25792: Modern Control
Course Name: Modern Control
Course Number: 25792
Prerequisite(s): 25411 (Linear Control Systems) and 25871 (Linear Algebra) or 25872 (Mathematical Methods in Engineering)
Co-requisite(s): -
Units: 3
Level: Undergraduate
Last Revision: Spring 2015

Description: 
In this course, we will review fundamental concepts and then delve into solving state equations for linear systems. We’ll study the structural properties of linear systems, explore concepts of controllability and observability, and define stability.
 
Syllabus:
  • Introduction and General Definitions:
    • Overview of vector spaces, representation, and essential properties of linear transformations
    • Study of inner product structures in linear spaces, results related to their existence, and transformations
    • Investigation of normed spaces
  • System Properties and State-Space Representation:
    • Review of system properties (linearity, time-invariance, causality, etc.)
    • Mathematical description of dynamic systems using Lagrange and Hamilton equations
    • Utilization of simulation plots for describing state-space in time-invariant linear systems
    • Various canonical forms
  • Solving State Equations:
    • Solution methods for time-varying and time-invariant linear systems
    • Calculation of state transition matrices and their properties
    • Modal decomposition
    • Input-output description using Markov parameters
    • Systems affected by coordinate changes
    • Companion matrices and alternate representations
  • Structural Properties of Linear Systems:
    • Study of time-varying and time-invariant linear systems in ballistic and servo control
    • Concepts of reachability (controllability from the origin) and controllability (controllability to the origin)
    • Observability and reconstruction of states from output measurements
    • Investigation of accessible, observable, and standard control/observable subspaces
    • Kalman and Ho canonical forms
  • Controllability and Stability:
    • Controllability as a structural property in proving the pole-placement theorem
    • Feedback-based state and output control for single-input systems
    • Effects of state and output feedback on system properties
    • Stability concepts and Lyapunov stability
  • Observer Design:
    • Types of state observers (full-order and reduced-order)
    • Design of state observers for time-varying and time-invariant linear systems
    • Invariant observers and separation principle
  • Stability Concepts:
    • Stability in time-varying and time-invariant linear systems
    • Zero-input and nonzero-input stability
    • Lyapunov stability

References:
  • C. T. Chen, Linear System Theory and Design, HRW, 1984
  • T. Kailath, Linear Systems, Prentice Hall, 1980
  • Z. A. Zadeh, and C. A. Desoer, Linear System Theory, McGraw Hill, 1963

 
Last Update: 2024-07-10