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Chapter 12

Chapter 12. Direct Synthesis. ( G includes G m , G v ). 1. Specify closed-loop response (transfer function). Chapter 12. 2. Need process model, (= G P G M G V ). 3. Solve for G c ,. (12-3b). Specify Closed – Loop Transfer Function. (first – order response, no offset). Chapter 12.

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Chapter 12

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  1. Chapter 12

  2. Direct Synthesis ( G includes Gm, Gv) 1. Specify closed-loop response (transfer function) Chapter 12 2. Need process model, (= GPGMGV) 3. Solve for Gc, (12-3b)

  3. Specify Closed – Loop Transfer Function (first – order response, no offset) Chapter 12 But other variations of (12-6) can be used (e.g., replace time delay with polynomial approximation)

  4. Derivation of PI Controller for FOPTD Process Consider the standard first-order-plus-time-delay model, Chapter 12 Specify closed-loop response as FOPTD (12-6), but approximate Substituting and rearranging gives a PI controller, with the following controller settings:

  5. Time Delay Compensation • Model-based feedback controller that improves closed-loop performance when time delays are present • Effect of added time delay on PI controller performance for a second order process (t1 = 3, t2 = 5) shown below Chapter 16

  6. Chapter 16

  7. Chapter 16 No model error: (sensitive to model errors > +/- 20%)

  8. Chapter 16

  9. Direct Synthesis Approach (Smith Predictor) Assume time delay between set-point change and controlled variable (same as process time delay,  ). If Chapter 16 then From Block Diagram, Equating...

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