Question

Ks) Sw I Where .(s) is the Laplace transform of the motor's speed w (t) V(s)Is the Laplace transform ofvoltage r(t) · . K 3 and r 0.5 Find the system's step response and its three performance specifications. Hint: The system's transfer function can be rewritten as: G (s)-K sta for a = 1/τ. The step response would be: c(t) = K[1-e-alu (t) and the three performance specifications are the same as those of sta **USE MATLAB* Problem Statement: write a matlab m-file (program) to obtain the closed loop system transfer function Mn(s), for 1sns4, for each of the following feedback schemes

2. SW2=1; SW1=SW3=0

Using KP=0.1, KI=4 and KD=0.3. Your program should display the transfer functions

M1(s),M2(s),M3(s) and M4(s)

you must use matlab and include the codes.

Answer 1

SOLUTION

Given That data is closed loop transfer function of requirement is

SW2=1; SW1=SW3=0

Using KP=0.1, KI=4 and KD=0.3

MATLAB code is given below in bold letters:

clc;
close all;
clear all;

s = tf('s');

K = 3;
a = 1/0.5;
G = K*a/(s+a);
KP = 0.1;
KI = 4;
KD = 0.3;
% closed loop transfer function for the given case
% switch 1 is closed switch 2 and switch 3 are closed as well
T = feedback(G,KP+KD*s+KI/s); % feedback loop transfer function
T

figure; step(T); grid on;
title('Step response of closed loop system');

T =

6 s
--------------------
2.8 s^2 + 2.6 s + 24

Continuous-time transfer function.