Digital Control Systems

Links

• Textbooks
  • Introduction to Applied Digital Control, Greg Starr, University of New Mexico
    • Greg's ME481/ME581 web pages contain solutions to the book problems and other things.
  • Optimal Sampled-Data Control Systems, Chen & Francis
  • Digital Control System Analysis and Design, 3rd Ed., Philips
  • Control Systems and Control Engineering

MATLAB/Octave

• Octave Control Systems Toolbox This is not the same thing that is on Octave Forge here.

Z Transforms

• Relationship between the Laplace and Z transforms
• Convolution and Z Transforms
  • Z Transforms and Convolution
  • Here is an animation of discrete convolution. To convolve $x(t)$ with $h(t)$, you flip shift $h(t)$ into $h(t-t_0)$ on the $t_0$ axis, then you multiply it by $x(t_0)$ to get $x(t_0)h(t-t_0)$, then you integrate with respect to $t_0$, so that the convolution is: $x(t)*h(t)=\underset{-\mathrm{\infty }}{\overset{\mathrm{\infty }}{\int }}x(t_0)h(t-t_0)d{t}_0$. The animation shows this happening with sampled waveforms: $x_s(t)=x(t)\sum _{n=0}^{\mathrm{\infty }}\delta (t-nT)=\sum _{n=0}^{\mathrm{\infty }}x(nT)\delta (t-nT)$ and $h_s(t)=h(t)\sum _{n=0}^{\mathrm{\infty }}\delta (t-nT)=\sum _{n=0}^{\mathrm{\infty }}h(nT)\delta (t-nT)$.
    • More discrete convolution animations
      • This one lets you try several functions.
      • This one shows what happens if your signals happen prior to time zero.
  • Notice that this becomes the same as Polynomial Multiplication.