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Control Systems/System Modeling

The Control Process
It is the job of a control engineer to analyze existing systems, and to design new systems to meet specific needs. Sometimes new systems need to be designed, but more frequently a controller unit needs to be designed to improve the performance of existing systems. When designing a system, or implementing a controller to augment an existing system, we need to follow some basic steps:

 * 1) Model the system mathematically
 * 2) Analyze the mathematical model
 * 3) Design system/controller
 * 4) Implement system/controller and test

The vast majority of this book is going to be focused on (2), the analysis of the mathematical systems. This chapter alone will be devoted to a discussion of the mathematical modeling of the systems.

External Description
An external description of a system relates the system input to the system output without explicitly taking into account the internal workings of the system. The external description of a system is sometimes also referred to as the Input-Output Description of the system, because it only deals with the inputs and the outputs to the system.

If the system can be represented by a mathematical function h(t, r), where t is the time that the output is observed, and r is the time that the input is applied. We can relate the system function h(t, r) to the input x and the output y through the use of an integral:

 * $$y(t) = \int_{-\infty}^\infty h(t, r)x(r)dr$$

This integral form holds for all linear systems, and every linear system can be described by such an equation.

If a system is causal (i.e. an input at t=r affects system behaviour only for $$t \ge r$$) and there is no input of the system before t=0, we can change the limits of the integration:

 * $$y(t) = \int_0^t h(t, r)x(r)dr$$

Time-Invariant Systems
If furthermore a system is time-invariant, we can rewrite the system description equation as follows:

 * $$y(t) = \int_0^t h(t - r)x(r)dr$$

This equation is known as the convolution integral, and we will discuss it more in the next chapter.

Every Linear Time-Invariant (LTI) system can be used with the Laplace Transform, a powerful tool that allows us to convert an equation from the time domain into the S-Domain, where many calculations are easier. Time-variant systems cannot be used with the Laplace Transform.

Internal Description
If a system is linear and lumped, it can also be described using a system of equations known as state-space equations. In state-space equations, we use the variable x to represent the internal state of the system. We then use u as the system input, and we continue to use y as the system output. We can write the state-space equations as such:

 * $$x'(t) = A(t)x(t) + B(t)u(t)$$
 * $$y(t) = C(t)x(t) + D(t)u(t)$$

We will discuss the state-space equations more when we get to the section on modern controls.

Complex Descriptions
Systems which are LTI and Lumped can also be described using a combination of the state-space equations, and the Laplace Transform. If we take the Laplace Transform of the state equations that we listed above, we can get a set of functions known as the Transfer Matrix Functions. We will discuss these functions in a later chapter.

Representations
To recap, we will prepare a table with the various system properties, and the available methods for describing the system:

 * {| class="wikitable"

!Properties !! State-Space Equations !! Laplace Transform !! Transfer Matrix
 * Linear, Time-Variant, Distributed || no || no || no
 * Linear, Time-Variant, Lumped || yes || no || no
 * Linear, Time-Invariant, Distributed || no || yes || no
 * Linear, Time-Invariant, Lumped || yes || yes || yes
 * }
 * Linear, Time-Invariant, Distributed || no || yes || no
 * Linear, Time-Invariant, Lumped || yes || yes || yes
 * }
 * }

We will discuss all these different types of system representation later in the book.

Analysis
Once a system is modeled using one of the representations listed above, the system needs to be analyzed. We can determine the system metrics and then we can compare those metrics to our specification. If our system meets the specifications we are finished with the design process. However if the system does not meet the specifications (as is typically the case), then suitable controllers and compensators need to be designed and added to the system.

Once the controllers and compensators have been designed, the job isn't finished: we need to analyze the new composite system to ensure that the controllers work properly. Also, we need to ensure that the systems are stable: unstable systems can be dangerous.

Frequency Domain
For proposals, early stage designs, and quick turn around analyses a frequency domain model is often superior to a time domain model. Frequency domain models take disturbance PSDs (Power Spectral Densities) directly, use transfer functions directly, and produce output or residual PSDs directly. The answer is a steady-state response. Oftentimes the controller is shooting for 0 so the steady-state response is also the residual error that will be the analysis output or metric for report.

Brief Overview of the Math
Frequency domain modeling is a matter of determining the impulse response of a system to a random process.

 * $$S_{YY}\left(\omega\right)=G^*\left(\omega\right)G\left(\omega\right)S_{XX}= \left | G\left(\omega\right)\right \vert S_{XX}$$

where
 * $$S_{XX}\left(\omega\right)$$ is the one-sided input PSD in $$\frac{magnitude^2}{Hz}$$
 * $$G\left(\omega\right)$$ is the frequency response function of the system and
 * $$S_{YY}\left(\omega\right)$$ is the one-sided output PSD or auto power spectral density function.

The frequency response function, $$G\left(\omega\right)$$, is related to the impulse response function (transfer function) by

 * $$g\left(\tau\right)=\frac{1}{2 \pi} \int_{-\infty}^{\infty}e^{i\omega t}H\left(\omega\right)\,d\omega$$

Note some texts will state that this is only valid for random processes which are stationary. Other texts suggest stationary and ergodic while still others state weakly stationary processes. Some texts do not distinguish between strictly stationary and weakly stationary. From practice, the rule of thumb is if the PSD of the input process is the same from hour to hour and day to day then the input PSD can be used and the above equation is valid.

Modeling Examples
Modeling in Control Systems is oftentimes a matter of judgement. This judgement is developed by creating models and learning from other people's models. ControlTheoryPro.com is a site with a lot of examples. Here are links to a few of them

 * Hovering Helicopter Example
 * Reaction Torque Cancellation Example
 * List of all examples at ControlTheoryPro.com

Manufacture
Once the system has been properly designed we can prototype our system and test it. Assuming our analysis was correct and our design is good, the prototype should work as expected. Now we can move on to manufacture and distribute our completed systems.

title: Control Systems/System Modeling


text:
Control Systems/Sampled Data Systems

Ideal Sampler
In this chapter, we are going to introduce the ideal sampler and the Star Transform. First, we need to introduce (or review) the Geometric Series infinite sum. The results of this sum will be very useful in calculating the Star Transform, later.

Consider a sampler device that operates as follows: every T seconds, the sampler reads the current value of the input signal at that exact moment. The sampler then holds that value on the output for T seconds, before taking the next sample. We have a generic input to this system, f(t), and our sampled output will be denoted f*(t). We can then show the following relationship between the two signals:

 * $$f^{\,*}(t)=f(0)\big(\mathrm{u}(t\,-\,0)\,-\,\mathrm{u}(t\,-\,T)\big)\,+\,f(T)\big(\mathrm{u}(t\,-\,T)\,-\,\mathrm{u}(t\,-\,2T)\big)\,+\;\cdots\;+\,f(nT)\big(\mathrm{u}(t\,-\,nT)\,-\,\mathrm{u}(t\,-\,(n\,+\,1)T)\big)\,+\;\cdots$$

Note that the value of f* at time t = 1.5 T is the same as at time t = T. This relationship works for any fractional value.

Taking the Laplace Transform of this infinite sequence will yield us with a special result called the Star Transform. The Star Transform is also occasionally called the "Starred Transform" in some texts.

Geometric Series
Before we talk about the Star Transform or even the Z-Transform, it is useful for us to review the mathematical background behind solving infinite series. Specifically, because of the nature of these transforms, we are going to look at methods to solve for the sum of a geometric series.

A geometric series is a sum of values with increasing exponents, as such:

 * $$\sum_{k=0}^{n} ar^k = ar^0+ar^1+ar^2+ar^3+\cdots+ar^n \,$$

In the equation above, notice that each term in the series has a coefficient value, a. We can optionally factor out this coefficient, if the resulting equation is easier to work with:

 * $$a \sum_{k=0}^{n} r^k = a \left(r^0+r^1+r^2+r^3+\cdots+r^n \,\right)$$

Once we have an infinite series in either of these formats, we can conveniently solve for the total sum of this series using the following equation:

 * $$a \sum_{k=0}^{n} r^k = a\frac{1-r^{n+1}}{1-r}$$

Let's say that we start our series off at a number that isn't zero. Let's say for instance that we start our series off at n = 1 or n = 100. Let's see:

 * $$\sum_{k=m}^{n} ar^k = ar^m+ar^{m+1}+ar^{m+2}+ar^{m+3}+\cdots+ar^n \,$$

We can generalize the sum to this series as follows:

 * $$\sum_{k=m}^n ar^k=\frac{a(r^m-r^{n+1})}{1-r}$$

With that result out of the way, now we need to worry about making this series converge. In the above sum, we know that n is approaching infinity (because this is an infinite sum). Therefore, any term that contains the variable n is a matter of worry when we are trying to make this series converge. If we examine the above equation, we see that there is one term in the entire result with an n in it, and from that, we can set a fundamental inequality to govern the geometric series.

 * $$r^{n+1} < \infty$$

To satisfy this equation, we must satisfy the following condition:

 * $$r \le 1$$

Therefore, we come to the final result: The geometric series converges if and only if the value of r is less than one.

The Star Transform
The Star Transform is defined as such:

 * $$F^*(s) = \mathcal{L}^*[f(t)] = \sum_{k = 0}^\infty f(kT)e^{-skT}$$

The Star Transform depends on the sampling time T and is different for a single signal depending on the frequency at which the signal is sampled. Since the Star Transform is defined as an infinite series, it is important to note that some inputs to the Star Transform will not converge, and therefore some functions do not have a valid Star Transform. Also, it is important to note that the Star Transform may only be valid under a particular region of convergence. We will cover this topic more when we discuss the Z-transform.

Star ↔ Laplace
The Laplace Transform and the Star Transform are clearly related, because we obtained the Star Transform by using the Laplace Transform on a time-domain signal. However, the method to convert between the two results can be a slightly difficult one. To find the Star Transform of a Laplace function, we must take the residues of the Laplace equation, as such:

 * $$X^*(s) = \sum \bigg[ \text{residues of } X(\lambda)\frac{1}{1-e^{-T(s-\lambda)}}\bigg]_{\text{at poles of E}(\lambda)}$$

This math is advanced for most readers, so we can also use an alternate method, as follows:

 * $$X^*(s)=\frac{1}{T}\sum_{n=-\infty}^\infty X(s+jm\omega_s)+\frac{x(0)}{2}$$

Neither one of these methods are particularly easy, however, and therefore we will not discuss the relationship between the Laplace transform and the Star Transform any more than is absolutely necessary in this book. Suffice it to say, however, that the Laplace transform and the Star Transform are related mathematically.

