Chapter 8 Feedback Controllers Chapter 8 Error Signal
Chapter 8 Feedback Controllers
Chapter 8
Error Signal
Proportional Control
Chapter 8
Reverse or Direct Acting Controller • Direct-Acting (Kc < 0): “output increases as input increases" • Reverse-Acting (Kc > 0): “output increases as input decreases"
Chapter 8
Proportional Band (PB) PB is the error (% of the range of controlled variable) required to move the output from its lowest to its highest value.
Chapter 8 • Example 2: Flow Control Loop Assume FT is direct-acting. 1. ) Air-to-open (fail close) valve ==> ? 2. ) Air-to-close (fail open) valve ==> ? • Consequences of wrong controller action? ?
Chapter 9
Chapter 8 Example 3: Liquid Level Control • Control valves are air-to-open • Level transmitters are direct acting Question: Type of controller action?
Chapter 8 INTEGRAL CONTROL ACTION
Proportional-Integral (PI) Controller
Reset Time Reset time is the time that the integral mode repeats the action of proportional mode.
Example: Heat Exchanger Control Loop
Reset Windup
Reset Windup
Anticipatory or Derivative Control Action
Proportional-Integral-Derivative (PID) Control Now 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 (see Table 8. 1, page 194) • Next, we consider the three most common forms.
Parallel Form of PID Control
Effects of Anticipatory (Derivative) Control Action
Drawbacks of Anticipatory (Derivative) Control Action
Chapter 8
Parallel-Form PID Controller with Derivative Filter
Derivative and Proportional Kicks One 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.
Elimination of Derivative and Proportional Kicks in Parallel. Form Controllers
Series Form of PID Control
Elimination of Derivative Kick in Series-Form Controllers
Expanded (Non-interacting) Form of PID Control
Chapter 8
Chapter 8 Typical Response of Feedback Control Systems Consider response of a controlled system after a sustained disturbance occurs (e. g. , step change in disturbance variable)
Chapter 8
Chapter 8
Automatic and Manual Control Modes Chapter 8 • 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-up plant shut-down emergencies • Percentage of controllers "on manual” ? ? (30% in 2001, Honeywell survey)
Digital PID Controller Chapter 8 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) ( pd)- incremental change
Chapter 8 Controller Comparison P -Simplest controller to tune (Kc). -Offset with sustained disturbance or set point change. PI -More complicated to tune (Kc, I). -Better performance than P -No offset -Most popular FB controller PID -Most complicated to tune (Kc, I, D). -Better performance than PI -No offset -Derivative action may be affected by noise
Chapter 8 Summary of the Characteristics of the Most Commonly Used Controller Modes 1. Two Position: Inexpensive. Extremely simple. 2. Proportional: Simple. Inherently stable when properly tuned. Easy to tune. Experiences offset at steady state. 3. Proportional plus integral: No offset. Better dynamic response than reset alone. Possibilities exist for instability due to lag introduced.
Chapter 8 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 reset plus rate: Most complex Rapid response No offset. Difficult to tune. Best control if properly tuned.
Chapter 8 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. Example 1: Temperature control of jacketed vessel.
On-Off Controllers Chapter 8 Synonyms: “two-position” or “bang-bang” controllers. Controller output has two possible values.
Chapter 8 Practical case (dead band)
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