CDS 101: Principles of Feedback and Control Lecture 2.1: System Modeling 7 October 2002

Lecture

This lecture provides an overview of modeling for control systems. We discuss what a model is and what types of questions it can be used to answer. The concepts of state, dynamics, inputs and outputs are described, including running examples to demonstrate the concepts. Several different modeling techniques are summarized: finite state automata, difference equations, differential equations, and Markov chains. Two examples are included to demonstrate the main concepts.

• Lecture Presentation

Mud card responses [advanced search]:

• What does ode45 do?
• How do we learn how to translate MATLAB equations into the Simulink diagrams?
• What is a stochastic system?
• What is a state? How does one determine what is a state and what is not?
• Can we get a more solid description of what it means for a system to be robust?
• Why is the parameter "a" in the predator-prey problem used as both death of rabbit and birth of foxes?
• On slide 17, does 'omega' describe the driving frequency?
• Problem set #1 has taken a long time and problem set #2 looks longer. Can you shorten the problem sets?
• Why is the slope of the hill an input, not a parameter? (Isn't it constant?)
• Doesn't GM test their tractor-trailers going uphill with loads before selling them? Why didn't the R&D lab catch this before putting the truck on the market?

Reading Material and Handouts

Handouts from lecture

• Lecture handout
• Homework #2

Required reading

• K. J. Astrom, Control Systems Design, Sections 3.1-3.2, 3.6
  

Supplemental reading

• K. J. Astrom, Control Systems Design, Section 3.3

Homework Set #2

This homework set demonstrates the construction and use of models for control systems. The first problem asks the student to identify the states, inputs, outputs, and dynamics for some sample systems. The second problem consists of a detailed construction of a vehicle model that can be used for cruise control. The last three problems (CDS 110 only) explore different modeling techniques, including both symbolic and MATLAB-based analysis.

• Homework Assignment [pdf]
• SIMULINK cruise control module (for problem #2): hw1cruise.mdl, documentation
• Detailed directions for problem #3 (traffic controller)

Modifications to the homework (link above is always the latest version):

• 13 Oct 02
  • Made changes announced in class on 10/9: set m1 = m2 in problem 6 and use m1=m2=250, k=50, b=10.
• 8 Oct 02:
  • Changed description for problem #2 (clarified terms, notation)
  • Posted detailed directions for problem #3
• 7 Oct 02: handed out in class

Frequently asked questions on homework and TA hints:

• Some of the questions on homework #2 required lecture #3.1 to solve. Why did you do this?