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 convolution with continuous signals. Look at it so you understand what is happening with the mechanics of 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: $x(t)*h(t)=\int _{-\infty }^{\infty }x(t_{0})h(t-t_{0})dt_{0}$. The first animation shows this happening with sampled waveforms: $x_{s}(t)=x(t)\sum _{n=0}^{\infty }\delta (t-nT)=\sum _{n=0}^{\infty }x(nT)\delta (t-nT)$ and $h_{s}(t)=h(t)\sum _{n=0}^{\infty }\delta (t-nT)=\sum _{n=0}^{\infty }h(nT)\delta (t-nT)$.
    • Discrete convolution animations
      • Here is an animation of discrete convolution to illustrate the above equations.
      • This one lets you try several functions.
      • This one shows what happens if your signals happen prior to time zero.
  • Notice that this is really the same as Polynomial Multiplication.

Discretization

• This is how the c2d zero order hold works in MATLAB/octave. It uses the "exact" solution to the discretization problem.
• Also check Chapter 7.3 of Greg Starr's book.