text:
Umbraco/Help Out

Help Out
How to help out with Umbraco.

Report Bugs
Information on reporting bugs and defects in Umbraco can be found at http://www.umbraco.org/frontpage/documentation/bugs.aspx

The bugreporting page at umbraco.org is not working so here is a link to http://bugs.umbraco.org/Issues.aspx?m=1

Make a Donation
Information on donating to the Umbraco project can be found here http://www.umbraco.org/frontpage/about/donate.aspx

Donations are needed to finish Umbraco V3 - http://umbraco.org/frontpage/sponsorumbracov3.aspx

Contribute to the Wiki
Need I explain?

 * Typical errors

title: Umbraco/Help Out


text:
User talk:68.174.121.28

You must learn circular breathing to play continueous music
This information is correct, so you shouldn't have removed it.203.214.25.238

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: User talk:68.174.121.28


text:
Umbraco/Samples and Articles/Dot Net Controls/Access Umbraco Data With Dot NET Controls

Access Umbraco Data with .NET controls
This is based on an original article at http://www.umbraco.org/frontpage/documentation/implementingnetcontrols/accessingumbracodata.aspx

Getting Started
You can access all umbraco content by creating a reference to the umbraco.dll. Use the node factory located at umbraco.presentation.nodeFactory to manipulate the XML used to store all of Umbracos data.

First include: using umbraco.presentation.nodeFactory;

To get the current node for the page the control is on use the Node.GetCurrent method:

Node curNode = Node.GetCurrent;

Using your newly created node object, you can use work on the current node directly, or use it as a starting point to traverse the entire tree.


text:
Umbraco/Reference/Umbraco XML Format

Umbraco XML Format
All published content in umbraco are stored in an Xml Document which has the following format: First the Node (which often is a page) is represented by a ”Node” element. This node element has a number of attributes with basic information about the structure, type, name and create/update dates. The data on the page – the generic properties defined in the document type – is then represented as “Data” elements which is children of the “Node” element. The node can also have other nodes as children, and representing the structure of the site.

Confused – don't be; lets have a look:

The attributes of the node element

 * id: The Identifier of the page (node)
 * version: Identifier of the version id for the page
 * parentID: Identifier of the parent node
 * level: The depth of the placement of the node
 * template: Identifier of the template
 * sortOrder: The order of the node
 * createDate: The createdate of the node
 * updateDate: The date of the latest update (publishing time)
 * nodeName: The title of the node
 * urlName: Used by the umbraco request handler
 * writerName: The name of the user who published the node
 * nodeTypeAlias: The alias of the document type
 * path: A comma-separated string representing all parent-nodes

The attributes of the data element

 * version: The identifier of the version id for the page which this property belongs to
 * alias: The alias of the Property Type (as defined in the document type)

title: Umbraco/Reference/Umbraco XML Format


text:
Control Systems/Gain

What is Gain?
Gain is a proportional value that shows the relationship between the magnitude of the input to the magnitude of the output signal at steady state. Many systems contain a method by which the gain can be altered, providing more or less "power" to the system. However, increasing gain or decreasing gain beyond a particular safety zone can cause the system to become unstable.

Consider the given second-order system:
 * $$T(s) = \frac{1}{s^2 + 2s + 1}$$

We can include an arbitrary gain term, K in this system that will represent an amplification, or a power increase:

 * $$T(s) = K\frac{1}{s^2 + 2s + 1}$$

In a state-space system, the gain term k can be inserted as follows:

 * $$x'(t) = Ax(t) + kBu(t)$$
 * $$y(t) = Cx(t) + kDu(t)$$

The gain term can also be inserted into other places in the system, and in those cases the equations will be slightly different.

Responses to Gain
As the gain to a system increases, generally the rise-time decreases, the percent overshoot increases, and the settling time increases. However, these relationships are not always the same. A critically damped system, for example, may decrease in rise time while not experiencing any effects of percent overshoot or settling time.

Gain and Stability
If the gain increases to a high enough extent, some systems can become unstable. We will examine this effect in the chapter on Root Locus. But it will decrease the steady state error.

Conditional Stability
Systems that are stable for some gain values, and unstable for other values are called conditionally stable systems. The stability is conditional upon the value of the gain, and often the threshold where the system becomes unstable is important to find.

title: Control Systems/Gain


text:
Umbraco/Samples and Articles/XSLT/Extend Xsl

Extend XSL using Javascript, VB or C#
Originally from http://www.umbraco.org/frontpage/documentation/articles/sampleofthemonth.aspx

When developing using xsl, the language sometimes falls short or its difficult and time consuming to accomplish what is easily done in other programming languages.

Answering a question in the umbraco mailing list, revealed that it wasn't common knowledge that you could extend xsl with inline code of your favorite programming language, but it is in fact very easy to do so.

An example using inline server interpreted Javascript.

     <![CDATA[ function random{ return Math.random; } 						]]>

This above example shows how to get a random node from a nodeset, using a wrapper to the "Math.random" function from Javascript, in order to generate a random seed.

The javascript is executed serverside - in fact any defined function is compiled to MSIL (wrapped in a class definition), and thus should have little effect on the general performance - other scenarios could result in performance overheads, but - in the soon to be released Umbraco v. 2.1 - it possible to cache the output of your macroes and therefore it should be possible to maintain high performance and at the same time flexibility in the development.

You can use different programming languages, a complete list and further information can be found at http://msdn.microsoft.com/library/default.asp?url=/library/en-us/cpguide/html/cpconXSLTStylesheetScriptingUsingMsxslscript.asp

Author: Kasper Bumbech Andersen


text:
User:Goldkear

Hmm, my very own wiki page, huh? If you really feel like it you can go ahead and write all you want here, you can even write something nasty if you want, as long as you don't delete anything I wrote. I won't promise that nasty remarks will stay around, but you can write them anyway :)

Jacob Clark (thats me!)
First off, Jacob Clark is mearly a pen name. Not that I feel the need to be secretive or anything, but it is pretty cool to have a pen name. I was born and raised in Minot, ND and I am currently enrolled at North Dakota State University (NDSU) in Fargo, ND (yes, the place the movie 'Fargo' is named after). My major is currently Architecture with a minor in Interior design, however I will probably change to a major in Interior design and a minor in Photography. In my free time I love photography and both visual and performing arts, However durring the cold months (which is most of them for ND) I play plenty of video games. During the summer I work as a lifegaurd and I love to spend my time by the pool or at the lake.

Various Wikis that I read/contribute to

 * MapleStory
 * Blender 3D: Noob to Pro
 * Dofus wikicity

Non-wiki links

 * Flyff oficial english site for my favorite MMORPG
 * IAB Good for when you are bored
 * Worth1000 my stuff, browse around the site too, very cool
 * Digikitten cool site, good for finding desktop backrounds

Contact

 * [mailto:coldgear@gmail.com E-mail]
 * Aim/Yahoo/X-fire - coldgear
 * MSN - coldgear@hotmail.com

title: User:Goldkear


text:
Umbraco/Plugins And Extensions

Plugins and Extensions

 * umbracoUtilities For 2.1
 * E-Commerce Server
 * Commerce4umbraco
 * Language Packs
 * Foldout Menu
 * Log Viewer
 * Umbraco Stats
 * Flat URL's for TextGen.aspx
 * Upload progress bar
 * Static HTML export
 * Blog Package - http://web.archive.org/web/20061126102545/http://umbraco.bruunebonen.com/media/440/umbracoblog.zip

title: Umbraco/Plugins And Extensions


text:
Umbraco/Plugins And Extensions/umbracoUtilities For 2.1

Features

 * AutoForm. The fastest way ever to build dynamic web applications. You can build full .net applications just using a mouse and a web browser. You can watch the screencast here for how to build a Gallery in five minutes.
 * Search. Full text search of all umbraco content – the package even index everything automatically upon install
 * SubscribeUnsubscribe. Easy management of newsletters that integrates into the new mass mailer in umbraco 2.1
 * ContentType. Change the mime type of templates, making it easy to output umbraco data as xml or csv.

Installation

 * Download the .umb file (and make sure it isn’t renamed as .zip when you download) to your desktop or another location where you can find it.
 * Login to your umbraco installation, click on the developer icon (bottom left corner), right-click macro and choose “Import Package”.
 * In the window that open up, click “choose” and locate the umbracoUtilities.umb file on your desktop. Press “Load Package” and follow on screen instructions.


text:
User talk:Seductionreport.com

Come introduce yourself at the new users page. If you have any questions, you can ask there or contact me personally.

I know you have been adding some content on Wikibooks for a little while, but I want to thank you for coming here and participating, and coming back to add more content.

One minor concern I have is over the new Wikibook names Fast seduction. I found similar content listed here: http://www.seductionreport.com/bodylanguage.htm

The concern I have is that this is potentially a copyright violation. While we try to assume good faith, and assume that you have read the warning at the bottom of the edit window that you have not submitted copyrighted works without permission, sad experience in the past suggests that some individuals don't know or understand this concept. If possible, please add a note somewhere on Talk:Fast seduction that you are indeed the author and that you have granted permission for this to be added to Wikibooks. I ask this for all substantial text content additions, just to be safe and not even remotely violate copyright, so we can protect authors who may not even know about Wikibooks. If there is on-line content hosted elsewhere, that usually is a warning that it may be a copyright violation.

