The Major Issue In The Economy Essay Example | Topics and Well Written Essays - 750 words

The Major Issue In The Economy - Essay Example The protests of the Occupy Wall Street state its objectives: â€Å"to end corruption in Wall Street and the political process.† This straightforward statement and the protest that expresses it appeared to be a very rational extension of opinionated dialogue. This has been a voiced proclamation by the presidential candidates, as well as activists for a very long time. On the other hand, under entrepreneurship, there is just no way to get rid of the greed and the sleaze from Wall Street, or to â€Å"get cash out of politics.† Known that takings are already entrenched in the ‘goods’ exchanged on Wall Street, ‘voracity’ is utterly, totally, and necessarily inherent from the very outset. Capitalism has been found to be the systemization of gluttony and that Wall Street is its figural and fiduciary quintessence. Trying to get rid of greed in Wall Street is like trying to get blood out of the body and commanding it to walk around. Gluttony is the bloo d of free enterprise and Wall Street is the heart. To do away with the supremacy of systemic greed, we cannot remove greediness from Wall Street; we must get rid of Wall Street from the world itself (Van 112). Supplementary, the free enterprise is in a condition of systemic crisis. This makes its paroxysms felt across the globe and in every locality thereof. The era of ‘progressive’ reformism had ended, and it is not going to come back. This is lucid if one takes a view at Europe, where old-age reforms are being undone, country after country.

Holocaust, The Situation of Depression Essay Example | Topics and Well Written Essays - 1500 words

Holocaust, The Situation of Depression - Essay Example According to the essay "Holocaust: The Situation of Depression" findings, in terms of the manner of labor inside the Ghetto, forced labor is very much imminent. People have to work so hard in return for nothing. Bribery must be done sometimes to at least escape from the harsh working conditions. This only shows how inhumane the treatment to the Jews and other Europeans happened back then. The manner of implementation of things somehow satisfies a very sadist culture for the German soldiers who have been so happy seeing the suffering of Jews. This has been the common cases of Genocides. One finds happiness in the suffering of others. If we shall observe more carefully the Ghetto life, it is deeply rooted in the grand political narrative of Hitler: superiority. At the same time, these Ghetto camps can be considered safe havens somehow but not that safe in reality. People may just be working, forced under harsh circumstances that dehumanize them further. Solomon Radasky back then has us ed bribery as well just to see his sister who is already dead. This only shows that his frustration about the situation during the war is very incommensurable. At the same time, he has experienced the work inside the Ghetto camps which I have described to be so harsh and demeaning the one who worked would most likely do not want to work there since there is no hope of getting comfort and be treated humanely. In this case, violence has been so triumphant in Europe during the war. There is no significant difference in it when the other wars have occurred.

What is faith Essay Example | Topics and Well Written Essays - 1500 words

What is faith - Essay Example In many cases, faith becomes the equivalent of what we call a "world view," a context or framework within which life can be lived. The world view need not be optimistic, as it is above. Faith now includes trust and reliance on an authority, even though all the experience of the speaker suggests that the authority is wrong. The extent of the trust has now been enlarged. The evidence that a compass offers has a high degree of assurance behind it; compasses do not lie, cheat, change their minds, or get fooled very often. There is greater risk involved in this kind of faith, for it is trust in a person. Trust (and risk) has now been further enlarged (Cimino, Latin 2001). The same thing happens when a person (a) undergoes anesthesia and surgery, (b) sits in the back seat of a moving vehicle, (c) eats a meal someone else has prepared, (d) marries, (e) shares a secret. These random examples cumulatively begin to tell us something about the meaning of faith as we ordinarily use the word, and what they tell us will be useful when we develop a working definition. Faith clearly has some sort of content, drawn out of our own experience or out of the common experience of the past, and our engagement with it involves us in varying degrees of commitment to that content, involving both trust and risk. Consequently we act on the basis of the degree of trust we possess: we continue the lab experiments, we endure dungeon, fire, and sword, we sail north-northeast, we buy the painting, we stay out of the airplane, we remain confident in the space capsule. There are many number of ways to argue that faith must lead to action, that action is the proving ground of faith, and that what we affirm in our hearts or minds is not truly affirmed until it is translated into deed. Those who say love and who live hate are not only denying their neighbors but negating their affirmations as well. Better still, they are demonstrating what their true affirmations are, when put to the test (Dennett 2006). The incident is instructive in many ways, not least for indicating that it often takes someone else to confront us with the kind of challenge that puts our faith to the test and insists that we act upon it. In religion, faith plays a special role determining the course of actions and moral behavior of followers. In religion, faith is associated with God and his divine power. To believe in God is to believe that he is on the side of the oppressed, which means in turn that the believer must be on the side of the oppressed unless he wishes to deny his belief. The struggle for faith involves him in faith for the struggle. Faith for the struggle, involvement in the concerns of love and justice, vindicates the ongoing struggle for faith. For religious believers, faith and action become virtually indistinguishable from one another; a key word is "praxis" (Dennett 2006) reflection and action to transform the world. In religion, faith symbolizes universal knowledge and truth. Faith can be described as "God's benevolence," his goodwill toward his children (Dennett 2006). This is not merely a psychological insight propounded to protect mortal men from prideful assertions that they can create faith themselves or work their way up into God's presence by dutiful striving. Rather, the recognition that faith is a gift is one of the consequences of the content of this particular kind of faith. The nature of this particular promise is that it comes to us in personal terms, in a life to which we can make response. It comes to us, more importantly, in a

