document of control technology

1. @farhan. M Lecture: 14 PID Controller 1
Hello Class
Lecture 14
Topic: PID Controller
Prepared by
Engr. Dr. Muhammad Farhan
Email: mfarhan@gcuf.edu.pk
Control Systems
Course Lecture Series
for
Undergraduate BSc Electrical, Electronics
& Computer Systems Engineering
EngiTech
Learn
Plex
Lecture: 14 PID Controller

2. • 80% of industrial control applications are installed by
feedback control loop and devices.
• Unlike simpler control algorithms, PID controller can adjust
process inputs based on the history and rate of change of the
error signal, which gives more accurate and stable control.
• It can be shown mathematically that a PID loop will produce
accurate stable control in cases where other control
algorithms would either have a steady-state error or would
cause the process to oscillate.
2
Hello Class
@farhan. M Lecture: 14 PID Controller 2
PID Controller Theme---Background
Lecture: 14 PID Controller

3. • A (PID controller) is a generic controller widely used in industrial control
systems.
• It can be used to regulate flow, temperature, pressure, level, and many other
industrial process variables.
• It describes the mathematic calculations that are applied to calculate the
error between the current result and the desired set-point.
• Proportional term responds instantaneously to the current error (providing
(providing instaneous response).
• Integral term (past errors) responds to the accumulation of errors in the
in the form of average (providing a slow response that drives the steady-
state error towards Zero).
• Derivative term (future errors) responds to the rate at which the error is
error is changing (providing some anticipatory response).
3
Hello Class
@farhan. M Lecture: 14 PID Controller 3
PID controller
Lecture: 14 PID Controller

4. • With manual, all regulation tasks
will have to be done manually.
• For example: To keep constant
temperature of water discharged,
an operator will have to watch a
temperature gauge and adjust a
fuel gas valve accordingly
• If the water temperature
becomes too high or too cold for
some reason, the operator has to
close the gas valve.
4
Hello Class
@farhan. M Lecture: 14 PID Controller 4
Life before PID controller –Manual Control
Lecture: 14 PID Controller

5. • Through PID controller Set
Point feature, operator can set
the desired temperature ranges.
• The Controller’s Output (CO)
sets the position of the control
valve.
• When everything is functional,
PID controller compares the PV
to its SP and calculates the
difference b/w the two signals
as an Error (E). 5
Hello Class
@farhan. M Lecture: 14 PID Controller 5
Life with PID Controller
Lecture: 14 PID Controller

6. • In a PID loop, the correction that's added is calculated from the error
in three ways
• To cancel out the present error (proportional mode)
• Average out past errors (Integral mode)
• Anticipate the future a bit from the slope of the error(s) over time
(Derivative mode).
6
Hello Class
@farhan. M Lecture: 14 PID Controller 6
PID CONTROLLER BASICS
Lecture: 14 PID Controller

7. • In PID each of the three parts of the equation are given a K constant. However,
PID controllers having the Integral and Derivative constants are represented as
• Ti is defined as the time required by the integral term to generate an output
equivalent to the proportional term.
• Td is defined as the time required by the proportional term to repeat the output
provided by the derivative term. With these substitutions, our equation now
becomes:
• The proportional term (Kp), has an amplifying effect on the entire algorithm.
7
Hello Class
@farhan. M Lecture: 14 PID Controller 7
PID Equation
Lecture: 14 PID Controller

8. • Proportional: To handle the present, the error is multiplied by a negative
constant P and added to the controlled quantity.
• Note: When error is zero, proportional controller's output is zero.
• Integral: To handle the past, error is integrated (added up) over a time period,
multiplied by a negative constant I and added to the controlled quantity. I finds
output's average error from the setpoint.
• A simple proportional system oscillates around the setpoint, because there's
the error.
• By adding a negative proportion of the average error from the process input,
difference between the process output and the setpoint is reduced and the process
settle at the setpoint.
• Derivative: To handle the future, the first derivative (slope) of the error is
calculated, multiplied by negative constant D, and added to the controlled
• The larger this derivative term, more rapidly the controller responds to changes
output.
• The D term dampens a controller's response to short term changes. 8
Hello Class
@farhan. M Lecture: 14 PID Controller 8
PID Control----Terms
Lecture: 14 PID Controller

9. 9
Hello Class
@farhan. M Lecture: 14 PID Controller 9
PID PROCESS CONTROLLER
Lecture: 14 PID Controller

10. 10
Hello Class
@farhan. M Lecture: 14 PID Controller 10
PID CONTROLLER: CLOSED-LOOP MODEL
Lecture: 14 PID Controller

