# Teaching

COURSES AND EDUCATIONAL TALKS

Xu Chen

Department of Mechanical Engineering

University of Washington

• Basics: Arithmetic of LTI systems, Goals of feedback, Loop shaping, Tradeoffs
• Fundamental limitations
– Bandwidth
– Waterbed
– Unstable zeros
– Magnitude-phase relationship
• Practical control engineering
– Sampling time
– Delays
– Time-frequency relationship

• Control engineering or control systems engineering
• Automatic Control
– Stability/Safety
– Performance
– Cost
• Importance of Control Systems
• Example of Control Systems
– HDDs
– 3D Printing
– Challenges in Sensing, Controls, and Platforms
• Powder Bed Fusion

• Basic concepts of matrices and vectors
• Linear systems of equations
• Vector space
• Matrix defines linear transformations between vector spaces
• Matrix properties
• Matrix and linear equations
• Eigenvector and eigenvalue
• Similarity transformation
• Matrix inversion
• Spectral mapping theorem
• Inner product
• Norms
• Symmetric, skew-symmetric, and orthogonal matrices
• Singular value and singular value decomposition (SVD)

• Notations
• Big picture: differential equations, applications
• Basics of ODE: order, general form, initial-value problem
• Separable ODEs
• Common differentiation and integration formulas
• Exact ODE
• First-order linear ODE
• Second-order linear ODE
• Higher-order linear ODEs

• Basic concepts of PDEs
• PDEs solvable as ODEs
• Vibrating string and wave equation
– PDE modeling
– Solution by separating variables and Fourier series
– Alternative representations
• Heat flow
– One-dimensional heat equation
• Solving 2nd-order PDEs via the method of characteristics

• Main results, linear time-invariant (LTI) transfer function
• The underlying theory
– Definitions
– Derivations

• Background
– Periodic functions
– Orthogonal decomposition
• Fourier series
– Arbitrary period
– Even and odd functions
– Application example: ODE with special inputs
• Complex Fourier series
• Fourier integral
• Fourier transform
• Discrete Fourier analysis
– Discrete Fourier series
– Discrete-time Fourier transform (DTFT)
– Discrete Fourier transform (DFT)