1. Feedback Control System
Dr.-Ing. Erwin Sitompul

2. Textbook and Syllabus Textbook: Syllabus:
Gene F. Franklin, J. David Powell, Abbas Emami-Naeini, “Feedback Control of Dynamic Systems”, 6th Edition, Pearson International Edition.
Syllabus:
Introduction
Dynamic Models
Dynamic Response
A First Analysis of Feedback
The Root-Locus Design Method
The Frequency-Response Design Method
IDR 192,000
USD

3. Grade Policy
Final Grade = 10% Homework + 20% Quizzes % Midterm Exam + 40% Final Exam Extra Points
Homeworks will be given in fairly regular basis. The average of homework grades contributes 10% of final grade.
Homeworks are to be written on A4 papers, otherwise they will not be graded.
Homeworks must be submitted on time. If you submit late,
< 10 min.  No penalty
10 – 60 min.  –20 points
> 60 min.  –40 points
There will be 3 quizzes. Only the best 2 will be counted. The average of quiz grades contributes 20% of final grade.

4. Grade Policy
Midterm and final exam schedule will be announced in time.
Make up of quizzes and exams will be held one week after the schedule of the respective quizzes and exams, at the latest.
The score of a make up quiz or exam can be multiplied by 0.9 (the maximum score for a make up is 90).
Extra points will be given every time you solve a problem in front of the class. You will earn 1 or 2 points.

5. Feedback Control System
Chapter 1
INTRODUCTION
Feedback Control System
Dr.-Ing. Erwin Sitompul

6. Introduction
Control is a series of actions directed for making a system variable adheres to a reference value (can be either constant or variable).
The reference value when performing control is the desired output variable.
Process, as it is used and understood by control engineers, means the component to be controlled.
Fundamental structures of control are classified based on the information used along the control process:
Open-loop control / Feedforward control
Closed-loop control / Feedback control

7. Process Reference Disturbance Measurement noise Performance Input

8. Open-loop vs. Feedback Control
The difference:
In open-loop control, the system does not measure the actual output and there is no correction to make the actual output to be conformed with the reference value.
In feedback control, the system includes a sensor to measure the actual output and uses its feedback to influence the control process.

9. Examples Open-loop control Feedback control
Example: an electric toaster, a standard gas stove.
Example: automated filling up system, magic jar, etc.
The controller is constructed based on knowledge or experience.
The process output is not used in control computation.
The output is fed back for control computation.

10. Plus-Minus of Open-loop Control
Generally simpler than closed-loop control
Does not require sensor to measure the output
Does not, of itself, introduce stability problem
Has lower performance to match the desired output compared to closed-loop control

11. Plus-Minus of Feedback Control
More complex than open-loop control
May have steady-state error
Depends on the accuracy of the sensor
May have stability problem
Process controlled by well designed feedback control can respond to unforeseen events, such as: disturbance, change of process due to aging, wear, etc.
Eliminates the need of human to adjust the control variable  reduce human workload
Gives much better performance than what is possibly given by open loop control: ability to meet transient response objectives and steady-state error objectives

12. Feedback Control System
Chapter 2
DYNAMIC MODELS
Feedback Control System
Dr.-Ing. Erwin Sitompul

13. Dynamic Models A Simple System: Cruise Control Model u x (Position)
Write the equations of motion for the speed and forward motion of the car shown below, assuming that the engine imparts a force u, and results the car velocity v, as shown.
Using the Laplace transform, find the transfer function between the input u and the output v. u
(Force)
x (Position)
v (Velocity)

14. Dynamic Models
Applying the Newton’s Law for translational motion yields:
MATLAB (Matrix Laboratory) is the standard software used in control engineering:
In the end of this course, you are expected to be able to know how to use MATLAB for basic applications.

15. Dynamic Models With the parameters:
Response of the car velocity v to a step-shaped force u:
In MATLAB windows:

16. Dynamic Models A Two-Mass System: Suspension Model
m1 : mass of the wheel
m2 : mass of the car
x,y : displacements from equilibrium
r : distance to road surface
Equation for m1:
Equation for m2:
Rearranging:

17. Dynamic Models Using the Laplace transform:
to transfer from time domain to frequency domain yields:

18. Dynamic Models
Eliminating X(s) yields a transfer function:

19. Dynamic Models
Bridged Tee Circuit v1
Resistor
Inductor
Capacitor

20. Dynamic Models
RL Circuit v1
Further calculation and eliminating V1,

21. Feedback Control System
Chapter 3
DYNAMIC RESPONSE
Feedback Control System
Dr.-Ing. Erwin Sitompul

22. Review of Laplace Transform
Time domain
Frequency domain
Problem
difficult operations
easy operations
Solution

23. Properties of Laplace Transform
1. Superposition
2. Time delay
3. Time scaling
4. Shift in Frequency
5. Differentiation in Time

24. Properties of Laplace Transform
6. Integration in Time
7. Differentiation in Frequency
8. Convolution

25. Table of Laplace Transform
unit impulse
unit step
unit ramp

26. Laplace Transform
Example:
Obtain the Laplace transform of

27. Laplace Transform Example:
Find the Laplace transform of the function shown below.

28. Inverse Laplace Transform
The steps are:
Decompose F(s) into simple terms using partial-fraction expansion.
Find the inverse of each term by using the table of Laplace transform.
Example:
Find y(t) for

29. Inverse Laplace Transform
Comparing the coefficients

30. Initial and Final Value Theorem
Only applicable to stable system, i.e. a system with convergent step response
Example:
Find the final value of the system corresponding to

31. Initial and Final Value Theorem
Example:
Find the final value of the system corresponding to
WRONG
Since
NOT convergent
NO limit value

32. Initial and Final Value Theorem
Example:
Find the final value of
WRONG
Since
periodic signal
NOT convergent
NO limit value

33. Homework 1
2.6
3.4 (b)
3.5 (c)
3.6 (e)
Deadline: , 7:30 am.