MAE 524 Control of Mechatronic Systems
Summer 2008
Course Description Syllabus Homework
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
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
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