I also have some conern that this page largely duplicates the content here: Guide to Social Activity/Body Language

Just to let me and others know what you intend to do here, I'm curious what you intend to do with this new Wikibook that is going to be different from the Guide to Social Activity. I don't see anything specifically wrong with the content, and even the writing style is just fine for the most part (I havn't run it through a spell checker or a grammar checker, for instance). It just seems like a waste and duplication of effort when very similar content is found elsewhere, but I would like to give you the benefit of the doubt and see what you might want to do that would make this different. If this is a disagreement over editorial philosophies with another Wikibooks user, I can understand that as well.

Have fun here, and I hope to be seeing more of what you have written in the future! --Rob Horning 14:39, 12 April 2006 (UTC)

Most of the material here is from my own website: seductionreport.com. I am bringing new trafic from my own website. Soon more visitors will contribute their own ideas.

If you have time, please do run in through a spell checker.--Seductionreport.com 04:50, 13 April 2006 (UTC)

improper transwikis
You seem to be copying a lot of wikipedia articles and putting them here, which is no problem, but you need to log these on the transwiki log, and you need to provide links back to the wikipedia page for the contribution history (this is required by the GFDL, wich is the copyright covering both wikipedia and wikibooks.

An alternative that will (hopefully) soon be available is the import function, which brings the pages over with the contribution history in one fell swoop (only admins can do it, but there will be a request page). -- SB_Johnny | talk 15:54, 12 October 2006 (UTC)

title: User talk:Seductionreport.com


text:
User talk:ZS~enwikibooks

Wikipedia is not in the public domain
I noticed that you recently moved some contents to Wikibooks from Wikipedia.

Wikipedia is not in the public domain. The only way that Wikibooks can use content from Wikipedia is through the GNU Free Documentation License, which in section 4 requires – I will skip over the details – attribution (credit) to Wikipedia. Regardless of what the FDL says, I think that it is useful to know when a Wikibook has Wikipedian authors, in addition to Wikibookian authors. Thus I will be adding such a credit to the Need for Speed: Most Wanted page.

There is also an arrangement (Transwiki) to move content and leave the attribution on the talk page – when someone submits a page to the wrong project before someone moves the page. Further, the authors (copyright holders) are free to move their own content around. --Kernigh 16:04, 12 April 2006 (UTC)

Your account will be renamed
Hello,

The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

Unfortunately, your account clashes with another account also called ZS. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name ZS~enwikibooks that only you will have. If you like it, you don't have to do anything. If you do not like it, you can pick out a different name.

Your account will still work as before, and you will be credited for all your edits made so far, but you will have to use the new account name when you log in.

Sorry for the inconvenience.

Yours, Keegan Peterzell Community Liaison, Wikimedia Foundation 23:55, 17 March 2015 (UTC)

Renamed
 This account has been renamed as part of single-user login finalisation. If you own this account you can |log in using your previous username and password for more information. If you do not like this account's new name, you can choose your own using this form after logging in: . -- Keegan (WMF) (talk) 05:40, 19 April 2015 (UTC)

title: User talk:ZS~enwikibooks


text:
Category:Agar recipes

Recipes involving agar.

title: Category:Agar recipes


text:
Control Systems/Signal Flow Diagrams

Signal-flow graphs
Signal-flow graphs are another method for visually representing a system. Signal Flow Diagrams are especially useful, because they allow for particular methods of analysis, such as Mason's Gain Formula.

Signal flow diagrams typically use curved lines to represent wires and systems, instead of using lines at right-angles, and boxes, respectively. Every curved line is considered to have a multiplier value, which can be a constant gain value, or an entire transfer function. Signals travel from one end of a line to the other, and lines that are placed in series with one another have their total multiplier values multiplied together (just like in block diagrams).

Signal flow diagrams help us to identify structures called "loops" in a system, which can be analyzed individually to determine the complete response of the system.

Forward Paths
A forward path is a path in the signal flow diagram that connects the input to the output without touching any single node or path more than once. A single system can have multiple forward paths.

Loops
A loop is a structure in a signal flow diagram that leads back to itself. A loop does not contain the beginning and ending points, and the end of the loop is the same node as the beginning of a loop.

Loops are said to touch if they share a node or a line in common.

The Loop gain is the total gain of the loop, as you travel from one point, around the loop, back to the starting point.

Delta Values
The Delta value of a system, denoted with a Greek Δ is computed as follows:

 * $$\Delta = 1 - A + B - C + D - E + F......+ \infty$$

Where:
 * A is the sum of all individual loop gains
 * B is the sum of the products of all the pairs of non-touching loops
 * C is the sum of the products of all the sets of 3 non-touching loops
 * D is the sum of the products of all the sets of 4 non-touching loops
 * et cetera.

If the given system has no pairs of loops that do not touch, for instance, B and all additional letters after B will be zero.

Mason's Rule
Mason's rule is a rule for determining the gain of a system. Mason's rule can be used with block diagrams, but it is most commonly (and most easily) used with signal flow diagrams.

If we have computed our delta values (above), we can then use Mason's Gain Rule to find the complete gain of the system:

 * $$M = \frac{y_{out}}{y_{in}} = \sum_{k=1}^N \frac{M_k \Delta\ _k}{ \Delta\ }$$

Where M is the total gain of the system, represented as the ratio of the output gain (yout) to the input gain (yin) of the system. Mk is the gain of the kth forward path, and Δk is the loop gain of the kth loop.

Solving a signal-flow graph by systematic reduction : Two interlocking loops
This example shows how a system of five equations in five unknowns is solved using systematic reduction rules. The independent variable is $$x_{in}$$. The dependent variables are $$x_1$$, $$x_2$$, $$x_3$$, $$x_4$$, $$x_{out}$$. The coefficients are labeled $$a, b, c, d, e$$. Here is the starting flowgraph:

 * $$\begin{align}

x_1 &= x_\mathrm{in}+e x_3 \\ x_2 &= b x_1+a x_4 \\ x_3 &= c x_2 \\ x_4 &= d x_3 \\ x_\mathrm{out} &= x_4 \\ \end{align}$$

The steps for solving $$x_{out}$$ follow.

Removing edge c from x2 to x3

 * $$\begin{align}

x_1 &= x_\mathrm{in}+e x_3 \\ x_2 &= b x_1+a x_4 \\ x_3 &= c x_2 \\ x_3 &= c (b x_1+a x_4) \\ x_3 &= bc x_1+ca x_4 \\ x_4 &= d x_3 \\ x_\mathrm{out} &= x_4 \\ \end{align}$$

Removing node x2 and its inflows
$$x_2$$ has no outflows, and is not a node of interest.

Removing edge e from x3 to x1

 * $$\begin{align}

x_1 &= x_\mathrm{in}+e x_3 \\ x_1 &= x_\mathrm{in}+e (bc x_1+ca x_4) \\ x_1 &= x_\mathrm{in}+ bce x_1+ ace x_4 \\ x_2 &= b x_1+a x_4 \\ x_3 &= bc x_1+ca x_4 \\ x_4 &= d x_3 \\ x_\mathrm{out} &= x_4 \\ \end{align}$$

Remove edge d from x3 to x4

 * $$\begin{align}

x_1 &= x_\mathrm{in}+ace x_4 + bce x_1 \\ x_3 &= bc x_1+ac x_4 \\ x_4 &= d x_3 \\ x_4 &= d (bc x_1+ac x_4) \\ x_4 &= bcd x_1 + acd x_4 \\ x_\mathrm{out} &= x_4 \\ \end{align}$$

Node $$x_3$$ has no outflows and is not a node of interest. It is deleted along with its inflows.
 * $$\begin{align}

x_1 &= x_\mathrm{in}+ace x_4 + bce x_1 \\ x_4 &= bcd x_1 + acd x_4 \\ x_\mathrm{out} &= x_4 \\ \end{align}$$

Removing self-loop at x1

 * $$\begin{align}

x_1 &= x_\mathrm{in}+ace x_4 + bce x_1 \\ x_1 (1-bce) &= x_\mathrm{in}+ace x_4 \\ x_1 &= \frac{1}{1-bce}x_\mathrm{in}+\frac{ace}{1-bce} x_4   \\ x_4 &= bcd x_1 + acd x_4 \\ x_\mathrm{out} &= x_4 \\ \end{align}$$

Removing self-loop at x4

 * $$\begin{align}

x_1 &= \frac{1}{1-bce}x_\mathrm{in}+\frac{ace}{1-bce} x_4   \\ x_4 &= bcd x_1 + acd x_4 \\ x_4 (1-acd) &= bcd x_1 \\ x_4 &= \frac{bcd}{1-acd} x_1 \\ x_\mathrm{out} &= x_4 \\ \end{align}$$

Remove edge from x4 to x1

 * $$\begin{align}

x_1 &= \frac{1}{1-bce}x_\mathrm{in}+\frac{ace}{1-bce} x_4   \\ x_1 &= \frac{1}{1-bce}x_\mathrm{in}+\frac{ace}{1-bce} \times \frac{bcd}{1-acd} x_1   \\ x_4 &= \frac{bcd}{1-acd} x_1 \\ x_\mathrm{out} &= x_4 \\ \end{align}$$

Remove outflow from x4 to xout

 * $$\begin{align}

x_1 &= \frac{1}{1-bce}x_\mathrm{in}+\frac{ace}{1-bce} \times \frac{bcd}{1-acd} x_1   \\ x_\mathrm{out} &= \frac{bcd}{1-acd} x_1 \\ \end{align}$$ $$x_4$$'s outflow is then eliminated: $$x_\mathrm{out}$$ is connected directly to $$x_1$$ using the product of the gains from the two edges replaced.

$$x_4$$ is not a variable of interest; thus, its node and its inflows are eliminated.

