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CHE 185 – PROCESS CONTROL AND DYNAMICS

CHE 185 – PROCESS CONTROL AND DYNAMICS. PID CONTROLLER FUNDAMENTALS. CLOSED LOOP COMPONENTS. GENERAL DEFINITIONS OPEN LOOPS ARE MANUAL CONTROL FEEDBACK LOOPS ARE CLOSED EXAMPLE P&ID FOR FEEDBACK CONTROL LOOP. CLOSED LOOP COMPONENTS.

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CHE 185 – PROCESS CONTROL AND DYNAMICS

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  1. CHE 185 – PROCESS CONTROL AND DYNAMICS PID CONTROLLER FUNDAMENTALS

  2. CLOSED LOOP COMPONENTS • GENERAL DEFINITIONS • OPEN LOOPS ARE MANUAL CONTROL • FEEDBACK LOOPS ARE CLOSED • EXAMPLE P&ID FOR FEEDBACK CONTROL LOOP

  3. CLOSED LOOP COMPONENTS • GENERAL BLOCK DIAGRAM FOR FEEDBACK CONTROL LOOP (FIGURE 7.2.1 FROM TEXT)

  4. CLOSED LOOP COMPONENTS • OVERALL TRANSFER FUNCTION

  5. TYPICAL TRANSFER FUNCTIONS FOR A FEEDBACK LOOP • CONSIDER THE RESPONSE TO A DISTURBANCE • WITH CONSTANT S/P (Ysp(s) = 0) • REGULATORY CONTROL OR DISTURBANCEREJECTION • THIS REPRESENTS A PROCESS AT • STEADY STATE RESPONDING TO • BACKGROUND DISTURBANCES

  6. TYPICAL TRANSFER FUNCTIONS FOR A FEEDBACK LOOP • CONSIDER THE SETPOINT RESPONSE • WITH NO DISTURBANCE (D(s) = 0) • SETPOINT TRACKING OR SERVO CONTROL • THIS MODEL REPRESENTS THE SYSTEM RESPONSE TO A S/P ADJUSTMENT

  7. TYPICAL TRANSFER FUNCTIONS FOR A FEEDBACK LOOP • GENERALIZATIONS REGARDING THE FORM OF THE TRANSFER FUNCTIONS • THE NUMERATOR IS THE PRODUCT OF ALL TRANSFER FUNCTIONS BETWEEN THE INPUT AND THE OUTPUT • THE DENOMINATOR IS EQUAL TO THE NUMERATOR + 1

  8. TYPICAL TRANSFER FUNCTIONS FOR A FEEDBACK LOOP • CHARACTERISTIC EQUATION • oBTAINED BY SETTING THE DENOMINATOR = 0 • ROOTS FOR THIS EQUATION WILL BE: • OVERDAMPED LOOP • COMPLEX ROOTS, FOR AN OSCILLATORY LOOP • AT LEAST ONE REAL POSITIVE ROOT FOR AN UNSTABLE LOOP

  9. Feedback Control Analysis • The loop gain (KcKaKpKs) should be positive for stable feedback control. • An open-loop unstable process can be made stable by applying the proper level of feedback control.

  10. Characteristic Equation Example • Consider the dynamic behavior of a P-only controller applied to a CST thermal mixer (Kp=1; τp=60 sec) where the temperature sensor has a τs=20 sec and τais assumed small. Note that Gc(s)=Kc.

  11. Characteristic Equation Example- closed loop poles • When Kc =0, poles are -0.05 and -0.0167 which correspond to the inverse of τp and τs. • As Kc is increased from zero, the values of the poles begin to approach one another. • Critically damped behavior occurs when the poles are equal. • Underdamped behavior results when Kc is increased further due to the imaginary components in the poles.

  12. PID ALGORITHM - POSITION FORM • ISA POSITION FORM FOR PID: • FOR PROPORTIONAL ONLY

  13. Definition of Terms • e(t) - the error from setpoint [e(t)=ysp-ys]. • Kc- the controller gain is a tuning parameter and largely determines the controller aggressiveness. • τI - the reset time is a tuning parameter and determines the amount of integral action. • τD - the derivative time is a tuning parameter and determines the amount of derivative action.