Star + Laplace
In some systems, we may have components that are both continuous and discrete in nature. For instance, if our feedback loop consists of an Analog-To-Digital converter, followed by a computer (for processing), and then a Digital-To-Analog converter. In this case, the computer is acting on a digital signal, but the rest of the system is acting on continuous signals. Star transforms can interact with Laplace transforms in some of the following ways:

Convergence of the Star Transform
The Star Transform is defined as being an infinite series, so it is critically important that the series converge (not reach infinity), or else the result will be nonsensical. Since the Star Transform is a geometic series (for many input signals), we can use geometric series analysis to show whether the series converges, and even under what particular conditions the series converges. The restrictions on the star transform that allow it to converge are known as the region of convergence (ROC) of the transform. Typically a transform must be accompanied by the explicit mention of the ROC.

The Z-Transform
Let us say now that we have a discrete data set that is sampled at regular intervals. We can call this set x[n]:

x[n] = [ x[0] x[1] x[2] x[3] x[4] ... ]

we can utilize a special transform, called the Z-transform, to make dealing with this set more easy:

 * $$X(z) = \mathcal{Z}\left\{x[n]\right\} = \sum_{n = -\infty}^\infty x[n] z^{-n}$$

Like the Star Transform the Z Transform is defined as an infinite series and therefore we need to worry about convergence. In fact, there are a number of instances that have identical Z-Transforms, but different regions of convergence (ROC). Therefore, when talking about the Z transform, you must include the ROC, or you are missing valuable information.

Z Transfer Functions
Like the Laplace Transform, in the Z-domain we can use the input-output relationship of the system to define a transfer function.

The transfer function in the Z domain operates exactly the same as the transfer function in the S Domain:

 * $$H(z) = \frac{Y(z)}{X(z)}$$

 * $$\mathcal{Z}\{h[n]\} = H(z)$$

Similarly, the value h[n] which represents the response of the digital system is known as the impulse response of the system. It is important to note, however, that the definition of an "impulse" is different in the analog and digital domains.

Inverse Z Transform
The inverse Z Transform is defined by the following path integral:

 * $$ x[n] = Z^{-1} \{X(z) \}= \frac{1}{2 \pi j} \oint_{C} X(z) z^{n-1} dz \ $$

Where C is a counterclockwise closed path encircling the origin and entirely in the region of convergence (ROC). The contour or path, C, must encircle all of the poles of X(z).

This math is relatively advanced compared to some other material in this book, and therefore little or no further attention will be paid to solving the inverse Z-Transform in this manner. Z transform pairs are heavily tabulated in reference texts, so many readers can consider that to be the primary method of solving for inverse Z transforms. There are a number of Z-transform pairs available in table form in The Appendix.

Final Value Theorem
Like the Laplace Transform, the Z Transform also has an associated final value theorem:

 * $$\lim_{ n\to \infty} x[n] = \lim_{z \to 1} (z - 1) X(z)$$

This equation can be used to find the steady-state response of a system, and also to calculate the steady-state error of the system.

Star ↔ Z
The Z transform is related to the Star transform though the following change of variables:

 * $$z = e^{sT}$$

Notice that in the Z domain, we don't maintain any information on the sampling period, so converting to the Z domain from a Star Transformed signal loses that information. When converting back to the star domain however, the value for T can be re-insterted into the equation, if it is still available.

Also of some importance is the fact that the Z transform is bilinear, while the Star Transform is unilinear. This means that we can only convert between the two transforms if the sampled signal is zero for all values of n < 0.

Because the two transforms are so closely related, it can be said that the Z transform is simply a notational convenience for the Star Transform. With that said, this book could easily use the Star Transform for all problems, and ignore the added burden of Z transform notation entirely. A common example of this is Richard Hamming's book "Numerical Methods for Scientists and Engineers" which uses the Fourier Transform for all problems, considering the Laplace, Star, and Z-Transforms to be merely notational conveniences. However, the Control Systems wikibook is under the impression that the correct utilization of different transforms can make problems more easy to solve, and we will therefore use a multi-transform approach.

Z plane
z is a complex variable with a real part and an imaginary part. In other words, we can define z as such:

 * $$z = \operatorname{Re}(z) + j\operatorname{Im}(z)$$

Since z can be broken down into two independent components, it often makes sense to graph the variable z on the Z-plane. In the Z-plane, the horizontal axis represents the real part of z, and the vertical axis represents the magnitude of the imaginary part of z.

Notice also that if we define z in terms of the star-transform relation:

 * $$z = e^{sT}$$

we can separate out s into real and imaginary parts:

 * $$s = \sigma + j\omega$$

We can plug this into our equation for z:

 * $$z = e^{(\sigma + j\omega)T} = e^{\sigma T} e^{j\omega T}$$

Through Euler's formula, we can separate out the complex exponential as such:

 * $$z = e^{\sigma T} (\cos(\omega T) + j\sin(\omega T))$$

If we define two new variables, M and φ:

 * $$M = e^{\sigma T}$$

 * $$\phi = \omega T$$

We can write z in terms of M and φ. Notice that it is Euler's equation:

 * $$z = M\cos(\phi) + jM\sin(\phi)$$

Which is clearly a polar representation of z, with the magnitude of the polar function (M) based on the real-part of s, and the angle of the polar function (φ) is based on the imaginary part of s.

Region of Convergence
To best teach the region of convergance (ROC) for the Z-transform, we will do a quick example.

Laplace ↔ Z
There are no easy, direct ways to convert between the Laplace transform and the Z transform directly. Nearly all methods of conversions reproduce some aspects of the original equation faithfully, and incorrectly reproduce other aspects. For some of the main mapping techniques between the two, see the Z Transform Mappings Appendix.

However, there are some topics that we need to discuss. First and foremost, conversions between the Laplace domain and the Z domain are not linear, this leads to some of the following problems:

 * 1) $$\mathcal{L}[G(z)H(z)] \ne G(s)H(s)$$
 * 2) $$\mathcal{Z}[G(s)H(s)] \ne G(z)H(z)$$

This means that when we combine two functions in one domain multiplicatively, we must find a combined transform in the other domain. Here is how we denote this combined transform:

 * $$\mathcal{Z}[G(s)H(s)] = \overline{GH}(z)$$

Notice that we use a horizontal bar over top of the multiplied functions, to denote that we took the transform of the product, not of the individual pieces. However, if we have a system that incorporates a sampler, we can show a simple result. If we have the following format:

 * $$Y(s) = X^*(s)H(s)$$

Then we can put everything in terms of the Star Transform:

 * $$Y^*(s) = X^*(s)H^*(s)$$

and once we are in the star domain, we can do a direct change of variables to reach the Z domain:

 * $$Y^*(s) = X^*(s)H^*(s) \to Y(z) = X(z)H(z)$$

Note that we can only make this equivalence relationship if the system incorporates an ideal sampler, and therefore one of the multiplicative terms is in the star domain.

Z ↔ Fourier
By substituting variables, we can relate the Star transform to the Fourier Transform as well:

 * $$e^{sT} = e^{j \omega}$$
 * $$e^{(\sigma + j \omega)T} = e^{j \omega}$$

If we assume that T = 1, we can relate the two equations together by setting the real part of s to zero. Notice that the relationship between the Laplace and Fourier transforms is mirrored here, where the Fourier transform is the Laplace transform with no real-part to the transform variable.

There are a number of discrete-time variants to the Fourier transform as well, which are not discussed in this book. For more information about these variants, see Digital Signal Processing.

Reconstruction
Some of the easiest reconstruction circuits are called "Holding circuits". Once a signal has been transformed using the Star Transform (passed through an ideal sampler), the signal must be "reconstructed" using one of these hold systems (or an equivalent) before it can be analyzed in a Laplace-domain system.

If we have a sampled signal denoted by the Star Transform $$X^*(s)$$, we want to reconstruct that signal into a continuous-time waveform, so that we can manipulate it using Laplace-transform techniques.

Let's say that we have the sampled input signal, a reconstruction circuit denoted G(s), and an output denoted with the Laplace-transform variable Y(s). We can show the relationship as follows:

 * $$Y(s) = X^*(s)G(s)$$

Reconstruction circuits then, are physical devices that we can use to convert a digital, sampled signal into a continuous-time domain, so that we can take the Laplace transform of the output signal.

Zero order Hold

A zero-order hold circuit is a circuit that essentially inverts the sampling process: The value of the sampled signal at time t is held on the output for T time. The output waveform of a zero-order hold circuit therefore looks like a staircase approximation to the original waveform.

The transfer function for a zero-order hold circuit, in the Laplace domain, is written as such:

 * $$G_{h0} = \frac{1 - e^{-Ts}}{s}$$

The Zero-order hold is the simplest reconstruction circuit, and (like the rest of the circuits on this page) assumes zero processing delay in converting between digital to analog.

First Order Hold

The zero-order hold creates a step output waveform, but this isn't always the best way to reconstruct the circuit. Instead, the First-Order Hold circuit takes the derivative of the waveform at the time t, and uses that derivative to make a guess as to where the output waveform is going to be at time (t + T). The first-order hold circuit then "draws a line" from the current position to the expected future position, as the output of the waveform.

 * $$G_{h1} = \frac{1 + Ts}{T} \left[ \frac{1 - e^{-Ts}}{s}\right]^2$$

Keep in mind, however, that the next value of the signal will probably not be the same as the expected value of the next data point, and therefore the first-order hold may have a number of discontinuities.

Fractional Order Hold
The Zero-Order hold outputs the current value onto the output, and keeps it level throughout the entire bit time. The first-order hold uses the function derivative to predict the next value, and produces a series of ramp outputs to produce a fluctuating waveform. Sometimes however, neither of these solutions are desired, and therefore we have a compromise: Fractional-Order Hold. Fractional order hold acts like a mixture of the other two holding circuits, and takes a fractional number k as an argument. Notice that k must be between 0 and 1 for this circuit to work correctly.

 * $$G_{hk} = (1 - ke^{-Ts}) \frac{1 - e^{-Ts}}{s} + \frac {k}{Ts^2} (1 - e^{-Ts})^2$$

This circuit is more complicated than either of the other hold circuits, but sometimes added complexity is worth it if we get better performance from our reconstruction circuit.

