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Consider a first-order system Y(s) D(s) Y(s) = Gp(S) = U(s) KD tps+1* KP. The system is tps+1 affected by an independent unmeasured disturbance with first- order dynamics = Gp(s) = The overall output can be computed as Y(s) = U(s)Gp(s)+D(s)Gp(s). Steps of unit magnitude were applied to u(t) and d(t) at time t = 1, the results of which are sketched in the figure to right. Note that the steps were applied separately, and all variables are in deviation form. There is no measurement noise and all dynamics other than Gp(s) and GD (s) can be considered negligible. For all questions below, any references to controller tuning parameters assume that the controller is in ideal form such that U(s) E(s) 1.1. = Kc (1++ KDs). 3 €1 0 -1 -2 Open-Loop Responses to steps in u(t) and d(t) Response to step in u(t) Response to step in d(t) 10 15 20 25 Time Estimate the process parameters Kp, KD, Tp and Tp to the best of your ability. Explain briefly why you chose these values. 1.2. 1.3. We want to control this process under a proportional (P) closed-loop control scheme. For this process, determine the value of Kc that would be required for the closed-loop offset of this system to be of no greater magnitude than +0.2 when responding to a step change in the disturbance signal d(t). Reference lim (r(t) - y(t)). signal r(t) remains unchanged. Offset is defined as = = t-x On the same set of axes, sketch the response of the closed-loop system y(t) to a step in d(t) under P- control for the following values of Kc: a) Kc = the value you found in part (1.2). b) Kc>the one from part (1.2). c) Kc << the one from part (1.2). Closed-Loop Response to Step Change in r(t) 1.2

Consider a first-order system Y(s) D(s) Y(s) = Gp(S) = U(s) KD tps+1* KP. The system is tps+1 affected by an independent unmeasured disturbance with first- order dynamics = Gp(s) = The overall output can be computed as Y(s) = U(s)Gp(s)+D(s)Gp(s). Steps of unit magnitude were applied to u(t) and d(t) at time t = 1, the results of which are sketched in the figure to right. Note that the steps were applied separately, and all variables are in deviation form. There is no measurement noise and all dynamics other than Gp(s) and GD (s) can be considered negligible. For all questions below, any references to controller tuning parameters assume that the controller is in ideal form such that U(s) E(s) 1.1. = Kc (1++ KDs). 3 €1 0 -1 -2 Open-Loop Responses to steps in u(t) and d(t) Response to step in u(t) Response to step in d(t) 10 15 20 25 Time Estimate the process parameters Kp, KD, Tp and Tp to the best of your ability. Explain briefly why you chose these values. 1.2. 1.3. We want to control this process under a proportional (P) closed-loop control scheme. For this process, determine the value of Kc that would be required for the closed-loop offset of this system to be of no greater magnitude than +0.2 when responding to a step change in the disturbance signal d(t). Reference lim (r(t) - y(t)). signal r(t) remains unchanged. Offset is defined as = = t-x On the same set of axes, sketch the response of the closed-loop system y(t) to a step in d(t) under P- control for the following values of Kc: a) Kc = the value you found in part (1.2). b) Kc>the one from part (1.2). c) Kc << the one from part (1.2). Closed-Loop Response to Step Change in r(t) 1.2

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 step by step how ti solve these problems and include good explanations. I am most confused with graphing. Thank you, I will give positive feedback. The rest of the questions to this problem are submitted as a new questions due to the multiple part limit

Consider a first-order system Y(s) D(s) Y(s) = Gp(S) = U(s) KD tps+1* KP. The system is tps+1 affected by an independent unmeasured disturbance with first- order dynamics = Gp(s) = The overall output can be computed as Y(s) = U(s)Gp(s)+D(s)Gp(s). Steps of unit magnitude were applied to u(t) and d(t) at time t = 1, the results of which are sketched in the figure to right. Note that the steps were applied separately, and all variables are in deviation form. There is no measurement noise and all dynamics other than Gp(s) and GD (s) can be considered negligible. For all questions below, any references to controller tuning parameters assume that the controller is in ideal form such that U(s) E(s) 1.1. = Kc (1++ KDs). 3 €1 0 -1 -2 Open-Loop Responses to steps in u(t) and d(t) Response to step in u(t) Response to step in d(t) 10 15 20 25 Time Estimate the process parameters Kp, KD, Tp and Tp to the best of your ability. Explain briefly why you chose these values. 1.2. 1.3. We want to control this process under a proportional (P) closed-loop control scheme. For this process, determine the value of Kc that would be required for the closed-loop offset of this system to be of no greater magnitude than +0.2 when responding to a step change in the disturbance signal d(t). Reference lim (r(t) - y(t)). signal r(t) remains unchanged. Offset is defined as = = t-x On the same set of axes, sketch the response of the closed-loop system y(t) to a step in d(t) under P- control for the following values of Kc: a) Kc = the value you found in part (1.2). b) Kc>the one from part (1.2). c) Kc << the one from part (1.2). Closed-Loop Response to Step Change in r(t) 1.2
Transcribed Image Text:Consider a first-order system Y(s) D(s) Y(s) = Gp(S) = U(s) KD tps+1* KP. The system is tps+1 affected by an independent unmeasured disturbance with first- order dynamics = Gp(s) = The overall output can be computed as Y(s) = U(s)Gp(s)+D(s)Gp(s). Steps of unit magnitude were applied to u(t) and d(t) at time t = 1, the results of which are sketched in the figure to right. Note that the steps were applied separately, and all variables are in deviation form. There is no measurement noise and all dynamics other than Gp(s) and GD (s) can be considered negligible. For all questions below, any references to controller tuning parameters assume that the controller is in ideal form such that U(s) E(s) 1.1. = Kc (1++ KDs). 3 €1 0 -1 -2 Open-Loop Responses to steps in u(t) and d(t) Response to step in u(t) Response to step in d(t) 10 15 20 25 Time Estimate the process parameters Kp, KD, Tp and Tp to the best of your ability. Explain briefly why you chose these values. 1.2. 1.3. We want to control this process under a proportional (P) closed-loop control scheme. For this process, determine the value of Kc that would be required for the closed-loop offset of this system to be of no greater magnitude than +0.2 when responding to a step change in the disturbance signal d(t). Reference lim (r(t) - y(t)). signal r(t) remains unchanged. Offset is defined as = = t-x On the same set of axes, sketch the response of the closed-loop system y(t) to a step in d(t) under P- control for the following values of Kc: a) Kc = the value you found in part (1.2). b) Kc>the one from part (1.2). c) Kc << the one from part (1.2). Closed-Loop Response to Step Change in r(t) 1.2
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