Introduction_to_PID_control_basics .pptx

1. Mechatronics – 302050
Lecture Notes / PPT
UNIT VI

2. Syllabus
Control Systems
 P, I and D control actions,
 P, PI, PD and PID control systems,
 Transient response:- Percentage overshoot, Rise time, Delay
time, Steady state error
 PID tuning (manual)

3. Objectives
1. Understand key elements of Mechatronics system,
representation into block diagram
2. Understand concept of transfer function, reduction and analysis
3. Understand principles of sensors, its characteristics, interfacing
with DAQ microcontroller
4. Understand the concept of PLC system and its ladder
programming, and significance of PLC systems
5. in industrial application
6. Understand the system modeling and analysis in time domain
and frequency domain.
7. Understand control actions such as Proportional, derivative
and integral and study its significance in industrial
applications.

4. Outcomes
1. Identification of key elements of mechatronics system and its
representation in terms of block diagram
2. Understanding the concept of signal processing and use of
interfacing systems such as ADC, DAC, digital I/O
3. Interfacing of Sensors, Actuators using appropriate DAQ
micro-controller
4. Time and Frequency domain analysis of system model (for
control application)
5. PID control implementation on real time systems
6. Development of PLC ladder programming and implementation
of real life system

5. Assumed Knowledge
Dynamics:
 Engineering Mechanics
Electrical & Electronics
 Elements of Electrical Engineering
Mathematics
 Engineering Mathematics (I, II & III)

6. Reference Books
 Astrom & Hagglund, PID Controllers: Theory, Design &
Tuning, Chapter 2, 2nd Ed, Instrument Society of America,
1995.
 Golnaraghi & Kuo, Automatic Control System, Chapter 1/5/9,
9th Ed, John Wiley & Sons, 2009

7. Why is Controller Necessary?
 Blue response resembles an un-controlled system. This response is
oscillatory as well as it takes much longer to settle down.
 For a mechanical system, this could be due to Inertia effect,
friction, backlash etc
 The red response is of a controlled system. This response contains no
oscillations and it settles to equilibrium / steady state in lesser time.
 Job of a control system is to “generate a control input / effort that can
be used to drive the un-controlled system, albeit externally, to achieve
the desired performance”.

8. Illustration: What does Controller do?
-real +real
+imaginary
-imaginary
X
X
X Undesirable Open Loop Pole Location
X Desired Closed Loop Pole Location
X
u
u
Control is all about shifting of system
poles from un-desirable to desirable
location.
This shifting is done by the control
signal, u, provided the system allows it
i.e. the system is “controllable”

9. Analysis of Response: Transient Specifications
Unit Step Response of Second Order System

10. Transient Response Specifications
 Percentage Overshoot (% O.S): It is the amount that the
response overshoots the steady state, or final, value at the peak
time, expressed as a percentage of the steady-state value.
 Rise Time (Tr): Time required for the step response to rise from
10% to 90% of its final value.
 Delay Time (Td): Time required for the step response to reach
50% of final value
 Settling Time (Ts): Time required for the step response to
decrease and stay within ±2% of its final value
 Steady State Error (ess): It is the difference between the output
and the reference input after the steady state has reached

11. Feedback Controller
 Feedback controller generates an control signal / effort / external
disturbance based on the input signal it receives.
 The input signal is error; difference between measured value and
desired value, or set point.
 Feedback counters disturbance as well as variation in process
Block Diagram of Feedback Controller

12. Controllability
Advanced Learning (Out of Syllabus)
 Before a controller is implemented it is necessary to determine
is the system is controllable
 Test the “Controllability” of the system
 Controllability is the ability of the system to be controlled
provided an external disturbance is available.

13. Proportional Integral Derivative Control
 PID stands for Proportional Integral Derivative Control.
 Being robust & easy to implement, it is one of the most widely used
closed loop control for precise operation of industrial applications and
processes.
Input PID Plant Output
∑
+
_
e u
Block Diagram of PID Controller

14. Proportional Control
 In Proportional Control, the control signal, u, is directly
proportional to the error, e.
 As the gain is increased the system responds faster to changes in
set-point but becomes progressively under damped and eventually
unstable.
    Offset


 e
K
t
u
t
u P
P

15. Proportional Control Action
P Control Signal

16. Proportional Control
Advantages:
 Simple and easy to design and tune
 Rapid Response / Reduces Rise Time
 Reduces Steady State Error
Disadvantages:
 Not possible to eliminate Steady State Error / Offset
 Could lead to instability / rise in overshoot/ oscillations
Applications:
 Float Valve, Thermostat etc

17. Derivative Control
 Derivative control produces a control signal proportional to the
rate at which the error is changing.
 Also known as rate controller.
 While sudden/rapid change in error leads to a control signal of
larger magnitude, gradual change leads to small magnitude.
 Even if the error is huge, the derivative control will generate no
signal if the error is constant
 Thus, not used alone; used with P control
     
dt
de
K
t
u
t
u D
D 


18. Derivative Control Action
D Control Signal

19. Derivative Control
Advantages:
 Reduces Settling time; Adds lead
 Reduces Overshoot; Adds more stability
Disadvantages:
 Not possible to eliminate Steady State Error / Offset
 Not possible to use alone
 Excessive use may make the system slow
 Amplifies Noise
Applications:
 In conjunction with P Control

