1. ECE 483. Digital Control Systems Analysis and Design
Instructor: Jianghai Hu
Office: MSEE 220
Tel:
Office Hours: Tu 4:15-5:15pm
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2. Lec. 1. Control Systems Overview
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
Environmental
Perturbations
Controller
Input
Physical Objects:
Plant, Process, System
output

3. Examples of (Digital) Control Systems
Digital thermostat
Digital DC servo control
Digital Automated Flight Computer System (AFCS)

4. Continuous-Time (Analog) Control Systems
Plants and controllers are continuous-time systems
continuous-time input and output signals
modeled by differential equations, or transfer functions
𝐺(𝑠)
Block diagram of a simple analog feedback control system:
controller
plant
𝑈(𝑠) +
𝑌(𝑠)
𝑠+2 𝑠+3
1 𝑠(𝑠+1) _

5. Example: Satellite 𝑓 𝜃
gas jet
Suppose that the antenna of the satellite needs to point to the earth.
Satellite is a system with:
Input: force f generated by reaction of gas jet
Output: orientation of the satellite as given by the angle 

6. Example: Satellite 𝑇=𝐽⋅ 𝜃 𝑇=𝑓⋅𝑙 𝑓 𝑙 Newton’s Second Law:
Torque generated by the thrust f:
𝑇=𝑓⋅𝑙 𝑓
gas jet 𝑙 𝜃
Newton’s Second Law:
𝑇=𝐽⋅ 𝜃
Total torque
Moment of inertia
Angular acceleration
System model (time domain):
System model (frequency domain):
Θ(𝑠) 𝐹 𝑠 = 𝑙 𝐽 𝑠 2
𝑓 𝑡 ⋅𝑙=𝐽⋅ 𝜃 (𝑡)
Laplace transform

7. Example: DC Motor System
armature resistance
𝑅 𝑎
torque 𝑇
Basic motor properties: 𝑖 +
Generated torque proportional to current: 𝜃 + 𝑒 -
𝑒 𝑚 𝐽
𝑇= 𝐾 𝑇 ⋅𝑖 -
Motor voltage proportional to shaft angular velocity:
Friction 𝐵
𝑒 𝑚 = 𝐾 𝑏 ⋅ 𝜃
Electro-mechanical system
Input: voltage source e(t)
Output: shaft angular position 𝜃(𝑡)
Basic circuit properties (KVL):
Newton law:
𝑒 𝑡 = 𝑅 𝑎 ⋅𝑖 𝑡 + 𝑒 𝑚 (𝑡)
𝑇=𝐽 𝜃 +𝐵 𝜃

8. Example: DC Motor System
System model:

9. Digital Control Systems
A typical digital feedback control system: T
r(t)
A/D
Computer
D/A
Data
Hold
Plant
y(t)
Sampling
Sensor
Idea: computers have enormous data processing power (intelligence)
Sampling and data hold:
Needed since computer’s clock is in discrete time and plants operate in continuous time
A/D and D/A units: needed since computer can only process binary strings

10. Example: Digital Motor Control𝑇 𝑢
A/D
Digital
Controller
D/A + + - 𝑇 - 𝜃 𝑖 +
𝑒 𝑚 𝜃 𝐽 -
Sensor

11. Diagram of Digital Motor Control
Digital Controller
Motor 𝑇
𝑢(𝑡)
𝜃(𝑡)
A/D
D/A
𝑧+0.1 𝑧+0.6
𝐾 1 𝑠(𝑠+𝑎) + -
Both continuous-time and discrete-time signals present
Both Laplace transforms and Z-transform used

12. Example: Remote Antenna Control
Digital reference
input signal
Antenna
Power
Amplifier q
Motor
Receiver
Decoder
D/A
1 𝑠(𝑠+𝑎) K
wireless communication
channel
Digital
Filter
Receiver
Decoder
Encoder
Binary code

13. Other Forms of Digital Control Systems

14. Digital Control System Analysis
Plant: still modeled by a Laplace transfer function G(s)
Computer as the digital controller
Input and output are both discrete-time signals, hence a digital filter
Modeled using a linear difference (recursion) equation
Or through z-transform as a transfer function in z
So a mixture of s-transfer functions and z-transfer functions
What about the A/D, D/A, sampling, and data hold?
They cannot be modeled as transfer functions!
This is the key difficulty of analyzing digital control systems

15. Digital Controller Design
For a given system, design the digital controller for
Reduced steady-state error
Faster transient response
Disturbance rejection
Low sensitivity to modeling error
Design methods
Root locus design
Frequency response design
Direct design method

16. State-Variable Approach
Modern perspective
Systems with different internal structures may have the same TF
Internal variables are of interest as well: input/output no longer enough
Intrinsic system model
More powerful design methods
Cellular biosynthesis process
Automated flight control system

17. Summary of Course Content
Digital System Modeling
How to construct math model of a digital controller/system?
Digital Control System Analysis
What is system output under an arbitrary input?
Digital Controller Design
How to design digital controller so that the system output behaves desirably?