Arthur Miller Essay Example for Free

Arthur Miller Essay An important theme in Arthur Millers play All My Sons is the responsibility a man has for another man. Miller stressed that people must be held accountable for their actions to society and they will be held accountable by the inevitable justice found in the universe: karma. This theme is expressed through action as well as characters throughout the entire play; it is subtle at first but slowly becomes more prominent until Joe Keller finally realizes exactly how his actions affected people outside of his family. To begin, Kellers character is important to the theme because he represents the opposite of being responsible for his actions and being held accountable to society. Joe Keller seems like a simple kind of man. His greatest wishes are to obtain the American dream for his wife and to create a legacy to pass on to his son. However, he harbors a dark secret that explains how he achieved those dreams for his family- he knowingly shipped out faulty airplane parts during wartime. Up until the time of the play, Keller did not believe he did a terrible thing by shipping those parts out. As he explains, when he came home from jail he was like an expert on the whole jail thing and, over time, the children got it confused and [he] ended up a detective(29). Or, more clearly, he went from being the bad guy to being the good guy. In Kellers mind, he was the good guy because he saved his family from being poor and having their reputations in the gutter. He says to his wife, you wanted money, so I made money(76). To him, he simply did what he had to do to protect and take care of his family. At that point in his life he was not able to see the big picture of things; he was only able to see one little contour, just one small piece, of what makes up the universe. Furthermore, it is evident that Kellers small piece of the universe, his family, is what is most important to him. Throughout the play he tells Chris that everything he has done with the business , including sending out cracked gear heads, was for Chris: it was a chance and I took it for you(70). Keller believed that he had to send out those parts so that he would still have a business to pass on to his son. Chris replies what is that, the world- the business?(70). He is asking his father if the whole world is the business. And the answer in Kellers mind is, as long as it takes care of his family, yes it is the world. Slowly, though, Keller begins to see just what his actions have caused to happen to other people. Take, for example, when he speaks to Ann about her father, Steve. He finds out that Ann and George never visit Steve in jail and that they dont even write to him. Keller is unable to understand why the children would crucify their father and he pleads with Ann to not make a murderer out of him(32). He realizes that Steves life was ruined and his relationships with his children, something that Keller gives very high value to, are ruined as well. It is also easy to believe that Keller doesnt want to see Steve crucified because if he is, that means that Keller should be too. And if Keller was punished for his actions, that means there is something bigger in the world than the relationship between father and son. The whole ordeal with Steve and Steves children gives Keller a clue that there may be bigger things in the world than familial relationships and also that there may be consequences to wrongful actions. Finally, Chris and Larry (posthumously) work to enlighten Keller that theres a universe of people outside and that [hes] responsible to it(84). Chris character alone serves as a guidepost to this revelation. He is the epitome of the idea of responsibility and accountability to society because he is the person that reaches for something he wants but pulls back because other people will suffer(16). Chris takes other peoples feelings and well-being into account before he acts. He learned to be so self-less in the war, as he watched his men kill themselves for each other. He describes it as a kind of responsibility. Man for man(35-36). He learned that you cannot only look out for yourself in this world, but you have to help other people out as well. And Larry, whom Keller thought shared his ideas on the way the world was made (with a forty-foot front), had a good sense that people must consider the good of the many before they act for the few. It is his letter to Ann, in which he states he cant bear to live anymore(83) because of what his father did, that brings everything crashing down around Keller. In the same way Larrys memorial tree came crashing down and allowed more light to shine into the arbor, his letter shined light onto the true ways of the universe. Everything that Keller stood for, everything he believed in was wrong. He finally realized that he did a terrible thing that killed not only strangers, but people who were fathers, brothers, and sons. In essence, he killed the thing he lives for; he killed family. This revelation drives home the idea that justice will inevitably be brought to the wrong-doers. Kellers karma comes back and makes him not only set everything right in the universe again but pay the ultimate price for his actions: death by his own hand. Chris, Ann, and Kate can now move forward, not bogged down by shame and guilt, and they can live.