Eliminating self-loop at x1

 * $$\begin{align}

x_1 &= \frac{1}{1-bce}x_\mathrm{in}+\frac{ace}{1-bce} \times \frac{bcd}{1-acd} x_1   \\ x_1 (1-\frac{ace}{1-bce} \times \frac{bcd}{1-acd}) &= \frac{1}{1-bce}x_\mathrm{in}    \\ x_1  &= \frac{1}{(1-bce) \times (1-\frac{ace}{1-bce} \times \frac{bcd}{1-acd}) }x_\mathrm{in}    \\ x_\mathrm{out} &= \frac{bcd}{1-acd} x_1 \\ \end{align}$$

Eliminating outflow from x1, then eliminating x1 and its inflows

 * $$\begin{align}

x_1  &= \frac{1}{(1-bce) \times (1-\frac{ace}{1-bce} \times \frac{bcd}{1-acd}) }x_\mathrm{in}    \\ x_\mathrm{out} &= \frac{bcd}{1-acd} x_1 \\ x_\mathrm{out} &= \frac{bcd}{1-acd} \times \frac{1}{(1-bce) \times (1-\frac{ace}{1-bce} \times \frac{bcd}{1-acd}) }x_\mathrm{in} \\ \end{align}$$ $$x_1$$ is not a variable of interest; $$x_1$$ and its inflows are eliminated
 * $$\begin{align}

x_\mathrm{out} &= \frac{bcd}{1-acd} \times \frac{1}{(1-bce) \times (1-\frac{ace}{1-bce} \times \frac{bcd}{1-acd}) }x_\mathrm{in} \\ \end{align}$$

Simplifying the gain expression
$$\begin{align} x_\mathrm{out} &= \frac{-bcd}{bce+acd-1} x_\mathrm{in} \\ \end{align}$$

Solving a signal-flow graph by systematic reduction: Three equations in three unknowns
This example shows how a system of three equations in three unknowns is solved using systematic reduction rules. The independent variables are $$y_1$$, $$y_2$$, $$y_3$$. The dependent variables are $$x_1$$, $$x_2$$, $$x_3$$. The coefficients are labeled $$c_{jk}$$. The steps for solving $$x_1$$ follow:

Electrical engineering: Construction of a flow graph for a RC circuit

This illustration shows the physical connections of the circuit. Independent voltage source S is connected in series with a resistor R and capacitor C. The example is developed from the physical circuit equations and solved using signal-flow graph techniques. Polarity is important: The unknown variable of interest is the voltage across capacitor C.
 * S is a source with the positive terminal at N1 and the negative terminal at N3
 * R is a resistor with the positive terminal at N1 and the negative terminal at N2
 * C is a capacitor with the positive terminal at N2 and the negative terminal at N3.

Approach to the solution:
 * Find the set of equations from the physical network. These equations are acausal in nature.
 * Branch equations for the capacitor and resistor. The equations will be developed as transfer functions using Laplace transforms.
 * Kirchhoff's voltage and current laws
 * Build a signal-flow graph from the equations.
 * Solve the signal-flow graph.

Branch equations
The branch equations are shown for R and C.

Resistor R (Branch equation $$B_R$$)
The resistor's branch equation in the time domain is:
 * $$V_R(t) = R I_R(t) $$

In the Laplace-transformed signal space:
 * $$V_R(s) = R I_R(s) $$

Capacitor C (Branch equation $$B_C$$)
The capacitor's branch equation in the time domain is:
 * $$V_C(t) = \frac{Q_C(t)}{C} = \frac{1}{C}\int_{t_0}^t I_C(\tau) \mathrm{d}\tau + V_C(t_0)$$

Assuming the capacitor is initially discharged, the equation becomes:
 * $$V_C(t) = \frac{Q_C(t)}{C} = \frac{1}{C}\int_{t_0}^t I_C(\tau) \mathrm{d}\tau $$

Taking the derivative of this and multiplying by C yields the derivative form:
 * $$I_C(t) = \frac{\mathrm{d}Q(t)}{\mathrm{d}t} = C\frac{\mathrm{d}V_C(t)}{\mathrm{d}t}$$

In the Laplace-transformed signal space:
 * $$I_C(s) = V_C(s) sC $$

Kirchhoff's Voltage Law equation $$\mathrm{KVL}_1$$
This circuit has only one independent loop. Its equation in the time domain is:
 * $$V_R(t) + V_C(t) - V_S (t) =0 $$

In the Laplace-transformed signal space:
 * $$V_R(s) + V_C(s) - V_S (s) =0 $$

Kirchhoff's Current Law equations $$\mathrm{KCL}_1, {KCL}_2, {KCL}_3 $$
The circuit has three nodes, thus three Kirchhoff's current equations (expresses here as the currents flowing from the nodes):

\begin{align} I_S(t) + I_R (t) & = 0 & & \mathrm{(KCL_1)} \\ I_C(t) - I_R (t) & = 0 & & \mathrm{(KCL_2)} \\ I_S(t) - I_C (t) & = 0 & & \mathrm{(KCL_3)} \\ \end{align} $$ In the Laplace-transformed signal space:

\begin{align} I_S(s) + I_R (s) & = 0 & & \mathrm{(KCL_1)} \\ I_C(s) - I_R (s) & = 0 & & \mathrm{(KCL_2)} \\ I_S(s) - I_C (s) & = 0 & & \mathrm{(KCL_3)} \\ \end{align} $$ A set of independent equations must be chosen. For the current laws, it is necessary to drop one of these equations. In this example, let us choose $$\mathrm{KCL}_1, {KCL}_2$$.

Building the signal-flow graph
We then look at the inventory of equations, and the signals that each equation relates:

The next step consists in assigning to each equation a signal that will be represented as a node. Each independent source signal is represented in the signal-flow graph as a source node, therefore no equation is assigned to the independent source $$\mathrm{V_S}$$. There are many possible valid signal flow graphs from this set of equations. An equation must only be used once, and the variables of interest must be represented.

The resulting flow graph is then drawn

The next step consists in solving the signal-flow graph.

Using either Mason or systematic reduction, the resulting signal flow graph is:

title: Control Systems/Signal Flow Diagrams


text:
Control Systems/Root Locus

The Problem
Consider a system like a radio. The radio has a "volume" knob, that controls the amount of gain of the system. High volume means more power going to the speakers, low volume means less power to the speakers. As the volume value increases, the poles of the transfer function of the radio change, and they might potentially become unstable. We would like to find out if the radio becomes unstable, and if so, we would like to find out what values of the volume cause it to become unstable. Our current methods would require us to plug in each new value for the volume (gain, "K"), and solve the open-loop transfer function for the roots. This process can be a long one. Luckily, there is a method called the root-locus method, that allows us to graph the locations of all the poles of the system for all values of gain, K

Root-Locus
As we change gain, we notice that the system poles and zeros actually move around in the S-plane. This fact can make life particularly difficult, when we need to solve higher-order equations repeatedly, for each new gain value. The solution to this problem is a technique known as Root-Locus graphs. Root-Locus allows you to graph the locations of the poles and zeros for every value of gain, by following several simple rules. As we know that a fan switch also can control the speed of the fan.

Let's say we have a closed-loop transfer function for a particular system:

 * $$\frac{N(s)}{D(s)} = \frac{KG(s)}{1 + KG(s)H(s)}$$

Where N is the numerator polynomial and D is the denominator polynomial of the transfer functions, respectively. Now, we know that to find the poles of the equation, we must set the denominator to 0, and solve the characteristic equation. In other words, the locations of the poles of a specific equation must satisfy the following relationship:

 * $$D(s) = 1 + KG(s)H(s) = 0$$

from this same equation, we can manipulate the equation as such:

 * $$1 + KG(s)H(s) = 0$$

 * $$KG(s)H(s) = -1$$

And finally by converting to polar coordinates:

 * $$\angle KG(s)H(s) = 180^\circ$$

Now we have 2 equations that govern the locations of the poles of a system for all gain values:

 * $$1 + KG(s)H(s) = 0$$

 * $$\angle KG(s)H(s) = 180^\circ$$

Digital Systems
The same basic method can be used for considering digital systems in the Z-domain:

 * $$\frac{N(z)}{D(z)} = \frac{KG(z)}{1 + K\overline{GH}(z)}$$

Where N is the numerator polynomial in z, D is the denominator polynomial in z, and $$\overline{GH}(z)$$ is the open-loop transfer function of the system, in the Z domain.

