1. Dr. D.Y.Patil Institute of Engineering, Management and Research
Mechatronics
UNIT -VI
Mrs. Amruta Adwant

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

4. Outcomes
Identification of key elements of mechatronics system and its representation in terms of block diagram
Understanding the concept of signal processing and use of interfacing systems such as ADC, DAC, digital I/O
Interfacing of Sensors, Actuators using appropriate DAQ micro-controller
Time and Frequency domain analysis of system model (for control application)
PID control implementation on real time systems
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,
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?
-imaginary
X Undesirable Open Loop Pole Location
X Desired Closed Loop Pole Location X u
-real X
+real
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” u
Note: This is just to give an example. The undesirable open loop and the desired closed loop pole location is dependent on the application!
Question: Does the dynamics of the system remain the same? X
+imaginary

9. Analysis of Response: Transient Specifications
Performance of the un-controlled as well as the controlled system is defined in terms of the transient specifications. Thus, the specifications, which were mentioned in Unit V, are mentioned here again. In Unit VI, no numerical treatment on transient specifications is expected.
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. Block Diagram of 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

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.
Controllability is discussed for understanding purpose only. No questions will be asked on this in the End Sem Examination.
However, knowledge of controllability is important as far as control system implementation is concerned.

13. Proportional Integral Derivative Controlu + ∑
Input
PID
Plant
Output _
Block Diagram of PID Controller
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.

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.

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

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.

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.
Integral Windup is discussed for understanding purpose only. No questions will be asked on this in the End Sem Examination.
However, knowledge of Integral Windup is important as far as control system implementation is concerned.

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

25. Transfer Function of Series Form

26. Transfer Function of Series Form

27. PID: Parallel / Non-Interacting Form
Ideal Form
Derivative Action does not Interact with Integral Action

28. Transfer Function of Parallel Form

29. Parallel Form: PI Control
Proportional Integral (PI) Control helps minimise rise time, settling time as well as eliminate steady state error.

30. PI Control

31. Parallel Form: PD Control
Proportional Derivative (PD) Control helps reduce rise time, settling time as well as minimize overshoot.

32. Proportional Derivative Control

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

34. Effect of P, I & D on Transient Specifications

35. P, I & D Control Action

36. PID: Stepwise Procedure for Manual Tuning
Obtain an open-loop response and determine what needs to be improved
Add a proportional control to improve the rise time
Add a derivative control to improve the overshoot
Add an integral control to eliminate the steady-state error
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.
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.

37. PID: Stepwise Procedure for Manual Tuning
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!

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