Uninterruptible Power Supply

Uninterruptible Power Supply In the United Kingdom over the past half century, the use of electricity has been increasing year on year (Figure 1). This increase in demand means that the supply of electricity is becoming more critical to the consumer and how much everyday life requires the use of electricity. Disruption to the supply can cause major issues and potential financial difficulty to many consumers who require a constant supply. Electricity disturbances can come in many different arrangements which affect the AC waveform and influence electrical loads in different ways. Common disturbances are shown in Figure 2 Depending on the criticality of the load devices can be placed between the supply and the load to eliminate these issues. Common devices used to eliminate disturbances are Uninterruptible power supplies Power Filters/Conditioners Different UPS systems can be used to eliminate disturbances through different configurations and setups. Power conditioners operate to illuminate certain aspects of the disturbances but wont eliminate disturbances like interruptions UPS systems can incorporate power conditioners to eliminate all these common disturbances to help give a constant supply for consumers. 1.1 Aims The principle aim of this final year individual project is to design and build an Uninterruptible Power Supply to eliminate interruptions up to 5 minutes. On failure of the supply, the system will pick up the load and continue to provide power until the main supply has returned after 5 minutes 1.2 Objectives Research and develop an understand of existing UPS configurations Design and build a standby UPS system including An AC to DC rectifier to supply an input to a DC Buck Charger A DC to DC converter to reduce input voltage to charge retrospective batteries A DC to AC inverter to make an AC voltage of 24V RMS An AC to AC converter to transfer between the duty and standby supply Develop an Arduino interface to control and display UPS parameters including Control of the switching of the DC to AC inverter Control of the AC to AC transfer switch Manual Control of UPS Display of UPS circuit position Voltage parameter readings for AC and DC AC load current and voltage readings Battery Temperature readings Evaluate UPS and discuss further work 1.3 Motivation The motivation for this final year project has come from time spent on placement at Phillip66 Humber Refinery working on the maintenance of primarily double conversion and rotary UPS systems. Through this experience, it has given an understanding of the systems and an interest to design and build a UPS. 2.1 UPS Configurations An uninterruptible Power supply is a system designed to maintain power or provide power when the input power fails or is disrupted. A UPS can be designed as a DC or AC back up, but most common UPS systems in the UK are designed to give AC because this is how electricity is supplied through the grid. [3] An AC UPS output can be produced using either a rotating machine (Rotary UPS) or a semiconductor based inverter (Static UPS). Batteries are the main energy source for both systems but for rotary systems, other rotating energy sources can be used. The UPS configurations as shown in Table 1 shows the different arrangements of a UPS 2.2 UPS Operation 2.2.1 Rotary UPS The rotary UPS generally consists of a motor and generator set but how these are configured depends on of the type of rotary UPS. Fixed Flywheel UPS (Figure 3a) [3] [4] Mains electricity operates an AC motor that is connected through a specially designed flywheel to an AC generator to produce an AC output. While the motor is driving the generator the flywheel rotates which stores kinetic energy.ÂÂ   When the main supply fails the kinetic energy in the flywheel continues to turn the generator for a short duration until another supply is provided by a backup generator. Battery backed (Figure 3B C) Mains electricity is converted to DC to charge a battery bank this DC is then used to operate a DC motor directly or through an inverter to an AC motor depending on the configuration. The motor is then directly coupled to a generator to supply the load. Diesel Backed (Figure 4) This UPS operates similarly to a flywheel UPS in normal operation an AC motor rotates a flywheel to store energy while a generator is producing power to the output. Instead of an external diesel generator set being used a diesel engine is coupled directly to the AC generator to produce power when the main supply fails. 