20. Integral Control
 Rate of change of integral control signal is proportional to
error.
 Control signal proportional to integral of error.
 When the error is zero, the control signal is a constant value.
 When the error is constant, the control signal varies at constant
rate.
    

 edt
K
t
u
t
u I
I

21. Integral Control Action
I Control Signal

22. Integral Control
Advantages:
 Eliminates steady state error/offset
 Decreases Rise Time
Disadvantages:
 Causes Integral Wind Up
 Leads to minor increase in overshoot
 Could make the system less stable
 Increases Settling time
Applications:
 In conjunction with P Control

23. Integral Wind Up
Advanced Learning (Out of Syllabus)
 Caused by actuator saturation.
What Happens?
 Feedback loop is broken and the system runs in open loop because the
actuator remains saturated.
 While the error is zero, the integral term will keep building and become very
large over a period of time. This in turn would lead to saturation of control
signal.
 The condition will prevail even when the error changes and it may take a long
time before the integrator and the controller output comes inside the
saturation range.
 The consequence is that there are large time delay.

24. PID: Parallel / Non-Interacting Form
 Ideal Form
 Derivative Action does not Interact with Integral Action
ysp y
plant


-
Kp
e
+
+
+
u
+
ud
ui
up
Ki
Kp
Kds
s

25. Transfer Function of Parallel Form
 
       
 
signal
measured
&
reference
between
Difference
Error
Where,
:
Signal
Control
Gain
Derivative
Gain
Integral
Gain,
al
Proportion
Where,
:
Function
Transer















e
dt
de
K
edt
K
e
K
t
u
t
u
t
u
t
u
K
K
K
s
K
s
K
K
s
H
D
I
P
D
I
P
D
I
P
D
I
P

26. Parallel Form: PI Control
 Proportional Integral (PI) Control helps minimise rise time,
settling time as well as eliminate steady state error.
 
      








edt
K
e
K
t
u
t
u
t
u
K
K
s
K
K
s
H
I
P
I
P
I
P
I
P
Gain
Integral
Gain,
al
Proportion
Where,

27. PI Control

28. Parallel Form: PD Control
 Proportional Derivative (PD) Control helps reduce rise time,
settling time as well as minimize overshoot.
 
       
dt
de
K
e
K
t
u
t
u
t
u
K
K
s
K
K
s
H
D
P
D
P
D
P
D
P
Gain
Derivative
Gain,
al
Proportion
Where,









29. Proportional Derivative Control

30. Response of P, I & D w.r.t Error

31. Action Rise
Time
Overshoot Settling
Time
SS
Error
KP Decrease Increase Small
Change
Decrease
KI Decrease Increase Initially
Decrease then
Increase
Eliminate
KD Small
Change
Decrease Decrease Small
Change
Effect of P, I & D on Transient Specifications

32. P, I & D Control Action

33. 1. Obtain an open-loop response and determine what needs to be
improved
2. Add a proportional control to improve the rise time
3. Add a derivative control to improve the overshoot
4. Add an integral control to eliminate the steady-state error
5. Adjust each of P, I & D until you obtain a desired overall
response referring to the table shown previously to find out
which controller controls what characteristics.
6. It is not necessary to implement all three controllers (P, I & D)
into a single system. For example, if a PI controller gives a good
enough response, then you don't need to add D control to the
system. Simple is better.
PID: Stepwise Procedure for Manual Tuning

34. PID: Series / Interacting Form
 Derivate Action interacts with Integral Action
 Modification in derivative time constant affects integral action
 Commercially used controller
P
D I
e u
+
+
+
+

35. Transfer Function of Series Form
  
PD
PI
P
TF
Constant
Time
Derivative
Constant,
Time
Integral
where,
4
since
0
PID
term
The
PID
PI
PD
P
TF
Controller
Derivative
D
Controller
Integral
I
,
Controller
al
Proportion
P
where,
I
1
PD
P
:
series
in
PID
of
Function
Transer

















d
i
d
i
T
T
T
T

36. Transfer Function of Series Form
           
 
signal
measured
&
reference
between
Difference
Error
Where,
:
series
in
PID
for
Signal
Control









e
dt
de
K
K
edt
K
K
e
K
t
u
t
u
t
u
t
u
t
u
t
u
D
P
I
P
P
D
P
I
P
P

37. NOTE
It is not necessary to implement all three controllers (P, I & D)
into a single system.
For example, if a PI controller gives a good enough response,
then you don't need to add D control to the system. Simple is
better!
PID: Stepwise Procedure for Manual Tuning

38. 90% processes are controlled using PID.
1. Regulation of Processes in Industry; for e.g.
1. Flow
2. Temperature
3. Pressure etc
2. Servo / DC motor Control
3. Linear Position Control
Applications of PID Control