Direction: Read the following passages carefully and answer the question that follows.
Regardless of how the state's feedback control law is designed, it is almost always necessary to implement it, using estimates of the state obtained from an observer. Hence, it is necessary to insure so that the desirable properties of the state feedback design do not vanish when the state estimate are used. It is proven in linear system theory courses that the command response is unaffected by the presence of the observer. However, the response to initial conditions will affect the system output. It is suggested that the observed poles should be made faster than the state feedback poles by an amount that depends upon the level of measurement noise. These conclusions are generally based upon transient time response properties of the system, and not on feedback properties such as robustness margins, We now present a procedure for tuning an observer so that, under appropriate conditions, the feedback properties of a state feedback design are recovered.

Direction: Read the following passages carefully and answer the question that follows.
Seven-year -old Jim came home from the park without his new bicycle. "An old man and a little boy borrowed it. " he explained. "They are going to bring it back at four O'clock,". His parents were upset that he had given his expensive new bicycle, but were secretly proud of his kindness and faith. Came four O'clock, no bicycle. The parents were anxious. But at 4 :30, the door bell rang. and there stood a happy man and a boy , with the bicycle and a box of chocolates. Jim suddenly disappeared into his bedroom, and then came running out. ' All right , ' he said, after examining the bicycle. "You can have your watch back ! " .

Direction: Read the following passages carefully and answer the question that follows.
We know that gold and silver are elements. An element consists of atoms of only one kind, unlike water, which consists of both hydrogen and oxygen. Another element is radium. Radium is especially interesting, because it produces heat, When soil is carried by rivers down to the sea and falls to the bottom, it often carries radium in it. As more and more soil is washed down into the ocean. more and more radium is carried in it. There, as elsewhere, it constantly produces heat.