Chapter 8Feedback Controllers

Chapter 8

Error Signal

Proportional Control

Chapter 8

Reverse or Direct Acting ControllerDirect-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.

Example 2: Flow Control LoopAssume FT is direct-acting.

1.) Air-to-open (fail close) valve ==> ?2.) Air-to-close (fail open) valve ==> ?

Consequences of wrong controller action??Chapter 8

Chapter 9

Example 3: Liquid Level Control Control valves are air-to-open Level transmitters are direct actingChapter 8Question: Type of controller action?

Chapter 8INTEGRAL CONTROL ACTION

Proportional-Integral (PI) Controller

Reset TimeReset 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

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Parallel-Form PID Controller with Derivative Filter

Derivative and Proportional KicksOne 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

Typical Response of Feedback Control SystemsConsider response of a controlled system after a sustained disturbance occurs (e.g., step change in disturbance variable)Chapter 8

Chapter 8

Chapter 8

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

Digital PID Controller

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 changeChapter 8

PID-Most complicated to tune (Kc, I, D) .-Better performance than PI-No offset-Derivative action may be affected by noisePI-More complicated to tune (Kc, I) .-Better performance than P-No offset-Most popular FB controllerP-Simplest controller to tune (Kc).-Offset with sustained disturbance or set point change.Controller ComparisonChapter 8

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.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 complexRapid responseNo 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.

Chapter 8

On-Off ControllersSynonyms:two-position or bang-bang controllers.Controller output has two possible values.Chapter 8

Practical case (dead band)Chapter 8