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Class 27 pd, pid electronic controllers

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Manipal Institute of Technology
Manipal Institute of Technology

This document discusses proportional, derivative, and proportional-integral-derivative (PID) electronic controllers. It provides mathematical equations for proportional, derivative, and PID control modes. Examples are given to show how to calculate controller gains and design op amp circuits based on given control parameters and signal change periods. The document also provides reference information for the course on process instrumentation and control taught by Dr. S. Meenatchisundaram.

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ICE401: PROCESS INSTRUMENTATION AND CONTROL Class 27 PD, PID Electronic Controllers Dr. S. Meenatchisundaram Email: meenasundar@gmail.com Process Instrumentation and Control (ICE 401) Dr. S.Meenatchisundaram, MIT, Manipal, Aug – Nov 2015
Proportional Derivative Control Mode: Process Instrumentation and Control (ICE 401) Dr. S.Meenatchisundaram, MIT, Manipal, Aug – Nov 2015 1 2 2 3 3 0 1 3 1 3 1 3 out e out e dV dVR R R V R C V R C V R R dt R R R R dt       + = + +      + + +      1 3 1 3 R R R R R   =   + 
Derivative Control Mode: Process Instrumentation and Control (ICE 401) Dr. S.Meenatchisundaram, MIT, Manipal, Aug – Nov 2015 • If 2πfmaxR C = 0.1 , then, • where the proportional gain is Gp= R2/(R1+R3) and GD= R3C Try: • A proportional-derivative controller has a 0.4 to 2.0V input measurement range, a 0- to 5-V output, KP = 5 %/%, KD = 0.08% /(%/min). The period of the fastest expected signal change is 1.5 s. Implement this controller with an op amp circuit. 2 2 3 0 1 3 1 3 e out e dVR R V V R C V R R R R dt     = + +    + +   
Derivative Control Mode: Process Instrumentation and Control (ICE 401) Dr. S.Meenatchisundaram, MIT, Manipal, Aug – Nov 2015 Solution: • A KP = 5 %/% means 20% of PB. So, • KD = 0.08% /(%/min). • The period of the fastest expected signal change is 1.5 s. ( )( ) ( )( ) 100% 5 5 15.625 20% 1.6 0.32 P V V G V V = = = ( )( ) ( )( ) 4.8% 5 15sec 1% 1.6 D V G V = = ( ) ( ) 0.08% 60sec 4.8% 1min% / min % / s     =     1 3 1 3 0.1 1.5sec 0.024sec 2 R R C R R π = = +
Derivative Control Mode: Process Instrumentation and Control (ICE 401) Dr. S.Meenatchisundaram, MIT, Manipal, Aug – Nov 2015 • From KP, KD, we can write • Let C=100µF, then, R1 = 240 , R2 = 2.35 M , R3 = 150 k 2 1 3 1 3 1 3 15.625 , 15 , 0.0016P D R R G s G R C s V R R R R     = = = = =    + +   
Three Mode: Process Instrumentation and Control (ICE 401) Dr. S.Meenatchisundaram, MIT, Manipal, Aug – Nov 2015
Three Mode: Process Instrumentation and Control (ICE 401) Dr. S.Meenatchisundaram, MIT, Manipal, Aug – Nov 2015 2 2 2 1 1 1 1 (0)e out e e D D out I I dVR R R V V V dt R C V R R R C R dt       − = + + +            ∫ 2 1 1 , ,P I D D D I I R G G G R C R R C   = = =   
Three Mode Controller: Process Instrumentation and Control (ICE 401) Dr. S.Meenatchisundaram, MIT, Manipal, Aug – Nov 2015 Try: • A temperature-control system inputs the controlled variable as a range from 0 to 4 V. The output is a heater requiring 0 to 8 V. A PID is to be used with, KP = 2.4 %/%, KI = 9% /(%‒min), KD = 0.7% /(%/min). The period of the fastest expected signal change is 8 s. Implement this controller with an op amp circuit.
References: • Process Control Instrumentation Technology, by Curtis D. Johnson, Eighth Edition, Pearson Education Limited. Process Instrumentation and Control (ICE 401) Dr. S.Meenatchisundaram, MIT, Manipal, Aug – Nov 2015

