MAE 524 Control of Mechatronic Systems

Summer 2008

Course Description       Syllabus       Homework

CONTROL OF DYNAMICAL SYSTEMS: AN INTRODUCTORY APPROACH

 

Contents

1. Complex Dynamics Simplified

Equations; Equilibrium; Linearization

2. Converting to the State Space

Nonlinear State Equations; Equilibrium; Linearization; The Euler Method; The Runga-Kutta Method; Computer  Programming; Stability; Vector Methods     

3. Types of Dynamical Systems, Control Problems and Control Strategies

Applications; Properties of Dynamical Systems; Control Problems; Control Strategies

4. Motion in a Stability Region (Part I)

Free Undamped Vibration; Free Damped Vibration; Free Time Response; Comparison of Limiting Cases; Constant Excitation; Harmonic Excitation

5. Motion in a Stability Region (Part II)

Fourier Series; Steady-State Response to Periodic Excitation; Complex Fourier Series; Fourier Integral (Fourier Transform); Discrete Fourier Transform; Laplace Transform               

6. Tracking the Reference Path

Constructing the Reference Path; Calculating the Tracking Force

7.  Regulating the Reference Path (Continuously-Acting Actuators)

Displacement Feedback; Velocity Feedback; State Feedback; Integral Feedback; PID Feedback; Time Delays; Summary

8.  Regulating the Reference Path (Discretely-Acting Actuators)        

Bang-Bang Feedback; Impulse Feedback

9. System Concepts

Linear Operators; Block Diagrams; Separation Principle for Tracking and Regulation; Transfer Functions

10. Treating Multi-Dimensional Systems

Equations; The Eigenvalue Problem; Properties of the Eigenvalue Problem; Modal Equations of Motion; The Double Pendulum; Actuator Dynamics

11. Regulating Multi-Dimensional Systems

PID Regulation of Modes; Physical Forces; Regulating Settling Time; Regulating Settling Time and Peak-Overshoot; Regulating Settling Time, Peak-Overshoot and Steady-State Error; Full Regulation of a Double Pendulum; Non-Full Regulation

12. Regulating Steady-State Behavior

The Single Degree-of-Freedom System; The Two Degree-of-Freedom System; The Tuned Absorber

13. Sensitivity Analyses

Perturbation Analysis; Root-Locus

14. Linear Algebraic Equations

How to Minimize a Function of Several Variables; Matrix-Vector Notation; Types of Linear Algebraic Equations; Under-Determined Systems (Minimum-Norm Solutions); Uniquely Determined Systems (Unique Solutions); Over-Determined Systems (Least Squares Solutions); Weighting; Singular Value Decomposition

15. State Estimation

The Configuration Space; The State Space; Two Degree-of-Freedom Systems