The denominator D(z), by the definition of the characteristic equation is equal to:

 * $$D(z) = 1 + K\overline{GH}(z) = 0$$

We can manipulate this as follows:

 * $$1 + K\overline{GH}(z) = 0$$
 * $$K\overline{GH}(z) = -1$$

We can now convert this to polar coordinates, and take the angle of the polynomial:

 * $$\angle K\overline{GH}(z) = 180^\circ$$

We are now left with two important equations:

 * $$1 + K\overline{GH}(z) = 0$$

 * $$\angle K\overline{GH}(z) = 180^\circ$$

If you will compare the two, the Z-domain equations are nearly identical to the S-domain equations, and act exactly the same. For the remainder of the chapter, we will only consider the S-domain equations, with the understanding that digital systems operate in nearly the same manner.

The Root-Locus Procedure
In the transform domain (see note at right), when the gain is small, the poles start at the poles of the open-loop transfer function. When gain becomes infinity, the poles move to overlap the zeros of the system. This means that on a root-locus graph, all the poles move towards a zero. Only one pole may move towards one zero, and this means that there must be the same number of poles as zeros.

If there are fewer zeros than poles in the transfer function, there are a number of implicit zeros located at infinity, that the poles will approach.

First thing, we need to convert the magnitude equation into a slightly more convenient form:

 * $$KG(s)H(s) + 1 = 0 \to G(s)H(s) = \frac{-1}{K}$$

Now, we can assume that G(s)H(s) is a fraction of some sort, with a numerator and a denominator that are both polynomials. We can express this equation using arbitrary functions a(s) and b(s), as such:

 * $$\frac{a(s)}{b(s)} = \frac{-1}{K}$$

We will refer to these functions a(s) and b(s) later in the procedure.

We can start drawing the root-locus by first placing the roots of b(s) on the graph with an 'X'. Next, we place the roots of a(s) on the graph, and mark them with an 'O'.

Next, we examine the real-axis. starting from the right-hand side of the graph and traveling to the left, we draw a root-locus line on the real-axis at every point to the left of an odd number of poles or zeros on the real-axis. This may sound tricky at first, but it becomes easier with practice.

Now, a root-locus line starts at every pole. Therefore, any place that two poles appear to be connected by a root locus line on the real-axis, the two poles actually move towards each other, and then they "break away", and move off the axis. The point where the poles break off the axis is called the breakaway point. From here, the root locus lines travel towards the nearest zero.

It is important to note that the s-plane is symmetrical about the real axis, so whatever is drawn on the top-half of the S-plane, must be drawn in mirror-image on the bottom-half plane.

Once a pole breaks away from the real axis, they can either travel out towards infinity (to meet an implicit zero), or they can travel to meet an explicit zero, or they can re-join the real-axis to meet a zero that is located on the real-axis. If a pole is traveling towards infinity, it always follows an asymptote. The number of asymptotes is equal to the number of implicit zeros at infinity.

Root Locus Rules
Here is the complete set of rules for drawing the root-locus graph. We will use p and z to denote the number of poles and the number of zeros of the open-loop transfer function, respectively. We will use Pi and Zi to denote the location of the ith pole and the ith zero, respectively. Likewise, we will use ψi and ρi to denote the angle from a given point to the ith pole and zero, respectively. All angles are given in radians (π denotes π radians).

There are 11 rules that, if followed correctly, will allow you to create a correct root-locus graph.

We will explain these rules in the rest of the chapter.

Root Locus Equations
Here are the two major equations:

 * {| class="wikitable"

! S-Domain Equations !! Z-Domain Equations
 * $$1 + KG(s)H(s) = 0$$
 * $$1 + K\overline{GH}(z) = 0$$
 * $$\angle KG(s)H(s) = 180^o$$
 * $$\angle K\overline{GH}(z) = 180^o$$
 * }
 * $$\angle K\overline{GH}(z) = 180^o$$
 * }

Note that the sum of the angles of all the poles and zeros must equal to 180.

Number of Asymptotes
If the number of explicit zeros of the system is denoted by Z (uppercase z), and the number of poles of the system is given by P, then the number of asymptotes (Na) is given by:

 * $$N_a = P - Z$$

The angles of the asymptotes are given by:

 * $$\phi_k = (2k + 1)\frac{\pi}{P - Z}$$

for values of $$k = [0, 1, ... N_a - 1]$$.

Asymptote Intersection Point
The asymptotes intersect the real axis at the point:

 * $$\sigma_0 = \frac{\sum_P - \sum_Z}{P - Z}$$

Where $$\sum_P$$ is the sum of all the locations of the poles, and $$\sum_Z$$ is the sum of all the locations of the explicit zeros.

Breakaway Points
The breakaway points are located at the roots of the following equation:

 * $$\frac{dG(s)H(s)}{ds} = 0$$ or $$\frac{d\overline{GH}(z)}{dz} = 0$$

Once you solve for z, the real roots give you the breakaway/reentry points. Complex roots correspond to a lack of breakaway/reentry.

The breakaway point equation can be difficult to solve, so many times the actual location is approximated.

Root Locus and Stability
The root locus procedure should produce a graph of where the poles of the system are for all values of gain K. When any or all of the roots of D are in the unstable region, the system is unstable. When any of the roots are in the marginally stable region, the system is marginally stable (oscillatory). When all of the roots of D are in the stable region, then the system is stable.

It is important to note that a system that is stable for gain K1 may become unstable for a different gain K2. Some systems may have poles that cross over from stable to unstable multiple times, giving multiple gain values for which the system is unstable.

Here is a quick refresher:

 * {|class="wikitable"

! Region ! colspan=2 | S-Domain ! colspan=2 | Z-Domain ! Stable Region ! Marginally Stable Region ! Unstable Region
 * Left-Hand S Plane || $$ \sigma < 0$$|| Inside the Unit Circle || $$|z| < 1$$
 * The vertical axis || $$ \sigma = 0$$ || The Unit Circle || $$|z| = 1$$
 * Right-Hand S Plane || $$ \sigma > 0$$ || Outside the Unit Circle, || $$|z| > 1$$
 * }

Example: Root-Locus Using MATLAB/Octave
{{TextBox|1=Use MATLAB, Octave, or another piece of mathematical simulation software to produce the root-locus graph for the following system:

 * $$T(s) = K\frac{s^2+7s+12}{(s^2 + 3s + 6)}$$

First, we must multiply through in the denominator:

 * $$N(s) = S^2+7S+12$$
 * $$D(s) = S^2+3S+2$$

Now, we can generate the coefficient vectors from the numerator and denominator: num = [0 1 7 12]; den = [0 1 3 2]; Next, we can feed these vectors into the rlocus command: rlocus(num, den); Note:In Octave, we need to create a system structure first, by typing: sys = tf(num, den); rlocus(sys); Either way, we generate the following graph:

{{Control Systems/Nav|Jurys Test|Nyquist Stability Criteria}}

title: Control Systems/Root Locus


text:
Template:Control Systems/Page

''This template is the general TOC template for the Control Systems wikibook. This template will appear on the main page of the book, and will appear at the top of every page, so it should be kept short.''

title: Template:Control Systems/Page


text:
Talk:Control Systems

Templates
I have created a template for page headers for this book:

 * Template:Control Systems/Page
 * Template:Control Systems/Stub
 * :
 * /Stubs

--Whiteknight (talk) (current) 18:25, 12 April 2006 (UTC)

Proposed Sections
These sections are proposed as future additions to this book. Some of these topics are sufficiently advanced or specialized enough that they may not be appropriate for this text. Any comments, suggestions, changes, or comments are welcome. --Whiteknight (talk) (projects) 15:00, 5 June 2006 (UTC)

Section X: System Implementation

 * Microcontroller implementation
 * Digital Filter Implementation
 * HDL Implementation
 * Implementing in LabView
 * Implementing in MatLab

Section Y: Optimal/Robust Control

 * Optimality
 * Euler-Lagrange equation
 * Pontryagin's minimum principle
 * Bellman's equation
 * Kalman filter
 * H-infinity design

Section Z: Adaptive Control

 * Least squares estimation
 * Persistently exciting input signals
 * Direct and indirect adaptive prediction
 * Self-tuning regulators
 * One-step-ahead control
 * Levinson predictor

Section W: Nonlinear Control

 * Nonlinear systems
 * Phase Plane Analysis
 * Existence and uniqueness of solutions
 * Perturbation Analysis
 * Sliding Mode Control

HMI Control Aspects
I suggest some coverage of this, as integral with the underlying plant control. How one depicts control information, navigational links, popups, status' and modes. --Billymac00 18:04, 13 December 2006 (UTC)

 * I almost want to say that HMI is outside the scope of this book. There aren't really any good theoretical ways to model the HMI of a particular system. that subject would likely be better covered in a book dedicated to user-interfaces in general, and not have to stretch this book to try and include that kind of information. This book is primarily theoretical, and worries about actual implementation of systems (and the interaction between the systems and the human control engineers) is outside the scope of this book. --Whiteknight (talk) (projects) 18:22, 13 December 2006 (UTC)

= Process Control wikibook =

The following text excerpts were copied from the Process Control Wikibook, as part of the merge. Some of the text from that book does not fit here, so we will try to merge the extra text to more appropriate books. --Whiteknight (talk) (current) 20:25, 26 April 2006 (UTC)

Elastic Collisions
In an ideal elastic collision, total kinetic energy is conserved. An example of ideal elastic collision is the collisions between atoms in a gas. During the collision, kinetic energy is transferred from one object to the other object.