11. 11
Hello Class
@farhan. M Lecture: 14 PID Controller 11
PID Control Modes
Lecture: 14 PID Controller
Mode Combination Function Application
Proportional (P) To provide GAIN For small set points or small load
changes
Proportional–plus-
Integral (PI)
To eliminate OFFSETs For large and slow set points or
changes
Proportional –plus-
Derivative (PD)
To speed up the response
minimize the
For sudden set points or quick load
changes in a slow response system
Proportional –
Integral-Derivative
(PID)
To speed up the response,
minimize the
and eliminate OFFSETs
For large and sudden set points or
changes in a slow response system

12. • Use P, if system has small time constant, small disturbance
and allow steady state error (off sets).
• Use PI, if system has small time constant, small disturbance
and requires no steady state error.
• Use PD function, if system has large time constant and time
delay (speed up process response).
• Using PD if the system allows steady state error, then use PID
• Use more advanced control scheme, if system has large time
constant, large time delay and disturbance.
12
Hello Class
@farhan. M Lecture: 14 PID Controller 12
General rules of Design PID Controller
Lecture: 14 PID Controller

13. 13
Hello Class
@farhan. M Lecture: 14 PID Controller 13
Proportional Control Mode
Lecture: 14 PID Controller
“correction proportional to error”

14. • In Proportional mode, controller simply multiplies the Error by the
Proportional Gain (Kp) to get the controller output.
• Small proportional gain (Kp) is the safest way to get to setpoint, but your
controller performance will be slow.
• If the Kp is increased, Overshoot in the signal will be present.
• Proportional action is useful for improving the response of a stable system
but cannot control an unstable system by itself.
• Additionally, the gain is the same for all frequencies leaving the system
with a non-zero steady-state error.
14
Hello Class
@farhan. M Lecture: 14 PID Controller 14
Proportional Action
Lecture: 14 PID Controller

15. • The main purpose of the proportional control is
minimize the fluctuations that occur within the
system.
• A proportional constant or value as entered into
the controller will determine how large the
"proportional band" is.
• When process parameter is inside the
proportional band, controller output will vary the
amount of change required to reduce overshoot
of the SP.
• Proportional controller will also experience
"droop".
• when the process and set point values are equal,
the process will generally stabilize somewhere
below the set point.
• The amount of droop increases with larger
15
Hello Class
@farhan. M Lecture: 14 PID Controller 15
Role of proportional Controller
Lecture: 14 PID Controller

16. • Consider an example of a Proportional
controller with different Proportional
Gains.
• As the gain is increased the system time
response is faster , but system starts to
oscillates.
• Comments: Clearly, it is not possible to
achieve low steady state error and good
transient response using only proportional
control.
• As the gain is increased, the response
becomes faster, but it has a lower phase
margin.
• To remove the steady-state error and have 16
Hello Class
@farhan. M Lecture: 14 PID Controller 16
Proportional Gains
Lecture: 14 PID Controller

17. • The P-controller usually has steady-state errors unless the control gain is large.
• As the control gain becomes larger, issues arise with the stability of the feedback
loop.
• For instance, reducing the rise time implies a high proportional gain, and reducing
overshoot and oscillations implies a small proportional gain. This is not possible to
achieve in all systems.
17
Hello Class
@farhan. M Lecture: 14 PID Controller 17
Proportional Control- Limitations
Lecture: 14 PID Controller
process output of
proportional control

18. • The way to eliminate these steady-
state errors is by adding an integral
action.
• The integral term in the equation
drives the error to zero.
• Higher Integral constant (1 / Tt)
drives the error to zero sooner but
also invites oscillations and
instability.
• Watch out a sample process output
diagram when integral control is 18
Hello Class
@farhan. M Lecture: 14 PID Controller 18
Proportional control------Solution
Lecture: 14 PID Controller
Response shows the reduction of
overshoots and oscillations compared to
the picture before adding the integral
action.

19. • The use of proportional control alone has a large
drawback of offset.
• Offset is a sustained error that cannot be
eliminated by proportional control alone.
For example: let’s consider controlling the water
level in the tank with a proportional-only
controller.
• As long as the flow out of the tank remains
constant, the level will remain at its set point.
• But, if the operator should increase the flow out of
the tank, the tank level will begin to decrease due
to the imbalance between inflow and outflow.
• While the tank level decreases, the error increases
and our proportional controller increases the
controller output proportional to this error.
19
Hello Class
@farhan. M Lecture: 14 PID Controller 19
Proportional-only Controller Dilemma
Lecture: 14 PID Controller
Level control, with operator causing a disturbance

20. • Consequently, the valve controlling the flow into the tank
opens wider and more water flows into the tank.
• As the level continues to decrease, the valve continues to
open until it gets to a point where the inflow again matches
the outflow.
• At this point the tank level (and error) will remain constant.
Because the error remains constant our P-controller will keep
its output constant and the control valve will hold its position.
• The system now remains at balance, but the tank level
remains below its set point. This residual sustained error is
called Offset. 20
Hello Class
@farhan. M Lecture: 14 PID Controller 20
Proportional-only Controller Dilemma
Lecture: 14 PID Controller