  14. PID Controller Transfer Function

  15. PID ALGORITHM - POSITION FORM • FOR PROPORTIONAL/INTEGRAL: • FOR PROPORTIONAL/DERIVATIVE

  16. PID ALGORITHM - POSITION FORM • TRANSFER FUNCTION FOR PID CONTROLLER:

  17. PID ALGORITHM - POSITION FORM • DERIVATIVE KICK: • RESULTS FROM AN ERROR SPIKE (INCREASE IN ) WHEN A SETPOINT CHANGE IS INITIATED • CAN BE ELIMINATED BY REPLACING THE CHANGE IN ERROR WITH A CHANGE IN THE CONTROLLED VARIABLE IN THE PID ALGORITHM • RESULTING EQUATION IS CALLED THE DERIVATIVE-ON-MEASUREMENT FORM OF THE PID ALGORITHM

  18. DIGITAL VERSIONS OF THE PID ALGORITHM • DIGITAL CONTROL SYSTEMS REQUIRE CONVERSION OF ANALOG SIGNALS TO DIGITAL SIGNALS FOR PROCESSING. • DIGITAL VERSION OF THE PREVIOUS EQUATION IN DIGITAL FORMAT BASED ON A SINGLE TIME INTERVAL, Δt: YIELDS THE VELOCITY FORM OF THE PID ALGORITHM

  19. DIGITAL VERSIONS OF THE PID ALGORITHM • FOR INTEGRATION OVER A TIME PERIOD, t, WHERE n = t/Δt:

  20. DIGITAL VERSIONS OF THE PID ALGORITHM • PROPORTIONAL KICK • RESULTS FROM THE INITIAL RESPONSE TO A SETPOINT CHANGE • CAN BE ELIMINATED IN THE VELOCITY EQUATION BY REPLACING THE ERROR TERM IN THE ALGORITHM WITH THE SENSOR TERM

  21. First Order Process with a PI Controller Example

  22. PI Controller Applied to a Second Order Process Example

  23. PROPORTIONAL ACTION • USES A MULTIPLE OF THE ERROR AS A SIGNAL TO THE CONTROLLER, CONTROLLER GAIN, • HAS INVERSE UNITS TO PROCESS GAIN

  24. Proportional Action Properties • Closed loop transfer function base on a P-only controller applied to a first order process. • Properties of P control • Does not change order of process • Closed loop time constant is smaller than open loop τp • Does not eliminate offset.

  25. P-only Control Offset

  26. Proportional Response Action with a PI Controller

  27. PROPORTIONAL CONTROL • RESPONSE OF FIRST ORDER PROCESS TO STEP FUNCTION • OPEN LOOP - NO CONTROL • CLOSED LOOP - PROPORTIONAL CONTROL

  28. PROPORTIONAL CONTROL • PROPORTIONAL CONTROL MEANS THE CLOSED SYSTEM RESPONDS QUICKER THAN THE OPEN SYSTEM TO A CHANGE. • OFFSET IS A RESULT OF PROPORTIONAL CONTROL. AS t INCREASES, THE RESULT IS:

  29. Integral Action • The primary benefit of integral action is that it removes offset from setpoint. • In addition, for a PI controller all the steady-state change in the controller output results from integral action.

  30. INTEGRAL ACTION • WHERE PROPORTIONAL MODE GOES TO A NEW STEADY-STATE VALUE WITH OFFSET, INTEGRAL DOES NOT HAVE A LIMIT IN TIME, AND PERSISTS AS LONG AS THERE IS A DIFFERENCE. • INTEGRAL WORKS ON THE CONTROLLER GAIN • INTEGRAL SLOWS DOWN THE RESPONSE OF THE CONTROLLER WHEN PRESENT WITH PROPORTIONAL

  31. INTEGRAL ACTION • INTEGRAL ADDS AN ORDER TO THE CONTROL FUNCTION FOR A CLOSED LOOP • FOR THE FIRST ORDER PROCESS WITH PI CONTROL, THE TRANSFER FUNCTION IS: • WHERE AND

  32. Derivative Action Properties • THE DERIVATIVE MODE RESPONDS TO THE SLOPE • THIS MODE AMPLIFIES SUDDEN CHANGES IN THE CONTROLLER INPUT SIGNAL - INCREASES CONTROLLER SENSITIVITY

  33. Derivative Action Properties • DERIVATIVE MODE CAN COUNTERACT INTEGRAL MODE TO SPEED UP THE RESPONSE OF THE CONTROLLER. • DERIVATIVE DOES NOT REMOVE OFFSET • IMPROPER TUNING CAN RESULT IN HIGH-FREQUENCY VARIATION IN THE MANIPULATED VARIABLE • 7.6 DOES NOT WORK WELL WITH NOISY SYSTEMS

  34. Derivative Action Properties • Properties of derivative control: • Does not change the order of the process • Does not eliminate offset • Reduces the oscillatory nature of the feedback response • Closed loop transfer function for derivative-only control applied to a second order process.

  35. Derivative Action Response for a PID Controller

  36. Derivative Action • The primary benefit of derivative action is that it reduces the oscillatory nature of the closed-loop response.

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