Like all other collisions, total momentum is conserved in an elastic collision:

\begin{matrix} m_a\vec{v}_{a1} + m_b\vec{v}_{b1} = m_a\vec{v}_{a2} + m_b\vec{v}_{b2} \end{matrix} $$

In an ideal elastic collision, total kinetic energy is conserved: (This is what makes them different from Inelastic collisions):

 * $$\begin{matrix}

{1 \over 2}m_a v_{a1}^2 + {1 \over 2}m_b v_{b1}^2 = {1 \over 2}m_a v_{a2}^2 + {1 \over 2}m_b v_{b2}^2 \\ \end{matrix}$$

Let a head-on elastic collision occur between two bowling balls, one of mass 5kg with an initial velocity of 10 ms-1; and the other of mass 4kg which is initially stationary.

What happens when they collide ?

If we assume the collision is perfectly elastic, we can calculate what we expect to happen:

\begin{matrix} m_a &=& 5 kg \\ m_b &=& 4 kg \\ \vec{v}_{a1} &=& + 10 ms^{-1} \\ \vec{v}_{b1} &=& 0 \\ \end{matrix} $$

Then we plug those values into the above equations:

\begin{matrix} m_a\vec{v}_{a1} + m_b\vec{v}_{b1} &=& m_a\vec{v}_{a2} + m_b\vec{v}_{b2} \\ (5 kg)(10 ms^{-1}) + (4 kg)(0) &=& (5 kg)\vec{v}_{a2} + (4 kg)\vec{v}_{b2} \\ {1 \over 2}m_a v_{a1}^2 + {1 \over 2}m_b v_{b1}^2 &=& {1 \over 2}m_a v_{a2}^2 + {1 \over 2}m_b v_{b2}^2 \\ (5 kg)(10 ms^{-1})^2 + (4 kg)(0)^2 &=& (5 kg) v_{a2}^2 + (4 kg) v_{b2}^2 \\ \end{matrix} $$

Then we solve for the final velocities:

...

Thus it can be seen that a large object colliding with a small object under the rules of elastic collisions will cause the smaller object to move with a velocity greater than the larger object.

Physics with Calculus : Conservation_of_Momentum

Conservation of Momentum
Momentum is a property of an object that we are able to measure by a very simple means. Momentum is an extension of Newton's First Law in that a body with momentum will conserve that momentum, be it zero or non-zero. The formula that we use to describe the momentum of an object is the product of the object's mass and its velocity. Because velocity is a vector (having both magnitude and direction) and mass is a scalar quantity, by definition, a scalar multiplied by a vector is a vector. As a result, the momentum vector will have the same direction as the velocity vector.

Ergo,
 * $$\mathbf{p} = m\mathbf{v}$$

Conservation of Momentum, therefore, is by definition a zero change in the momentum of a system of objects. The initial momentum will then be equal to the final momentum.

single object
When a single object does not interact with other objects, we observe that its momentum always stays the same.

\begin{matrix} \Delta \mathbf{p} & = & \mathbf{p}_{final} - \mathbf{p}_{initial} \\        0        & = & \mathbf{p}_{f} - \mathbf{p}_{i} \\  \mathbf{p}_f   & = & \mathbf{p}_i\end{matrix} $$

Because the object does not change mass, it does not change velocity and hence momentum is conserved.

\begin{matrix} m_1\mathbf{v}_1 = m_1\mathbf{v}_2 \\ \mathbf{v}_1 = \mathbf{v}_2 \end{matrix} $$

two objects
When two objects (call them a and b) interact with each other, we observe that the total momentum of the entire systems always stays the same.

This is true whether the interactions are Elastic Collisions or Inelastic Collisions.

\begin{matrix} m_a\mathbf{v}_{a1} + m_b\mathbf{v}_{b1} = m_a\mathbf{v}_{a2} + m_b\mathbf{v}_{b2} \\ \end{matrix} $$

multiple objects
No matter how many objects interact with each other, we observe that the total momentum of the entire system always stays the same.

Possible sections
I am removing the optimal and robust control bullets from the main TOC, because we dont have material for those chapters yet. --Whiteknight (talk) (projects) 19:20, 18 April 2007 (UTC)

Optimal and Robust Control

 * Cost Functions
 * Pontryagin's maximum principle
 * Hamilton-Jacobi-Bellman equation
 * Linear-Quadratic Gaussian Control
 * State Regulator (Linear Quadratic Regulator)
 * Model Predictive Control
 * H-2 Control
 * H-Infinity Control
 * Robust Control

Blurb
The image used in this book's ad is a little bit hard to see. Would you have a better one around, perhaps? -- Kowey 19:35, 3 May 2007 (UTC)

 * I agree with you, i'll look for a better image, but I dont know that there are many others. I may need to make one. --Whiteknight (talk) 23:12, 3 May 2007 (UTC)

 * Just to check, you ok with the space shuttle? -- Kowey 14:08, 15 May 2007 (UTC)

Broken link
The link from System Metrics to Digital and Analog doesn't work -> it redirects to non-existent page "Analog and Digital".141.232.1.1 14:31, 13 July 2007 (UTC)

Main page headlines
I believe that since the preface is as a level 2 headline, apendixes and resources should be too. This way the actual contents are separeted from the "extras". I am changing it, anyway. --D1ma5ad (talk) 00:12, 11 March 2008 (UTC)

 * Thanks for taking the initiative! I never know how things are supposed to be spaced out like this. --Whiteknight (Page) (Talk) 01:01, 11 March 2008 (UTC)

Math displayed inconsistently
The math formulas in this book is displayed inconsistently. Sometimes in Latex-way, sometimes just as ordinary text. Maybe it should be always in Latex-way, when placed on separate rows? And in ordinary text font, when inline? Maybe you don't see this if you're logged in, and your preferences apply. Most of us read these books without being logged in. Try logout, and watch this page, so you see what I mean: Control Systems/Introduction. Mårten Berglund (talk) 18:21, 7 July 2008 (UTC)

PDF
The PDF print version has following issues
 * 1) Every page has a footer text "http://en.wikibooks.org/w/index.php?title=Control_Systems/Print_version&printable=yes". Even if there is a need of footer text have something better than this.
 * 2) Page no. 35 contains a commen, that too covering an equation.
 * 3) At the end of the same page, Some table starts but the content of which are shown in the next page.
 * 4) I really think we need to switch to some better fonts at least in the print version. For equations the letters seems to be a bit faded.

Aravind V R (discuss • contribs) 10:06, 19 April 2012 (UTC)

Update PDF Info
The PDF version info is out of date. The current version of the pdf file is about 4 mb which is about twice what it currently says on the current pdf download page. Can this information be updated so it looks like this book is still in active development? --Esj88 (discuss • contribs) 18:36, 12 May 2012 (UTC)

New PDF
I made a new pdf yesterday. --Dirk Hünniger (discuss • contribs) 08:33, 14 March 2013 (UTC)

The tables of the PDF doesn't show
The tables in the pdf are now codes instead of tables.Getlink2588 (discuss • contribs) 20:04, 22 December 2019 (UTC)

Thanks for the bug report. I updated the pdf things should be fixed now. @Getlink2588

--Dirk Hünniger (discuss • contribs) 20:09, 26 December 2019 (UTC)

Change to page Control Systems
User:Minorax, the page Control Systems transcludes into the page Control Systems/Print version; with your recent change they all the links become become erroneous redlinks. Wouldn't it be better to revert your change to Control Systems? -- Jules (Mrjulesd) 21:54, 20 December 2020 (UTC)
 * reverted, thanks. --Minorax (discuss • contribs) 05:21, 21 December 2020 (UTC)

New page: Eigenvalue Assignment for MIMO Systems
I have moved the content about controller design from the MIMO Systems page to a new page. It is not finished yet. I plan to add some references and "further reading" material. Please feel free to check, update and extend the stated material :)

--StephanSp3 (Page) (Talk) 14:35, 08 April 2021 (UTC)

title: Talk:Control Systems


text:
Category:Milk recipes

Recipes involving milk.

title: Category:Milk recipes


text:
GAMSAT Guide/Recommended Books

Below are recommendations from various candidates. Remember that your own educational background is crucial to your revision tactics so this is just what worked for them, not an official list...

Here are the main books I used to revise the GAMSAT with - my background was Psychology so my knowledge of most of these areas was quite sketchy at best so I was pretty much starting from scratch on the science front.

 * A self-teaching guide Chemistry (Houk and Post) - poor on quite a few parts but a good basic text to establish the base
 * Chemistry in Context (Hill and Holman) - fills in the spaces left by the previous book.
 * A self-teaching guide Physics (Kuhn) - similar to first book but seemed to cover all the physics I needed. Maybe a little too much of a spoon fed approach so if your physics are above minimal, you may want to opt for a more rapidly progressing text book.

