original process oscillation amplitude from filtered oscillation amplitude to better know actual process variability (measurement lags and filters provide a attenuated view of real world) (5) Attenuation Top Ten Concepts
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12. (6) Sensitivity- Resolution Top Ten Concepts Sensitivity o x x o x o o o o o o o o o x x x x x x x x Actual Transmitter Response True Process Variable Process Variable and Measurements Digital Updates 0 1 2 3 4 5 6 7 8 9 10 0.00% 0.09% 0.08% 0.07% 0.06% 0.05% 0.04% 0.03% 0.02% 0.01% 1.00%
13. (6) Sensitivity- Resolution Top Ten Concepts Resolution Digital Updates o o o o o o o o o o x x x x x x x x x x o x Actual Transmitter Response True Process Variable 0 1 2 3 4 5 6 7 8 9 10 0.00% 0.09% 0.08% 0.07% 0.06% 0.05% 0.04% 0.03% 0.02% 0.01% 1.00% Process Variable and Measurements
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15. (7) Hysteresis-Backlash Top Ten Concepts Hysteresis Hysteresis Digital Updates Process Variable and Measurements Actual Transmitter Response True Process Variable 0% 90% 80% 70% 60% 50% 40% 30% 20% 10% 100% 0 0 0 0 0 0 0 0 0 0 0 1 2 3 4 5 6 7 8 9 10 0 x x x x x x x x x x x x x x x x x x x x
16. (7) Hysteresis-Backlash Top Ten Concepts Backlash (Deadband) Deadband is 5% - 50% without a positioner ! Deadband Signal (%) 0 Stroke (%) Digital positioner will force valve shut at 0% signal Pneumatic positioner requires a negative % signal to close valve
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18. (8) Repeatability-Noise Top Ten Concepts Official definition of repeatability obtained from calibration tests Process Variable and Measurements Digital Updates 0 1 2 3 4 5 6 7 8 9 10 0% 90% 80% 70% 60% 50% 40% 30% 20% 10% 100% 0 Repeatability 0 0 0 0 0 0 0 0 0 0 Actual Transmitter Response True Process Variable
19. (8) Repeatability-Noise Top Ten Concepts Practical definition of repeatability as seen on trend charts Process Variable and Measurements Digital Updates 0 1 2 3 4 5 6 7 8 9 10 0% 90% 80% 70% 60% 50% 40% 30% 20% 10% 100% Repeatability 0 x 0 0 0 0 0 0 0 0 0 0 x x x x x x x x x x Actual Transmitter Response True Process Variable
20. (8) Repeatability-Noise Top Ten Concepts Noise as seen on trend charts Process Variable and Measurements Digital Updates 0 1 2 3 4 5 6 7 8 9 10 0% 90% 80% 70% 60% 50% 40% 30% 20% 10% 100% 0 0 0 0 0 0 0 0 0 0 0 x x x x x x x x x x x Noise Actual Transmitter Response True Process Variable
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22. (9) Offset-Drift Top Ten Concepts Offset (Bias) 0% 90% 80% 70% 60% 50% 40% 30% 20% 10% 100% 0 0 0 0 0 0 0 0 0 0 Digital Updates 0 1 2 3 4 5 6 7 8 9 10 Process Variable and Measurements Bias Actual Transmitter Response True Process Variable x x x x x x x x x x 0
23. (9) Offset-Drift Top Ten Concepts Drift (Shifting Bias) Process Variable and Measurements Months 0 1 2 3 4 5 6 7 8 9 10 0% 90% 80% 70% 60% 50% 40% 30% 20% 10% 100% 0 0 0 0 0 0 0 0 0 0 0 Actual Transmitter Response True Process Variable x Drift = 1% per month x x x x x x x x x x
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25. (10) Nonlinearity Top Ten Concepts 0% 90% 80% 70% 60% 50% 40% 30% 20% 10% 100% 0 0 0 0 0 0 0 0 0 0 Digital Updates 0 1 2 3 4 5 6 7 8 9 10 Process Variable and Measurements Nonlinearity Actual Transmitter Response True Process Variable x x x x x x x x x x x 0
26. Accuracy and Precision Top Ten Concepts Good Accuracy and Good Precision 2-Sigma Bias 2-Sigma True and Measured Values Frequency of Measurements True Value Measured Values Good Accuracy and Poor Precision 2-Sigma 2-Sigma Bias True and Measured Values True Value Measured Values Frequency of Measurements Poor Accuracy and Good Precision 2-Sigma Bias 2-Sigma True and Measured Values True Value Measured Values Frequency of Measurements Poor Accuracy and Poor Precision 2-Sigma 2-Sigma Bias True and Measured Values True Value Measured Values Frequency of Measurements
27. Self-Regulating Process Open Loop Response Time (seconds) % Controlled Variable (CV) or % Controller Output (CO) CO CV o p2 K p = CV CO CV CO CV Self-regulating process open loop negative feedback time constant Self-regulating process gain (%/%) Response to change in controller output with controller in manual observed total loop deadtime o or Maximum speed in 4 deadtimes is critical speed Improving Dynamics
28. Integrating Process Open Loop Response Maximum speed in 4 deadtimes is critical speed Improving Dynamics Time (seconds) o K i = { [ CV 2 t 2 ] CV 1 t 1 ] } CO CO ramp rate is CV 1 t 1 ramp rate is CV 2 t 2 CO CV Integrating process gain (%/sec/%) Response to change in controller output with controller in manual % Controlled Variable (CV) or % Controller Output (CO) observed total loop deadtime