Other Reconstruction Circuits

Another type of circuit that can be used is a linear approximation circuit.

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

title: Control Systems/Sampled Data Systems


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Control Systems/System Delays

Delays
A system can be built with an inherent delay. Delays are units that cause a time-shift in the input signal, but that don't affect the signal characteristics. An ideal delay is a delay system that doesn't affect the signal characteristics at all, and that delays the signal for an exact amount of time. Some delays, like processing delays or transmission delays, are unintentional. Other delays however, such as synchronization delays, are an integral part of a system. This chapter will talk about how delays are utilized and represented in the Laplace Domain. Once we represent a delay in the Laplace domain, it is an easy matter, through change of variables, to express delays in other domains.

Ideal Delays
An ideal delay causes the input function to be shifted forward in time by a certain specified amount of time. Systems with an ideal delay cause the system output to be delayed by a finite, predetermined amount of time.

Time Shifts
Let's say that we have a function in time that is time-shifted by a certain constant time period T. For convenience, we will denote this function as x(t - T). Now, we can show that the Laplace transform of x(t - T) is the following:

 * $$\mathcal{L}\{x(t - T)\} \Leftrightarrow e^{-sT}X(s)$$

What this demonstrates is that time-shifts in the time-domain become exponentials in the complex Laplace domain.

Shifts in the Z-Domain
Since we know the following general relationship between the Z Transform and the Star Transform:

 * $$z \Leftrightarrow e^{sT}$$

We can show what a time shift in a discrete time domain becomes in the Z domain:

 * $$x((n-n_s)\cdot T)\equiv x[n - n_s] \Leftrightarrow z^{-n_s}X(z)$$

Delays and Stability
A time-shift in the time domain becomes an exponential increase in the Laplace domain. This would seem to show that a time shift can have an effect on the stability of a system, and occasionally can cause a system to become unstable. We define a new parameter called the time margin as the amount of time that we can shift an input function before the system becomes unstable. If the system can survive any arbitrary time shift without going unstable, we say that the time margin of the system is infinite.

Delay Margin
When speaking of sinusoidal signals, it doesn't make sense to talk about "time shifts", so instead we talk about "phase shifts". Therefore, it is also common to refer to the time margin as the phase margin of the system. The phase margin denotes the amount of phase shift that we can apply to the system input before the system goes unstable.

We denote the phase margin for a system with a lowercase Greek letter φ (phi). Phase margin is defined as such for a second-order system:

 * $$\phi_m = \tan^{-1} \left[ \frac{2 \zeta}{(\sqrt{4 \zeta^4 + 1} - 2\zeta^2)^{1/2}}\right]$$

Oftentimes, the phase margin is approximated by the following relationship:

 * $$\phi_m \approx 100\zeta$$

The Greek letter zeta (ζ) is a quantity called the damping ratio, and we discuss this quantity in more detail in the next chapter.

Transform-Domain Delays
The ordinary Z-Transform does not account for a system which experiences an arbitrary time delay, or a processing delay. The Z-Transform can, however, be modified to account for an arbitrary delay. This new version of the Z-transform is frequently called the Modified Z-Transform, although in some literature (notably in Wikipedia), it is known as the Advanced Z-Transform.

Delayed Star Transform
To demonstrate the concept of an ideal delay, we will show how the star transform responds to a time-shifted input with a specified delay of time T. The function :$$X^*(s, \Delta)$$ is the delayed star transform with a delay parameter Δ. The delayed star transform is defined in terms of the star transform as such:

 * $$X^*(s, \Delta)

= \mathcal{L}^* \left\{ x(t - \Delta) \right\} = X(s)e^{-\Delta T s}$$

As we can see, in the star transform, a time-delayed signal is multiplied by a decaying exponential value in the transform domain.

Delayed Z-Transform
Since we know that the Star Transform is related to the Z Transform through the following change of variables:

 * $$z = e^{-sT}$$

We can interpret the above result to show how the Z Transform responds to a delay:

 * $$\mathcal{Z}(x[t - T]) = X(z)z^{-T}$$

This result is expected.

Now that we know how the Z transform responds to time shifts, it is often useful to generalize this behavior into a form known as the Delayed Z-Transform. The Delayed Z-Transform is a function of two variables, z and Δ, and is defined as such:

 * $$X(z, \Delta)

= \mathcal{Z} \left\{ x(t - \Delta) \right\} = \mathcal{Z} \left\{ X(s)e^{-\Delta T s} \right\}$$

And finally:

 * $$\mathcal{Z}(x[n], \Delta) = X(z, \Delta) = \sum_{n=-\infty}^\infty x[n - \Delta]z^{-n}$$

Modified Z-Transform
The Delayed Z-Transform has some uses, but mathematicians and engineers have decided that a more useful version of the transform was needed. The new version of the Z-Transform, which is similar to the Delayed Z-transform with a change of variables, is known as the Modified Z-Transform. The Modified Z-Transform is defined in terms of the delayed Z transform as follows:

 * $$X(z, m)

= X(z, \Delta)\big|_{\Delta \to 1 - m}        = \mathcal{Z} \left\{ X(s)e^{-\Delta T s} \right\}\big|_{\Delta \to 1 - m} $$

And it is defined explicitly:

 * $$X(z, m) = \mathcal{Z}(x[n], m) = \sum_{n = -\infty}^{\infty} x[n + m - 1]z^{-n}$$

title: Control Systems/System Delays


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Control Systems/MIMO Systems

Multi-Input, Multi-Output
Systems with more than one input and/or more than one output are known as Multi-Input Multi-Output systems, or they are frequently known by the abbreviation MIMO. This is in contrast to systems that have only a single input and a single output (SISO), like we have been discussing previously.

State-Space Representation
MIMO systems that are lumped and linear can be described easily with state-space equations. To represent multiple inputs we expand the input u(t) into a vector U(t) with the desired number of inputs. Likewise, to represent a system with multiple outputs, we expand y(t) into Y(t), which is a vector of all the outputs. For this method to work, the outputs must be linearly dependent on the input vector and the state vector.

 * $$X'(t) = AX(t) + BU(t)$$
 * $$Y(t) = CX(t) + DU(t)$$

Transfer Function Matrix
If the system is LTI and Lumped, we can take the Laplace Transform of the state-space equations, as follows:

 * $$\mathcal{L}[X'(t)] = \mathcal{L}[AX(t)] + \mathcal{L}[BU(t)]$$
 * $$\mathcal{L}[Y(t)] = \mathcal{L}[CX(t)] + \mathcal{L}[DU(t)]$$

Which gives us the result:

 * $$s\mathbf{X}(s) - X(0) = A\mathbf{X}(s) + B\mathbf{U}(s)$$
 * $$\mathbf{Y}(s) = C\mathbf{X}(s) + D\mathbf{U}(s)$$

Where X(0) is the initial conditions of the system state vector in the time domain. If the system is relaxed, we can ignore this term, but for completeness we will continue the derivation with it.

We can separate out the variables in the state equation as follows:

 * $$s\mathbf{X}(s) - A\mathbf{X}(s) = X(0) + B\mathbf{U}(s)$$

Then factor out an X(s):

 * $$\mathbf[sI - A]{X}(s) = X(0) + B\mathbf{U}(s)$$

And then we can multiply both sides by the inverse of [sI - A] to give us our state equation:

 * $$\mathbf{X}(s) = [sI - A]^{-1}X(0) + [sI - A]^{-1}B\mathbf{U}(s)$$

Now, if we plug in this value for X(s) into our output equation, above, we get a more complicated equation:

 * $$\mathbf{Y}(s) = C([sI - A]^{-1}X(0) + [sI - A]^{-1}B\mathbf{U}(s)) + D\mathbf{U}(s)$$

And we can distribute the matrix C to give us our answer:

 * $$\mathbf{Y}(s) = C[sI - A]^{-1}X(0) + C[sI - A]^{-1}B\mathbf{U}(s) + D\mathbf{U}(s)$$

Now, if the system is relaxed, and therefore X(0) is 0, the first term of this equation becomes 0. In this case, we can factor out a U(s) from the remaining two terms:

 * $$\mathbf{Y}(s) = (C[sI - A]^{-1}B + D)\mathbf{U}(s)$$

We can make the following substitution to obtain the Transfer Function Matrix, or more simply, the Transfer Matrix, H(s):

 * $$C[sI - A]^{-1}B + D = \mathbf{H}(s)$$

And rewrite our output equation in terms of the transfer matrix as follows:

 * $$\mathbf{Y}(s) = \mathbf{H}(s)\mathbf{U}(s)$$

If Y(s) and X(s) are 1 × 1 vectors (a SISO system), then we have our external description:

 * $$Y(s) = H(s)X(s)$$

Now, since X(s) = X(s), and Y(s) = Y(s), then H(s) must be equal to H(s). These are simply two different ways to describe the same exact equation, the same exact system.

Dimensions
If our system has q inputs, and r outputs, our transfer function matrix will be an r × q matrix.

Relation to Transfer Function
For SISO systems, the Transfer Function matrix will reduce to the transfer function as would be obtained by taking the Laplace transform of the system response equation.

For MIMO systems, with n inputs and m outputs, the transfer function matrix will contain n × m transfer functions, where each entry is the transfer function relationship between each individual input, and each individual output.

Through this derivation of the transfer function matrix, we have shown the equivalency between the Laplace methods and the State-Space method for representing systems. Also, we have shown how the Laplace method can be generalized to account for MIMO systems. Through the rest of this explanation, we will use the Laplace and State Space methods interchangeably, opting to use one or the other where appropriate.

Zero-State and Zero-Input
If we have our complete system response equation from above:

 * $$\mathbf{Y}(s) = C[sI - A]^{-1}\mathbf{x}(0) + (C[sI - A]^{-1}B + D)\mathbf{U}(s)$$

We can separate this into two separate parts:

 * $$C[sI - A]^{-1}X(0)$$ The Zero-Input Response.
 * $$(C[sI - A]^{-1}B + D)\mathbf{U}(s)$$ The Zero-State Response.

These are named because if there is no input to the system (zero-input), then the output is the response of the system to the initial system state. If there is no state to the system, then the output is the response of the system to the system input. The complete response is the sum of the system with no input, and the input with no state.

