#1 A rise in the expected future exchange rate shifts the demand for domestic assets to the ____and causes the domestic currency to____. A) left; depreciate B) right; appreciate C) left; appreciate D) right; depreciate #2 A rise in the expected import demand shifts the demand for domestic assets to the ___ and causes the domestic currency to ___. A) left; appreciate B) right; depreciate C) right; appreciate D) left; depreciate

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1. A tiltrotor aircraft shown in Figure 1-a is both an airplane and a helicopter. It can position its engine in a vertical position for takeoff and landing as a helicopter, and then rotate its engine 90 degrees to a horizontal configuration for cursing as an airplane. The altitude control system of the helicopter mode is shown in Figure 1-b. • Determine the root locus of this system as K varies between zero (0) and infinity (infinity). • Determine the range of K for a stable system • For K = 280, find the response y(t) to a unit step input r(t), and the corresponding Percentage overshoot (PO) and the settling time (T_s, with 2% criterion) • For K = 280, and r(t) = 0, find the response y(t) to a unit step disturbance 2. An arm of a space robot is shown in Figure 2-1 with its corresponding block diagram shown in Figure2-b. Perform the following tasks: • For a proportional controller Gc=Kp, determine the value of Kp such that the percentage overshoot P.O.-3%. • Plot the system response to a unit step input for the value of Kp determined in the previous task • Design a proportional -derivative controller (PD) using ITAE method with wn = 8 • Determine the required prefilter Gp(S). • Determine the system response to a step input after you add the PD and prefilter to the system. • Design a proportional-integral controller (PI) and a prefdilter using ITAE method. • Determine the system response to a step input after you add the Pi and prefilter to the system. • Design a proportional-integral-derivative controller (PID) and a prefilter using ITAE method such that the settling time T, <4 sec based on a 2% criterion. • What is your recommendation for the most appropriate controller among P, PD, PI, and PID for this system? TAs Controller Arm R- Gas) GO sEs+9 Fig 2-6 F’3 2-a Document Preview:

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1. (a) With reference to the phasor diagram, state what is meant by the load angle of a synchronous motor. (b) What is the value of this angle when the motor runs on no-load? 2. (a) Sketch the curve of the power factor characteristic of a synchronous motor as the excitation current changes.
(b) (i) With reference to the curve in part (a), when the excitation is increasing initially state whether the power factor is leading or lagging.
(ii) Explain, with the help of a phasor diagram for one phase, briefly what happens as the excitation increases further.
3. Explain briefly with the aid of phasor diagrams, how the synchronous machine stator current can be varied if the load is constant.
4. (a) State and explain briefly the main methods of excitation of a synchronous induction motor.
(b) Identify which method of excitation is most commonly used in modern machines.

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1. According to the EF, is the human population living at, beyond or below the Earth’s natural biocapacity? For how long has this been the case? Is this sustainable? (4 marks) 2. According to the EF, is the Chinese population living at, beyond or below China’s natural biocapacity? For how long has this been the case? Is this sustainable? (4 marks) 3. If you assume that EF grows at a constant yearly rate, what is the approximate slope of the EF relationship with time for China? And what is its units? Give the equation of, and sketch this line, with EF on the vertical axis and year on the horizontal axis. (EF for 2012 is 3.4 and for 1961 was approximately 1). (4 marks) 4. If you assume that biocapacity grows at a constant yearly rate, what is the approximate slope of the biocapacity relationship with time for China? And what is its units? Give the equation of, and sketch this line, with biocapacity on the vertical axis and year on the horizontal axis. (biocapacity for 2012 is 0.9 and for 1961 was approximately 1). (4 marks) 5. If this trend continues, what will EF and biocapacity be in 2050? (Hint: use your equation from questions 3 and 4.) What will biocapacity minus EF be in 2050? Will there be a deficit or reserve? (4 marks) 6. Use the data presented in Figure 1 to suggest a policy to make land use sustainable. (4 marks)
The model describes the evolution of a population over time ??. ??(??) = ??0?? (??-??)?? (1) where ??0 is the population at time ?? = 0. 1. If the initial population is ??0 = 2000, the annual birth rate ?? = 0.03 (3% exponential birth rate) and annual death rate ?? = 0.02 (2% exponential death rate), what is the population after 1 year? Explain this result. (4 marks) 2. Find an expression for the growth rate (population change) of the population in terms of time and the parameters. Hint: differentiating with respect to time gives a rate of change. (4 marks) 3. If ??
The model in equation (1) in Part A describes a population untouched by humans: there is no harvesting. We can model what happens if we harvest ?? individuals from the population each period. The unlimited population growth with harvesting model is given by ??(??) = ???? (??-??)?? + ??-???? (??-??)?? (??-??) (2) where ?? is the birth rate, ?? is the death rate, and ?? is the number of individuals taken from the population in each period. 1. Confirm that the rate of population change is ????(??) ???? = (?? – ??)??(??) – ??. (3) (5 marks) 2. Give the meaning of the expression in equation (3). (4 marks) 3. Let ??0 = ??(0) = 2000, ?? = 0.05 and ?? = 0.02. At what rate can the population be harvested sustainably? Hint: The sustainable harvest, ??, will be the value that causes no change in the overall population, i.e. ????(??) ???? = 0. (4 marks) 4. Suppose an ecosystem is being sustainably harvested at exactly its replacement rate, and the population is constant. Now suppose the population experiences a brief disease epidemic, which causes 4% of individuals to perish. What will happen to the population if harvesting continues at the same rate? (4 marks) 5. Suppose a population of fish that follows this model is being harvested sustainably, as before. What will happen in the long run if, one day, a fisherman decides to throw one of the fish back? (4 marks) 6. This type of model is often said to have a “knife-edge” equilibrium. Explain what this means. (4 marks) 7. Governments often levy fishing quotas in areas where populations are at risk. Does this model shed any light on the effectiveness (or otherwise) of these policies? (Hint: what if someone cheats?) (4 marks)
A model linking these ideas was first proposed by a French mathematician Pierre Verhulst in 1838. The Verhulst model can be written as: ??(??) = ??0?? ???? 1+ ??0(?? ????-1) ?? (4) where ??0 is the initial population level. For simplicity, we’ll write the net reproduction rate simply as ??, rather than in terms of births and deaths. 1. What is the growth rate if the initial population is zero? (4 marks) 2. When the population is initially at its carrying capacity, i.e. ??0 = ??, what is the population at time ??? How does the population level change when the growth rate r increases? (4 marks) 3. Differentiate (4) to show that the rate of population growth at time t is ????(??) ???? = ????(??) (1 – ??(??) ?? ) (5) Remember to use the quotient rule to differentiate (4). You will find it easier if you carefully look for the terms that you expect to see in the final expression, and factor those out. (5 marks) 4. Does the population grow faster when it is above the environment’s carrying capacity (N>K), or below it (??

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