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Consider a first-order system Y(s) Y(s) D(s) Kp Gp(S) The system is = KD tps+1° tps+1 affected by an independent unmeasured disturbance with first- order dynamics = GD(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 Gp(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) = =Kc (1++ KDs). 3 0 -1 Open-Loop Responses to steps in u(t) and d(t) Response to step in u(t) Response to step in d(t) -2 15 20 25 0 5 10 Time 1.4. 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). Consider the plot to right, which shows the response y(t) for a step change in the reference signal r(t) while under Pl-control using Kc = t = 1. Given this response, sketch on the same axes the response of y(t) to the same step in r(t) if: a) τι » 1. b) t, << 1. c) -> T→ ∞o (i.e., a P controller only). 1.2 Closed-Loop Response 10 0.4 0.6 0.8 0.2 Closed-Loop Response to Step Change in r(t) 0 0 5 10 15 20 20 Time 25 25 1.5. For this scenario, answer the following by saying YES or NO and explaining in one sentence maximum a) If a controller is stable for a bounded change in r(t), is it stable for a bounded change in d(t)? b) If a controller results in zero offset for a change in d(t), will it have zero offset for a change in r(t)? c) If bounded changes r(t) and d(t) result in stable closed-loop outputs when applied separately, is it guaranteed that the output will be stable when r(t) and d(t) are applied together?

Consider a first-order system Y(s) Y(s) D(s) Kp Gp(S) The system is = KD tps+1° tps+1 affected by an independent unmeasured disturbance with first- order dynamics = GD(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 Gp(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) = =Kc (1++ KDs). 3 0 -1 Open-Loop Responses to steps in u(t) and d(t) Response to step in u(t) Response to step in d(t) -2 15 20 25 0 5 10 Time 1.4. 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). Consider the plot to right, which shows the response y(t) for a step change in the reference signal r(t) while under Pl-control using Kc = t = 1. Given this response, sketch on the same axes the response of y(t) to the same step in r(t) if: a) τι » 1. b) t, << 1. c) -> T→ ∞o (i.e., a P controller only). 1.2 Closed-Loop Response 10 0.4 0.6 0.8 0.2 Closed-Loop Response to Step Change in r(t) 0 0 5 10 15 20 20 Time 25 25 1.5. For this scenario, answer the following by saying YES or NO and explaining in one sentence maximum a) If a controller is stable for a bounded change in r(t), is it stable for a bounded change in d(t)? b) If a controller results in zero offset for a change in d(t), will it have zero offset for a change in r(t)? c) If bounded changes r(t) and d(t) result in stable closed-loop outputs when applied separately, is it guaranteed that the output will be stable when r(t) and d(t) are applied together?

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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This is the last two questions of a previous question I just sent. Please show step by step with clear explanations as to what to do for these questions. I am very confused. Thank you, I will give positive feedback

Consider a first-order system Y(s) Y(s) D(s) Kp Gp(S) The system is = KD tps+1° tps+1 affected by an independent unmeasured disturbance with first- order dynamics = GD(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 Gp(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) = =Kc (1++ KDs). 3 0 -1 Open-Loop Responses to steps in u(t) and d(t) Response to step in u(t) Response to step in d(t) -2 15 20 25 0 5 10 Time
Transcribed Image Text:Consider a first-order system Y(s) Y(s) D(s) Kp Gp(S) The system is = KD tps+1° tps+1 affected by an independent unmeasured disturbance with first- order dynamics = GD(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 Gp(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) = =Kc (1++ KDs). 3 0 -1 Open-Loop Responses to steps in u(t) and d(t) Response to step in u(t) Response to step in d(t) -2 15 20 25 0 5 10 Time
1.4. 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). Consider the plot to right, which shows the response y(t) for a step change in the reference signal r(t) while under Pl-control using Kc = t = 1. Given this response, sketch on the same axes the response of y(t) to the same step in r(t) if: a) τι » 1. b) t, << 1. c) -> T→ ∞o (i.e., a P controller only). 1.2 Closed-Loop Response 10 0.4 0.6 0.8 0.2 Closed-Loop Response to Step Change in r(t) 0 0 5 10 15 20 20 Time 25 25 1.5. For this scenario, answer the following by saying YES or NO and explaining in one sentence maximum a) If a controller is stable for a bounded change in r(t), is it stable for a bounded change in d(t)? b) If a controller results in zero offset for a change in d(t), will it have zero offset for a change in r(t)? c) If bounded changes r(t) and d(t) result in stable closed-loop outputs when applied separately, is it guaranteed that the output will be stable when r(t) and d(t) are applied together?
Transcribed Image Text:1.4. 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). Consider the plot to right, which shows the response y(t) for a step change in the reference signal r(t) while under Pl-control using Kc = t = 1. Given this response, sketch on the same axes the response of y(t) to the same step in r(t) if: a) τι » 1. b) t, << 1. c) -> T→ ∞o (i.e., a P controller only). 1.2 Closed-Loop Response 10 0.4 0.6 0.8 0.2 Closed-Loop Response to Step Change in r(t) 0 0 5 10 15 20 20 Time 25 25 1.5. For this scenario, answer the following by saying YES or NO and explaining in one sentence maximum a) If a controller is stable for a bounded change in r(t), is it stable for a bounded change in d(t)? b) If a controller results in zero offset for a change in d(t), will it have zero offset for a change in r(t)? c) If bounded changes r(t) and d(t) result in stable closed-loop outputs when applied separately, is it guaranteed that the output will be stable when r(t) and d(t) are applied together?
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