1. Interactive Opportunity Assessment Demo and Seminar (Deminar) Series for Web Labs – Process Control Improvement Primer Sept 8, 2010 Sponsored by Emerson, Experitec, and Mynah Created by Greg McMillan and Jack Ahlers www.processcontrollab.com Website - Charlie Schliesser (csdesignco.com)

18. 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 Self-Regulating Process Open Loop Response  o or Maximum speed in 4 deadtimes is critical speed

19. Integrating Process Open Loop Response Maximum speed in 4 deadtimes is critical speed 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

20. 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  ’ p2  ’ o

21. 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 % % % Delay => Dead Time Lag =>Time Constant K i = K mv  (K pv /  p2 )  K cv 100% / span K c T i T d

24. 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

25. Ultimate Limit to Loop Performance Peak error is proportional to the ratio of loop deadtime to 63% response time Integrated error is proportional to the ratio of loop deadtime squared to 63% response time 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

26. Disturbance Speed and Attenuation Effect of load disturbance lag (  L ) can be estimated by replacing the open loop error with the exponential response of the disturbance during the loop deadtime The attenuation of oscillations van 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

27. 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 )

28. 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

29. Fastest Practical PID Tuning Settings (Practical Limit to Loop Performance) For runaway processes: For self-regulating processes: For integrating processes: short cut tuning method (near integrator approximation) short cut tuning method (near integrator approximation)

30. Effect of Tuning Speed on Oscillatory Disturbance 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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