2.2.2 Static UPS A static UPS generally comprises of a rectifier, inverter and a battery bank, how these are configured depends on the type of static UPS. Standby (Figure 5) [5] [6] In normal operation, a rectifier charges a set of batteries and the input is fed to the output through a transfer switch when the mains fails the transfer switch changes to take the supply from the batteries through an inverter. Standby-Ferro (Figure 6) [5] [6] This configuration is very similar to the standby UPS but has a ferroresonant transformer to reduce the time loss of power on a changeover from main to inverter supply, this transformer stores energy in a resonant circuit which supplies up to a half cycle of power to allow time for the inverter to start up and provide power. Double Conversion (Figure 7) [5] [6] In normal operation, mains electricity is converted to DC to charge the batteries which is then inverted back to AC filtered and supplied to the load. When power is lost the batteries supply the AC through the inverter. The static switch is used in the event that if the rectifier or inverter fails the load can be supplied directly from the load. Delta Conversion (Figure 8) [5] [6] In normal operation two converters are used to regulate current and voltage, the series converter is used to control current and a parallel converter to control the voltage. The converter operates to maintain a constant voltage and current output. When the supply is less than the load requires the batteries are used make up the difference. When too much power is provided the extra is used to charge the batteries through the bi-directional inverter. Line Interactive (Figure 9)[5] [6] In normal operation, the mains is supplied to the output while the bi-directional inverter is charging the batteries. When the main supply fails the inverter changed direction and supplies the load from the batteries. 2.3 UPS Comparisons To gain a better understanding of the UPS configurations and their capabilities a compassion was conducted as illustrated below (Table 2). UPS Configuration Power Rating Range (kVA) Cost per VA Efficiency Application Standby 0 0.5 Low Very High Interruptions Standby-Ferro 3- 15 High Low-Medium Interruptions Double Conversion 5-5000 Medium Low-Medium Transient, Interruptions, Sag/Swell, Distortion Delta Conversion 5-5000 Medium High Transient, Interruptions, Sag/Swell, distortion Line Interactive 0.5-5 Medium Very High Interruptions Flywheel Rotary 25-2500 Medium Medium to High Transient, Interruptions, Sag/Swell, Distortion Battery Backed Rotary Medium Medium to High Transient, Interruptions, Sag/Swell, Distortion Table 2: UPS Configuration Comparison [5] 2.4 Project Reasoning A standby UPS system was chosen due to its low cost, its simplicity and because it covers a single disruption. This type of UPS is basic to remove loss of power and to bridge the gap between power loss and back up operation starting 3.1 Work Breakdown Structure and Network Diagram A WBS is a key project deliverable that organises work into manageable sections and is the foundation of any project plan. All the project deliverables are selected and organised into key areas of activity. [7] A network diagram shows the sequence of activities which are in the WBS in order of time, these are then used to develop a Gantt chart. The WBS (Appendix 9.2.1: WBS) separated the project into 5 main sections which were then subdivided to develop a network diagram (Appendix 9.2.2: Network Diagram) Research Design Programming Build testing Report/ Presentation 3.2 Project Plan A project plan was developed as a Gantt chart from the network diagram, the time scale for the project was set to begin in September and complete the development of the UPS by December. This giving two months before the deadline to complete final checks and adjustments. The project plan was reviewed weekly and updated as the progress of the project developed. 3.3 Monthly Reports A monthly report was conducted to record and document my project progress on a regular basis, each monthly report is attached in Appendix 2 Project Planning. This report involved a document of the work I had conducted the month before and also a plan of what I would be doing for the next month including a number of hours that would be spent. 