Discrete MIMO Systems
In the discrete case, we end up with similar equations, except that the X(0) initial conditions term is preceded by an additional z variable:

 * $$\mathbf{X}(z) = [zI - A]^{-1}zX(0) + [zI - A]^{-1}B\mathbf{U}(z)$$
 * $$\mathbf{Y}(z) = C[zI - A]^{-1}zX(0) + C[zI - A]^{-1}B\mathbf{U}(z) + D\mathbf{U}(z)$$

If X(0) is zero, that term drops out, and we can derive a Transfer Function Matrix in the Z domain as well:

 * $$\mathbf{Y}(z) = (C[zI - A]^{-1}B + D)\mathbf{U}(z)$$

 * $$C[zI - A]^{-1}B + D = \mathbf{H}(z)$$

 * $$\mathbf{Y}(z) = \mathbf{H}(z)\mathbf{U}(z)$$

Controller Design
The controller design for MIMO systems is more extensive and thus more complicated than for SISO system. Ackermann's formula, the typical full state feedback design for SISO system, could not be used for MIMO systems because the additional inputs lead to an overdetermined system. This means, in case of MIMO systems, the feedback matrix K is not unique.

Approaches for the controller design are stated in Section Eigenvalue Assignment for MIMO Systems.

title: Control Systems/MIMO Systems


text:
User:Tom Tolnam

Tom Tolnam's page.

title: User:Tom Tolnam


text:
Cookbook:Cruller

| Dessert | Cuisine of France

A cruller is a type of doughnut. It is often covered in or topped with icing, which may be chocolate. It is often twisted (rather than round) in shape and unraised. The word comes from early 19th century Dutch kruller, from krullen "to curl." It is most commonly found in New England and the Mid-Atlantic and North Central states of the USA, but it is also common in California. It is also common in France.

title: Cookbook:Cruller


text:
Talk:Sociology of the Family

I'd suggest reverting the move to Wikiversity, books, text- or otherwise, should stay here.--Piotrus 02:45, 14 September 2006 (UTC)
 * Done. --Digitalme 22:00, 17 September 2006 (UTC)

I have copied the content to Wikipedia article on the subject, as it seems more intro/encyclopedic then a proper book anyway. See Sociology of the family. --Piotrus (talk) 18:40, 16 March 2009 (UTC)

title: Talk:Sociology of the Family


text:
Talk:Cell Biology/Organelles

There is a reference to Mitochondria being responsible for respiration-is this correct?

I can only find references that mention protein generation. However I am unable to find any reference to respiration.

--Xrayman 03:22, 14 September 2006 (UTC)

I have since modified it to read that it is responsible for metabolism within the cell. --Xrayman 03:43, 14 September 2006 (UTC)

day in the life of a cell
Xrayman- if you can't answer that question you should not be adding content to this article.

Are we sure we want a "day in the life of a cell" section? Out of place. I'm going to delete it unless someone objects.

title: Talk:Cell Biology/Organelles


text:
Talk:Dutch/Lesson 2

Untitled
een rood huis, een rode auto -- should we point out the exception for neuter nouns with an indefinite article here? It seems confusing.

 * I revised it, but the explanation is in part only given in the next lesson because nouns are discussed later. At first I thought this was aproblem but I kind of like it this way.

Iarlagab 14:01, 27 March 2007 (UTC)

title: Talk:Dutch/Lesson 2


text:
Bicycles/Maintenance and Repair/Pedals

Non-serviceable pedals
For standard platform and cage pedals: Most (if not all) modern (c.2006) non-clipless pedals (like the one shown at right) are made to be disposed of when they wear out. This includes many pedals with toe clips: the days when 'serious' cyclists used toe clips are long gone, and so the manufacturers don't bother with making pedals for the low end of the market that can be overhauled. This makes maintenance obvious: remove the old pedals and install some new ones. These disposable pedals can last a long time. Make sure the plastic plugs in the ends of the pedals don't fall out; this is where the water and dirt will enter and speed up bearing wear.

Serviceable Pedals

 * It's worth having pedals that you can service yourself. (You do like working on your bike, don't you?  That's why you're reading this book!)  If you're not a 'serious' cyclist (and let's face it, most people aren't; if you are, we've got more information for you coming soon) then being able to re-pack the bearings in your pedals will save you lots of money over the years.  It's also nice to not have to throw away gear that, but for want of a better design, could be renovated and used again.

Toe Clips, etc

 * Different pedal retention systems (or lack thereof) and how they interact with your feet and footwear. (Plain (do not use toe-clip-only pedals without toe clips!!!), toe clips, half clips, PowerGrips, clipless.)

 * The spindles (axles) of pedals are made from hardened steel and can be reused to make tools such as punches.
 * The most popular standard for pedals is 9/16", but some cheaper bicycles use 1/2" (based on nominal hole size).

Tools
Extra long spanners/wrenches are available for the removal of pedals. These typically have a head with a 9/16" opening on one side and a 15mm opening on the other side and long comfortable handle for extra leverage. If the pedal was installed properly, a pedal spanner is typically not required.  But often pedals become seized and the longer lever arm and comfortable handle are useful in removing the pedal.  Properly installed pedals should be removable with a standard spanner/wrench, mostly commonly 15mm.  Usually the flats of the pedal are too small for a shifting spanner/adjustable wrench, unless the tool is very small (6" in length or less). Some pedals have a 8mm allen hole on the frame side which can be used for removal and installation.

Removing Pedals
See the article on removing pedals

Installing Pedals
Pedals should always be greased before installing them, especially in areas where corrosion (i.e. from salt) is a problem. Any general purpose grease is acceptable. Ungreased pedals are very likely to become seized later and make for troublesome removal.

title: Bicycles/Maintenance and Repair/Pedals


text:
XForms/Calculator

One of the classic examples of a web application program is a calculator.

Discussion
The calculator program is about 300 lines long. But much of the code is just telling what actions should happen when a button gets pressed.

The model of the calculator is very simple. Just a five variables:

 * display - the visible display
 * displaybuffer - a secondary display that is not visible
 * first - the first operator
 * second - the second operator
 * memory - used by the memory function

Here is the trigger for the "5" button:

 5

The actions for the trigger is to do just two things:
 * 1) are to multiply the value of the display buffer by 10 (shifting the digits over by one) and then to add a five.
 * 2) copy the value of the display buffer to the display.

There are also scientific function calculators but they have a smiliar structure.

It is interesting to compare a JavaScript version to the XForms version. The JavaScript version is shorter but the JavaScript can take advantage of some of the tools that are available to JavaScript.

title: XForms/Calculator


text:
Embedded Systems/Cypress PSoC Microcontroller

The Cypress PSoC microcontroller, like all microprocessors, has its own quirks.

When you can't figure something out, and this FAQ doesn't help, the forums at are a good place to start.
 * http://www.psocdeveloper.com/, under "Forums"
 * http://www.psoczone.com/, under "Forums"
 * http://www.cypress.com/, under "Technical Support" then "Discussion Boards".

= User Documentation =

 * Embedded Systems/Cypress PSoC Microcontroller/Application Notes
 * Embedded Systems/Cypress PSoC Microcontroller/User Modules

= Cypress PSoC FAQ =

(If the answers I've sketched in are incorrect, *please* correct them).

Which PSoC to use
Some people recommend that hobbyists use the largest and most capable chip available in a DIP package—as of 2008-09, that is the CY8C29466 28-DIP.

CY8C29466 28-DIP—This is the same chip as in the CY8C29466 28-SSOP or 28-SOIC, and similar to the CY8C29566 44-TQFP, CY8C29666 48-SSOP or 48-QFN, and CY8C29866 100TQFP. The difference aside from the packages is the number of I/O pins. These parts have more Flash (32 KByte Flash) and more RAM (2 KByte RAM) and more digital blocks (16) and more analog blocks (12) than any other PSoC available (except the 27xxx series has the same number of analog blocks).

CY8C27143 8-DIP: more Flash (16 KByte Flash) and more digital blocks (8) and more analog blocks (12) and just as much RAM (256 bytes) of any 8-pin PSoC.

CY8CNP102: not yet available (as of 2008-09), but expected to have 256 KByte non-volatile storage and 2 KByte RAM.

(analogous to Embedded Systems/PIC Microcontroller)

Many PSoC development boards are available for under $100 each. They include:
 * Gainer PSoC Development Board
 * MP3 Trigger PSoC development board
 * freeSoC PSoC dev board
 * "PSoC FirstTouch Starter Kit"
 * "Schmartboard PSoC 5LP Development Board"
 * "PSoC 4 Pioneer Kit"

other FAQs
Q: It's not working! A: Have you gone through the "Software Checklist: Tips on Using PSoC" by Zlatko Saravanja, 2004 ? Tips on using the PSoC ? PSoC(R) Technical Reference Manual (TRM)? "Getting Started with PSoC (READ THIS FIRST) - AN2010"?

Q: I'm having problems trying to use my PSoC MiniProg to program a CY8C26443. A: The Miniprogrammer does not support the 25/26 families. You will have to use ICE-4000 or the ICE-cube. Or switch to a chip that the MiniProg does support, such as the 27/29 families. [FIXME: make a list of chips, and mark each with "Y -- known to work with MiniProg", "N -- doesn't work with MiniProg", or "? -- unknown"]. http://www.psocdeveloper.com/forums/viewtopic.php?t=2057 http://www.psocdeveloper.com/forums/viewtopic.php?t=2022 (Should we make this a table, with the various programmers -- m8cprogs open hardware, MiniProg, ICE-cube, etc. vs. the various chips?).

interrupt handler
Q: How do I write an interrupt handler in C? A: See "Software Checklist: Tips on Using PSoC". Also, inside the PSoC IDE, choose "Help", "Documentation", then "C Language Compiler User Guide". More discussion: http://www.psocdeveloper.com/forums/viewtopic.php?t=2089 and "Tips on using the PSoC" http://www.psocdeveloper.com/old/index.php?page=8&mode=article&k=11 http://www.psocdeveloper.com/forums/viewtopic.php?t=1902 http://www.psocdeveloper.com/forums/viewtopic.php?t=2102 http://www.psocdeveloper.com/forums/viewtopic.php?t=2099 http://www.psocdeveloper.com/forums/viewtopic.php?t=2089

warning: area 'myproject_RAM' not defined
Q: I'm getting the message:
 * warning: area 'myproject_RAM' not defined in startup file './obj/boot.o' and
 * does not have an link time address.