29. Runaway Process Open Loop Response Response to change in controller output with controller in manual o Noise Band Acceleration CV CO CV K p = CV CO Runaway process gain (%/%) % Controlled Variable (CV) or % Controller Output (CO) Time (seconds) observed total loop deadtime runaway process open loop positive feedback time constant For safety reasons, tests are terminated after 4 deadtimes or Maximum speed in 4 deadtimes is critical speed Improving Dynamics ’ p2 ’ o
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31. Phase Shift ( ) and Amplitude Ratio (B/A) A B time phase shift oscillation period T o If the phase shift is -180 o between the process input A and output B , then the total shift for a control loop is -360 o and the output is in phase with the input (resonance) since there is a -180 o from negative feedback (control error = set point – process variable). This point sets the ultimate gain and period that is important for controller tuning. Improving Dynamics For frequency response and Bode plot fans
32. Basis of First Order Approximation = Tan -1 ( ) negative phase shift (as approaches infinity, approaches -90 o phase shift) t = (-360 T o time shift B 1 AR = ---- = ----------------------- amplitude ratio A [1 + ( ] 1/2 Amplitude ratios are multiplicative (AR = AR 1 AR 2 ) and phase shifts are additive ( ) asis of first order approx method where gains are multiplicative and dead times are additive Improving Dynamics For a self-regulating process
33. Loop Block Diagram (First Order Approximation) p1 p2 p2 K pv p1 c1 m2 m2 m1 m1 K cv c c2 Valve Process Controller Measurement K mv v v K L L L Load Upset CV CO MV PV PID Delay Lag Delay Delay Delay Delay Delay Delay Lag Lag Lag Lag Lag Lag Lag Gain Gain Gain Gain Local Set Point DV First Order Approximation : o v p1 p2 m1 m2 c v p1 m1 m2 c1 c2 (set by automation system design for flow, pressure, level, speed, surge, and static mixer pH control) % % % Delay <=> Dead Time Lag <=>Time Constant For integrating processes: K i = K mv (K pv / p2 ) K cv 100% / span Hopefully p2 is the largest lag in the loop Improving Dynamics K c T i T d
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35. Ultimate Limit to Loop Performance Peak error is proportional to the ratio of loop deadtime to 63% response time (Important to prevent SIS trips, relief device activation, surge prevention, and RCRA pH violations) Integrated error is proportional to the ratio of loop deadtime squared to 63% response time (Important to minimize quantity of product off-spec and total energy and raw material use) For a sensor lag (e.g. electrode or thermowell lag) or signal filter that is much larger than the process time constant, the unfiltered actual process variable error can be found from the equation for attenuation Total loop deadtime that is often set by automation design Largest lag in loop that is ideally set by large process volume Improving Dynamics
36. Disturbance Speed and Attenuation Effect of load disturbance lag ( L ) on peak error can be estimated by replacing the open loop error with the exponential response of the disturbance during the loop deadtime For E i (integrated error), use closed loop time constant instead of deadtime Improving Dynamics
37. Effect of Disturbance Lag on Integrating Process Periodic load disturbance time constant increased by factor of 10 Adaptive loop Baseline loop Adaptive loop Baseline loop Primary reason why bioreactor control loop tuning and performance for load upsets is a non issue! Improving Dynamics
38. Accessing On-Demand and Adaptive Tuning Click on magnifying glass to get detail view of limits and tuning Click on Duncan to get DeltaV Insight for “On-Demand” and “Adaptive” tuning Improving Dynamics
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42. Contribution of Each PID Mode Improving Tuning - Part 1 Contribution of Each PID Mode for a Step Change in the Set Point ( and ) CO 2 = CO 1 SP seconds/repeat CO 1 Time (seconds) Signal (%) 0 kick from proportional mode bump from filtered derivative mode repeat from integral mode
43. Reset Gives Operations What They Want SP PV IVP 52 48 ? TC-100 Reactor Temperature steam valve opens water valve opens 50% set point temperature time PV Should steam or water valve be open ? Improving Tuning - Part 1
44. Open Loop Time Constant (controller in manual) CO Time (seconds) Signal (%) 0 o Dead Time (Time Delay) p Open Loop (process) Time Constant (Time Lag) CV SP Controller is in Manual Open Loop Error E o (%) 0.63 E o Improving Tuning - Part 1
45. Closed Loop Time Constant (controller in auto) CO Time (seconds) Signal (%) 0 o Dead Time (Time Delay) c Closed Loop Time Constant (Time Lag) Lambda ( ) CV SP Controller is in Automatic SP (%) 0.63 SP Improving Tuning - Part 1
