Question 2 Complete the following unfinished MATLAB code. % DC motor transfer function G1 = tf([0.8 1.6],[1 4 7.2]); % Cable reel transfer function G2 = tf([25],[1 1]); % System transfer fuction G=G1*G2 %% PID - Reaction curve method % Compute the step response of G and save it in [Y2,T2] [Y2,T2] = step(Tcl); % Compute the derivative of the step response % Finds the inflection point [M,I] % Time that the inflection point was observed % Magnitude of the step reponse at the inflection point % Gradient of the step reponse at the time of the inflection point % Find the X and Y intercepts % Compute the parameters for ZN PID tuning, i.e. "R" and "tau" % Obtain the PID gains Kp, Ti, Td and N using the ZN tuning rules for the Reaction Curve method. % Fine tune the gains Kp, Ti and Td to satisfy the control requirements (Peak time, overshoot, steady-state error) % Obtain the transfer function of the PID controller. Use the command "pidstd". % Obtain the closed-loop transfer function Tcl. Use the command "feedback" and save the result in the variable "Tcl" % In the following line we use the command "step" to save the the step response in the variables "y" and "t" [y,t] = step(Tcl); % Use the command "stepinfo" to obtain the characteristics of the step response and save the result in the variable "assessStep" % In the following line we compute the steady-state error and save it in the variable "ess" ess = abs(1 - y(end))
Question 2 Complete the following unfinished MATLAB code. % DC motor transfer function G1 = tf([0.8 1.6],[1 4 7.2]); % Cable reel transfer function G2 = tf([25],[1 1]); % System transfer fuction G=G1*G2 %% PID - Reaction curve method % Compute the step response of G and save it in [Y2,T2] [Y2,T2] = step(Tcl); % Compute the derivative of the step response % Finds the inflection point [M,I] % Time that the inflection point was observed % Magnitude of the step reponse at the inflection point % Gradient of the step reponse at the time of the inflection point % Find the X and Y intercepts % Compute the parameters for ZN PID tuning, i.e. "R" and "tau" % Obtain the PID gains Kp, Ti, Td and N using the ZN tuning rules for the Reaction Curve method. % Fine tune the gains Kp, Ti and Td to satisfy the control requirements (Peak time, overshoot, steady-state error) % Obtain the transfer function of the PID controller. Use the command "pidstd". % Obtain the closed-loop transfer function Tcl. Use the command "feedback" and save the result in the variable "Tcl" % In the following line we use the command "step" to save the the step response in the variables "y" and "t" [y,t] = step(Tcl); % Use the command "stepinfo" to obtain the characteristics of the step response and save the result in the variable "assessStep" % In the following line we compute the steady-state error and save it in the variable "ess" ess = abs(1 - y(end))
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
Complete the following unfinished MATLAB code.
% DC motor transfer function
G1 = tf([0.8 1.6],[1 4 7.2]);
% Cable reel transfer function
G2 = tf([25],[1 1]);
% System transfer fuction
G=G1*G2
%% PID - Reaction curve method
% Compute the step response of G and save it in [Y2,T2]
[Y2,T2] = step(Tcl);
% Compute the derivative of the step response
% Finds the inflection point [M,I]
% Time that the inflection point was observed
% Magnitude of the step reponse at the inflection point
% Gradient of the step reponse at the time of the inflection point
% Find the X and Y intercepts
% Compute the parameters for ZN PID tuning, i.e. "R" and "tau"
% Obtain the PID gains Kp, Ti, Td and N using the ZN tuning rules for the Reaction Curve method.
% Fine tune the gains Kp, Ti and Td to satisfy the control requirements (Peak time, overshoot, steady-state error)
% Obtain the transfer function of the PID controller. Use the command "pidstd".
% Obtain the closed-loop transfer function Tcl. Use the command "feedback" and save the result in the variable "Tcl"
% In the following line we use the command "step" to save the the step response in the variables "y" and "t"
[y,t] = step(Tcl);
% Use the command "stepinfo" to obtain the characteristics of the step response and save the result in the variable "assessStep"
% In the following line we compute the steady-state error and save it in the variable "ess"
ess = abs(1 - y(end))
Transcribed Image Text:0.8s + 1.6
Consider a DC motor with a dynamic model G₁(s) =
s² + 4s +7.2
controller using the Zielger Nichols Reaction Curve method. The closed loop system is shonw in the figure.
R(s) +
Σ
CPID(S)
▪ Peak Time: Tp ≤ 0.5 second
■ Overshoot: P.O. < 30%
▪ Zero steady-state error
, and is used to drive a cable reel with a dynamic model, G₂(s) =
The PID controller should have the following parallel form,
1
TD
CPID(S)= Kp(1+ +
Tis
TDS +1
The closed-loop step response should achieve the following objectives:
G₁ (s)
G₂ (s)
Y(s)
25
s+1
You are required to design a PID
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