3.4 Project Progress Review A PPR was conducted on Friday 2nd December by Dr Joe Cole this was designed as For the design and building of this standby UPS, it has been split into individual circuits to ease the understanding and to show the importance of each aspect of the UPS. The UPS has been divided as follows AC Rectification DC Inverter Battery Charging Transfer Switch Control of the UPSÂ   4.1 Bridge Rectifier (AC >> DC) 4.1.1 Calculation Theory An AC to DC converter is required to utilise the mains AC voltage to charge a set of batteries for use when the AC signal is lost. A rectifier circuit can be designed to utilise either full or half of the AC waveform, this can be achieved through the use of diodes or thyristors. Figure 10 shows the circuit configuration of a bridge rectifier which can use either component. The difference between using diodes and thyristors is the control over the voltage on the output, diodes give an output equal to the peak voltage of the AC waveform and thyristors voltage depends on the firing angle used to turn the thyristors on. To achieve a pure DC voltage filtering is required to remove the ripple of the sinusoidal waveform. Figure 11 shows how the DC can be filtered to give a pure DC voltage through the use of a capacitor. For this project, a constant DC voltage equivalent to the peak AC waveform can be used to supply the Buck Battery Charger because this will reduce the DC voltage to the required voltage to charge the retrospective batteries. For the purpose of this project, a diode full wave bridge rectifier can be used to supply 34V to the buck battery charger. 4.1.2 Simulation The circuit in figure 4.1.1 was modified to add a smoothing capacitor then it was built in Multisim as shown in Figure 9which gives the output as shown in Figure 13. 4.1.3 Building and Testing After simulation was complete the circuit was built on a breadboard so that its operation could be tested in practice before a PCB was designed. The practical testing is shown in Figure 14. It can be seen that the incoming 24V AC supply is changed to DC through the bridge rectifier which is shown as the peak voltage on channel 1 as 31.5 V DC Once the circuit was tested on a breadboard it was then produced on a PCB, this was soldered using the same components and tested to give the same results as in Figure 14. The PCB design and finished PCB can be observed below (Figure 15/16) 4.2 Inverter (DC >> AC) 4.2.1 Calculation Theory To convert the DC voltage stored in the batteries to make AC voltage a DC to AC inverter is required. There are three main types of DC to AC inverter which depend on the AC output waveform, these are square, modified sine and pure sine wave. The difference between the modified sine and the pure sine wave is that the modified sine rests on the 0 line for a small amount of time then either rises or falls whereas the sine wave goes straight through the 0 line. (Figure 17) For this application, a sine wave as close to the mains is required so a modified sine wave will be produced which will be filtered to make a sine wave. To change DC to AC an H bridge is required similar to that of an AC to DC converter. As can be seen in Figure 19 the switching of the H Bridge changes the current flow through the load and so creates AC. The issue with this circuit is that it will give an AC square wave, to adapt this to make a modified sine another bridge is required Figure 18to introduce a voltage step and make a multilevel inverter. Each bridge is use to add a square wave on top of each other so that an output Figure 20 can be produced. With an increase in H-bridges, this means an increase of switches and DC sources. The DC sources are required to make an AC RMS voltage equivalent to that of the mains input (24V RMS). The peak voltage of the AC waveform has to be matched by the total voltage of the DC, this means that a total DC voltage can be calculated by equation 1 which gives a value of 33.94 V. To achieve this voltage exactly through the use of DC sources would be hard so a voltage higher would be best through the use of four 9V or six 6V batteries used to get 36V, this would mean that by using six 6V batteries smaller steps are achieved but more bridges are required which would be more accurate than using 9V steps and having fewer bridges. To eliminate the repeated use of bridges a modified multilevel inverter circuit (Figure 21) can be developed to use 1 bridge and switch on each source as required so that switch numbers can be reduced from 24 switches to 10 switches. The reduction of switches can be observed through a comparison of the conventional and modified H-bridge. (Figure 21). For this inverter, it will be designed as a 13 level