How do I get rid of that warning? A: (from http://www.psocdeveloper.com/forums/viewtopic.php?t=1761 ) Open the boot.tpl. In the end, you will see many areas defined in RAM. Add the following line below the already existing RAM area declarations, just above the AREA bss declaration: AREA myproject_RAM (RAM, REL, CON) Then save the boot.tpl file and "Config" >> "generate application".

lookup table
Q: How do I create a lookup table in assembly language? A: See http://www.psocdeveloper.com/old/index.php?page=8&mode=article&k=10 (Um ... don't you also have to disable "code compression" during that table?)

gotchas
Q: Any gotchas I should watch out for? A: "Tips on using the PSoC" http://www.psocdeveloper.com/old/index.php?page=8&mode=article&k=11

simulator and other programming languages
Q: What alternatives are there to the (free) PSoC Designer and the ImageCraft PSoC C compiler ? (Because they haven't yet been ported to Linux) A1: m8cutils: http://m8cutils.sourceforge.net/ Werner is developing an assembler and a simulator and a programmer for Linux   http://www.psocdeveloper.com/forums/viewtopic.php?t=1616 A2: Forth/PSoC Forth: Christopher Burns wrote a PSoC Forth. The source code is available at http://www.psocdeveloper.com/tools/misc_dev_tools/. As of 2007, David Cary is maintaining it at Forth/PSoC Forth (was: http://forthfreak.net/index.cgi?M8cForth ). This Forth compiler will work with Linux, Mac, Windows, Solaris, Palm, and even VT-100 dumb terminals.

I/O pins
Q: How do I make output pins Hi and Lo ? A: Usually you connect the output pins to some digital "module" (such as a PWM block). If none of the "modules" do what you want, you can set them in software—see The GPIO reference http://www.psocdeveloper.com/articles/fundamentals_of_psoc_gpio/ the GPIO Read Write example project http://www.psocdeveloper.com/docs/example-project.html GPIO Help http://www.psocdeveloper.com/forums/viewtopic.php?t=83 http://www.psocdeveloper.com/forums/viewtopic.php?t=1950 (Warning: Be aware that the PRTxDR register is write-only—you can't read back from that register. If you read from the PRTxDR address, you are directly reading the value at the pins, which is often *not* what you just wrote. If you incorrectly assume they will be the same, you will sooner or later be bitten by the read-modify-write problem.). (Warning: "you cannot read a port that is configured for "interrupt on change from last read" from main code and have the ISR feature work reliably." See http://www.psocdeveloper.com/forums/viewtopic.php?t=2094 ). "How to set a single port pin?" http://www.cypress.com/portal/server.pt/gateway/PTARGS_0_652034_739_205_211_43/http%3B/sjapp20/cf_apps/design_supports/forums/messageview.cfm?catid=3&threadid=18055 PSoC I/O Pin-Port Configuration - AN2094 http://www.cypress.com/portal/server.pt?space=CommunityPage&control=SetCommunity&CommunityID=285&PageID=552&shortlink=DA_240474 "Mr. Zee's intro to GPIO", "Basic fundamentals of GPIO" by mrzee http://www.psocdeveloper.com/forums/viewtopic.php?t=2058 http://www.psocdeveloper.com/forums/viewtopic.php?t=1667

Q: What should I do with pins I'm not using? A: Nothing. The Designer will leave them in high-impedance mode by default. They'll be perfectly happy if left floating. If it really bothers you, set them to pull-up or pull-down.

QThe XRES should be connected to ... what ? A: Although it has an internal pull down it is good practice to connect it to ground via a 470,1K,... ohm resistor.

I/O pins
Q: How do I read the state of a single digital input pin? A: Usually you connect the input pins to some digital "module" (such as a timer block). If none of the "modules" do what you want, you can set them in software—see the GPIO references in the previous question.

interrupts
Q: How do I set up a digital input pin to trigger an interrupt? Where do I put the code to handle that interrupt? A: ??? http://www.psocdeveloper.com/forums/viewtopic.php?t=1586 "How to determine source of GPIO interrupt" http://www.psocdeveloper.com/forums/viewtopic.php?t=1524

How many bytes of stack do I really need?
Q: I'm running out of RAM—How many bytes of stack do I really *need*? A: the "stalkwalk" utility does static stack analysis http://www.psocdeveloper.com/forums/viewtopic.php?t=9 gives a conservative count of how many bytes are needed. (It still needs some work ...).

RS485
Q: How do I connect my PSoC to a RS485 bus? A1: http://www.psocdeveloper.com/forums/viewtopic.php?t=1640 mentions "Interrupt on 9th bit ... Application Note AN2269 "Implement 9-Bit Protocol on the PSoC™ UART" ". A2: Half-duplex issues are discussed at http://www.psocdeveloper.com/forums/viewtopic.php?t=1731 http://www.psocdeveloper.com/forums/viewtopic.php?t=2397

UART
Q: The UART isn't working! I'm pulling out my hair! A: Please restate in the form of a question.

mixing C and assembly language
Q: How do I call a C function from assembly? A: You can call C functions in assembly by adding an underscore before the function name. For example, if you want to call a C function called foo from assembly you would use call _foo . This applies for C functions that do not take any parameters. If you want to call functions that take parameters then you need to pass these parameters to the stack before calling it. The parameters are pushed from right to left and MSB first. Example: C function to be called: void foo(WORD Arg1, WORD Arg2) assembly code: mov A,[Arg2 MSB] push A mov A,[Arg2 LSB] push A mov A,[Arg1 MSB] push A mov A,[Arg1 LSB] push A xcall _foo add SP,-4

interrupts
Q: How do I call a C function from an assembly ISR? A1: The simple method: Use "#pragma interrupt_handler" to mark the C function. From the ISR side, LJUMP to the C function (don't bother pushing anything on the stack). Refer to the answer of question "How do I write an interrupt handler in C?". The C function marked with "#pragma interrupt_handler" can call normal C functions (and normal assembly functions) -- but normal C functions *cannot* call any C function marked with "#pragma interrupt_handler".

A2: If you insist that your assembly ISR *must* "call" a normal C function, it gets tricky.

You need to take care of saving and restoring virtual registers used by the C function. Open the .lst file and check what are the virtual registers used by the C function. For example, if the C function foo uses virtual registes __r0 and __r1: (assumes void foo(void). See "How do I call a C function from assembly?" if foo has parameters.)

mov A,[__r0] push A mov A,[__r1] push A xcall _foo pop A mov [__r1],A pop A mov [__r0],A

Apart from saving and restoring virtual registers, A and X also have to be saved and restored. In case you are using a program with LMM enabled, then the paging mode has to be restored to native paging before calling the C function and also the paging registers have to be saved and restored.

This is all stuff that the compiler would have handled automatically for you, if you had marked that C function with "#pragma interrupt_handler", and had your assembly language LJUMP to that C function.

object code size
Q: How can I optimize object code size generated by the PSoC C Compiler ?

A1: On MCUs with more than 256 bytes of SRAM, do not use LMM if at all possible. The overhead from page management is significant.

A2: Do not use 32-bit variables unless absolutely necessary.

A3: If possible, stick to 8-bit variables of type BYTE, and only use 16-bit WORDs if necessary.

A4: If readability does not overly suffer, try to only use global variables.

A5: Stay away from pointers to structures, and arrays of structures. This particularly means avoiding the passing of structure pointers to functions.

A6: Consider limiting the number of function parameters, and making common data global that can be accessed directly by all functions.

JTAG
Q: Does the PSoC do JTAG ? A: No. But much of the JTAG functionality can be done other ways. PSoC boundary scan using "m8cbscan"

Q: Is there a way that the program running in the PSoC can modify the flash in that same PSoC? (instead of the normal process of burning the program into the PSoC, then never modifying the program) ? A1: ... use the EEPROM module ... A2: ... some tips in the "Flash Write Routine" thread ... A3: ... Forth/PSoC Forth gives an example of a program running in the PSoC that modifies the flash in that same PSoC.


text:
Literary Criticism/Comparison Exercises

Comparison Exercise 1
Write a critical discussion of the following TWO passages, pointing out features of comparison and/or contrast. (a)    "How sad it is!" murmured Dorian Gray with his eyes still fixed upon his own portrait. "How sad it is! I shall grow old, and horrible, and dreadful. But this picture will remain always young. It will never be older than this particular day of June. . . . If it were only the other way! If it were I who was to be always young, and the picture that was to grow old! For that--for that--I would give everything! Yes, there is nothing in the whole world I would not give! I would give my soul for that!" The painter stared in amazement. It was so unlike Dorian to speak like that. What had happened? He seemed quite angry. His face was flushed and his cheeks burning. "Yes," he continued. “How long will you like me? Till I have my first wrinkle, I suppose. I know, now, that when one loses one's good looks, whatever they may be, one loses everything. Your picture has taught me that. Lord Henry Wotton is perfectly right. Youth is the only thing worth having. When I find that I am growing old, I shall kill myself." Hallward turned pale and caught his hand. "Dorian! Dorian!" he cried, "don't talk like that. I have never had such a friend as you, and I shall never have such another. You are not jealous of material things, are you?-- you who are finer than any of them!" "I am jealous of everything whose beauty does not die. I am jealous of the portrait you have painted of me. Why should it keep what I must lose? Every moment that passes takes something from me and gives something to it. Oh, if it were only the other way! If the picture could change, and I could be always what I am now! Why did you paint it? It will mock me some day- mock me horribly!" Excerpt from Oscar Wilde The Picture of Dorian Gray

(b)              Mirror

I am silver and exact. I have no preconceptions.

Whatever I see I swallow immediately.

Just as it is, unmisted by love or dislike.

I am not cruel, only truthful –

The eye of a little god, four-cornered.

Most of the time I meditate on the opposite wall.

It is pink, with speckles. I have looked at it so long

I think it is a part of my heart. But it flickers.

Faces and darkness separate us over and over.

Now I am a lake. A woman bends over me.

Searching my reaches for what she really is.

Then she turns to those liars, the candle or the moon.

I see her back. I reflect it faithfully.

She rewards me with tears and the agitation of hands.

I am important to her. She comes and goes.

Each morning it is her face that replaces the terrible darkness.

In me she has drowned a young girl, and in me an old woman

Rises toward her day after day like a terrible fish.

Sylvia Plath

Questions and Suggested Answer to Comparison Exercise 1
1)How do Dorian Gray and the persona in the poem feel about their appearance?

