1. ECE 382. Feedback Systems Analysis and Design
Instructor: Jianghai Hu
Office: MSEE 220
Tel:
Office hours: Mon 1-2pm
TA: Vineeth Ravi
Office hours: Wed 2-3:30pm, Fri 2-3pm
Grader: Gonghao Sun

2. Lec 1. Introduction and Overview
What is control?
Use of algorithms and feedback to affect the operation of physical objects of interest to achieve some desired performance
Environmental
Perturbations
Controller
Input
Physical Objects:
Plant, Process, System
output

3. Example: Thermostat
Turning on/off heater/cooler to maintain the room temperature at a pre-specified level
Similar example: Cruise control of cars (maintaining constant speed)

4. Example: Robotic Arm
Control the voltage applied on the motors so that the robot hand moves along a specified trajectory (and grasps some object)

5. Example: Process Control

6. Example: Traffic Control
Ground Traffic
Air Traffic
Air traffic controllers control traffic flows for maximum throughput and safety
Similar example: Internet congestion control

7. Example: Biological Control

8. Observations Control is everywhere
Other examples: electrical, mechanical, ecological, and financial systems
Physical processes under control can be very complicated
Often need to work in adverse situations
Environmental noises, part failure, human errors, etc

9. Two Control Methodologies
Black box approach
Learn by training
Example: adaptive neural network, fuzzy logic, expert systems
Advantage: no need for deep physical understanding
Disadvantage: hard to analyze, not good for high performance sys.
Model-based approach (this class!)
Build a math model to relate the system input and output
Advantage: easy to analyze, high performance
Disadvantage: physical models complicated, not always available

10. Open-Loop vs. Closed-Loop Control
Open-Loop Control
Controller
Input
Physical Objects
Plant, Process, System
output
Controller determines the plant input without looking at plant output
Controller
Physical Objects
Plant, Process, System
Input
output
Closed-Loop (Feedback) Control
Controller uses plant output to help determine the plant input

11. Advantages of Feedback
Robustness of performance with respect to
Model inaccuracy
External and internal disturbances
Open loop control is used only when one has accurate knowledge of system and environment behaviors.
A simple example to demonstrate the above advantages

12. Example: Cruise Control
Environmental disturbances
(road grade w)
Controller
Reference
speed r
Input
Output
(throttle
angle u)
Sensor
(speedometer)
measured
speed y’
(speed y)
Actuator (engine)
Controlled object (car)
Goal: design controller so that the actual speed y of the car is as close to the reference speed r as possible, despite variations in road grade w.

13. Environmental disturbances
Model Construction
Observation 1: speed y increases with throttle angle u
Observation 2: speed y decreases with road grade w
Model (static):
Model (dynamic):
Environmental disturbances
(road grade w)
Input
Output
(throttle
angle u)
(speed y)
Actuator (throttle)
Controlled object (car)

14. Block Diagram of Static Model
road grade w
Input
Output
(throttle
angle u)
(speed y)
Actuator (throttle)
Controlled object (car) 10
0.5 + -
Input u
Grade w
Speed y
Graphical Representation +
summation 5
multiplication

15. An Open-Loop Controller
Grade w
controller gain
0.5
0.1
reference
speed r
Controller -
Speed y
Input u 10 + +
Plant
The throttle angle u is set proportionally to the reference speed r
Question: Set r=65 mph. What is the actual speed of the car under this controller for different road grades?

16. Analysis of Open-Loop Controller
Grade w
controller gain
0.5
0.1
reference
speed r
Controller -
Speed y
Input u 10 + +
Plant
Assume r=65 mph
Road grade w
Actual speed y
Error e
Error
Percentage 65 0% 1 60 5
7.69% 2 55 10
15.38%
Actual Speed:
Tracking Error:

17. A Feedback Controller - - + +
Grade w
Feedback
controller
0.5
reference
speed r -
Speed y +
Input u + 10 10 + + -
controller gain
Plant
Use the difference between the measured speed and the reference speed to determine the throttle angle (assuming no measurement error):

18. Analysis of Feedback Controlled System10
0.5 + -
Input u
Speed y
Plant
reference
speed r
Feedback
controller
Grade w
Assume r=65 mph
Road grade w
Actual speed y
Error e
Error
Percentage
64.36
0.64
0.99% 1
64.31
0.69
1.07% 2
64.26
0.74
1.14%
Actual Speed:
Tracking Error:

19. Comparison of Open vs Closed-Loop
Open loop controller
Feedback controller w
Actual speed y
Error e
Error
Percentage 65 0% 1 60 5
7.69% 2 55 10
15.38% w
Actual speed y
Error e
Error
Percentage
64.36
0.64
0.99% 1
64.31
0.69
1.07% 2
64.26
0.74
1.14%
Open loop controller
No error on level ground
Error increases rapidly with w
Feedback controller
A small error on level ground
Reduced sensitivity to grade disturbances
Reduced sensitivity to model inaccuracy (not shown here)

20. More Discussions By increasing controller gain of feedback controller
Tracking error can be further reduced
May cause instability in general
Design problem:
how to choose the controller gain so that the error on level ground is within 0.05%?
Dynamic models?

21. Course Content System Modeling Control System Analysis
How to construct math model of a system?
Control System Analysis
How does system output change under certain inputs?
Root locus analysis
Frequency response analysis
Control System Design
How to design controller so that the system output behaves desirably?

22. Digital Control Systems
A digital control system:
D/A
Computer
D/A
Physical Objects
Plant, Process, System
Input
output
Digital Control Theory will be studied in ECE 483