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Chapter 8Feedback Controllers
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On-off Controllers Simple Cheap Used In residential heating and domestic refrigerators Limited use in process control due to continuous cycling of controlled variable excessive wear on control valve.
ExamplesBatch process control (PLC = programmable logic controller)Solenoid in home heating unitSprinkler systemsCruise control?
Chapter 8
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On-Off ControllersSynonyms:two-position or bang-bang controllers.Controller output has two possible values.Chapter 8e = error = set point measured variable
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Practical case (dead band)Chapter 8system never reaches steady-state = tolerance
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Chapter 8
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Three Mode (PID) Controller Proportional Integral DerivativeProportional Control Define an error signal, e, by e = Ysp YmwhereYsp = set pointYm = measured value of the controlled variable (or equivalent signal from transmitter) Chapter 8
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Since signals are time varying,e(t) = Ysp(t) - Ym (t)n.b. Watch units!!
For proportional control: where, p(t) = controller output = bias value (adjustable) Kc = controller gain (dimensionless, adjustable)Chapter 8
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Figures 8.4, 8.5in TextChapter 8Standards (ISO/ISA)
3 15 psi4 - 20 ma0 10 VDC
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Proportional Band, PB
Reverse or Direct Acting Controller Kc can be made positive or negative Recall for proportional FB control: or Direct-Acting (Kc < 0)output increases as input increases"p(t) Ym(t)
Reverse-Acting (Kc > 0)output increases as input decreases"Chapter 8
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Example 2: Flow Control LoopAssume 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 of wrong controller action??Chapter 8
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Transfer Function for Proportional Control:Let Then controller input/output relation can written as
Take Laplace transform of each side,
or
INTEGRAL CONTROL ACTIONSynonyms: "reset", "floating control"
I reset time (or integral time) - adjustableChapter 8
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Proportional-Integral (PI) Control Response to unit step change in e:Chapter 8integral provides memory of emost popular controller
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Chapter 8 Integral action eliminates steady-state error (i.e., offset) Why??? e 0 p is changing with time until e = 0, where p reaches steady state. Transfer function for PI control
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Derivative Control Action Ideal derivative action
Used to improve dynamic response of the controlled variable Derivative kick (use -dym/dt ) Use alone?
Some controllers are calibrated in 1/I ("repeats per minute") instead of I .Chapter 8 For PI controllers,is not adjustable.
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Chapter 8
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Chapter 8Proportional-Integral-Derivative (PID) ControlNow we consider the combination of the proportional, integral, and derivative control modes as a PID controller.Many variations of PID control are used in practice.Next, we consider the three most common forms.Parallel Form of PID ControlThe parallel form of the PID control algorithm (without a derivative filter) is given by
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Chapter 8The corresponding transfer function is:Series Form of PID ControlHistorically, it was convenient to construct early analog controllers (both electronic and pneumatic) so that a PI element and a PD element operated in series.Commercial versions of the series-form controller have a derivative filter that is applied to either the derivative term, as in Eq. 8-12, or to the PD term, as in Eq. 8-15:
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Chapter 8Expanded Form of PID ControlIn addition to the well-known series and parallel forms, the expanded form of PID control in Eq. 8-16 is sometimes used:Features of PID ControllersElimination of Derivative and Proportional KickOne disadvantage of the previous PID controllers is that a sudden change in set point (and hence the error, e) will cause the derivative term momentarily to become very large and thus provide a derivative kick to the final control element.
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Chapter 8
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Automatic and Manual Control Modes Automatic Mode Controller output, p(t), depends on e(t), controller constants, and type of controller used. ( PI vs. PID etc.) Manual Mode Controller output, p(t), is adjusted manually. Manual Mode is very useful when unusual conditions exist:plant start-upplant shut-downemergencies Percentage of controllers "on manual ?? (30% in 2001, Honeywell survey)Chapter 8
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Digital PID Controller
finite difference approximation
where,= the sampling period (the time between successive samples of the controlled variable)= controller output at the nth sampling instant, n=1,2,= error at the nth sampling unit
velocity form - see Equation (8-19)(pn)- incremental changeChapter 8
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Chapter 8
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Typical Response of Feedback Control SystemsConsider response of a controlled system after a sustained disturbance occurs (e.g., step change in disturbance variable); y > 0 is off-spec.Chapter 8
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Chapter 8
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Chapter 8integral action ~
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Summary of the Characteristics of the Most Commonly Used Controller Modes1. Two Position:Inexpensive.Extremely simple.2. Proportional:Simple.Inherently stable when properly tuned.Easy to tune.Experiences offset at steady state. (OK for level control)3. Proportional plus integral:No offset.Better dynamic response than reset alone.Possibilities exist for instability due to lag introduced.Chapter 8
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4. Proportional plus derivative:Stable.Less offset than proportional alone (use of higher gain possible).Reduces lags, i.e., more rapid response.5. Proportional plus integral plus derivative:Most complexRapid responseNo offset.Best control if properly tuned.Chapter 8
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Example 3: Liquid Level Control Control valves are air-to-open Level transmitters are direct actingChapter 8
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Chapter 8Question:1. Type of controller action? Select Kc so that air-to-open valve: sign of Kv?sign of process gain?
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Chapter 8Previous chapterNext chapter
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