Dorian Gray is a narcissist and he regards his appearance, his young look - as "the only thing worth having", and sees that "when one loses one's good looks", "one loses everything". When he looks into the portrait of himself, he suddenly feels that he will be ageing and he will lose his youth and this clearly scares him. He desires to look young forever, he simply cannot stand seeing himself grow to be an old man, we can see his desire to "stay young" in "When I find that I am growing old, I shall kill myself". He is willing to sacrifice everything in order to protect his youth, or in other words, look better in appearance. We can see that he is getting mad as he discovers he would eventually grow old one day, he would rather sacrifice his "soul", and he even gets angry at the portrait as it can remain "young" forever. He believes his own portrait would "mock" him "horribly" one day, when he finds that he himself becomes an old man. He sees an appearance with "youth" above all things.

The woman in the poem "Mirror" has great dislike on her appearance. Like Dorian Gray, she has seen her trueself in the "lake"(mirror) as it reflects her appearance "faithfully". However when she comes face to face with her actual appearance, she "rewards" the "lake" with "tears" and "the agitation of hands", clearly shows that her hatred for her appearance, which is, probably very ugly and not pleasing. Both Dorian Gray and the woman are very much concerned about their appearances, however, Dorian Gray still views himself very perfect at the moment, the reason why he feels unhappy is that he realizes that someday he would grow "old", "horrible" and "dreadful", but the portrait would remain the same forever. For the woman in "Mirror", she apparently dislikes her appearance a lot and because of this, she turns to the "liars" - the "candle" or the "moon", which never tell who she really is, she rejects the "faithful" lake which reveals her true appearance.

2)What kind of relationship is there between Dorian and his portrait, and between the mirror and the woman it belongs to?

Dorian compares his own appearance to that of his portrait. He envies his portrait for escaping age and change in the appearance. He is "jealous" of the portrait, and wishes to have things "the other way round", to have himself staying the same and the portrait to grow old and ugly. He is also angry, for he know that his portrait's beauty will out live his own. "His face (is) flushed and his cheeks burning" when he thinks about this. The portrait helps Dorian to realize that someday he will "grow old, and horrible, and dreadful", it arouses his terrible fear for growing old and that his "beauty", which he treasures so much, which is the reason why people love him, will die. A portrait is supposed to be admired and loved by its owner, but Dorian's portrait, on the contrary, not only rouses its owner's jealousy and hatred, but also gave its owner the idea of fear and death. Dorian, after looking at his own portrait, is filled with fear, and in this fear, he gets the idea to "kill" himself when he finds himself growing old. To Dorian, the portrait is a threat. As a narcissist, he treasures his youth more than anything, even life. Dorian imagines that the portrait is taking his beauty from him, so as to keep the youth shown in the portrait. Dorian cannot stand the portrait existing with himself, it is his enemy. It shows him the reality and the truth, which he doesn't want to face, it will "mock him someday".

By thinking of the way Oscar Wilde put the conversation between Dorian Gray and his portrait,and involving myself in the similar position,i shouldn't agree with the fact that Dorian's hate lies behind the conversation.It is hard to believe that a young person could not admire to own beautiful picture,so it led me to think another way about it.I suppose that Dorian's dissatisfaction and dialogue is just Oscar Wilde's idea to start the novel's main plot-unbelievable story about handsome Dorian who stay young for years while his matches grow old.It is also the key moment to make up for the presence of Devil,who no one has been mentioned in the book,one fantastic idea,that Oscar achieved by means of this introduction dialog led by Dorian and his portrait.

The mirror is very "important" to the woman in the poem. It shows "no preconceptions", like a faithful friend telling her the truth without bias. The girl has to rely on the mirror to know and "search" for "what she really is". It has become her habit to look into the mirror "each morning" to look at her own reflection throughout the years. The mirror and the girl are like good friends, friends that know each other for a long time.By showing the girl her reflection "unmisted by love or dislike", the mirror shows the girl her face, turning from "a young girl" to "an old woman". The girl is saddened by her old and ugly reflection shown in the mirror and "rewards" the mirror's faithfulness with "tears" and "the agitation of hands". The mirror gives the girl sadness and frustration through showing the girl her true reflection.

3)Compare how Dorian sees himself with how the other people in the passage see him. Compare the mirror's attitude with that of the woman.

Dorian sees himself as being young and good-looking at the time of speaking, but he knows well that good looks do not last forever. He thinks it will fade away and eventually he will dislike his own look, and people will also dislike him. By then his portrait will be a horrible contrast to his shrivelled look when he is old. However his friend Hallward thinks that beauty does not rely on good outward appearance, but what is inside, he knows that Dorian is a person deeper than what material matter means to him.in fact all human are more superior than materials because they've got a soul and a mind. He knows that even when Dorian grows old, he will still like him as a friend.

Similarly, the woman looking in the mirror has noticed the problem of her ageing, yet the mirror is almost emotionless, it can judge things with no "preconceptions", it does not feel anything towards the woman's fading youth. She noticed that she has changed from a innocent young girl to an old lady who has experience all the dark side of human nature, the hypocrisy of people. Looking into the mirror she realized that she is no longer the old her. The mirror's calmness and the woman's sadness is a contrast. The mirror reflects the truth, and it has no much feelings. However, her reaction towards the fact shown in the mirror is vigorous. She cries and complains about the reality with "the agitation of hands".

4)Do the passages invite you to be sympathetic towards or critical of the characters? How would you describe the tone of each passage?

For A, the passage doesn't make us feel sympathetic towards the character, but for B, it gains our sympathy. This is because the tone and perspective of the main character of the two passage are different. For A, the character feels angry for knowing he will look ugly and old, "He seemed quite angry. His face was flushed and his cheeks burning." he points out that youth is "the only thing worth having", and express to us that he agrees that he is perfect now. and He is afraid of being old and he is " jealous of everything whose beauty does not die". The fact that he is being too proud, too arrogant towards his appearance make readers dislike his character. The way he shows hatred and admit to his jealousy shows his shallow-mindedness and superficiality, thus readers do not feel sympathetic towards his desires to be forever young.

For B, the poem invites our sympathy. The mirror gives a reflection of how the woman has a low self opinion of herself and how helpless she feels when she sees her true self. "Tears" fall and her hand "agitates" display her utter state of sadness. She doesn't even have the courage to come out in the light, as the poem describes how she "turns to those liars, the candle or the moon" and escaping from the mirror. The image the poem creates is one that is void of light. In the line "drowned a young girl, and in me an old woman" implying that the woman feels much older than she is and has buried any signs of her youth and has become an "old" woman. The woman feels inferior and does not have the courage to face life gains readers' sympathy.the agitations of her hands and the tears created her a helpless fragile image.She cannot avoid getting old, nor change the darkness she experienced. Perhaps the most pathetic part is that its her experience in life, the darkness she experienced all these years that make her old and sad. the mirror is truthful, time is fair, everyone gets old and many of them will accept aging as a natural process. the woman failed to accept the reality and her life remain miserable. this may arouse reader's sympathy.

However, we can also look it from a different perspective. We can feel sympathetic towards Dorian and critical towards the woman.

In the prose passage, Dorian shows his indulgence in his beauty. His eccentric addiction and his narcissism easily portrait him as a mad man (and in fact he does turn mad when his wish is granted and the portrait grows old instead of him). To readers, he may seem rather silly as to make a wish that the portrait will grow old instead of himself. He is a man who is too obsessed with his own beauty. Readers all know that ageing is natural, and is a process what we must all experience, yet Dorian rejects the laws of nature and thinks that looking old and ugly is "sad". Moreover, he makes the impractical wish of hoping that his soul can be exchanged for his youth. His indulgence will may arouse readers' sympathy.

In the poem, the woman is reluctant to face the reality. She first searches for "what she really is", and when she finds out the ugly truth that her prime of life cannot stay forever, she "turns to those liars", candles and moon, who are changeable and has no fixed state, on the contrary of the mirror which is "exact", to comfort herself. Yet she "comes and goes", she wants to accept the fact but every time she lacks the courage and turns her back to it. She keeps repeating the action, escaping from the reality while deep down she knows she needs the mirror to tell her the truth. Her hesitation and fickleness may annoy readers thus feeling critical towards the woman.

Comparison Exercise 2
Write a critical discussion of the following TWO passages, pointing out features of comparison and/or contrast.

a)	The author describes the experience of accompanying a Burmese prisoner to his execution while he worked with the British Colonial Police Force in Burma in the 1920s.

It was about forty yards to the gallows. I watched the bare brown back of the prisoner marching in front of me. He walked clumsily with his bound arms, but quite steadily. At each step, his muscles slid neatly into place, the lock of hair on his scalp danced up and down, his feet printed themselves into the wet gravel. And once, in spite of the men who gripped him by each shoulder, he stepped slightly aside to avoid a puddle on the path. It is curious, but till that moment I had never realized what it means to destroy a healthy, conscious man. When I saw the prisoner step aside to avoid the puddle, I saw the mystery, the unspeakable wrongness, of cutting a life short when it is in full tide. This man was not dying; he was alive just as we are alive. All the organs in his body were working – bowels digesting food, skin renewing itself, nails growing, tissues forming – all toiling away in solemn foolery. His nails would still be growing when he stood on the drop, when he was falling through the air with a tenth of a second to live. His eyes saw the yellow gravel and the grey walls, and his brain still remembered, foresaw, reasoned – even about puddles. He and we were a party of men walking together, seeing, feeling, understanding the same world; and in two minutes, with a sudden snap, one of us would be gone – one mind less, one world less. From ‘Burmese Days’ by George Orwell (1903-1950)

b)	In this blues song, Allen describes the bodies of black Americans who have been killed by racist gangs.

Strange Fruit

Southern trees bear strange fruit,

Blood on the leaves and blood at the root,

Black bodies swinging in the southern breeze,

Strange fruit hanging from the poplar trees.

Pastoral scene of the gallant  south,

The bulging eyes and the twisted mouth,

Scent of magnolias, sweet and fresh,

Then the sudden smell of burning flesh.

Here is fruit for the crows to pluck,

For the rain to gather, for the wind to suck,

For the sun to rot, for the trees to drop,

Here is a strange and bitter crop.

Lewis Allen (1890 – 1954)

Suggested Answer to Comparison Exercise 2
1) Are we invited to empathise with the victims in these passages or to feel alienated from them?

Both passages invite the readers to empathise with the victims.

