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Linear System

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

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Linear System

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

  2. 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

  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 controlsystem? • 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. • A system is linear if and only if it satisfies • 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. 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

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