Murray Wiki - User contributions [en]

What is bandwidth? What is meant by 'not giving too much bandwidth if there is a RHP zero'?

2008-11-20T02:10:27Z

Buzi:

Bandwidth is the frequency range over which the gain has not decreased by more than 1/sqrt(2). For a lot of systems this is closely related to the gain crossover frequency (frequency at which the open loop gain is 1). Both those concepts can be found in AM08 (pg 322) or in the Monday lecture slides.

RHP zeros impose limitations on how big the bandwidth or the gain crossover frequency can be. This is what is meant by not giving too much bandwidth. See AM08 section 11.5 and especially Example 11.7.

'--[[User:Buzi|Buzi]] 18:10, 19 November 2008 (PST)'
[[Category: CDS 101/110 FAQ - Lecture 8-2]]
[[Category: CDS 101/110 FAQ - Lecture 8-2, Fall 2008]]

What is meant/useful about transfer functions between 2 blocks in a block diagram?

2008-11-04T00:59:21Z

Buzi:

The transfer functions are between two signals, not blocks. Usually blocks in a block diagram represent transfer functions. A direct link between two blocks means that the output of the first block (transfer function) serves as the input to the second one. Using the rules shown in class, one can combine different blocks (transfer functions) into a single block (transfer function), which makes it easier to reason about the system.
'--[[User:Buzi|Buzi]] 16:59, 3 November 2008 (PST)'
[[Category: CDS 101/110 FAQ - Lecture 6-1]]
[[Category: CDS 101/110 FAQ - Lecture 6-1, Fall 2008]]

CDS210 Problem 4 typo

2008-10-15T05:38:50Z

Buzi:

For CDS210 problem 4, V should be an R^n->R function not R^n->R^n.

'--[[User:Buzi|Buzi]] 22:38, 14 October 2008 (PDT)'
[[Category: CDS 101/110 FAQ - Homework 2]]
[[Category: CDS 101/110 FAQ - Homework 2, Fall 2008]]

CDS 210 - Stability Analysis

2008-10-14T06:02:53Z

Buzi:

{{cds101-fa08}}

Instructions for downloading SEDUMI and SOSTOOLS [[Media:InstallSOSTOOLS.pdf|InstallSOSTOOLS.pdf]]

Instructions for downloading YALMIP [[Media:InstallYalmip.pdf|InstallYalmip.pdf]]

Examples using YALMIP [[Media:Yalmipexamples.m|Yalmipexamples.m]]

File:Yalmipexamples.m

2008-10-14T05:55:17Z

Buzi:

File:InstallYalmip.pdf

2008-10-14T05:54:55Z

Buzi:

CDS 210 - Stability Analysis

2008-10-07T00:49:05Z

Buzi:

{{cds101-fa08}}
Instructions for downloading SEDUMI and SOSTOOLS [[Media:InstallSOSTOOLS.pdf|InstallSOSTOOLS.pdf]]

File:InstallSOSTOOLS.pdf

2008-10-07T00:18:58Z

Buzi: Instructions for downloading and installing SEDUMI and SOSTOOLS.

Instructions for downloading and installing SEDUMI and SOSTOOLS.

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?

2008-10-06T23:40:35Z

Buzi:

The condition for stability states that '''for all''' epsilon>0 exists a delta>0 ... This condition would be violated for the case above since you can just take epsilon=r/2 (r radius of the circle).
--[[User:Buzi|Buzi]] 16:40, 6 October 2008 (PDT)
[[Category: CDS 101/110 FAQ - Lecture 2-1]]
[[Category: CDS 101/110 FAQ - Lecture 2-1, Fall 2008]]

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?

2008-10-06T23:32:56Z

Buzi:

Generally no.
A Lyapunov function can only be used to show the stability of a fixed point.
However there are some cases when the equilibrium point is a "source", i.e. a fixed point that is asymptotically stable if we run the time backwards.
In this case, we can use Lyapunov functions since we can modify the system by reversing time and search for a Lyapunov function for the fixed point of the new system.
-[[User:Buzi|Buzi]] 16:30, 6 October 2008 (PDT)
[[Category: CDS 101/110 FAQ - Lecture 2-1]]
[[Category: CDS 101/110 FAQ - Lecture 2-1, Fall 2008]]

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?

2008-10-06T23:30:45Z

Buzi:

Generally no.
A Lyapunov function can only be used to show the stability of a fixed point.
However there are some cases when the equilibrium point is a "source", i.e. a fixed point that is asymptotically stable if we run the time backwards.
In this case, we can use Lyapunov functions since we can modify the system by reversing time and search for a Lyapunov function for the fixed point of the new system.
-[[User:Buzi|Buzi]] 16:30, 6 October 2008 (PDT)
[[Category: CDS 101/110 FAQ - Lecture w-m]]
[[Category: CDS 101/110 FAQ - Lecture w-m, Fall 2008]]

The additional material and schedule of cds210.

2008-09-30T02:36:32Z

Buzi:

CDS210 Friday lecture will be complementary to the topics covered on Monday and Wednesday. It will generally try to expand on the material covered on the previous lectures as well as introduce some more advanced concepts and treatments of the material.
Tentative topics to be covered include
Lyapunov Theory; Lyapunov equation, Optimization and Linear Matrix Inequalities, Reachability and Observability; Norms and Transfer Functions; Robust Stability and Performance, Algebraic and Analytical Constrains ; LQR

--[[User:Buzi|Buzi]] 19:36, 29 September 2008 (PDT)
[[Category: CDS 101/110 FAQ - Lecture 1-1]]
[[Category: CDS 101/110 FAQ - Lecture 1-1, Fall 2008]]

Is kp (the gain of the system) dimensionless?

2008-09-30T01:54:45Z

Buzi:

Yes.
It is useful to think of the gains of the system as dimensionless and avoid dealing with the units when designing a controller. You still have to deal with the units, but one should decouple that from choosing the appropriate gains for the system.
--[[User:Buzi|Buzi]] 18:54, 29 September 2008 (PDT)
[[Category: CDS 101/110 FAQ - Lecture 1-1]]
[[Category: CDS 101/110 FAQ - Lecture 1-1, Fall 2008]]