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. (c) Suppose that you want the pitch angle to increase at a constant acceleration of 1 deg/s². To achieve this, you set the desired pitch angle to a parabolic function, r(t) = ½/t² · us(t), where us(t) is the unit step function. What is the system type n? Calculate the steady-state error ess of the closed-loop system as a function of K. Submit your calculations. (d) Compute the closed-loop transfer function, Hc₁ (s) = Y(s)/R(s). Write the characteristic equation of the closed-loop system in the form 1 + KL(s) = 0. Submit your calculations. (e) Plot the positive root locus for the closed-loop system in MATLAB using the command rlocus (L). Use this plot to find the range of K for which the closed-loop system is stable. Submit your MATLAB plot and explain how you used it to find the range of K. W (1) Now we introduce a disturbance input W(s) = kwhere W is a constant, into the feedback controller as shown below. The transfer functions H(s) and C(s) are the same as in parts (c)-(e), and we set R(s) = 0. What type of disturbance input W(s) (step, ramp, or parabola) can the system reject (i.e., the steady-state error ess is a nonzero constant)? Submit your calculations. W(s) R(s) o C(s) + H(s) - Y(s)

. (c) Suppose that you want the pitch angle to increase at a constant acceleration of 1 deg/s². To achieve this, you set the desired pitch angle to a parabolic function, r(t) = ½/t² · us(t), where us(t) is the unit step function. What is the system type n? Calculate the steady-state error ess of the closed-loop system as a function of K. Submit your calculations. (d) Compute the closed-loop transfer function, Hc₁ (s) = Y(s)/R(s). Write the characteristic equation of the closed-loop system in the form 1 + KL(s) = 0. Submit your calculations. (e) Plot the positive root locus for the closed-loop system in MATLAB using the command rlocus (L). Use this plot to find the range of K for which the closed-loop system is stable. Submit your MATLAB plot and explain how you used it to find the range of K. W (1) Now we introduce a disturbance input W(s) = kwhere W is a constant, into the feedback controller as shown below. The transfer functions H(s) and C(s) are the same as in parts (c)-(e), and we set R(s) = 0. What type of disturbance input W(s) (step, ramp, or parabola) can the system reject (i.e., the steady-state error ess is a nonzero constant)? Submit your calculations. W(s) R(s) o C(s) + H(s) - Y(s)

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
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(c) Suppose that you want the pitch angle to increase at a constant acceleration of 1 deg/s². To achieve this, you set the desired pitch angle to a parabolic function, r(t) = ½t² · us(t), where us(t) is the unit step function. What is the system type n? Calculate the steady-state error ess of the closed-loop system as a function of K. Submit your calculations. (d) Compute the closed-loop transfer function, Hcz (s) = Y(s)/R(s). Write the characteristic equation of the closed-loop system in the form 1 + KL(s) = 0. Submit your calculations. (e) Plot the positive root locus for the closed-loop system in MATLAB using the command rlocus (L). Use this plot to find the range of K for which the closed-loop system is stable. Submit your MATLAB plot and explain how you used it to find the range of K. W (1) Now we introduce a disturbance input W(s) = where W is a constant, into the feedback sk controller as shown below. The transfer functions H(s) and C(s) are the same as in parts (c) (e), and we set R (s) = 0. What type of disturbance input W(s) (step, ramp, or parabola) can the system reject (i.e., the steady-state error ess is a nonzero constant)? Submit your calculations. R(s) 0- C(s) + W(s) H(s) - Y(s)
Transcribed Image Text:(c) Suppose that you want the pitch angle to increase at a constant acceleration of 1 deg/s². To achieve this, you set the desired pitch angle to a parabolic function, r(t) = ½t² · us(t), where us(t) is the unit step function. What is the system type n? Calculate the steady-state error ess of the closed-loop system as a function of K. Submit your calculations. (d) Compute the closed-loop transfer function, Hcz (s) = Y(s)/R(s). Write the characteristic equation of the closed-loop system in the form 1 + KL(s) = 0. Submit your calculations. (e) Plot the positive root locus for the closed-loop system in MATLAB using the command rlocus (L). Use this plot to find the range of K for which the closed-loop system is stable. Submit your MATLAB plot and explain how you used it to find the range of K. W (1) Now we introduce a disturbance input W(s) = where W is a constant, into the feedback sk controller as shown below. The transfer functions H(s) and C(s) are the same as in parts (c) (e), and we set R (s) = 0. What type of disturbance input W(s) (step, ramp, or parabola) can the system reject (i.e., the steady-state error ess is a nonzero constant)? Submit your calculations. R(s) 0- C(s) + W(s) H(s) - Y(s)
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