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ECE 483. Digital Control Systems
Analysis and Design
Instructor: Jianghai Hu
Course Administration
- Textbooks
- Digital Control System Analysis and Design, C. L. Phillips and H. T. Nagle, 3rd edition, ISBN 0-13-309832-X
- Prerequisite
- Homework
- Exams
- Two midterms and one final exam
- Grading policy
- Homework: 15%
- Two midterms: 45%
- Final: 39.5%
- Completing course evaluation: 0.5%
- Course website
dynamo.ecn.purdue.edu/~jianghai/ECE
Lec 1. Control Systems
• Reading: Chapter 1
• What is control?
- Use of algorithms and feedback to affect the operation
of physical objects of interest (systems) to achieve
some desired performance
Physical Objects: Plant, Process, System
Input output
Example: Room Temperature Control
Turning on/off heater/cooler to maintain the room temperature at a pre-specified level
Similar examples: Cruise control of cars (maintaining constant speed)
Some Observations
- Control is everywhere
- Other examples: electrical, mechanical, ecological, and financial systems
- Physical process under control can be very complicated
- Air traffic control example
- Bioengineering example
- Often need to work in adverse situations
- Environmental noises
- Part failure
- Human errors, etc
Two Perspectives of Systems
- Black box
- Learn by training
- Example: adaptive neural network, fuzzy logic, expert systems
- Advantage: no need of physical understanding
- Disadvantage: hard to analyze, not suitable for high performance sys.
- Model-based (this course)
- Build a math model to relate the system input and output
- Advantage: easy to analyze, high performance
- Disadvantage: physical models not always available
Example: Satellite
Suppose that the antennas of the satellite need to point to the earth. Thus the satellite can only rotate around a particular axis
(courtesy of Lawrence Berkeley National Laboratory)
gas jet
Output: orientation of the satellite is given by the angle θ
Input: A force F can be generated by reaction jet, which is controllable
Satellite is a system
Satellite System Model
Total torque (^) Moment of interia
Angular acceleration
Newton’s Second Law:
Take Laplace transform (assuming
Torque generated by the thrust F: zero initial condition)
gas jet
System model (time domain):
System model (frequency domain): i.e., transfer function:
Task of Control
- For a given system, adjust the input signal in a
proper manner to achieve, e.g.,
- Reduced steady-state error
- Faster transient response
- Disturbance rejection
- Low sensitivity to model error
Open Loop vs. Closed Loop Control
Controller Physical Objects Plant, Process, System
Input output
Open Loop Control
Controller Physical Objects Plant, Process, System
Input output
Closed Loop (Feedback) Control
Using output to help determine the controlled input (emphasis of this course)
Controller determines the controlled input directly (in a pre-programmed way)
Control = Sensing + Computation + Actuation
Sensing (speedometer)
Actuate (gas pedal)
Computation (human controller)
We will focus on computation part. Sensing and Actuation parts will be covered by other courses
process
Modern Digital Control Systems
- The signal that the digital controller bases its decision on is sampled at discrete time
- The command the digital controller sends to actuators is also discrete time
Actuators System Sensors
D/A Computer A/D
noises (^) noises
Digital controller
y(t)
y(kT ) u(kT )
Data hold
u ¯(t)
k = 0, 1 ,... k = 0, 1 ,...
