a | Lecture Chemical process control - Chapter 8 Feedback Controllers Chapter 8 On-off Controllers • Simple • Cheap Chapter 8 • Used In residential heating and domestic refrigerators • Limited use in process control due to continuous cycling of controlled variable excessive wear on control valve. Examples Batch process control (PLC = programmable logic controller) Solenoid in home heating unit On-Off Controllers Synonyms: “two-position” or “bang-bang” controllers. Chapter 8 e = error = set point – measured variable Controller output has two possible values. Practical case (dead band) Chapter 8 δ = tolerance system never reaches steady-state Chapter 8 Three Mode (PID) Controller • Proportional • Integral • Derivative Proportional Control Chapter 8 • Define an error signal, e, by e = Ysp – Ym where Ysp = set point Ym = measured value of the controlled variable (or equivalent signal from transmitter) Since signals are time varying, e(t) = Ysp(t) - Ym (t) . Watch units!! Chapter 8 • p(t) = p + K ce(t) p = p p For proportional control: where, p(t) = controller output p = bias value (adjustable) Kc = controller gain (dimensionless, adjustable) Figures , Chapter 8 in Text Standards (ISO/ISA) 3 – 15 psi 4 - 20 ma 0 – 10 VDC • Proportional Band, PB 100% PB Kc • Reverse or Direct Acting Controller • Kc can be made positive or negative • Recall for proportional FB control: p(t) = p + K c e(t) Chapter 8 or p( t ) p K c Ysp ( t ) Ym ( t ) • Direct-Acting (Kc < 0) “output increases as input increases" p(t) Ym(t) • Reverse-Acting (Kc > 0) “output increases as input decreases" • Example 2: Flow Control Loop Chapter 8 Assume FT is direct-acting. Select sign of Kc so that KcKv > 0 1.) Air-to-open (fail close) valve ==> ? 2.) Air-to-close (fail open) valve ==> ? • Consequences
