### Control Systems Problem**Objective:** Find values of $ K_1 $ and $ K_2 $ to yield poles at $ s = -1 \pm j 3 $.**Options:**- (a) $ K_1 = 2, K_2 = 11 $- (b) $ K_1 = 2, K_2 = 9 $- (c) $ K_1 = 9, K_2 = 2 $- (d) $ K_1 = 1, K_2 = 2 $**Question:** When $ K_1 = 6 $ and $ K_2 = 9 $, find the poles of the system.**Calculated Poles:**- (a) $ s_1 = -3, s_2 = -3 $- (b) $ s_1 = -4, s_2 = -3$- (c) $ s_1 = -3 + j 3, s_2 = -3 - j 3 $- (d) $ s_1 = 2.5, s_2 = 4 $**Diagram Analysis:**The block diagram represents a control system. The components include:1. **Integrator ($\int$):** Symbolized by a block with an integration sign, indicating the integration of the input signal.2. **Negative Feedback (-K1):** A block representing a multiplication with the constant $-K_1$.3. **Additional Feedback (1-K2):** A block indicating the system output is multiplied by $1-K_2$ before feeding back to the system input.4. **Summing Junction:** Located at the circuit junctions with typical plus and minus signs indicating the addition and subtraction of signals.5. **Signal Path:** The lines connecting each block highlight the flow of control signals through the system.The goal is to manipulate the values $ K_1 $ and $ K_2 $ such that the system provides a desired response characterized by specific pole placements.

Answered: Image /qna-images/answer/186a1d86-222e-4e8e-90af-3587f4c21517.jpg

x₂ (t) AS (a) K₁ = 2, K₂ = 11 (b) K₁ = 2, K₂ = 9 (c) K₁ = 9, K₂ = 2 (d) K₁ = 11, K₂ = 2 -K₂ Find values of K, and K₂ to yield poles at s = -1 ±j3. x, (t) When K₁ = 6 and K₂ = 9, find the poles of the system. (a) S₁ = -3, S₂ = -3 (b) s₁ = -3+j3, S₂ = -3-j3 (c) s₁ = -3+j, $₂ = -3-j (d) $₁ = -2, S₂ = -4

x₂ (t) AS (a) K₁ = 2, K₂ = 11 (b) K₁ = 2, K₂ = 9 (c) K₁ = 9, K₂ = 2 (d) K₁ = 11, K₂ = 2 -K₂ Find values of K, and K₂ to yield poles at s = -1 ±j3. x, (t) When K₁ = 6 and K₂ = 9, find the poles of the system. (a) S₁ = -3, S₂ = -3 (b) s₁ = -3+j3, S₂ = -3-j3 (c) s₁ = -3+j, $₂ = -3-j (d) $₁ = -2, S₂ = -4

Power System Analysis and Design (MindTap Course List)

6th Edition

ISBN:9781305632134

Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Publisher:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Chapter6: Power Flows

Section: Chapter Questions

Problem 6.4P

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