46. Conversion of Signals for PID Algorithm To compute controller tuning settings, the process variable and controller output must be converted to % of scale and time units of deadtimes and time constants must be same as time units of reset time and rate time settings! Improving Tuning - Part 1 Sensing Element Control Valve AO PID SCLR AI SCLR SCLR % % % SUB CV SP % CO OUT (e.u.) Process Equipment Smart Transmitter PV - Primary Variable SV - Second Variable* TV - Third Variable* FV - Fourth Variable* PV (e.u.) PID DCS MV (e.u.) The scaler block (SCLR) that convert between engineering units of application and % of scale used in PID algorithm is embedded hidden part of the Proportional-Integral-Derivative block (PID) Final Element Measurement * - additional HART variables PV (e.u.)
47. Practical Limit to Loop Performance Peak error decreases as the controller gain increases but is essentially the open loop error for systems when total deadtime >> process time constant Integrated error decreases as the controller gain increases and reset time decreases but is essentially the open loop error multiplied by the reset time plus signal delays and lags for systems when total deadtime >> process time constant Peak and integrated errors cannot be better than ultimate limit - The errors predicted by these equations for the PIDPlus and deadtime compensators cannot be better than the ultimate limit set by the loop deadtime and process time constant Open loop error for fastest and largest load disturbance Improving Tuning - Part 1
48. Implied Deadtime from Slow Tuning Slow tuning (large Lambda) creates an implied deadtime where the loop performs about the same as a loop with fast tuning and an actual deadtime equal to the implied deadtime ( i ) For most aggressive tuning Lambda is set equal to observed deadtime (implied deadtime is equal to observed deadtime) Money spent on improving measurement and process dynamics (e.g. reducing measurement delays and process deadtimes) will be wasted if the controller is not tuned faster to take advantage of the faster dynamics You can prove most any point you want to make in a comparison of control system performance, by how you tune the PID. Inventors of special algorithms as alternatives to the PID naturally tend to tune the PID to prove their case. For example Ziegler-Nichols tuning is often used to show excessive oscillations that could have be eliminated by cutting gain in half Improving Tuning - Part 1
49. Effect of Implied Deadtime on Allowable Digital or Analyzer Delay In this self-regulating process the original process delay (dead time) was 10 sec. Lambda was 20 sec and the sample time was set at 0, 5, 10, 20, 30, and 80 sec (Loops 1 - 6) The loop integrated error increased slightly by 1%*sec for a sample time of 10 sec which corresponded to a total deadtime (original process deadtime + 1/2 sample time) equal to the implied deadtime of 15 seconds. http://www.modelingandcontrol.com/repository/AdvancedApplicationNote005.pdf sample time = 0 sec sample time = 5 sec sample time = 10 sec sample time = 20 sec sample time = 30 sec sample time = 80 sec Effect depends on tuning, which leads to miss-guided generalities based on process dynamics Improving Tuning - Part 1
50. Lambda Tuning for Self-Regulating Processes Self-Regulation Process Gain: Controller Gain Controller Integral Time Lambda (Closed Loop Time Constant) Lambda tuning excels at coordinating loops for blending, fixing lower loop dynamics for model predictive control, and reducing loop interaction and resonance Improving Tuning - Part 1
51. Lambda Tuning for Integrating Processes Integrating Process Gain: Controller Gain: Controller Integral (Reset) Time: Lambda (closed loop arrest time) is defined in terms of a Lambda factor ( f ): Closed loop arrest time for load disturbance Controller Derivative (Rate) Time: To prevent slow rolling oscillations: secondary lag Improving Tuning - Part 1
52. Fastest Possible Tuning (Lambda Tuning Method) For max load rejection set lambda equal to deadtime Substitute Into Tuning for max disturbance rejection (Ziegler Nichols reaction curve method gain factor would be 1.0 instead of 0.5) For setpoint response to minimize overshoot Improving Tuning - Part 1
53. Near Integrator Approximation (Short Cut Tuning Method) For “Near Integrating” gain approximation use maximum ramp rate divided by change in controller output The above equation can be solved for the process time constant by taking the process gain to be 1.0 or for more sophistication as the average ratio of the controlled variable to controller output Tuning test can be done for a setpoint change if the PID gain is > 2 and the PID structure is “ PI on Error D on PV” so you see a step change in controller output from the proportional mode Improving Tuning - Part 1
