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16.30

Feedback Control Systems

4-1-7 units · Undergraduate

Studies state-space representation of dynamic systems, including model realizations, controllability, and observability. Introduces the state-space approach to multi-input-multi-output control system analysis and synthesis, including full state feedback using pole placement, linear quadratic regulator, stochastic state estimation, and the design of dynamic control laws. Also covers performance limitations and robustness. Extensive use of computer-aided control design tools. Applications to various aerospace systems, including navigation, guidance, and control of vehicles. Laboratory exercises utilize a palm-size drone. Students taking graduate version complete additional assignments.

Fall 2010

Topics

  • Introduction
  • Basic root locus: analysis and examples
  • Frequency response methods
  • Control design using Bode plots
  • Introduction to state-space models
  • Developing state-space models based on transfer functions
  • State-space models: basic properties
  • System zeros and transfer function matrices
  • Midterm 1
  • State-space model features
  • Controllability
  • Full-state feedback control
  • Pole placement approach
  • LQ servo introduction
  • Open-loop and closed-loop estimators
  • Combined estimators and regulators
  • Adding reference inputs
  • LQ servo: improving transient performance
  • Midterm 2
  • Deterministic linear quadratic regulator (LQR)
  • Linear quadratic Gaussian (LQG)
  • Digital control basics
  • Systems with nonlinear functions
  • Analysis of nonlinear systems
  • Anti-windup
  • Closed-loop system analysis

Readings

Spring 2004 · Estimation and Control of Aerospace Systems

Topics

  • Introduction
  • Frequency Response Bode Plot Rules
  • Frequency Response (cont.) Gain / Phase Margins
  • Bode Plot Exercises
  • Bode Plots for Unstable Open - Loop Systems
  • Root - Locus Review
  • Root - Locus Examples
  • Compensation Design Principles
  • Compensation Design Principles (cont.)
  • Proportional Control
  • Lag and PID Compensation
  • Lead and PID Compensation
  • Examples
  • High Frequency Roll-off Notch and Plant Inversion
  • Design Example Lead-Lag Compensation
  • Examples (cont.)
  • More Examples
  • Control of Unstable Plants
  • Control of Unstable Plants (cont.)
  • Models of Nonlinearities
  • Common Effects of Nonlinearities
  • Prof. David Trumper’s Lecture
  • Describing Functions Introduction and Motivation
  • Describing Function Analysis
  • Computing DFs
  • DF Analysis: Example 1, Stability of Boat Autopiloot
  • DF Analysis: Example 1 (cont.)
  • DF Analysis: Limit Cycling
  • DF Analysis: Jump Resonance
  • DF-based Compensation Design
  • DF-based Compensation Design (cont.)
  • Phase-Plane Analysis Introduction and Motivation
  • Phase Plane Drawing Rules
  • Phase - Plane Example I Carry-on Suitcase
  • Phase - Plane Example II Satellite System
  • Phase - Plane Example III Satellite System
  • Phase - Plane and Parameter Dependence of System Dynamics
  • Phase - Plane and Parameter Dependence of System Dynamics (cont.)

Readings

Prerequisites & course information

Subject meets with 16.31 Prereq: 16.06 or permission of instructor U (Fall) 4-1-7 units

Sources