Linear System

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Linear System
by C.J.Lin

• Office Room H116
• Lab. H830-1
• Telephone 4100

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

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Scoring Criterion

• 20 Homework
• 30 Middle Test
• 30 Final Test
• 20 Final Oral Report

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Outline

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

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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?

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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.

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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.
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• 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.

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• 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.

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Linear System

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

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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

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

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Design process