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Problem 1: Fig. 1 shows a proposed method to eliminate the undesirable effects of a measurable load force in a robotic application. You are asked to compare the controlled system design (with and without force feedforward controller G(s). In Fig. 1, Gp, GL are known. The rate-sensor gain k, and the controllers (G. and Gr) are to be designed. F(s) G(s) Switch GL(s) R(s) G(s) G,(s) C(s) The plant transfer function is given by ks 20 G,(s) = Fig. 1 s(s+1)(s+4) 1) Consider F(s) = 0 and G(s) = 1: a) Redraw the block-diagram into the following form, and determine the open-loop and closed-loop transfer functions of the unity-feedback system in terms of the rate-sensor gain k. E(s) R(s) G(s) → C(s) b) Determine the value of k such that the closed-loop complex poles is -1 ± j2.4. Find the corresponding damping ratio and natural frequency, and third pole. c) Use the value of k determined in (1b), determine the steady-state error of the closed loop system when R(s) is a unit ramp-input.

Problem 1: Fig. 1 shows a proposed method to eliminate the undesirable effects of a measurable load force in a robotic application. You are asked to compare the controlled system design (with and without force feedforward controller G(s). In Fig. 1, Gp, GL are known. The rate-sensor gain k, and the controllers (G. and Gr) are to be designed. F(s) G(s) Switch GL(s) R(s) G(s) G,(s) C(s) The plant transfer function is given by ks 20 G,(s) = Fig. 1 s(s+1)(s+4) 1) Consider F(s) = 0 and G(s) = 1: a) Redraw the block-diagram into the following form, and determine the open-loop and closed-loop transfer functions of the unity-feedback system in terms of the rate-sensor gain k. E(s) R(s) G(s) → C(s) b) Determine the value of k such that the closed-loop complex poles is -1 ± j2.4. Find the corresponding damping ratio and natural frequency, and third pole. c) Use the value of k determined in (1b), determine the steady-state error of the closed loop system when R(s) is a unit ramp-input.

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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Problem 1: Fig. 1 shows a proposed method to eliminate the undesirable effects of a measurable load force in a robotic application. You are asked to compare the controlled system design (with and without force feedforward controller G(s). In Fig. 1, Gp, GL are known. The rate-sensor gain k, and the controllers (Go and Gf) are to be designed. F(s) GAs) Switch GL(s) R(s) G(s) G,(s) C(s) The plant transfer function is given by ks 20 G,(s) = Fig. 1 s(s+1)(s+4) 1) Consider F(s) = 0 and G(s) = 1: a) Redraw the block-diagram into the following form, and determine the open-loop and closed-loop transfer functions of the unity-feedback system in terms of the rate-sensor gain k. E(s)[ G(s) R(s)- C(s) b) Determine the value of k such that the closed-loop complex poles is -1 t j2.4. Find the corresponding damping ratio and natural frequency, and third pole. c) Use the value of k determined in (1b), determine the steady-state error of the closed loop system when R(s) is a unit ramp-input.
Transcribed Image Text:Problem 1: Fig. 1 shows a proposed method to eliminate the undesirable effects of a measurable load force in a robotic application. You are asked to compare the controlled system design (with and without force feedforward controller G(s). In Fig. 1, Gp, GL are known. The rate-sensor gain k, and the controllers (Go and Gf) are to be designed. F(s) GAs) Switch GL(s) R(s) G(s) G,(s) C(s) The plant transfer function is given by ks 20 G,(s) = Fig. 1 s(s+1)(s+4) 1) Consider F(s) = 0 and G(s) = 1: a) Redraw the block-diagram into the following form, and determine the open-loop and closed-loop transfer functions of the unity-feedback system in terms of the rate-sensor gain k. E(s)[ G(s) R(s)- C(s) b) Determine the value of k such that the closed-loop complex poles is -1 t j2.4. Find the corresponding damping ratio and natural frequency, and third pole. c) Use the value of k determined in (1b), determine the steady-state error of the closed loop system when R(s) is a unit ramp-input.
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