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CHE 185 – PROCESS CONTROL AND DYNAMICS

CHE 185 – PROCESS CONTROL AND DYNAMICS. Dynamic Behavior of Ideal Systems. Ideal Dynamic Behavior. Idealized dynamic behavior can be effectively used to qualitatively describe the behavior of industrial processes.

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CHE 185 – PROCESS CONTROL AND DYNAMICS

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  1. CHE 185 – PROCESS CONTROL AND DYNAMICS Dynamic Behavior of Ideal Systems

  2. Ideal Dynamic Behavior Idealized dynamic behavior can be effectively used to qualitatively describe the behavior of industrial processes. Certain aspects of second order dynamics (e.g., decay ratio, settling time) are used as criteria for tuning feedback control loops

  3. CATEGORIZATION OF PROCESS INPUTS • PRIMARY TYPES OF INPUTS ARE REPRESENTED BY FIGURE 6.2.1 IN THE TEXT: • THESE REPRESENT THE MOST COMMON TYPES OF SIGNALS USED IN CONTROL LOOPS

  4. STEP INPUT • THIS MAY BE A SINGLE INSTANTANEOUS CHANGE IN SET POINT SIGNAL • THE LaPLACE TRANSFORM FOR THE SIGNAL IS FOR A STEP OF MAGNITUDE A THAT IS IMPOSED AT t = 0. • THE MAXIMUM SLOPE FOR THE STEP FUNCTION IS AT t = 0 • THE TIME REQUIRED TO REACH 63.2% OF THE FINAL CHANGE IS ONE TIME CONSTANT.

  5. REGULAR PULSE INPUT • THIS IS A SERIES OF TWO STEP INCREASES WITH THE SIGNAL RETURNING TO THE ORIGINAL VALUE • THE PULSE HAS A LaPLACE COMPOSED OF TWO COMPONENTS: • WHERE τpIS THE DURATION OF THE PULSE AND A IS THE MAGNITUDE

  6. IMPULSE INPUT • SPECIAL CASE OF THE PULSE FUNCTION • DURATION IS ZERO • MAGNITUDE A IS THE TOTAL INTEGRAL OBTAINED BY TAKING THE LIMIT AS THE DURATION GOES TO ZERO • LaPLACEIS U(s) = A • THIS IS NOT POSSIBLE IN INDUSTRIAL INSTALLATIONS

  7. RAMP INPUT • CAN REPRESENT THE SIGNAL FROM A PLC FOR DRIVING A PROCESS TO A NEW STEADY STATE OVER A PERIOD OF TIME • LaPLACEIS BASED ON THE RATE OF CHANGE a,

  8. SINUSOIDAL INPUT • CAN BE THE RESULT OF NOISE IN AN UPSTREAM SYSTEM THAT IS TRANSFERRED AS A SIGNAL TO A DOWNSTREAM UNIT • CHARACTERISTICS IN TERMS OF FREQUENCY RESPONSE OF OUTPUT TO INPUT

  9. SINUSOIDAL INPUT • THE RADIAN FREQUENCY IS, ω • PERIOD IS THE TIME DURATION OF ONE FULL CYCLE AND IS EQUAL TO 2π/ω. • PHASE ANGLE IS THE PHASE DIFFERENCE BETWEEN INPUT AND OUTPUT SIGNALS • AMPLITUDE RATIO IS THE RATIO OF OUTPUT MAGNITUDE TO INPUT MAGNITUDE • LaPLACEFOR A SINUSOIDAL SIGNAL IS

  10. FIRST ORDER PROCESSES • ARE BASED ON THE RESPONSE OF A LUMPED PARAMETER SYSTEM • GENERAL FORM OF THE DIFFERENTIAL EQUATION

  11. FIRST ORDER PROCESSES • GENERAL FORM OF THE TRANSFER FUNCTION • Note that gain and time constant define the behavior of a first order process.

  12. FIRST ORDER PROCESSES • RESPONSE TO A STEP INPUT WHERE THE FINAL VALUE OF THE STEP CHANGE IS AKp: • RESPONSE TO AN IMPULSE OF MAGNITUDE C:

  13. FIRST ORDER PROCESSES • THE AMPLITUDE RATIO FOR A FIRST ORDER SYSTEM (SEE SECTION 9.2) IS ALWAYS LESS THAN THE PROCESS GAIN Kp AND DECREASES MONOTONICALLY:

  14. FIRST ORDER PROCESSES • THE AMPLITUDE RATIO FOR A FIRST ORDER SYSTEM (SEE SECTION 11.2) • Open-loop bode plot shows frequency response

  15. TYPICAL FIRST ORDER PROCESSES

  16. TYPICAL FIRST ORDER PROCESSES

  17. TYPICAL RESPONSE CURVE • FOR A FIRST ORDER SYSTEM HAS THE FOLLOWING SHAPE AND CHARACTERISTICS

  18. TYPICAL RESPONSE CURVE • FOR A FIRST ORDER the amount of change is: • 63.2% one time constant • 95% three time constants • 98% four time constants

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