I am a journalism graduate with an A Level In biology, so was starting from scratch with Chem and Physics. I passed Gamsat science using these books:

 * Chemistry: For basic GCSE refresher and a bit more, I started with Barron's Review Course Series 'Let's Review: Chemistry The Physical Setting. It's an American book aimed at 16-18 year olds and really easy to grasp.

Then I moved to Ramsden's A Level Chemistry book but found it to be insufferably dry and too full of facts and not enough explanation of concepts behind the facts, so I switched to Chemistry: The Central Science, by Brown, LeMay and Bursten - another US book aimed at 1st year college students - excellent explanation of concepts - particularly in thermochemistry, kinetics, equilibria, acids and bases, which are all key. I also used Ramsden's Calculations for A Level Chemistry, but not a lot.

Because there is so much organic chemistry, I bought (I kid you not) Organic Chemistry for Dummies and it is brilliant! Does exactly what it says on the tin. AcerGamsat.com also provides a great chemistry GAMSAT study guide called - The Holy Grail Organic Chemistry Book

 * Biology: I covered all the animal biology from Biology 2nd Edition by Mike Boyle and Kathryn Senior from the Collins Advanced Science Series. Nice and easy book to understand tho it may not quite be detailed enough for some of the more complex questions at Gamsat.

I also purchased The Biology holy grail book from AcerGamsat.com, which provided all the content needed for GAMSAT biology.

 * Physics: I didn't overdo it, since it is only 20% of the science section. So I used Barron's Review Course Series Let's Review: Physics. Again, an American book but really gets to grips with forces, vectors and basic electricity and light geometrics that you'll be asked about.

Preparation Materials:

Hi there folks, coming from a non-science background. I can see non-classic GAMSAT texts listed above. The ones I went with are only branded for the GAMSAT:
 * Mr Shum's Classroom (e.g. http://mrshum.com/pre-med/organic-chemistry/hydrocarbons/), which was great for succinct and easy-to-understand definitions, particularly if you haven't got a background in science (like me). Downside was that it lacked a question bank, and didn't cover the verbal section
 * GradReady GAMSAT is one of the most reputable GAMSAT preparation companies, and they provide lots of free preparation materials. You can sign up for their Free Trial to get access to 50 Free MCQs, example marked essays, textbook chapters, explanation videos, and a week-by-week GAMSAT study guide for each topic. You can also sit a one-of-a-kind GAMSAT practice test which mimics the actual ACER GAMSAT in detail, allowing you to familiarise yourself with the online delivery of the exam before test day.
 * Fraser's GAMSAT has probably the best content available for GAMSAT, with lots of free resources across all three sections. Their courses are excellent, however are a big investment of both time and money, taking over 3 months in most cases.
 * Gold Standard GAMSAT has a great question bank, both from their books and through online subscriptions. A considerable amount of content has been added since their first edition in 2010 as a single hardcover book then and its current edition of at least 4 GAMSAT books discussing specific strategies in Sections 1 and 2 with chapter review questions. One significant improvement in their new edition is that the books include 4 new chapters called "Chapter Zero" for each of the 4 sciences with the intention to summarise the subject in more common language, life experience, and practice questions that show the difference between conventional exams and GAMSAT. Probably the most helpful when it comes to GAMSAT-level practice out there is their Heaps Book with 10 full-length mock exams: GAMSAT Practice Tests
 * ExamKrackers, which like Mr. Shum's Classroom, has nice illustrations. I used this alongside Mr Shum's quite a bit. A great combo. Can't stress how good these are!
 * There are also a few others around like Medired and Guru Method, but perhaps someone else can elaborate on these, who has a better background
 * Preparation Materials:- GAMSAT materials or books are available to take your GAMSAT preparation to the next level. Note that some students use MCAT material to prepare for the GAMSAT such as Khan Academy or similar content.

title: GAMSAT Guide/Recommended Books


text:
Control Systems/Bode Plots

Bode Plots
A Bode Plot is a useful tool that shows the gain and phase response of a given LTI system for different frequencies. Bode Plots are generally used with the Fourier Transform of a given system.

The frequency of the bode plots are plotted against a logarithmic frequency axis. Every tickmark on the frequency axis represents a power of 10 times the previous value. For instance, on a standard Bode plot, the values of the markers go from (0.1, 1, 10, 100, 1000, ...) Because each tickmark is a power of 10, they are referred to as a decade. Notice that the "length" of a decade decreases as you move to the right on the graph. (note that this description doesn't match the chart above... there are 10 tickmarks per decade, not one, but since it is a log chart they are not evenly spaced).

The bode Magnitude plot measures the system Input/Output ratio in special units called decibels. The Bode phase plot measures the phase shift in degrees (typically, but radians are also used).

Decibels
A Decibel is a ratio between two numbers on a logarithmic scale. To express a ratio between two numbers (A and B) as a decibel we apply the following formula for numbers that represent amplitudes (numbers that represent a power measurement use a factor of 10 rather than 20):

 * $$dB = 20 \log\left({A \over B}\right)$$

Where dB is the decibel result.

Or, if we just want to take the decibels of a single number C, we could just as easily write:

 * $$ dB = 20 \log(C)$$

Frequency Response Notations
If we have a system transfer function T(s), we can separate it into a numerator polynomial N(s) and a denominator polynomial D(s). We can write this as follows:

 * $$T(s) = \frac{N(s)}{D(s)}$$

To get the magnitude gain plot, we must first transit the transfer function into the frequency response by using the change of variables:

 * $$s = j\omega$$

From here, we can say that our frequency response is a composite of two parts, a real part R and an imaginary part X:

 * $$T(j\omega) = R(\omega) + jX(\omega)$$

We will use these forms below.

Straight-Line Approximations
The Bode magnitude and phase plots can be quickly and easily approximated by using a series of straight lines. These approximate graphs can be generated by following a few short, simple rules (listed below). Once the straight-line graph is determined, the actual Bode plot is a smooth curve that follows the straight lines, and travels through the breakpoints.

Break Points
If the frequency response is in pole-zero form:

 * $$T(j\omega) = \frac{\prod_n|j\omega + z_n|}{\prod_m|j\omega + p_m|}$$

We say that the values for all zn and pm are called break points of the Bode plot. These are the values where the Bode plots experience the largest change in direction.

Break points are sometimes also called "break frequencies", "cutoff points", or "corner points".

Bode Gain Plots
Bode Gain Plots, or Bode Magnitude Plots display the ratio of the system gain at each input frequency.

Bode Gain Calculations
The magnitude of the transfer function T is defined as:

 * $$|T(j\omega)| = \sqrt{R^2 + X^2}$$

However, it is frequently difficult to transition a function that is in "numerator/denominator" form to "real+imaginary" form. Luckily, our decibel calculation comes in handy. Let's say we have a frequency response defined as a fraction with numerator and denominator polynomials defined as:

 * $$T(j\omega) = \frac{\prod_n|j\omega + z_n|}{\prod_m|j\omega + p_m|}$$

If we convert both sides to decibels, the logarithms from the decibel calculations convert multiplication of the arguments into additions, and the divisions into subtractions:

 * $$Gain = \sum_n20\log(|j\omega + z_n|) - \sum_m20\log(|j\omega + p_m|)$$

And calculating out the gain of each term and adding them together will give the gain of the system at that frequency.

Bode Gain Approximations
The slope of a straight line on a Bode magnitude plot is measured in units of dB/Decade, because the units on the vertical axis are dB, and the units on the horizontal axis are decades.

The value ω = 0 is infinitely far to the left of the bode plot (because a logarithmic scale never reaches zero), so finding the value of the gain at ω = 0 essentially sets that value to be the gain for the Bode plot from all the way on the left of the graph up till the first break point. The value of the slope of the line at ω = 0 is 0 dB/Decade.

From each pole break point, the slope of the line decreases by 20 dB/Decade. The line is straight until it reaches the next break point. From each zero break point the slope of the line increases by 20 dB/Decade. Double, triple, or higher amounts of repeat poles and zeros affect the gain by multiplicative amounts. Here are some examples:

 * 2 poles: -40 dB/Decade
 * 10 poles: -200 dB/Decade
 * 5 zeros: +100 dB/Decade

Bode Phase Plots
Bode phase plots are plots of the phase shift to an input waveform dependent on the frequency characteristics of the system input. Again, the Laplace transform does not account for the phase shift characteristics of the system, but the Fourier Transform can. The phase of a complex function, in "real+imaginary" form is given as:

 * $$\angle T(j\omega) = \tan^{-1}\left(\frac{X}{R}\right)$$

Bode Procedure
Given a frequency response in pole-zero form:

 * $$T(j\omega) = A\frac{\prod_n|j\omega + z_n|}{\prod_m|j\omega + p_m|}$$

Where A is a non-zero constant (can be negative or positive).

