Ps4 - EE 428 PROBLEM SET 4 DUE 12 OCT 2007 Reading assignment Please read chapter 4 sections 4.2 through 4.4 Problem 14(20 points This problem

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EE 428 PROBLEM SET 4 DUE: 12 OCT 2007 Reading assignment: Please read chapter 4 sections 4.2 through 4.4. Problem 14: (20 points) This problem considers the efects oF a single ±nite zero on the transient response oF the second-order system Y ( s ) U ( s ) = ( s/αζω n )+1 ( s/ω n ) 2 +2 ζ ( s/ω n . The zero is located at s = αζω n . IF α is large, than the zero is Far removed From the poles and will have little efect on the response. In Fact, as α →∞ , we have lim α →∞ Y ( s ) U ( s ) = 1 ( s/ω n ) 2 ζ ( s/ω n . 1. (8 points) Let ζ =0 . 5and ω n = 1 rad/sec. Using MATLAB, plot the unit-step response For α =1 , 2 , 4 , and 100 in a single ±gure. Label the individual responses using the legend command . In order to obtain the Greek symbol α in the legend, use the MATLAB symbol \alpha . Add your name and section using gtext ,an include a copy oF the m-±le speciFying the commands used to generate the plots. 2. (7 points) ²or each system in part 1, sketch the pole-zero map, and using MATLAB, determine the percent peak overshoot, the time-to-peak, rise-time, and settling time. (You may wish to use the Function From Problem Set 2, Problem 9). Based on these time response characteristics, summarize the efect oF moving the zero towards the imaginary axis in two or three short sentences. 3. (5 points) In part 1 the zero is always located in the leFt-halF plane. Now consider the afect oF an unstable zero , that is, a zero located in the right-halF plane. With ζ . ω n = 1 rad/sec, simulate the step-response For α = 1 using MATLAB. In comparison to the results obtained in part 1, what is the salient Feature oF the step-response obtained with a system that has an unstable zero? Problem 15: (15 points) Consider the Following second order system with an added pole H ( s )= 1 ( s/p +1)( s 2 + s +1) . 1. (8 points) Let p = α/ 2 and plot the unit-step response using MATLAB For α . 1 , 1 , and 10 in a single ±gure. Label the responses using the legend command and add your name and section number using gtext . Include a copy oF an m-±le showing the MATLAB commands used to generate the plots. 2. (7 points) ²or each system in part 1, sketch the pole-zero map, and using MATLAB, determine the percent peak overshoot, the time-to-peak, rise-time, and settling time. (You may wish to use the Function From Problem Set 2, Problem 9). Based on these time response characteristics, summarize the efect oF moving the pole towards the imaginary axis in two or three short sentences.
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Problem 16: (15 points) Many physical systems are represented as the cascade of a fast and slow subsystem as shown in Figure 1. This situation often arises in electromechanical systems, such as the DC motor. In this problem we show that the behavior of the cascade system can be adequately described by a reduced order model. Suppose that H f ( s )= 4 f +1 H s ( s 0 . 5 s , where the fast system has a time constant τ f =0 . 1 s while the slow system has a time constant τ s =1 .
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This note was uploaded on 07/23/2008 for the course EE 428 taught by Professor Schiano during the Fall '07 term at Pennsylvania State University, University Park.

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Ps4 - EE 428 PROBLEM SET 4 DUE 12 OCT 2007 Reading assignment Please read chapter 4 sections 4.2 through 4.4 Problem 14(20 points This problem

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