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Question 2 The block diagram of a digital position controller for a robotic arm is shown in Fig. 1. The sampling period of the D/A converter, T, is 0.25 s, and the controller is programmed with the following algorithm: m(k)= 23.6[e(k) - 0.76e(k-1)] c(KT) r(KT) m(kT) m(t) G.(z) D/A (s+5)³ Topbo digital processor (a) Write an expression for the 2-transform of Fig. 1 2s c(1) (i) the digital processor, G.(z)=M(z)/E(z) and (ii) the digital representation of the plant, G,W(z)=C(z)/M(z) A/D c(KT) (b) Determine the following closed-loop transfer functions: (i) C(z)/R(z): relating sampled values of the output signal to sampled values of the reference input, and (ii) M(z)/R(z): relating sampled values of the manipulated signal to sampled values of the reference input. (c) Calculate the steady-state value of m(kT) for a unit step input.

Question 2 The block diagram of a digital position controller for a robotic arm is shown in Fig. 1. The sampling period of the D/A converter, T, is 0.25 s, and the controller is programmed with the following algorithm: m(k)= 23.6[e(k) - 0.76e(k-1)] c(KT) r(KT) m(kT) m(t) G.(z) D/A (s+5)³ Topbo digital processor (a) Write an expression for the 2-transform of Fig. 1 2s c(1) (i) the digital processor, G.(z)=M(z)/E(z) and (ii) the digital representation of the plant, G,W(z)=C(z)/M(z) A/D c(KT) (b) Determine the following closed-loop transfer functions: (i) C(z)/R(z): relating sampled values of the output signal to sampled values of the reference input, and (ii) M(z)/R(z): relating sampled values of the manipulated signal to sampled values of the reference input. (c) Calculate the steady-state value of m(kT) for a unit step 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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Question 2 The block diagram of a digital position controller for a robotic arm is shown in Fig. 1. The sampling period of the D/A converter, T, is 0.25 s, and the controller is programmed with the following algorithm: m(k)= 23.6[e(k) - 0.76e(k-1)] r(KT) c(KT) G₂(z) digital processor m(kT) m(t) (a) Write an expression for the 2-transform of D/A Fig. 1 2s (s+5)³ (i) the digital processor, G.(z)=M(z)/E(z) and (ii) the digital representation of the plant, G,W(z)=C(z)/M(z) c(1) A/D c(KT) (b) Determine the following closed-loop transfer functions: (i) C(z)/R(z): relating sampled values of the output signal to sampled values of the reference input, and (ii) M(z)/R(2): relating sampled values of the manipulated signal to sampled values of the reference input. (c) Calculate the steady-state value of m(kT) for a unit step input.
Transcribed Image Text:Question 2 The block diagram of a digital position controller for a robotic arm is shown in Fig. 1. The sampling period of the D/A converter, T, is 0.25 s, and the controller is programmed with the following algorithm: m(k)= 23.6[e(k) - 0.76e(k-1)] r(KT) c(KT) G₂(z) digital processor m(kT) m(t) (a) Write an expression for the 2-transform of D/A Fig. 1 2s (s+5)³ (i) the digital processor, G.(z)=M(z)/E(z) and (ii) the digital representation of the plant, G,W(z)=C(z)/M(z) c(1) A/D c(KT) (b) Determine the following closed-loop transfer functions: (i) C(z)/R(z): relating sampled values of the output signal to sampled values of the reference input, and (ii) M(z)/R(2): relating sampled values of the manipulated signal to sampled values of the reference input. (c) Calculate the steady-state value of m(kT) for a unit step input.
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