In the first prose written by George Orwell, Orwell gives a detailed description of the prisoner to be executed and the process of proceeding to the gallows. By describing the "bare brown back" readers are told that the prisoner's upper torso must be naked. He does not even have clothes on. The diction of "marching" seems to suggest the dignity he still holds and that he has accepted the fact that he cannot rebel, and his only choice is to accept his fate. That he is walking himself closer to his death step by step makes us empathize with him. Orwell describes the experience of sending the man to death as "the mystery, the unspeakable wrongness, of cutting life short when it is in full tide", showing his sense of guilt and sympathy towards the prisoner. He also suggests the prisoner is actually "not dying", he is "alive" like everyone of us; the seconds in his life go on, still all the same as all men on Earth, "walking together", "seeing", "feeling", "understanding the same world".

The only twist is, "in two seconds" and "a sudden snap", the prisoner would be gone, and "one mind less, one world less" - we lost a men in our world within such swiftness, one less man to share our mind and world. Orwell points out the cruelty of death.

Looking at the context of the political situation in Burma, this prisoner was probably a political prisoner who is persecuted under the barbaric regime. During the time period, hundreds of Burmese prisoners were tortured and killed each day. Genocide against minority nations on the borders took place, as well as the imprisonment and killing of people who dared to speak the truth about the political situation. This is similar to the blues song, where innocent people are persecuted of their identity. Because these people have not done anything wrong but are killed, this rouses readers' sympathy.

In the blues song, Allen compares the dead bodies of black Americans to a "strange fruit". Allen describes the scene of dead bodies in details; "blood" on the bodies which are "hanging" and "swinging" from the poplar tress in the southern breeze. By describing the horrible scene, "bulging eyes and the twisted mouth" and with smell of "burning flesh", the black Americans are killed without any sympathy from others, and they die painfully, the author points out the cruelty of the cold-blooded racists; he condemns them as what they have done destroy the peace in the "gallant south", contrasted with the original serenity, as depicted in "sweet and fresh" and "scent of magnolias". The originally peaceful pastures are no longer peaceful now, the blood of the "strange fruit" - "strange", as of an odd colour, in the racists' eyes - shed on them, and the tragedy will continue, for there will always be other races and more racists who will persecute people different from them--"here is a strange and bitter crop".

As the two passages both portray the pain and suffering of the victims, it is reasonable to assume that the authors are to arouse readers' sympathy and invite the readers to empathize with them.

2) How is imagery used in each passage?

In the first passage, one imagery used is the “puddle”, the prisoner stepped slightly aside to avoid a puddle on the path. On one hand it shows that he is mentally and physically healthy and vigilant, on the other hand the puddle may foreshadow his doomed fate of being executed, and that his vain attempts to avoid the puddles will not be able to help him to escape from it. The “yellow gravel” and “grey walls” paint a picture of the monotonous splashes of colours at the prison, or perhaps the image may relate to grave (which is a symbol of death).This emphasizes the fact that the prisoner is doomed, and providing a touch of depression or death by making use the dull colours.

In the second passage, “strange fruit” bore by the southern trees is the symbol of the black people (strange as in different in skin colour) that will be ruthlessly killed. There is "blood on the leaves" and "blood at the root", depicting the large amounts of blood shed by these poor black people who have lost their lives to racists.

3) Which passage do you find more shocking? Why?

The poem is more shocking. The atmosphere is mysterious and creepy, and the moment of "scent of magnolias" being replaced by "smell of burning flesh" is a twisting point. It indicates how a life is beaten by death in a glimpse. Also, "blood on the leaves" and "blood at the root" is a description of an unusual scene, it makes readers feel uncomfortable. Especially when he poet uses the "strange fruit" to symbolize the heads of the black people being hanged. The prose passage is a description of a prison on the way to execution, the author's feelings are what usual people will feel about the scene, so it does not surprise readers much. Comparing to it, the poet uses irony to emphasize his detestation to the racists irrational killings of black people.

What is the author's stance in each passage?

The author of the prose passage does not think the prisoner deserves death. When the prisoner avoids stepping on the puddle, the author realizes that he is same as any of the others. He sees what others see. The author thinks sentencing a healthy men to death is an "unspeakable wrongness" and inhumane. He thinks all human beings are equal, there is no difference among any of us as human beings, and executing men is taking away one's right to live. He is sad to see a healthy man being executed, as he thinks he is as important as any other human beings, to the author, the death of the Burmese prisoner means "one world less".

Although the poet seems to be a calm narrator, he actually feels sad for the black people and thinks it is brutal to kill them. The author shows how he thinks about black people in stanza 2. "Pastoral" and "gallant" suggests that the author is being sarcastic, he is using some positive words 'praising' the scene of killed people being hanged all around. He describes the "bulging eyes" and "twited mouth" as "gallant", which shows his sadness and sympathy towards the black people. Here the author presented his unpleasant feeling, he disagrees on the act of killing black people. The scene described after the tree being destroyed is unpleasant, crows will "pluck", wind will "suck", sun will "rot" the fruit. It is a place where people will not want to get near to. Through the unpleasant atmosphere created in the poem, we can see that the poet doesn't think killing black people because of racial discrimination is right.

4) Can you find instances of contrast and irony? What effect do they have?

Contrast can be seen in A. When the prisoner still alive, the author describes his moments, how his muscles and his body functioned in detailed. "muscles slid nearlty into plave", "the lock of hair on his scalp danced up and down", "bowels digesting food"," skin renewing itself" etc, the detailed description of his body movement emphasizes the fact that he is still alive, still a living thing. A contrast will be formed when later on the author said " with a sudden snap", "one mind less, one world less", he just simply uses few words to describe when the prisoner dead, "one mind less, one world less", a contrast is created, when he is alive, author uses terms and different phrases, to depict it, however after the prisoner dead, no movement, living cell is dead already, so no need further explain of describe.

In passage B, "fruits" is used to compare and make a big contrast to the dead bodies of the defeated, because fruits are like new born lives, while the bodies are actually dead and their lives come to an end. It is also an irony in the sense that in the comparison, one thing is born (fruit), one thing is killed. In the scene which "bulging eyes and twisted mouth" is associated with "pastoral scene of the gallant south", is more ironic when human being who are supposed to gain respect from all things now being treated as an object or a fruit "for the crows to pluck, rain to gather, wind to suck, sun to rot, and trees to drop" The irony presented shows that dead bodies are useless and being treat as an object, gaining no respect. Or on the other hand, it shows that the poet think death as a trivial thing which doesn't need to be fear.

Comparison Exercise 3
Write a critical discussion of the following TWO passages, pointing out features of comparison and/or contrast.

A)

Do you know the road I live in – Ellesmere Road, West Bletchley ? Even if you don’t, you know fifty others exactly like it. You know how these streets fester all over the inner-outer suburbs. Always the same. Long, long rows of little semi-detached houses – the numbers in Ellesmere Road run to 212 and ours is 191 –as much alike as council houses and generally uglier. The stucco front, the creosoted  gate, the privet  hedge, the green front door. The Laurels, the Myrtles, the Hawthorns, Mon Abri, Mon Repos, Belle Vue. At perhaps one house in fifty some anti-social type who'll probably end up in the workhouse has painted his front door blue instead of green.

That sticky feeling round my neck had put me in a demoralized kind of mood. It’s curious how it gets you down to have a sticky neck. I had no illusions about myself that morning. It’s almost as if I could stand at a distance and look at myself coming down the road, with my fat, red face and my false teeth and my vulgar clothes. A chap like me is incapable of looking like a gentleman. Even if you saw me at two hundred yards’ distance, you’d know immediately – not, perhaps, that I was in the insurance business, but that I was some kind of tout or salesman.

The clothes I was wearing were practically the uniform of the tribe. Grey herring-bone suit, a bit the worse for wear, blue overcoat costing fifty shillings, bowler hat, and no gloves. ‘Five to ten quid a week’, you’d say as soon as you saw me. Economically and socially I’m about at the average level for Ellesmere Road.

From Coming Up For Air by George Orwell (1903-1950)

B) Executive

I am a young executive. No cuffs than mine are cleaner;

I have a Slimline briefcase and I use the firm’s Cortina.

In every roadside hostelry from here to Burgess Hill

The maitres d’hotel all know me well and let me sign the bill.

You ask me what it is I do. Well actually, you know,

I’m partly a liaison man and partly P.R.O.

Essentially I integrate the current export drive

And basically I’m viable from ten o’clock till five.

I do some mild developing. The sort of place I need

Is a quiet country market town that’s rather run to seed.

A luncheon and a drink or two, a little savoir faire -

I fix the planning officer, the town clerk and the mayor.

And if some preservationist attempts to interfere

A ‘dangerous structure’ notice from the borough engineer

Will settle any buildings that are standing in our way –

The modern style, sir, with respect, has really come to stay.

John Betjeman (1906 – 1984)

Comparison Exercise 4
Write a critical discussion of the following TWO passages, pointing out features of comparison and/or contrast.

a)

In Flanders Fields

In Flanders fields the poppies blow

Between the crosses, row on row

That mark our place; and in the sky

The larks, still bravely singing, fly

Scarce heard amid the guns below.

We are the Dead. Short days ago

We lived, felt dawn, saw sunset glow,

Loved and were loved, and now we lie

In Flanders fields.

Take up our quarrel with the foe:

To you from failing hands we throw

The torch; be yours to hold it high.

If ye break faith with us who die

We shall not sleep, though poppies grow

In Flanders fields. John McCrea

B)

The Outpost Trench was about 200 yards from the main trench, which was now our front line. It had been solidly made, ten feet deep, with timbered fire-steps, splayed sides, and timbered steps at intervals to front and rear and to machine-gun emplacements. Now it was wrecked as though by earthquake and eruption. Concrete strong-posts were smashed, and tilted sideways; everywhere the chalky soil was pocked and pitted with huge shell-holes; and wherever we looked the mangled effigies  of the dead were our memento mori. Shell-twisted and dismembered, the Germans maintained the violent attitudes in which they had died. The British had mostly been killed by bullets or bombs, so they looked more resigned. But I can remember a pair of hands (nationality unknown) which protruded from the soaked ashen soil like the roots of a tree turned upside down; one hand seemed to be pointing at the sky with an accusing gesture. Each time I passed that place the protest of those fingers became more expressive of an appeal to God in defiance of those who made the War. Who made the War? I laughed hysterically as the thought passed through my mud-stained mind. But I only laughed mentally, for my box of Stokes gun ammunition left me no breath to spare for an angry guffaw. And the dead were the dead; this was no time to be pitying them or asking silly questions about their outraged lives. Such sights must be taken for granted, I thought, as I gasped and slithered and stumbled with my disconsolate crew. Floating on the surface of the flooded trench was the mask of a human face which had detached itself from the skull.