modified multilevel inverter which requires 8 control signals to switch on each 6V source and also to change the polarity across the load. 4.2.2 Simulation A 13 level modified cascaded inverter was built in Multisim using 8 pulsed signals that represent the signals obtainable from the microcontroller. This gives a modified sine wave output that is operating at 50Hz with a peak to peak of 72 V. 4.2.3 Testing 4.3 Battery Charger (DC >> DC) 4.3.1 Calculation Theory To charge the six 6 V batteries for the inverter and single 12-volt battery to supply the Arduino it is required to reduce the 34V produced from the AC rectifier to a suitable level for the retrospective batteries to charge. This is normally 1.15 times the voltage of the rated battery voltage which gives 6.9 volts and 13.8 volts which are confirmed in the datasheet for each battery. To reduce the DC voltage a chopper circuit is required, these can be categorised as either switched or linear, and to understand the characteristic a comparison of both is shown below [8] (Table 3). Linear Switched Function Can only reduce voltage Can increase or decrease voltage depending on design Efficiency As difference in voltage increases efficiency decreases High efficiency Complexity Low usually only requiring a regulator and capacitors Medium to high due to inductor, capacitor calculations Cost Low Medium to high depending on design Output Ripple Low Medium to high due to switching rate Table 3: Chopper Comparison [8] For best efficiency a switched inverter will be used, this is required to give each battery half an amp of current at 6.9 Volt and 13.8 volts. 4.3.2 Simulation 4.3.3 Testing 4.4 Transfer Switch (AC >> AC) 4.4.1 Calculation Theory An AC to AC converter is required to change the supply to the output between mains voltage and back up supply from the DC AC inverter. This type of AC converter works as a switch to turn either AC source on respectively when it is required (Figure 23), other types of AC to AC converter can be used to change aspects of the AC waveform but this is not required in this application. A contactor or a semiconductor device circuit can be designed to make this transfer switch, each of which has its advantages but for this project, a semiconductor device was used, the common devices use to make an AC AC converter are SCRs or thyristors. To utilise either device a double circuit of back to back devices is used so that each half of the cycle is seen at the output. (Figure 24). To prevent using 2 SCRs or thyristors back to back, a triac can be used to do this job instead. This means that the use of two triacs with a common output and separate inputs can be used as a transfer switch. (Figure 25) 4.4.2 Simulation To show the operation of the transfer switch 2 different AC signals of different frequencies are used to show the transfer. (Figure 26). When the control signal is supplied to Triac 1 the output waveform is shown as 25Hz but when the control signal is changed to Triac 2 the output changes to 50Hz. (Figure 27) To isolate the Triac from the microcontroller an optocoupler will be used so that in the event of a fault the microcontroller doesnt come in contact with the AC voltage 4.4.3 Testing The transfer switch was built on a prototyping board using two TIC246M Triacs which are then operated through two MOC3021 triac optocouplers, these use the AC signal to turn on each triac. To test the transfer switch a method similar to that of the simulation was adopted, but instead of using 2 different frequencies, 2 different phases where used then the output was compared to each to show that the transfer switch is operational. Due to the risk of shorting two phases if an issue occurred each side of the transfer switch was tested for operation individually. Once this was tested and operational the input signal for each phase was placed on channel 1 and 2 of the oscilloscope and the output positioned on channel 3. (Figure 28). This meant that as each triac was turned on it could be compared with the corresponding input to ensure the triac was operating as required. As we see below figure 4.4.3.2 shows the output when triac 1 is operating and figure 4.4.3.3 shows when the second is operational. When the transfer switch was tested and operational a PCB design was developed on circuit wizard, this also incorporated a CT to measure the output current and a bridge rectifier chip to take a reading of the output voltage peak voltage. These would be sent to the microcontroller to display.

