The document describes various controller modes including: 1. ON-OFF/two position controller - provides discontinuous control by switching between maximum and minimum output values. 2. Proportional (P) control - controller output is proportional to the error. Provides fast response but steady state error. 3. Integral (I) control - controller output is proportional to the integral of error over time. Eliminates steady state error but increases response time. 4. Derivative (D) control - controller output is proportional to the rate of change of error. Increases damping but can amplify noise and cause instability. Composite modes like PI, PD, and PID combine the advantages of the individual modes to provide

1. Controller Modes
1.
2.
3.
4.
5.
6.
7.
8.
ON-OFF controller/two position controller
Three-position controller
Proportional Action Control
Integral/Reset Action Control
Derivative/Rate Action Control
P+I Control
P+D Control
P+I+D Control

2. ON-OFF Control
•
•
•
•
•
Discontinuous control mode
Also called two-position control
The simplest form of control
It is very commonly used in industry
The manipulated variable is quickly changed to
either a maximum or a minimum value
• The minimum value of the manipulated variable
is usually zero (off)
• Transmit only two output signals: ON (100%), OFF
(0%)
• Only responds when it’s above or below the
setpoint

3. ON-OFF Controller
• Example :
Process : Water tank of 10 litres
Target: Reach + maintain a temperature of
o
90 C.
Water : 10 Litres
Heater
Sensor

10. Two-positions controller with hysteresis

11. ON-OFF Controller made from Op- amps
Vin reaches VH  Comparator ON state(V0)
Vin falls below a value VL  Comparator OFF
state (0)
The HIGH (ON) or V1=Vsp switch
voltage is
VH = Vsp
Vsp = Setpoint voltage
The LOW (OFF) switch voltage is
VL = Vsp – R1/R2 V0

12. Vout
(ON) V0
(OFF)
0
VL
VH
Vin

13. Example:
Level measurement in a sump tank is provided
by a transducer scaled as 0.2 V/m. A pump is to
be turned on by application of +5V when the
sump level exceeds 2.0m. The pump is to be
turned back off when the sump level drops to
1.5m. Find R2 if R1 is given 5kΩ

14. Three-Position Controller made from Op- amps

15. • In this circuit assumed:
The output of the comparators is 0V for the
OFF state
Vo volts for the ON state
• The summing amplifier includes a bias voltage
input VB which allows the three-position
mode response to be biased up or down in
voltage to suit particular needs.
• The inverter is to convert the sign of the
inverting action of the summing amplifier

16. • Equation presented the generic three-mode
controller response:
Vin < Vsp1
Vout = VB
Vsp1 < Vin < Vsp2 Vout = VB + R3/R1 Vo
Vin > Vsp2
Vout = VB + R3/R1 Vo + R3/R2 Vo

17. Response of the three-position controller with the bias
equal to zero

18. Example:
The level in a sump tank is to be controlled with a
three-position controller. The following
specifications are given:
1. The level measurement sensor has a transfer
function of 0.45 V/m
2. The valve is linearly driven from fully open to
fully closed by a voltage from 0 to 8V
3. The following specifications are given:
level < 2m
valve 20% open
level > 2m < 3m
valve 65% open
level > 3m
valve 100% open

19. Comparators are available that have outputs of
0 V for OFF and 5V for ON. Design a three
position op amp controller. R3 is given by 10kΩ

20. Proportional Controller (P Mode)
• Continuous control mode
• Typical behavior/characteristics:
 The signal output of a controller is proportional to
the input or error
 Stay at the same ratio
• Proportional control is a pure gain adjustment
acting on the error signal to provide the driving
input to the process.

21. • Implementation of this mode requires a circuit
which has a response given by
Where: U =controller output (0 100%)
K = Proportional gain (controller transfer function)
PB = proportional band in percentage
Ep = error in percent of variable range
Pp = controller output with no error (bias)

23. Example:
A proportional controller has the scale 0-10 volts
corresponds to a 0-100% output. If R2 = 10 KΩ,
and full scale error is 10 volt, find the value of V0
and R1 to support a 20% proportional band about
a 50% zero-error controller output.

24. Advantages:
 Simple
 Easiest of the continuous controllers tune
 Provides good stability, rapid response and
relatively stable.
Disadvantages:
 Only control results in offset – Never reaches SP
 Action is instantaneous – As soon as error is
produced, control action is taken.
 Used to stabilize unstable output

25. Integral Action Control
• Also called Reset Action Control
• Continuous control mode
• Typical behavior/characteristic:
- The controller output is proportional to the
integral of the error with respect to time
- The value of the controller output is changed
at a rate proportional to the error “e”
• Used to removed offset
• As long as error exist, integral action will work
to eliminate the error

26. Integral control is implemented through the
introduction of an integrator. Implementation of this
mode requires a circuit which has a response given by

28. Example:
• Suppose that V(0)=0 for an integral controller.
• It is required that the controller output should
saturate 15 seconds after a constant 5% error
is applied.
• The input range is 0-5 volts and the output
range is 0-10 volts. Calculate the integration
gain and the suitable values of R and C.
Assume C=50μF

29. Derivative Control
• Also called Rate Control Action
• Continuous control mode
• Typical behavior/characteristic:
- The controller output is proportional to the rate
of the error (time derivative)
• Faster/quick response compared to P
• Can cause the damage to the FCE because of too
fast rate of change of the error
• Can amplify the noise in the system
• Cannot compensating the system error: e = w-x=0

30. • The derivative mode is never used alone
because it cannot provide a controller output
when the error is zero.
• Implementation of this mode requires a circuit
which has a response given by

31. The value of R1 is selected so that the circuit will be
stable for high frequencies by setting
where f is the frequency in Hz.

32. Summary
Remark: Each mode has its advantages and drawbacks
individually
• P mode Advantage: Fast response action
• Drawback: Produces steady state error (offset)
• I mode Advantage: Steady state error is null
• Drawback: Increases the response time
• D Mode Advantage: increases the damping of the system
• Drawback: Amplifies the noise which can cause problems
including instability
• Therefore, the pure controller mode (P or I or D) is seldom
used in process control because of the advantage of
composite modes in providing good control.

33. Composite Controller
Proportional- Integral Control (PI Mode)
This controller can:
 eliminate an offset due to integral action
 the system response is slow due to lag introduced = -90o
 better dynamic response than integral alone
 I action repeats P action in Ti seconds
 the slope depends on Ti
Kp
Ki
Parallel controller - Mathematical
Gp

34. Gp
100/PB
1/Ti
Series controller - Practical
I
t
Ti – Time for integral action
after the proportional
action
I
t
I
P+I
t

36. Example:
PI controller has a proportional band of 30% and an
integration time =10 seconds. The 4-20mA input volts
converts to a 0.4-2 volt error signal and the controller
output range is 0-10 volts.Calculate values of Kp, KI,
R1, and R2. C is given by 10μF

37. Proportional-Derivative Control (PD Mode)
This controller can:
 experience the offset but less than proportional only
 the system response is faster due to lead introduced = -90o
 better dynamic response than integral alone
 I action repeats P action in Ti seconds
 the slope depends on Ti

38. Proportional-Derivative Control (PD Mode)

40. Three term Controller (PID Mode)