From Memoirs of an Infantry Officer by Siegfried Sassoon

Answers to Comparison Exercise 4
Both (A) and (B) are about war. For (A), the line 'Take up our quarrel with the foe' suggests the dead died in the war. For (B), ' the War' is mentioned and the 'trench' and 'Germans' also suggest the Second World War. However, different attitudes towards wars are shown in the two sources. (A), written in the dead's point of view, supports the idea of wars. The dead died with regrets, as they 'shall not sleep' if the people who are alive 'break faith with [them]'. They wanted to take revenge against their enemies. They ask the ones who are alive to take 'the torch' which they throw to them. A completely different attitude is shown in (B), which is written in the point of view of a living person who once experienced the war. He asked 'who made the War', showing his disapproval of the War. He does not want to take revenge, as he says the 'dead were the dead'. He believes it is not the time 'to be pitying them or asking silly questions about their outraged lives'.

The setting is also described in detail in (A) and (B). For (A), the whole of the first stanza is contributed to describe the 'Flanders field' in which the dead lie. For (B), the outpost trench is described in great details: the exact measurements of the depth of the trench, how far it was from the main trench, what it was made of etc. the settings are similar in a sense that they both are associated with death/destruction. The Flanders field is where the dead lie whereas the trench was where many lost their lives. But different moods are created by the two setting. For (A), the Flanders fields seem to be rather peaceful, with the 'poppies [blowing] between the crosses' and 'the lark, still bravely singing'. But for (B), the trench was 'wrecked as though by earthquake and eruption' and 'concrete srong-posts were smashed, and tilted sideways;...' Things are destroyed in the war and it creates a gloomy feeling.

The scene in poem A is set in a graveyard - Flanders Fields, while that of poem B is set when a soldier is fighting in a war. The mood of poem A is more calm and peaceful compared to that of poem B. Poem B describes the war scene in vivid detail, portraying a more realistic picture.

Poem A opens with a description of the graveyard where the dead soldiers lie. The mood here is quiet and serene. "and in the sky The larks, still bravely singing, fly Scarce heard amid the guns below." This phrase suggests that the souls of the dead are like the larks, looking down at the war still going on from above. The dead are portrayed as brave, courageous souls who have lost their lives for an honourable cause.

Readers are able to feel a sense of poignancy in stanza 2. "Short days ago We lived, felt dawn, saw sunset glow,Loved and were loved, and now we lie In Flanders fields." In this phrase, the dead express their sadness as their lives came to an abrupt end. However, although they are dead, their souls linger and live on because of unfinished business. "To you from failing hands we throw The torch; be yours to hold it high." Here the "failing hands" refer to the dead soldiers. The throwing of the torch symbolizes the dead soldiers handing over their duty to the living who are still fighting in the war. Because they did not live to see the battle won, they hope that the living will be able to lead the battle to ultimate victory.

Poem B has a rather different point of view concerning war and the dead. Soldiers seem to die with feelings of hatred and blame, instead of sadness and bravery. "one hand seemed to be pointing at the sky with an accusing gesture." The writer believes that the soldiers die blaming God for war and death. "this was no time to be pitying them or asking silly questions about their outraged lives." We sense no poignancy in this sentence, even at the time of death. Rather, the soldier regards his life as "silly" and "outraged" and deserves no pity. "Floating on the surface of the flooded trench was the mask of a human face which had detached itself from the skull." The last sentence symbolizes that the soul dies along with the human body, which differs greatly from the idea presented in poem A.

---

Poem A is set in the Flanders Field, which is rather peaceful, while passage B 's setting is a battlefield full of horrible scenes of death and destruction of war.

Poem A 's beginning has a calmer and more serene atmosphere. In the field  poppies blow, larks, still bravely singing but the last line of the stanza  Scarce heard the amid guns below suggests the theme of war. Still it is not so terrible.However, passage B already starts with violent and disturbing scenes of a war. The trench, which was supposed to be strong, was  wrecked as though by earthquake and eruption, pitted with huge shell-holes.  wherever we looked the mangled effigies of the dead were momento mori. gives readers a sense of horror.

The personae of Poem A and the narrator of Passage B hold a completely different attitude towards war. The personae in Poem A, who are dead soldiers have a more positive attitude. It seems they will never give up fighting their enemies and their morale will always remain high as the lines  Take up our quarrel with the foe and  If ye break with us who die/We shall not sleep demonstrate. They might even feel gratified for their death for the war as they are Loved and were loved. But the narrator in passage B, who is an officer in war, has a negative attitude. He can sense  the protest of those fingers became more expressive of an appeal to god in defiance of those who made the war. which probably shows that he opposes to the war. And he is possibly very desperate and sad about fighting in a war since he  laughed hysterically  about the idea  Who made the war?

Poem A only shows the idealistic side of war, with images of dawn  and  sunset, only  guns suggest there is violence. Passage B describes war in horrifying details.'' the Germans maintained the violent attitudes in which they had died. The British had mostly been killed by bullets and bombs, so they looked more resigned proves dying for a war is not gratifying.The appalling  Floating on the surface of the flooded trench was the mask of a human face which had detached itself from the skull'' arouses feelings of fear of war among the readers.

The poem and the passage are probably aimed at spreading messages of war in different views. The poem, with the gratified feelings of the dead soldiers and their determination to drive away foes, possibly encourages readers to join the war to serve their country since they can beLoved and were loved.The passage, with the detailed terrifying scenario of war, like horrible deaths of soldiers, destruction of land, the officer's desperate feelings of war,promotes the message of peace and opposition to war through deriving the sense of fear from readers by the horrible imageries of the reality of war.

title: Literary Criticism/Comparison Exercises


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XForms/References

The following are some references to XForms

 * Wikipedia XForms page
 * Go to IBM Alphaworks and then try: demo/flash/display/cxde3 IBM GUI Demo
 * Here is a nice intro from the IBM developer works. The Wikibook spam filter does not allow the direct link so you will have to put in the link to the IBM developer works web site and add "xml/library/x-xformsintro1/?ca=dnw-732"

title: XForms/References


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Persian/Phrasebook

 * Colors
 * Days of the Week
 * Directions
 * Family
 * Seasons and Months
 * Shapes

title: Persian/Phrasebook


text:
Talk:Persian/Introduction

the link is unreachable...--140.113.91.221 07:01, 14 September 2006 (UTC)

Needs Serious Reworking
This page needs serious rewriting, much of it is written from the first-person point of view and it contains some graffitti and references to Dutch.Poppy 11:22, 25 February 2007 (UTC)

Moved Section here for discussion
I removed the following section to here as I do feel it makes many interesting points but they are personal to the author:

"Persian speakers and learning Persian in the west I am not a native speaker of Persian but am a devout student of Persian, I have also lived in Iran for a short time. For the serious student of Persian here in the West there are some serious problems that may arise. In Iran a westerner that can say more then hello, how are you and goodbye in Persian really stands out. On IranAir, the stewardess was surprised I could order a water-in Persian. This attitude pretty much is typical.
 * The First and most unfortunate is the native Persian speaker. It has dawned on me that whilst Persian speakers (speaking primarily of Iranians)think its really nice and interesting that a non-Iranian would learn Persian, and more often then not they are more then willing to be of help in the language. Unfortunately I have definitely seen (both here and in Iran) that after a certain point, Iranians definitely think its weird that a westerner would be interested in Persian beyond a beginners level/interest. The dichotomy is that Persian speakers rave about the beauty of the language, its ancient history, its poets, its stories, but yet also feel that a westerner would have little interest in learning their language.

Really all that exists (even in Iran) are Academic Texts which can be mind-boggling for those who are not students of Linguistics or ridiculously simplistic tourist or beginner texts. Additionally most western universities don't offer Persian. I am planning on eventually putting up a critique of the most widely available Persian textbooks.
 * The second problem is lack of materials. Unfortunately this is a HUGE problem.

Of course learning Persian can be done but it takes effort and a bit of gumption to find the texts needed and of course to find Persian speakers who are sympathetic to your efforts."

Above is not my writing but what I removed from the Introduction. Poppy 11:35, 25 February 2007 (UTC)

Here is another section I have removed from the introduction as I feel it is personal to the author and makes some decicions about the book which could be better discussed here:

"Lastly and most importantly, I am not going to use any colloquial Persian at all (except for a few really common and obvious words). My reasons are thus: It seems like many of native Persian speakers think that the best way to help a newbie to the language is teach the "slangy" ways to pronounce words. In fact there are a number of teach yourself Persian books which teach ONLY colloquial Persian. I'm so totally against this because its really hard to actually grasp any language, on any level without a solid understanding of the grammar and vocabulary and additionally each region, even each city and village in Iran has their own slang, accent and way of pronouncing words, so just knowing colloquial Persian can be really confusing. Additionally when one learns standard (i.e. book-based) language, it is easier to learn slang and colloquial. I know some may disagree but this is my personal belief and my experiences relate to it. If a student of language language spends any amount of time around native speakers of that language they will inevitably pick up dialectal ways to saying things."

Poppy 13:19, 25 February 2007 (UTC)

title: Talk:Persian/Introduction


text: Template:Meta

title: Template:Meta


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User talk:65.9.228.133

Thanks for experimenting with the page Calculus/Limits on Wikibooks. Your test worked, and has been reverted or removed. Please use the sandbox for any other tests you want to do. Take a look at the welcome page if you would like to learn more about contributing to our project. Thanks.

Az1568 07:49, 14 September 2006 (UTC)

title: User talk:65.9.228.133


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Category:Interwiki link templates

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title: Category:Interwiki link templates


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User talk:Ravidreams

Leave messages at w:ta:user talk:ravidreams--Ravidreams 08:15, 14 September 2006 (UTC)

title: User talk:Ravidreams


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title: User:Ravidreams


text:
User:SBJohnny/sandbox3

 category=Weed profiles category=Garden plants order=descending namespace=0 replaceintitle=/A Wikimanual of Gardening/, *

Trying to get "or" to work
 category=Weed profiles OR category= Garden plants order=descending namespace=0 replaceintitle=/A Wikimanual of Gardening/, *

title: User:SBJohnny/sandbox3


text:
User:VolkmarGlauche

About me

 * SPM user and developer
 * Freiburg Brain Imaging

title: User:VolkmarGlauche