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06_Feedback_E2009 - 28150 Introduction to process control 6...

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1 28150. Introduction to process control 6. Feedback controllers Krist V. Gernaey 5 October 2009 28150 Learning objectives • At the end of this lesson you should be able to: – Explain advantages and disadvantages of different feedback controllers – Explain the effect of PID controller parameters on the response of a controlled process – Implement a PI controller and experiment with it (exercises) 5 October 2009 28150 Outline • Introduction • On-off controller • Basic control modes • PID controller: typical responses • PID controller formulation for digital control systems 5 October 2009 28150 Outline Introduction • On-off controller • Basic control modes • PID controller: typical responses • PID controller formulation for digital control systems 5 October 2009 28150 Feedback control Distinguishing feature: measure the controlled variable – Important distinction between negative feedback and positive feedback Advantages: – Corrective action is taken regardless of the source of the disturbance – Reduces sensitivity of the controlled variable to disturbances and changes in the process (shown later) Disadvantages: – No corrective action occurs until after the disturbance has upset the process (after y differs from y sp ) – Very oscillatory responses, or even instability… 5 October 2009 28150 Blending tank example
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2 5 October 2009 28150 Feedback control: block diagram Error signal : e = y sp – y m With: y sp = set point y m = measured value of the controlled variable 5 October 2009 28150 Bioreactor example: pH control 5 October 2009 28150 Bioreactor example: block diagram 5 October 2009 28150 Outline • Introduction On-off controller • Basic control modes • PID controller: typical responses • PID controller formulation for digital control systems 5 October 2009 28150 Characteristics of on-off controllers • Controller output: Where: e = error = set point – measured value • Synonyms: “two-position” or “bang-bang” controllers. • Simple (only two controller outputs), cheap • Limited use in process control due to continuous cycling of controlled variable • Example: pH control, residential heating system, refrigerator, etc. e 0 u min u max ( ) < = 0 0 min max e if u e if u t u 5 October 2009 28150 Fed-batch bioreactor example V S F X S K S S K S Y V S F dt dS O O O S SX F - + + - = max μ V X F X S K S S K S V X F dt dX O O O S F - + + + = max μ V P F X S K S S K S Y V P F dt dP O O O S XP F - + + + = max μ F dt dV = ( ) V S F X S K S S K S Y Y S S a K V S F dt dS O O O O S SX SO O O L F O O - + + - - + = max * , μ
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3 5 October 2009 28150 Fed-batch bioreactor example Volume Biomass Substrate Product Dissolved oxygen, no control 5 October 2009 28150 Fed-batch bioreactor example u y 5 October 2009
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