{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# ps4 - EE 428 PROBLEM SET 4 DUE 12 OCT 2007 Reading...

This preview shows pages 1–3. Sign up to view the full content.

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 effects of a single finite 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 ) + 1 . 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 effect on the response. In fact, as α → ∞ , we have lim α →∞ Y ( s ) U ( s ) = 1 ( s/ω n ) 2 + 2 ζ ( s/ω n ) + 1 . 1. (8 points) Let ζ = 0 . 5 and ω n = 1 rad/sec. Using MATLAB, plot the unit-step response for α = 1 , 2 , 4 , and 100 in a single figure. 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-file specifying the commands used to generate the plots. 2. (7 points) For 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 effect 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 affect of an unstable zero , that is, a zero located in the right-half plane. With ζ = 0 . 5 and 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 = 0 . 1 , 1 , and 10 in a single figure. Label the responses using the legend command and add your name and section number using gtext . Include a copy of an m-file showing the MATLAB commands used to generate the plots. 2. (7 points) For 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 effect of moving the pole towards the imaginary axis in two or three short sentences.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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 + 1 , where the fast system has a time constant τ f = 0 . 1 s while the slow system has a time constant τ s = 1 . 0 s.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}