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T(t) s(t) Figure Q4-Spinning disc The equation of motion in terms of angular speed of the spinning disc (represented in figure Q4). supported on bearings and driven by a DC motor, may be written as, Jn(t) + kn(t) = T(t) (4.1) where J is the polar moment of inertia of the disc, k, is a term representing friction in the system, denotes the angular speed of the disc and T is the torque supplied to the disc. The torque T is supplied by a proportional controller, T(t) = k,(a – 52(t)) where is the speed demanded (constant input) and k, is a constant. a) Copy and complete the following block diagram of the system corresponding to Equations (4.1) and (4.2): Na(s) S2(s) b) From the block diagram, determine the closed-loop transfer function and the speed (s (4.2) c) Show that the steady state error (difference between the demanded speed and the limit response) is given by = fa ke kịp th d) The torque is now supplied by a proportional plus integral (PI) controller,

T(t) s(t) Figure Q4-Spinning disc The equation of motion in terms of angular speed of the spinning disc (represented in figure Q4). supported on bearings and driven by a DC motor, may be written as, Jn(t) + kn(t) = T(t) (4.1) where J is the polar moment of inertia of the disc, k, is a term representing friction in the system, denotes the angular speed of the disc and T is the torque supplied to the disc. The torque T is supplied by a proportional controller, T(t) = k,(a – 52(t)) where is the speed demanded (constant input) and k, is a constant. a) Copy and complete the following block diagram of the system corresponding to Equations (4.1) and (4.2): Na(s) S2(s) b) From the block diagram, determine the closed-loop transfer function and the speed (s (4.2) c) Show that the steady state error (difference between the demanded speed and the limit response) is given by = fa ke kịp th d) The torque is now supplied by a proportional plus integral (PI) controller,

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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Question 4 C Figure Q4-Spinning disc The equation of motion in terms of angular speed of the spinning disc (represented in figure Q4). supported on bearings and driven by a DC motor, may be written as, Jn(t) + k,n(t) = T(t) (4.1) where J is the polar moment of inertia of the disc, k, is a term representing friction in the system, denotes the angular speed of the disc and I' is the torque supplied to the disc. The torque T is supplied by a proportional controller, T(t) s(t) T(t) = kp(nd-(t)) where is the speed demanded (constant input) and kp is a constant. a) Copy and complete the following block diagram of the system corresponding to Equations (4.1) and (4.2): Na(s) n(s) + (4.2) b) From the block diagram, determine the closed-loop transfer function and the speed (s c) Show that the steady state error (difference between the demanded speed and the limit response) is given by Ess=d7 kv ko thể d) The torque is now supplied by a proportional plus integral (PI) controller,
Transcribed Image Text:Question 4 C Figure Q4-Spinning disc The equation of motion in terms of angular speed of the spinning disc (represented in figure Q4). supported on bearings and driven by a DC motor, may be written as, Jn(t) + k,n(t) = T(t) (4.1) where J is the polar moment of inertia of the disc, k, is a term representing friction in the system, denotes the angular speed of the disc and I' is the torque supplied to the disc. The torque T is supplied by a proportional controller, T(t) s(t) T(t) = kp(nd-(t)) where is the speed demanded (constant input) and kp is a constant. a) Copy and complete the following block diagram of the system corresponding to Equations (4.1) and (4.2): Na(s) n(s) + (4.2) b) From the block diagram, determine the closed-loop transfer function and the speed (s c) Show that the steady state error (difference between the demanded speed and the limit response) is given by Ess=d7 kv ko thể d) The torque is now supplied by a proportional plus integral (PI) controller,
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