Laplace transforms

Laplace transforms Laplace Transforms – Motivation convenience – differential eqns become algebraic eqns. – easy to handle time delays – frequency response analysis to determine how the system responds to oscillating inputs Block Diagram Algebra – doing math with pictures – arithmetic for manipulating dynamic components using boxes and arrows Laplace Transform – Review Given a function f(t) Notes f(t) defined for t from 0 to infinity f(t) suitably â€Å"well-behaved† – piecewise continuous, integrable Linearity of Laplace Transforms the Laplace transform is a linear operation we will use Laplace transforms to analyze linear dynamic systems if our models arent linear, then we will linearize Useful Laplace Transforms for Process Control We need a small library of Laplace transforms for – differentiation – step input – pulse/impulse functions – exponentials – oscillating functions because these are common functions that we will encounter in our equations Lets think about a simple linear differential equation example: with V and F as constants Library of Useful Transforms differentiation – initial conditions disappear if we use deviation variables that are zero at an in initial steady state unit step function (Heaviside fn.) Library of Transforms exponential – exponentials appear in solutions of differential equations  » a provides information about the speed of the response when the input changes. If a is a large negative number, the exponential decays to zero quickly  » What happens if a is positive? – After we have done some algebra to find a solution to our ODEs in the Laplace domain, we must invert the Laplace transform if we want to get a solution in the time domain. We sometimes use partial fraction expansion to express the Laplace expressions in a form that can be easily inverted. CSTR Example Transform Model (in deviation variables) using our library of transforms, the Laplace transform of the model is: For a step change in feed concentration at time zero starting from steady state. Tank Example Solution Solve for CA(s) If we like, we can rearrange to the form: This is the solution in the Laplace domain. To find the solution in the time domain, we must invert the Laplace transforms CSTR Example Solution inverse Laplace transform – Can be determined using a complex integral easiest approach is â€Å"table lookup† Use Table 4-1, entry 5 Maple is good at inverting Laplace transforms too The Impulse Function limit of the pulse function (with unit area) as the width goes to zero and height becomes infinite transform CSTR Impulse Response physically dump some pure A into reactor, all at once input function Transform time response Interpretation of Impulse Response dump a bag of reactant into the reactor in a very very short time we see an instantaneous jump to a new concentration due to the impulse input concentration then decays back to the original steady-state concentration Time-Shifted Functions Representation of Delays Laplace transform for function with time delay Just pre-multiply by an exponential. How could we prove this? – change of variables in integration in expression for Laplace Transform (see p. 103 of Marlin, p. 115 in first ed.) Reactor Example with Time Delay Suppose we add a long length of pipe to feed – assume plug flow – It will take a time period, q minutes, before the change in concentration reaches the tank, and begins to influence cA – delay differential equation  » difficult to solve directly in time domain  » easy to solve with Laplace transforms Tank Example with Time Delay – Solutionresponse to step input in cA0 time response Final Value Theorem An easy way to find out what happens to the output variable if we wait a long time. We dont have to invert the Laplace transform! Why is it true? – Consider the Laplace transform of a time derivative now let s approach zero provided dy/dt isnt infinite between t=0 and t ®Ã‚ ¥ (i.e y(t) is STABLE) This will be true if Y(s) is continuous for s ³0 Using the Final Value Theorem Step Response Reactor example final value after a step input What can we do with Laplace Transforms so far. Take Laplace transforms of linear ODEs (in deviation variables). Substitute Laplace transform expressions for different kinds of inputs we are interested in: – Steps, pulses, impulses (even with dead time) Solve for the output variable in terms of s. Invert the Laplace transform using Table 4.1 to get the solution in the time domain. Find the final steady state value of the output variable, for a particular input change, even without inverting the Laplace transform. Laplace transforms are mostly used by control engineers who want to determine and analyze transfer functions. compact way of expressing process dynamics relates input to output p(s), q(s) polynomials in s – q(s) will also contain exponentials if time delay is present Once we know the transfer function of the process, we can use it to find out how the process responds to different types of input changes:

Spirituality and Edna St. Vincent Millays Works Essay -- Edna St. Vin

The assimilation of human feeling with nature impacted the writings of Edna St. Vincent Millay throughout the entirety of her career. At an early age, on the coast of Maine, Millay had a quasi-religious experience while nearly drowning, that when written down ten years later became the foundation of one of her most staggering works, â€Å"Renascence.† The way in which Millay confronts and interacts with nature, namely the sky, is unnerving, raw, and beautiful. She transcends time and is enabled to take part in an empathetic experience with the entirety of what she perceives around her. This poem serves as a precursor to later poems that deal with the human and its counterpart in existence, nature. Over the course of her work, Millay was constantly reconfiguring her notion of God, humanity, and nature and how they were interrelated. This examination and understanding of a oneness with things is the theme found throughout her writing. In addition to â€Å"Renascence†, it is found in â€Å"Spring† as well as â€Å"Epitaph for the Race of Man.† The constant it seems is her communion with that around her in the natural world. Her offerings of interpretations and meditations on the earthly goods of nature and humanity showcase a pantheistic view of the world, in which everything equals God. The poem â€Å"Renascence†, which garnered Edna St. Vincent Millay instant fame as a poet and allowed her entry into her life as a writer was written when she was only eighteen, ten years after a near drowning incident off of coastal Maine. The poem deals with the spiritual experience of accepting man’s suffering and offers an extended and meditative view of nature as a presence that pushes and awakens the sense of empathy in man. The beauty of â€Å"Renas... ...even if these connections are made by the shared experience of death. It is in this connection to larger ideas and showing then, the connections to smaller entities therein, that Edna Millay is able to project a pantheistic sensibility, even if this is in the minor chord of foreboding destruction. The humanity that Millay is privy to in the understandings she obtains from the observation of earth, sky, season, and the cycle of existence is the paramount essence of her writing. The poetry of Edna St. Vincent Millay is the poetry of evaluation of that which is shared and experienced. In each of her writings above, Millay has reconfigured the notion of nature and humanity, not as separate things existing in the same world, but rather two forces occupying each other’s space long enough that there is an indelible reference to each in the existence of the other.