54. Fastest Controller Tuning ( ultimate oscillation method*) K c K u T i = 1.0 * u T d = 0.1 u For integrating processes or for self-regulating processes where p >> o , double the factor for reset time (0.5 => 1.0) and add rate time if the process noise is negligible. The oscillations associated with quarter amplitude decay is about ½ the ultimate gain. Thus if we use quarter amplitude decaying oscillations for the test, we take ½ of the controller gain that caused these oscillations to get ¼ of the ultimate gain These tuning equations provide maximum disturbance rejection but will cause some overshoot of setpoint response Improving Tuning - Part 1 * - Ziegler Nichols method closed loop modified to be more robust and less oscillatory
55. Fastest Controller Tuning (reaction curve method*) For runaway processes: For self-regulating processes: For integrating processes: Near integrator ( p2 >> o ): Near integrator ( ’ p2 >> o ): Deadtime dominant ( p2 << o ): Improving Tuning - Part 1 These tuning equations provide maximum disturbance rejection but will cause some overshoot of setpoint response * - Ziegler Nichols method closed loop modified to be more robust and less oscillatory
56. Ultimate Period and Ultimate Gain Improving Tuning - Part 1 Time (min) Measurement (%) Ultimate Gain is Controller Gain that Caused these Nearly Equal Amplitude Oscillations (K u ) Set Point Ultimate Period T u 0 If p o then T u If p o then u
57. Damped Oscillation - (Proportional Only Control) Time (min) Measurement (%) Offset 110% of o Quarter Amplitude Period T q 0 Improving Tuning - Part 1 Set Point
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62. On-Demand Tuning Algorithm Time (min) Ultimate Period T u 0 Set Point d a Ultimate Gain 4 d K u = e n e = sq rt (a 2 - n 2 ) If n = 0, then e = a alternative to n is a filter to smooth PV Signal (%) Improving Tuning - Part 2
71. Output comes off high limit at 36.8 o C 0.30 o C overshoot Bioreactor Adaptive Tuning Gain 40 Reset 500 Improving Tuning - Part 2
72. Output comes off high limit at 35.9 o C 0.12 o C overshoot Bioreactor Adaptive Tuning Gain 40 Reset 5,000 Improving Tuning - Part 2
73. 0.13 o C overshoot Output comes off high limit at 36.1 o C Bioreactor Adaptive Tuning Gain 40 Reset 10,000 Improving Tuning - Part 2
74. 0.20 o C overshoot Output comes off high limit at 36.4 o C Bioreactor Adaptive Tuning Gain 40 Reset 15,000 Improving Tuning - Part 2
75. 0.11 o C overshoot Output comes off high limit at 36.1 o C Bioreactor Adaptive Tuning Gain 80 Reset 15,000 Improving Tuning - Part 2
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77. MIT Anna India University Lab Setup Improving Tuning - Part 2 http://www.controlglobal.com/articles/2010/LevelControl1002.html
78. Improving Tuning - Part 2 Gravity discharge flow makes the level response self-regulating (increase in level head increases flow through discharge valve) Increase in cross sectional area with level increases process time constant making process response slower Conical Tank Detail
79. Improving Tuning - Part 2 Conical Tank Linear Level Controller Performance
85. Nonlinear Control Valve Lab Improving Tuning - Part 2 Process gain is approximately proportional to flow for equal percentage flow characteristic
86. Nonlinear Control Valve Lab Improving Tuning - Part 2 Identification Out Limit that sets deadzone should be set approximately equal to valve deadband and stick-slip near closed position
If the temperature is below set point, should the steam or water valve be open? Based on looking at a faceplate or digital value of temperature on a graphic display, the operator will expect the steam valve to be open. Reset will work towards this end. However, the proper position of the control valves depends upon the trajectory of the process variable (PV). If the temperature is rapidly increasing with a sharp upward slope, the coolant valve should be open. Gain and rate action will recognize the approach to the set point and position the valves correctly to prevent overshoot. In contrast, reset has no sense of direction, and sacrifices long term results for short term gratification, much like corporate policies that cater to Wall Street. The human tendency to be impatient and not visualize the projected response (especially if it is slow or noisy) results in too much reset and not enough gain and rate action.
The offset from proportional only control is inversely proportional to the controller gain. For level and temperature loops, where the controller gain can be set high, very little reset action is need to eliminate offset..