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Class 27 pd, pid electronic controllers

  • 1. ICE401: PROCESS INSTRUMENTATION AND CONTROL Class 27 PD, PID Electronic Controllers Dr. S. Meenatchisundaram Email: meenasundar@gmail.com Process Instrumentation and Control (ICE 401) Dr. S.Meenatchisundaram, MIT, Manipal, Aug – Nov 2015
  • 2. Proportional Derivative Control Mode: Process Instrumentation and Control (ICE 401) Dr. S.Meenatchisundaram, MIT, Manipal, Aug – Nov 2015 1 2 2 3 3 0 1 3 1 3 1 3 out e out e dV dVR R R V R C V R C V R R dt R R R R dt       + = + +      + + +      1 3 1 3 R R R R R   =   + 
  • 3. Derivative Control Mode: Process Instrumentation and Control (ICE 401) Dr. S.Meenatchisundaram, MIT, Manipal, Aug – Nov 2015 • If 2πfmaxR C = 0.1 , then, • where the proportional gain is Gp= R2/(R1+R3) and GD= R3C Try: • A proportional-derivative controller has a 0.4 to 2.0V input measurement range, a 0- to 5-V output, KP = 5 %/%, KD = 0.08% /(%/min). The period of the fastest expected signal change is 1.5 s. Implement this controller with an op amp circuit. 2 2 3 0 1 3 1 3 e out e dVR R V V R C V R R R R dt     = + +    + +   
  • 4. Derivative Control Mode: Process Instrumentation and Control (ICE 401) Dr. S.Meenatchisundaram, MIT, Manipal, Aug – Nov 2015 Solution: • A KP = 5 %/% means 20% of PB. So, • KD = 0.08% /(%/min). • The period of the fastest expected signal change is 1.5 s. ( )( ) ( )( ) 100% 5 5 15.625 20% 1.6 0.32 P V V G V V = = = ( )( ) ( )( ) 4.8% 5 15sec 1% 1.6 D V G V = = ( ) ( ) 0.08% 60sec 4.8% 1min% / min % / s     =     1 3 1 3 0.1 1.5sec 0.024sec 2 R R C R R π = = +
  • 5. Derivative Control Mode: Process Instrumentation and Control (ICE 401) Dr. S.Meenatchisundaram, MIT, Manipal, Aug – Nov 2015 • From KP, KD, we can write • Let C=100µF, then, R1 = 240 , R2 = 2.35 M , R3 = 150 k 2 1 3 1 3 1 3 15.625 , 15 , 0.0016P D R R G s G R C s V R R R R     = = = = =    + +   
  • 6. Three Mode: Process Instrumentation and Control (ICE 401) Dr. S.Meenatchisundaram, MIT, Manipal, Aug – Nov 2015
  • 7. Three Mode: Process Instrumentation and Control (ICE 401) Dr. S.Meenatchisundaram, MIT, Manipal, Aug – Nov 2015 2 2 2 1 1 1 1 (0)e out e e D D out I I dVR R R V V V dt R C V R R R C R dt       − = + + +            ∫ 2 1 1 , ,P I D D D I I R G G G R C R R C   = = =   
  • 8. Three Mode Controller: Process Instrumentation and Control (ICE 401) Dr. S.Meenatchisundaram, MIT, Manipal, Aug – Nov 2015 Try: • A temperature-control system inputs the controlled variable as a range from 0 to 4 V. The output is a heater requiring 0 to 8 V. A PID is to be used with, KP = 2.4 %/%, KI = 9% /(%‒min), KD = 0.7% /(%/min). The period of the fastest expected signal change is 8 s. Implement this controller with an op amp circuit.
  • 9. References: • Process Control Instrumentation Technology, by Curtis D. Johnson, Eighth Edition, Pearson Education Limited. Process Instrumentation and Control (ICE 401) Dr. S.Meenatchisundaram, MIT, Manipal, Aug – Nov 2015