MASON ECE 421 - First-Order System Example #1 (11 pages)

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First-Order System Example #1



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First-Order System Example #1

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Pages:
11
School:
George Mason University
Course:
Ece 421 - Classical Systems and Control Theory

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1 First Order System Example 1 A Overview Two di erent first order systems will be presented in this example The first system G1 s will have its one open loop pole located at the origin of the s plane that is at s 0 The second system G2 s will have its one open loop pole located at some other place along the real axis Neither of these systems will have a zero in its transfer function Thus neither of these systems represents the most general first order system model but the two of them together do represent the most general strictly proper first order system models The reason for di erentiating between G1 s and G2 s in terms of the location of the open loop pole will be discussed in the following sections For each of these systems the corresponding closed loop transfer function will be developed under the assumption of unity feedback that is with H s 1 The closed loop responses of these systems to a unit step input and to a unit ramp will be developed using partial fraction expansion Several transient response and steady state response characteristics will be defined in terms of the parameters in the open loop transfer functions These characteristics will be useful in comparing the time domain performance of di erent first order systems and they will also serve as a basis for the more general characteristics of second order systems to be studied later B System 1 B 1 The System Models The first system to be considered is given by the following transfer function which will be placed in the forward path of a unity feedback closed loop system K K 0 1 s where K is a positive real number serving as the gain of the open loop system This transfer function can also be written in the following forms by simple algebraic manipulation G1 s 1 G1 s 1 K s 1 Ts 2 where T 1 K is defined as the time constant of the system All of the various time domain characteristics that will defined for this first order system will be expressed in terms of the time constant Using the last form for



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