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Consider the unit feedback control system shown in Fig. 4 for the control of a single- link rotational manipulator that includes a command shaping gain K as shown. The moment of inertia I = 5 kg m2 and the rotational viscous friction coefficient is br = 2 N m s/rad. a) Find the closed loop transfer function from the command angular velocity input ωr(t) to the angular response output ω(t) in terms of the system parameters I, br and K. b) For a unit step angular velocity reference input ωr(t) find the value of the gain K such that perfect tracking is achieved, i.e., the error e(t) = ωr(t) - ω(t) has steady-state value ess = 0 when t → ∞. c) Use Laplace Transform methods to find the closed-loop response ω(t) for the above values of the system parameters and gain K.

Consider the unit feedback control system shown in Fig. 4 for the control of a single- link rotational manipulator that includes a command shaping gain K as shown. The moment of inertia I = 5 kg m2 and the rotational viscous friction coefficient is br = 2 N m s/rad. a) Find the closed loop transfer function from the command angular velocity input ωr(t) to the angular response output ω(t) in terms of the system parameters I, br and K. b) For a unit step angular velocity reference input ωr(t) find the value of the gain K such that perfect tracking is achieved, i.e., the error e(t) = ωr(t) - ω(t) has steady-state value ess = 0 when t → ∞. c) Use Laplace Transform methods to find the closed-loop response ω(t) for the above values of the system parameters and gain K.

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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Consider the unit feedback control system shown in Fig. 4 for the control of a single- link rotational manipulator that includes a command shaping gain K as shown. The moment of inertia I = 5 kg m2 and the rotational viscous friction coefficient is br = 2 N m s/rad.
a) Find the closed loop transfer function from the command angular velocity input ωr(t) to the angular response output ω(t) in terms of the system parameters I, br and K.
b) For a unit step angular velocity reference input ωr(t) find the value of the gain K such that perfect
tracking is achieved, i.e., the error
e(t) = ωr(t) - ω(t) has steady-state value ess = 0 when t → ∞.
c) Use Laplace Transform methods to find the closed-loop response ω(t) for the above values of the system parameters and gain K.

Consider the unit feedback control system shown in Fig. 4 for the control of a single- link rotational manipulator that includes a command shaping gain K as shown. The moment of inertia I = 5 kg m? and the rotational viscous friction coefficient is b, =2 N m s/rad. a) Find the closed loop transfer function from the command angular velocity input w,(t) to the angular response output @(t) in terms of the system parameters I, b, and K. b) For a unit step angular velocity reference input @r(t) find the value of the gain K such that perfect tracking is achieved, i.e., the error e(t) = 0,(t) - @(t) has steady-state value ess = 0 when t → 0. c) Use Laplace Transform methods to find the closed-loop response o(t) for the above values of the system parameters and gain K. T(s) W(s) + 1 K Is+br Fig 4: Unit feedback single-link manipulator control block diagram
Transcribed Image Text:Consider the unit feedback control system shown in Fig. 4 for the control of a single- link rotational manipulator that includes a command shaping gain K as shown. The moment of inertia I = 5 kg m? and the rotational viscous friction coefficient is b, =2 N m s/rad. a) Find the closed loop transfer function from the command angular velocity input w,(t) to the angular response output @(t) in terms of the system parameters I, b, and K. b) For a unit step angular velocity reference input @r(t) find the value of the gain K such that perfect tracking is achieved, i.e., the error e(t) = 0,(t) - @(t) has steady-state value ess = 0 when t → 0. c) Use Laplace Transform methods to find the closed-loop response o(t) for the above values of the system parameters and gain K. T(s) W(s) + 1 K Is+br Fig 4: Unit feedback single-link manipulator control block diagram
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