Here are the steps involved in sketching the approximate Bode magnitude plots:

Here are the steps to drawing the Bode phase plots:

title: Control Systems/Bode Plots


text:
Category:Diets

Special diets and eating habits.

nl:Categorie:Speciaal dieet

title: Category:Diets


text:
Category:Spice mix recipes

Recipes for spice mixtures.

title: Category:Spice mix recipes


text:
Control Systems/Physical Models

Physical Models
This page will serve as a refresher for various different engineering disciplines on how physical devices are modeled. Models will be displayed in both time-domain and Laplace-domain input/output characteristics. The only information that is going to be displayed here will be the ones that are contributed by knowledgeable contributors.

Electrical Systems

 * {|class="wikitable"

!Component || Time-Domain || Laplace || Fourier !Resistor !Capacitor !Inductor
 * R || R || R
 * $$i = C\frac{dv}{dt}$$ || $$G(s) = \frac{1}{sC}$$ || $$G(j\omega) = \frac{1}{j\omega C}$$
 * $$v = L\frac{di}{dt}$$ || $$G(s) = sL$$ || $$G(j\omega) = j\omega L$$
 * }

title: Control Systems/Physical Models


text:
US History/Iran

Operation Merlin
Operation Merlin is an alleged United States covert operation under the Clinton Administration to provide Iran with a flawed design for building a nuclear weapon in order to delay the Iranian nuclear weapons program.

In his book State of War, author and New York Times intelligence correspondent James Risen claims that the CIA chose a defected Russian nuclear scientist to provide deliberately flawed nuclear warhead blueprints to Iranian officials in February 2000. Operation Merlin backfired when the Russian scientist noticed the flaws and pointed them out to the Iranians. Instead, the book alleges, it may have accelerated Iran's nuclear program by providing useful information, once the flaws were identified. Critics' contention Risen's citation of Seymour Hersh as well as anonymous sources make the book's claims somewhat suspicious.

Modern Crisis
On August 14th 2002, Alireza Jafarzadeh revealed the existence of two nuclear sites (Natanz, Arak) previously unknown to the International Atomic Energy Agency. This had many people worried that Iran might, now or later, get the capability to make a nuclear bomb. Since the revelation, the so-called EU-3 (Germany, France and Britain) have tried to pressure Iran to abandoning uranium enrichment. However, Iran has shown no sign of backing down, and after a few "voluntary suspensions", it began enriching uranium yet again.

Ultimately, the IAEA referred Iran to the UN Security Council, the body that can impose sanctions on Iran, or even authorize military action against the country, if Iran does not comply with its demands. Thus far, the Security Council has only agreed on a presidential statement, the weakest action that the body can take, demanding that Iran halt uranium enrichment. After the 30-days deadline passed without compliance by Iran, talks between Europe, Russia, China and the United States have begun yet again about how to handle the Iranian issue. The chance of getting China and Russia, supporters of Iran, to agree with sanctions was slim, but the Bush administration decided to take a gamble. Breaking with nearly 30 years of policy (not recognizing the Iranian regime), the administration offered bilateral talks with Iran on the nuclear issue, if Iran would halt uranium enrichment. It also offered some Euro-American economic and technological incentives for Iran, and the implicit threat of sanctions, if Iran does not accept the deal. Currently, the Iranians are deciding whether or not to accept the offer. President George W. Bush has said that Iran has weeks, not months to accept or reject the deal.

Involvement in 9/11
In July of 2004, the 9/11 Commission unearthed evidence that Iran might have offered safe passage to Al-Qaeda members, who were later involved in the September 11th attacks. However, the CIA had found "no direct connection between Iran and the attacks of Sept. 11." Ultimately, the 9/11 Commission found that Iran did allow safe passage for Al-Qaeda members, but that it had no part in, and was probably not aware of the plot to strike New York and Washington.

Announcement of Enriched Uranium
Then on April 12, 2006, came the news that Iran had completed the enrichment of uranium and sought to increase the enrichment to create industrial grade uranium. What was next? Weapons grade uranium? Many people in the West feared that the United States was planning military action against Iran, in part because of the resemblance between Bush's diplomatic campaign against Iraq and Iran. Also, the American president's harsh rhetoric against Iran has contributed to that perception. Bush, in a State of the Union message, said that Iraq, Iran and North Korea were part of an "Axis of Evil." In the 2006 State of the Union speech, he had mentioned that he wanted Iran to become democratic and free, because the current theocratic dictatorship does not reflect the wishes of the people of Iran, according to Bush. However whether or not there was to be a war was yet to be seen. Bush has not ruled out an attack against Iran, but he is apparently trying to downplay it.

Enriched Uranium Matter
The matter about possible uranium enrichment in Iran was mentioned after the War in Iraq. Enrichment refers to the percentage of 238Uranium to 235Uranium.

Definition
Enriched uranium is a kind of uranium in which the percent composition of uranium-235 has been increased through the process of isotope separation. Natural uranium is 99.284% 238U isotope, with 235U only constituting about 0.711% of its weight. However, 235U is the only isotope existing in nature (in any appreciable amount) that is fissionable by thermal neutrons.

Enriched uranium is a critical component for both civil nuclear power generation and military nuclear weapons. The International Atomic Energy Agency attempts to monitor and control enriched uranium supplies and processes in its efforts to ensure nuclear power generation safety and curb nuclear weapons proliferation.

During the Manhattan Project enriched uranium was given the codename oralloy, a shortened version of Oak Ridge alloy, after the location of the plants where the uranium was enriched. The term oralloy is still occasionally used to refer to enriched uranium. There are about 2,000 metric tons of highly enriched uranium in the world, produced mostly for nuclear weapons, naval propulsion, and smaller quantities for research reactors.

The 238U remaining after enrichment is known as depleted uranium (DU), and is considerably less radioactive than even natural uranium, though still extremely dense. It is useful for armor- penetrating weapons, and other applications requiring very dense metals, though at the present time, only 5% of it is put to any use; the rest remains in storage at the enrichment facilities.

International View on Crisis
Russia and China so far are against any use of sanctions to make Iran abandon its enrichment program. Iran has always condemned U.S hegemony over it. Pakistan is afraid of U.S threats; otherwise it is also very close to Iran.

Arrest of Ramin Jahanbegloo
In May 2006, after he came back from India to Iran, he was arrested by the Iranian government, speculated to have a relation to his recent interview with a Spanish newspaper about Ahmadinejad's comments concerning the Holocaust.

On May 3, Iran judiciary branch officials confirmed that he has been arrested and now he is imprisoned in the Evin Prison. Additionally, an unconfirmed source told the Fars News Agency that he was charged with spying.

On May 4, a friend of his told CBC News that he has been transfered to a hospital.

On May 5, Human Rights Watch expressed concern about Ramin Jahanbegloo being detained without charge and stated that he must immediately be released.

On May 6, The Ottawa Citizen published an article containing concerns voiced by friends of Mr. Jahanbegloo that he was being tortured. These concerns become more urgent Friday, when it became known that Jahanbegloo had been examined twice in the medical clinic at Tehran's notorious Evin prison for political prisoners. Boston University Professor Houchang Chehabi, an Iranian friend of Mr. Jahanbegloo, indicated this was a "bad sign" because it "may mean he's been tortured..."

Kavoshgar-1
Kavoshgar-1 (Explorer-1) is the name of the first Iranian rocket type that is able to reach space. The first launch was conducted on February 4, 2008, as announced by state-run television (or maybe on February 25, 2007, as it is unknown if the two rockets launched are of the same type). Kavoshgar-1 is not, or not yet, able to carry a satellite, but only instruments to measure the higher atmosphere. The rocket launched on February 4, 2008, was a liquid propellant driven rocket, probably a derivate of the Shahab 3, that reached an orbit in space at an altitude of 200-250 km and successful returned science data according to the Iranian News Agency.

On February 19, 2008, Iran offered new information about the rocket and announced that Kavoshgar-1 is a two staged rocket. The first stage separated after 100 seconds and returned to earth with the help of a parachute. The second stage continued its ascend to the altitude of 200 kilometers. However it was not intended to reach orbital velocity.

UN Resolution
The U.N. Security Council imposed another round of sanctions on Iran for refusing to suspend uranium enrichment, but Iran defiantly vowed Monday to continue its nuclear program despite the nearly unanimous censuring vote.

The resolution authorized a third set of sanctions targeting individuals, companies and equipment that could be used in Iran's nuclear program. It was adopted on a vote of 14-0, with Indonesia abstaining.

Two previous sanctions resolution were adopted unanimously, but diplomats said this vote still sent a strong message to the Tehran government that there is global concern that Iran is trying to produce nuclear weapons. Iran insists the program is aimed only at generating power.

The council imposed limited sanctions in December 2006 and has been ratcheting them up in hopes of pressuring Iran to suspend enrichment and start negotiations on its nuclear program. Iran has repeatedly defied the demand and has stepped up enrichment activities.

Iranian Ambassador Mohammad Khazee said just before Monday's vote that his government would not comply with what he called "unlawful action" against Iran's "peaceful nuclear program." He said the Security Council was being "downgraded to a mere tool of the national foreign policy of just a few countries."

"Iran cannot and will not accept a requirement which is legally defective and politically coercive," Khazee said. "History tells us that no amount of pressure, intimidation and threat will be able to coerce our nation to give up its basic and legal rights."

