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FAQ (Frequently Asked Questions)
Category:
CDS 101/110 Fall 2003
Identifiers: FN H0 H1 H2 H3 H4 H5 H6 H7 H8 L0.0 L1.1 L1.2 L10.1 L2.1 L2.2 L3.1 L3.2 L4.1 L4.2 L5.1 L5.2 L6.2 L8.1 L9.1 L9.2
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Isn'nt Bell in dB named after the circuit theorist Bell, rather than Bell labs?
Submitted by: mreiser
Submitted on: October 20, 2003
Identifier:
L4.1
The 'Bel' in dB is named in honor of Alexander Graham Bell, the "inventor" (since he filed his patent just a few hours ahead of the competition) of the telephone. Of course, the the deciBel is one-tenth of a Bel, a now forgotten unit. Bell labs is also named after A.G. Bell, since it was the name for the engineering labs at American Bell (later AT&T), a company established by Bell. Bell labs is still around as Lucent Technlogies. Bell labs has played a significant role in 20th century technology, here is a short history .
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What are the ways to look at a state-space model and identify whether it is linear or not?
Submitted by: mreiser
Submitted on: October 20, 2003
Identifier:
L4.1
In general a state-space model is one where we write a system of first order ODEs in a specific form, where we can directly read off the state vector. So of course there can be nonlinear models in state space form - the inverted pendulum on a cart dynamics (from HW 4 and Lecture 4.1 slide # 16) have been put into this form. There are (at least) 2 ways to determine that the system is linear, and they turn out to be equivalent:
1) You've got a linear system if you can arrange the dynamics into the standard form: x_dot = Ax + Bu, y = Cx + Du, where A, B, C, D are matrices of the appropriate dimensions. In the general case, you might have a linear, time-varying system, in which A(t), B(t), etc. are matrices whose entries can depend on time, though we have yet to see a system like this in class.
2) You also have a linear system if you can convince yourself that the basic linearity properties hold (e.g. see slide #3 in Lecture 4.1). This is harder to do (directly) form the state-space form, since we care about linearity of the solutions of these systems.
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Are all systems linearizable?
Submitted by: waydo
Submitted on: October 20, 2003
Identifier:
L4.1
The full question was: "Do we have to worry about whether a system is 'linearizable', or are all systems linearizable?
All systems are 'linearizable'(about an equilibrium point), though the linearization may or may not tell us anything interesting about the behavior of the actual system. For example, the system xdot = x^2 has the linearization xdot = 0 about the equilibrium at x = 0, which clearly doesn't tell us anything about the original system. Usually, however, linearization is a very useful tool to help us evaluate stability and approximate the behavior of a complex system.
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For LAST WEEK... we need some harder Lyapunov function examples.
Submitted by: lars
Submitted on: October 21, 2003
Identifier:
L4.1
, L3.2
, H3
Noted. We acknowledge that the Lyapunov function homework problem requires more effort than that presented in class. We'll be more conscientious about teaching the class at a consistent level.
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Are there tools for symbolic solving of systems, like MATLAB is for numerical solving?
Submitted by: lars
Submitted on: October 21, 2003
Identifier:
L4.1
If we specify "systems" as sets of algebraic equations or ODEs , then yes, there are a few tools available.
MATLAB has it's own symbolic toolbox (which you can investigate through MATLAB Help), but is somewhat limited in the classes of equations it can solve symbolically (MATLAB is generally limited to algebraic equations.
Mathematica and MAPLE are two other packages that have extensive symbolic math capabilities.
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