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Consider the following second-order UNSTABLE open-loop transfer function: -2s+1 Y(s) Gp(S) U(s) (5s - 1)(s + 1) This process is to be controlled using a feedback loop and a PI controller. The controller outputs a pressure signal P(s) that causes a control element to change the input to the system U(s) with negligible dynamics: Gy(s) = U(s) 4 P(s) 5 The structure of this controller can be assumed to be in PARRALEL form: GC P(s) E(s) = Kc + − S Where I = 1 is nothing more than the inverse of the integral time constant and is represented this way for the sake of easier algebra. 1. 2. 3. Кс I TI Explain in 1-2 sentences ONLY why the Ziegler-Nichols tuning correlations cannot be used to find stable controller parameters for this system. If the desired value of Y(s) is R(s), draw a simple closed-loop block diagram of this process under Pl feedback control. Label all transfer functions and signals. Perform a Routh-Hurwitz analysis on the closed-loop system to determine the mathematical conditions that must be followed when selecting KC and I to ensure a stable closed-loop process. Report the THREE conditions required for this problem as: < I < f(Kc) 4. where where is a number. is a number. where f(KC) is some nonlinear function of Kc you need to find. Visualize your findings from question 3.3 by plotting the "feasible set" of Kc and I that result in a closed-loop stable process. Then, select one combination of Kc and I that is stable, and one that is outside of the feasible set (choose something close but outside).

Consider the following second-order UNSTABLE open-loop transfer function: -2s+1 Y(s) Gp(S) U(s) (5s - 1)(s + 1) This process is to be controlled using a feedback loop and a PI controller. The controller outputs a pressure signal P(s) that causes a control element to change the input to the system U(s) with negligible dynamics: Gy(s) = U(s) 4 P(s) 5 The structure of this controller can be assumed to be in PARRALEL form: GC P(s) E(s) = Kc + − S Where I = 1 is nothing more than the inverse of the integral time constant and is represented this way for the sake of easier algebra. 1. 2. 3. Кс I TI Explain in 1-2 sentences ONLY why the Ziegler-Nichols tuning correlations cannot be used to find stable controller parameters for this system. If the desired value of Y(s) is R(s), draw a simple closed-loop block diagram of this process under Pl feedback control. Label all transfer functions and signals. Perform a Routh-Hurwitz analysis on the closed-loop system to determine the mathematical conditions that must be followed when selecting KC and I to ensure a stable closed-loop process. Report the THREE conditions required for this problem as: < I < f(Kc) 4. where where is a number. is a number. where f(KC) is some nonlinear function of Kc you need to find. Visualize your findings from question 3.3 by plotting the "feasible set" of Kc and I that result in a closed-loop stable process. Then, select one combination of Kc and I that is stable, and one that is outside of the feasible set (choose something close but outside).

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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Please explain each step clearly and include a proper image of what the block diagram and plot must look like. thank you

Consider the following second-order UNSTABLE open-loop transfer function: -2s+1 Y(s) Gp(S) U(s) (5s - 1)(s + 1) This process is to be controlled using a feedback loop and a PI controller. The controller outputs a pressure signal P(s) that causes a control element to change the input to the system U(s) with negligible dynamics: Gy(s) = U(s) 4 P(s) 5 The structure of this controller can be assumed to be in PARRALEL form: GC P(s) E(s) = Kc + − S Where I = 1 is nothing more than the inverse of the integral time constant and is represented this way for the sake of easier algebra. 1. 2. 3. Кс I TI Explain in 1-2 sentences ONLY why the Ziegler-Nichols tuning correlations cannot be used to find stable controller parameters for this system. If the desired value of Y(s) is R(s), draw a simple closed-loop block diagram of this process under Pl feedback control. Label all transfer functions and signals. Perform a Routh-Hurwitz analysis on the closed-loop system to determine the mathematical conditions that must be followed when selecting KC and I to ensure a stable closed-loop process. Report the THREE conditions required for this problem as: < I < f(Kc) 4. where where is a number. is a number. where f(KC) is some nonlinear function of Kc you need to find. Visualize your findings from question 3.3 by plotting the "feasible set" of Kc and I that result in a closed-loop stable process. Then, select one combination of Kc and I that is stable, and one that is outside of the feasible set (choose something close but outside).
Transcribed Image Text:Consider the following second-order UNSTABLE open-loop transfer function: -2s+1 Y(s) Gp(S) U(s) (5s - 1)(s + 1) This process is to be controlled using a feedback loop and a PI controller. The controller outputs a pressure signal P(s) that causes a control element to change the input to the system U(s) with negligible dynamics: Gy(s) = U(s) 4 P(s) 5 The structure of this controller can be assumed to be in PARRALEL form: GC P(s) E(s) = Kc + − S Where I = 1 is nothing more than the inverse of the integral time constant and is represented this way for the sake of easier algebra. 1. 2. 3. Кс I TI Explain in 1-2 sentences ONLY why the Ziegler-Nichols tuning correlations cannot be used to find stable controller parameters for this system. If the desired value of Y(s) is R(s), draw a simple closed-loop block diagram of this process under Pl feedback control. Label all transfer functions and signals. Perform a Routh-Hurwitz analysis on the closed-loop system to determine the mathematical conditions that must be followed when selecting KC and I to ensure a stable closed-loop process. Report the THREE conditions required for this problem as: < I < f(Kc) 4. where where is a number. is a number. where f(KC) is some nonlinear function of Kc you need to find. Visualize your findings from question 3.3 by plotting the "feasible set" of Kc and I that result in a closed-loop stable process. Then, select one combination of Kc and I that is stable, and one that is outside of the feasible set (choose something close but outside).
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