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Unformatted text preview: EE 428 PROBLEM SET 5 DUE: 29 OCT 2007 Reading assignment: Please read chapter 4 sections 4.2 through 4.4. Problem 19: (15 points) For each of the following polynomials 1. s 2 + as + b = 0, where a > 0 and b > 0. What happens if either a or b is zero or negative? 2. s 3 + 4 s 2 + 6 s + 6 = 0 3. s 5 + s 4 + 5 s 3 + 5 s 2 + 4 s + 4 = 0 4. s 4 + s 3 + 3 s 2 + 2 s + K = 0 5. s 5 + s 4 + 2 s 3 + s 2 + s + K = 0 determine: • the number of poles in the right-half plane, • the location of any complex conjugate roots on the ω axis, and • if there is an adjustable parameter K appearing in the polynomial, determine the range of K for which the polynomial is Hurwitz. Problem 20: (20 points) Figure 1 shows the block diagram of an automated arc welding system. To insure consistent quality, the system regulates the puddle diameter by varying the level of arc current. The system uses a video system to measure puddle width, and cascade compensation to achieve desired steady-state accuracy and transient response characteristics. Figure 1: Automated arc welding system. 1. (6 points) What is the largest value of K for which the closed-loop system remains BIBO stable? 2. (7 points) For half of the maximum value of K found in part 1, determine the roots of the characteristic equation and estimate the percent overshoot and rise-time of the system when it is driven by a unit-step input. 3. (7 points) For half of the maximum value of K found in part 1, determine the position error constant and the corresponding steady-state error for a unit-step input. Problem 21: (15 points) Once again consider the closed-loop system in Problem 20. • Construct a SIMULINK block diagram of the closed-loop system. Attach to your solutions a printout of the SIMULINK block diagram....
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