Thursday, July 10, 2014

CHAPTER 2: CONTROLLER PRINCIPLE

Figure 1 : Controller Principle block diagram

SP  = Set point
MV = Measured value
Controller is a device which receives input from two points :
(i)            a value which is sent by transmitter
(ii)          a value which is set by set point


There are two types of controller :

1. ON OFF Controller
         -like switch

2. Analog Controller
         -Proportional controller
         -Integral controller
         -Derivative controller



TWO POSITION MODE 

A  two  position  controller  is  a  device  that  has  two  operating  conditions:    completely  on  or completely off. Figure 1 shows the input to output, characteristic waveform for a two position controller that switches from its "OFF" state to its "ON" state when the measured variable increases above these tpoint.    Conversely,  it  switches  from  its  "ON"  state  to  its  "OFF"  state  when  the  measured variable decreases below the set point.  This device provides an output determined by whether the error signal is above or below the set point.  The magnitude of the error signal is above or below the setpoint.  The magnitude of the error signal past that point is of no concern to the controller.

Figure 1 : Two position controller
Example of Two Position Control

A system using a two position controller is shown in Figure 2.The controlled process is the volume of water in the tank.  The controlled variable is the level in  the  tank.    It  is  measured  by  a  level  detector  that  sends  information  to  the  controller.    The output  of  the  controller  is  sent  to  the  final  control  element,  which  is  a  solenoid  valve,  that controls the flow of water into the tank.As the water level decreases initially, a point is reached where the measured variable drops below the set point.   This creates a positive error signal.   The controller opens the final control elementfully.   Water is subsequently injected into the tank, and the water level rises.   As soon as the water  level  rises  above  the  setpoint,  a  negative  error  signal  is  developed.   The  negative  error signal causes the controller to shut the final control element. This opening and closing of the final control element results in a cycling characteristic of the measured variable.
 Figure 2   Two Position Control System

TYPES OF CONTROLLER

There are a few types of controller used to control a process either in a form of Proportional output to the error, Proportional and Integral to the error or Proportional and Derivative output to the first error.Controller can be used in the form of single mode of Proportional, Integral, or Derivative, two mode of Proportional and Integral (P+I) and Proportional and Derivative(P+D), and three mode of Proportional, Integral and Derivative (P+I+D). 


Proportional Controller (P-Controller)

One of the most used controllers is the Proportional Controller (P-Controller) who produce an output action that is proportional to the deviation between the set point and the measured process value.
OP = -kP Er         (1)
where
OP = output proportional controller
kP = proportional gain or action factor of the controller
Er = error or deviation between the set point value and the measured value
The gain or action factor - kP
  • influence on the output with a magnitude of kP
  • determines how fast the system responds. If the value is too large the system will be in danger to oscillate and/or become unstable. If the value is too small the system error or deviation from set point will be very large.
  • can be regarded linear only for very small variations.
The gain kP can be expressed as
kP = 100 / P         (1b)
where
P = proportional band
The proportional band P, express the value necessary for 100% controller output. If P = 0, the gain or action factor kP would be infinity - the control action would be ON/OFF. A proportional controller will have the effect of reducing the rise time and will reduce, but never eliminate, the steady-state error.


Integral Controller (I-Controller)

With integral action, the controller output is proportional to the amount of time the error is present. Integral action eliminates offset.
OI = - kI Σ(Er dt)         (2)
where
OI = output integrating controller
kI = integrating gain or action factor of the controller
dt = time sample
The integral controller produce an output proportional with the summarized deviation between the set point and measured value and integrating gain or action factor.
Integral controllers tend to respond slowly at first, but over a long period of time they tend to eliminate errors.
The integral controller eliminates the steady-state error, but may make the transient response worse. The controller may be unstable.
The integral regulator may also cause problems during shutdowns and start up as a result of the integral saturation or wind up effect. An integrating regulator with over time deviation (typical during plant shut downs) will summarize the output to +/- 100%. During start up the output is set to 100%m which may be catastrophic.


Derivative Controller (D-Controller)

With derivative action, the controller output is proportional to the rate of change of the measurement or error. The controller output is calculated by the rate of change of the deviation or error with time.
OD = - kD dEr / dt         (3)
where
OD = output derivative controller
kD = derivative gain or action factor of the controller
dEr = deviation change over time sample dt
dt = time sample
The derivative or differential controller is never used alone. With sudden changes in the system the derivative controller will compensate the output fast. The long term effects the controller allow huge steady state errors.
A derivative controller will in general have the effect of increasing the stability of the system, reducing the overshoot, and improving the transient response.


Proportional, Integral, Derivative Controller (PID-Controller)

The functions of the individual proportional, integral and derivative controllers complements each other. If they are combined its possible to make a system that responds quickly to changes (derivative), tracks required positions (proportional), and reduces steady state errors (integral).
Note that these correlations may not be exactly accurate, because P, I and D are dependent of each other. Changing one of these variables can change the effect of the other two.



Control Mode Proportional and integral (P + I) 

The process uses a large space Proportional to reduce cycle are usually fixed error (offset). Another great space Proportional or more large load changes, improved error is greater still. With the integration mode is required. Use proportional integral response but reduce the return on set point is more important. When the integral is used it will continue to change as long as there is an error output until the error becomes zero. 

Control Mode Proportional and integral (P + I) are: - 


       P (t) = + Kp KpEp 

   available from Ep area under the graph (%) versus time (t



 Mod Kawalan Berkadaran + Terbitan (P+D)

Pengawal jenis ini tidak dapat menghindarkan ralat tetap.  Tetapi berguna untuk prosees yang mengalami perubahan beban  dengan pantas selagi ralat tetap yang ditimbulkan boleh diterima.

Mod kawalan nya ialah:-

   




CONTROLLER

ADVANTAGES

DISADVANTAGES
Proportional
Faster response when load is changing
Offset exist
Integral
Eliminate offset
Longer recovery time
Derivative
Reduce offset
No output when no error
Proportional + Derivative
Reduce recovery time and offset
Offset still occurs
Proportional + Integral
Can eliminate offset
Longer recovery time





QUESTION

1. Design the schematic circuit for controller action types below.
            (i)         Proportional controller (P)
            (ii)        Integral controller (I)
            (iii)       Derivative controller (D)

2. Give the advantages and disadvantages of Proportional, Integral, Derivative, Proportional + Derivative and Proportional + Integral.

3. Explain the operation of three mode controller system (P+I+D)

4. Sebuah pengawal numat jenis berkadaran digunakan untuk mengawal suhu dalam proses melebur.  Suhu titik set ialah 750°C dan julat alat suhu ialah 0 - 1000°C. Ruang berkadaran ditentukan pada 15%.  Julat keluaran tekanan dari pengawal ialah 20 –100 kN/m2 dan nilai keluaran tekanan meningkat apabila suhu meningkat.  Jika nilai keluaran keluaran tekanan diset pada 60kN/m2 untuk titik set suhu, cari:

a)             Nilai suhu untuk keluaran tekanan 20 kN/m2
b)            Nilai suhu untuk keluaran tekanan 100 kN/m2
c)             Nilai tekaaaanan bila suhu 735°C




       




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