Iran Expelled
Iran has been kicked out of an international defense show in Malaysia for exhibiting missile equipment in violation of U.N. rules, an official said Thursday. Malaysian Deputy Prime Minister Najib Razak said Iranian companies were ordered out of the Defense Services Asia show Tuesday because their exhibition was deemed "offensive."

"Unfortunately, when we came around to inspecting their stand, they displayed equipment that clearly contravened the U.N. resolution — equipment such as missiles and missile systems and others," Najib told reporters.

"The moment they crossed the line, we had no option but to terminate them," Najib added.

Najib said the exhibit was in defiance of U.N. resolutions that ban Iranian arms exports and forbid countries from providing Iran with technical and financial assistance that could contribute to its alleged nuclear weapons program.

Iran is under three sets of U.N. Security Council sanctions for its refusal to suspend uranium enrichment and meet other council demands designed to ease fears that its civilian nuclear program is a cover for attempts to make atomic weapons.

Tehran has denied ever trying to make nuclear arms.

Complaint
Iran has lodged a formal protest at the United Nations about comments by Senator Hillary Rodham Clinton that the United States would “totally obliterate” Iran if it attacked Israel with nuclear weapons, the state-run IRNA news agency reported Thursday.

Iran’s deputy ambassador to the United Nations, Mehdi Danesh-Yazdi, sent a letter of protest on Wednesday to the United Nations secretary general and the United Nations Security Council denouncing the remarks, according to IRNA.

Mrs. Clinton made the comments in an interview on ABC last week. “I want the Iranians to know that if I’m the president, we will attack Iran,” she said when she was asked what she would do if Iran attacked Israel with nuclear weapons. “In the next 10 years, during which they might foolishly consider launching an attack on Israel, we would be able to totally obliterate them,” she added.

Mr. Danesh-Yazdi wrote in the letter that Mrs. Clinton’s comments were “provocative, unwarranted and irresponsible” and “a flagrant violation” of the United Nations charter, IRNA reported.

“I wish to reiterate my government's position that the Islamic Republic of Iran has no intention to attack any other nation,” the letter said.

Nonetheless “Iran would not hesitate to act in self-defense to respond to any attack against the Iranian nation and to take appropriate defensive measures to protect itself,” the letter added.

Secretary Rice
Secretary of State Condoleezza Rice raised fresh doubts Thursday about the nature of Iran's nuclear program, saying if the clerical state really wanted only an avenue to peaceful atomic energy it could quickly have it. Instead, Iran is stonewalling on an attractive deal to trade away only the part of the program that could result in a nuclear weapon, Rice said ahead of a gathering of the U.N. nations that have presented a carrot-or-stick package to Iran.

"I continue to suspect this is not at all about a civil nuclear program," Rice told reporters traveling with her. Iran's insistence that it be able to enrich uranium on its terms seems at cross-purposes with that goal, Rice said.

"One has to wonder what is going on here."

U.S. intelligence agencies concluded in a report last year that Iran shelved an active weapons-development program years ago, a finding that undercut the Bush administration's claim that Iran was using a public energy development program to hide a secret drive for a bomb. An unclassified summary of the report, known as a National Intelligence Estimate, said Iran could resume a weapons program and might evade detection if it did. Rice did not say whether she thought that had happened and did not directly accuse Iran of lying.

Problem left to Successor
The United States and the European Union told Iran on Tuesday they were ready to impose more sanctions over its nuclear enrichment program.

But President George W. Bush acknowledged the limits of U.S. influence over Tehran and, in the twilight of his presidency, appeared resigned to leaving the standoff to his successor.

"I leave behind a multilateral framework to work on this issue," Bush said after a U.S.-EU summit at a Slovenian castle.

"A group of countries can send a clear message to the Iranians, and that is: We're going to continue to isolate you ... we'll find new sanctions if need be, if you continue to deny the just demands of the free world, which is to give up your enrichment program," he said.

He stopped short of repeating the U.S. position that all options, including military action, remain open. "Now is the time for there to be strong diplomacy," Bush said.

Iranian Responce to Election 2008
President Mahmoud Ahmadinejad of Iran told reporters during a trip to New Delhi, the Indian capital, that he believed neither Mrs. Clinton nor Barack Obama, the other Democratic presidential candidate, had a chance of winning the presidential election.

“Do you think a black candidate would be allowed to be president in the U.S.?” he asked, the semiofficial Mehr News Agency reported. “We don’t think Mr. Obama will be allowed to become the U.S. president,” he said.

Referring to Mrs. Clinton, he said: “Presidency of a woman in a country that boasts its gunmanship is unlikely.”

According to the Iranian
Also in the Iranian, an Iranian newsletter, it was said, "Her ideology has contributed to the nation's moral bankruptcy, the loss of over one million lives, and the depletion of America’s treasury. These neoliberals who have driven us into a quagmire, elaborated it would serve America’s interest to promote the Democratic peace theory. Scholars, university professors, and neoliberal jurists presented the concept that sovereignty, as it stood in international law did not provide immunity from attack to states engaging in systematic human rights abuses or amassing weapons of mass destruction. These would be considered ‘pariah’ states to be attacked by democratic coalitions with a warrant to liberalize them.3 Candidate Hillary comes from this stock. It seems that the only thing which differentiates her from McCain is the conduct of the war in Iraq, not the immoral and illegal war itself."

Gordon Brown on Iran and Israel
Gordon Brown threatened Iran with tougher sanctions as he became the first British prime minister to address the Israeli parliament.

At the conclusion of his first trip to Jerusalem as Premier, Mr Brown vowed that Britain would stand by Israel's side as it faced threats to its existence.

Condemning as "abhorrent" Iranian president Mahmoud Ahmadinejad's call for Israel to be wiped from the map, he said he would not stand by as Tehran sought to acquire nuclear weapons.

The Prime Minister also urged Israel to seize the opportunity of lasting peace with the Palestinians. He was heckled at one point as he raised again the need for Israelis to withdraw from settlements on Palestinian land - an issue over which he clashed with his opposite number, Ehud Olmert, on Sunday.

Mr Brown, who was greeted at the Knesset with a red carpet and guard of honor, pleased his audience of MPs and visitors with a Hebrew phrase soon into his speech, "Shalom aleichem", meaning peace be unto you.

He went on to describe his long-standing admiration for Israel, stemming from his churchman father's fascination with, and frequent visits, to the country. He said his premiership would ensure that Britain remained Israel's "true friend".

Syria and Iran Blame U.S. in Blast on Iraq Border
Iran joined Syria on Monday in condemning what they described as an attack by four United States helicopters on the Syrian side of the border with Iraq that they said killed eight people.

Reach of War
The United States confirmed that a special operations mission took place in the area on Sunday but a senior military official gave no more details for now.

The incident comes at a time when the United States is trying to negotiate a strategic agreement with Iraq that would allow American troops to remain in the country and carry out military operations. The pact faces strenuous opposition from neighboring countries, especially Syria and Iran, because of concerns that the United States might use Iraqi territory to carry out attacks on them.

Syria’s state-run news channel reported that United States helicopters on Sunday attacked an area within Syria near the town of Abu Kamal. The official news agency, SANA, cited an anonymous official as saying four American helicopters had “launched aggression on a civilian building under construction,” killing eight people, giving the details of those it said were killed, and that the Syrian deputy foreign minister had summoned the chargé d’affaires from the American and Iraqi Embassies in protest.

Syria also said that United States soldiers on the ground had stormed a building in the area, Reuters reported.

In Tehran, an Iranian Foreign Ministry spokesman, Hassan Qashqavi, condemned the attack, saying a violation of the territorial integrity of any sovereign state was unacceptable.

“Iran condemns in strongest terms any form of aggression or violation of the states’ territorial integrity which leads to the death of innocent civilians,” he told reporters, according to the official news agency IRNA.

Syria’s state-run media also intensified its criticism of the United States on Monday, with the government newspaper Tishrin accusing American forces of committing “a war crime,” Agence France-Presse said.

Iran asks India to be more active in gas pipeline plan
Iran's oil minister called on India to play a more active role in development of a multi-billion dollar gas pipeline from Iran to Pakistan and India, semi-official Mehr news agency reported. "In the light of the many wasted opportunities in the pipeline project because of stalling by India, we asked this country to be more active," Gholam Hossein Nozari said after meeting Indian Foreign Minister Pranab Mukherjee. The 7.5 billion dollar project for the 2,600 kilometer (1,600 miles) Iran-Pakistan-India (IPI) pipeline was launched in 1994 but has been held up by disagreements between India and Pakistan. Iran and Pakistan agreed last month to go ahead with the pipeline on a bilateral basis. Mukherjee, who was in Tehran for an official visit, said India "has no intention of quitting the project," Mehr reported. He also raised the possibility of a three-way meeting between Iran, Pakistan and India, though no date has yet been set.

New Delhi has been under pressure from the United States not to do business with Iran, viewed in Washington as a state sponsor of terrorism that is bent on acquiring nuclear weapons.

Iran holds the world's second largest gas reserves after Russia but remains a small-scale exporter because of heavy domestic consumption and the lack of exploitation of some of its gas fields.

title: US History/Iran