1. Office Room: H116 Lab. : H830-1 Telephone: 4100
Linear System
by C.J.Lin
Office Room: H116
Lab. : H830-1
Telephone: 4100

2. Textbook: Linear system theory, Linear system, 1980
Ferenc Szidarovszky and A. Terry Bahill
Reference books:
Linear system theory and design,
Chi-Tsong Chen
Linear system, 1980
Thomas Kailath

3. Scoring Criterion 20% : Homework 30% : Middle Test 30% : Final Test
20% : Final Oral Report

4. Outline Mathematical Background
Mathematical Description of Dynamic System
Characterization of systems
Stability analysis
Controllability
Observability
Canonical forms
Realization
Estimation and design

5. Chapter 0. Introduction What is a system? What is a control system?
What is input and output of a control system?
What are the basic components of a control system?
Types of control system?
What is a Linear System?
How to describe a linear system?

6. General system
A system is a collection of components which interact with each other and with the environment (by information or energy links) from which the system is separated by a notational boundary.

7. Control System
A control system is a system capable of monitoring and regulating the operation of a process or a plant. The study of control system is essentially a study of an important aspect of systems engineering and its applications.

8. Process: the device, plant, or system under control.
Sensor: a device to measure signal of interest
Actuator: a device to amplify the control signal and to drive the plant.

9. Open-loop control
An open-loop control is applied to achieve desired system response using a controller or an actuator without feedback.
Closed-loop/feedback control
A closed-loop control is used to achieve desired system response using a controller with the output measurement as a feedback signal. The use of feedback enables us to improve system performance at the cost of introducing the measurement noise and stability problem.

10. Linear System A system is linear if and only if it satisfies
the principle of superposition.
the principle of homogeneity
the principle of additivity.

11. The methods to describe a system
The Nth-order differential equation model
Signal-Flow graph / Block diagram
Transfer Function ( by Laplace Transform)
The unit impulse response
The State-space Model

12. Differential Equations
Signal flowgraph/
Block diagram
Differential Equations
State Equations
Impulse response
Transfer function
Frequency response

13. Control system design
Engineering design is the main task of the engineer.
Specifications
The closed-loop control system performance specifications include:
1) good regulation against disturbance,
2) desirable responses to commands,
3) realistic actuator signal,
4) low sensitivity, and
5) robustness
The design is to achieve appropriate design specifications and rests on
four characteristics: complexity, tradeoffs, gaps and risk.

14. Design process