1 Feedback Control

Activities for Introduction to Applied Digital Controls

Chapter 1. Introduction to Digital Controls

• 1.1 Feedback Response
  Compares the response of a system with feedback and without feedback

Chapter 2. Linear Discrete Systems and the Z-Transform

• 2.4 Pole Locations and Responses
  Shows the initial value response for first and second order systems based on the pole/zero locations in the z-plane
• 2.6 Frequency Response of Discrete Systems
  Shows the amplitude and phase response of a discrete system. The activity graphs the ouput of a discrete transfer function with varying pole locations when the input is a sinusoidal of varying frequencies.

Chapter 3. Discrete Simulation of Continuous Systems

• 3.2 Comparison of left-half s-Plane with the z-Plane
  Compares the left-half of the s-plane with corresponding regions in the z-plane for forward, backward, and trapezoidal mappings.
• 3.6 Direct and Cannonical Realization of Difference Equations
  Simulates a program written in C that implements a transfer function using either direct or a cannonical realization.

Chapter 4. Sampled Data Systems

• 4.3 Aliasing
  Shows a plot a signal with varying frequencies and the corresponding aliased signal.
• 4.4 Frequency Spectra and Fourier Series
  Shows a plot the a square wave and its corresponding frequency spectrum. The activity show the effects of changing the sampling time and number of samples on the time domain signal, including aliasing.
• 4.4 Frequency Analyzer Simulation
  Simulates the frequency analyzer lab experiment described in the textbook.

Chapter 5. Design Using Transform Methods

• 5.2.1 Steady-State Accuracy
  Compares the response of Type 0, Type 1 and Type 2 systems for step, ramp and parabolic inputs.
• 5.2.2 Transient Response
  Plots a second order response and shows the effects of changing ζ and ω_n on the time domain response.
• 5.2.2 Design Parameters in the z-Plane
  Compares lines of constant damping, natural frequency and settling time in the s-plane to those in the z-plane.
• 5.4 Direct Design in the z-Plane
  Illustrates the process of designing a controller for the antenna problem in chapter 5. The activity lets the user change design values and see corresponding changes in system performance.

Chapter 7. Digital Controller Design using State Space Methods

• 7.4 Pole Placement Example
  Illustrates design process using pole placement. The activity lets the user change design values and see corresponding changes in system performance.
• 7.6 Control Law and Estimator Design
  Illustrates the design process using an estimator and controller. The activity lets the user change design values and see corresponding changes in system performance - includes MATLAB commands and results for different design parameters.
• 7.10 Stick Balancer—Design Example
  Illustrates the process for designing an estimator and controller for the stick balancer problem in the textbook. The activity lets the user change design values and see corresponding changes in system performance.

Chapter 8. System Identification

• 8.5.3 Identification Example
  Illustrates the process of using least-squares for system identification. The activity shows the affect of changing quantization error and the number of data points used for identification.

Appendix

• System Identification Project Data
  Data and video for the system identification project in Appendix B and C.

Extras

• MATLAB Quick Reference
  Provides a quick reference for MATLAB commands used in the textbook.