CDS 101/110 - System Modeling
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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, with emphasis on differential equations. Two examples are included to demonstrate the main concepts.
This lecture provides a more detailed introduction to the use of ordinary differential equations (ODEs) for modeling dynamical systems. A brief review of the solutions of second order linear ODEs is provided to make connection with prior coursework. The general form of nonlinear and linear ODEs is provided, along with an overview of some of the techniques for solving linear ODEs in special forms (scalar and diagonal systems). Analysis tools, including stability and frequency response, are illustrated. Finally, the use of block diagrams in control systems is introduced, including the standard symbology used in the text and an extended example (insect flight).
Friday: Review of Linear Algebra and ODE - Mary Dunlop (Lecture Notes)
This lecture will provide a review of key concepts from linear algebra and differential equations, tuned to the needs of the course.
|Monday|| Wednesday (CDS 110)
- K. J. Åström and R. M. Murray,, Preprint, 2006..
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 a sample systems. The second problem consists of a detailed construction of a vehicle model that can be used for cruise control. The last two problems (CDS 110 only) explore different modeling techniques, including both discrete time, analytical, and MATLAB-based analysis of dynamical systems.
- SIMULINK speed control module (for problem #2): hw1cruise.mdl,
- Can a Lyapunov function be used to show/prove a system is unstable at an equilibrium point similar to the way it can be used to show asymp stability?
- How do we read the simulated predator-prey graph?
- How is the Internet a feedback system?
- I'm a 101/110 student. Can I sit in on the 210 lectures on Fridays without being enrolled in 210?
- In slide 12, what is special about the red cycle as opposed to the blue curves?
- In slide 9, why did you only linearize around the downward equilibrium point?
- Is q1 a function of time
- Is there any open source software we can use instead of MATLAB?
- What are the Di parameters in the power grid model?
- What does the 45 mean in ode45?
- What does the at symbol mean in front of a function in matlab?
- What is a finite state machine and how does it relate to the traffic example?
- What is the significance of having eigenvalues that are 0? I think I heard you say "in that case you don't know anything". Does that mean you cannot determine if the system is stable or asymptotically stable?
- What's the difference between control "over" network and control "of" network?
- Where can I find a theoretical definition of dynamical system?
- Why is dB defined as 20log 10?
- Why was there only one damper in the mass/spring model?
- You mentioned "aggressive" dynamics a couple of times. Please define. How/when is it useful?
- You said spiraling out to a bounded circle is unstable, but doesn't that still satisfy the epsilon-delta condition of stability? Or are there limits on epsilon?
- CDS210 Problem 4 typo
- Do we have to consider complex states when trying to find equilibrium points analytically?
- In problem 3 (CDS 110), please use a different V2(x).
- Problem 1 -- Can I use Maple or Mathematica to solve this?
- Problem 1 -- Why don't the units work?
- Problem 2 - Actuator block
- Problem 2 -- Saturation of signal u
- Problem 2b -- Do I need to include the controller and feedback?
- Problem 3 -- Does "output get smaller as k gets larger" mean it gets more negative or more closer to zero?
- There are some problems with Ex 6
- Why are the initial conditions of the integrator and engine in hw1cruise.mdl set to 55*50?