Using the following Matlab commands (as needed): tf, step, impulse, stepinfo

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Using the following Matlab commands (as needed): tf, step, impulse, stepinfo, Use Matlab to determine the step response and impulse response for the process below. The transfer process for the function is: G(s) = P / ((1 + Ts)^3) P = 1.5 k = 0.2 T = 1

The Correct Answer and Explanation is:

To determine the step response and impulse response of the given transfer function using MATLAB, we first need to define the transfer function parameters and then use MATLAB’s built-in functions to generate the responses.

Given:

Transfer function:
G(s) = P / (1 + Ts)^3
Where:

  • P = 1.5
  • T = 1
  • k = 0.2 (This value is not directly used unless specified elsewhere)

We can write the transfer function as:
G(s) = 1.5 / (1 + s)^3

MATLAB Code:

matlabCopyEdit% Parameters
P = 1.5;
T = 1;

% Define the transfer function
s = tf('s');
G = P / (1 + T*s)^3;

% Display the transfer function
disp('Transfer Function:');
G

% Step Response
figure;
step(G)
title('Step Response of G(s)')
grid on

% Step Response Info
step_info = stepinfo(G);
disp('Step Response Information:')
disp(step_info)

% Impulse Response
figure;
impulse(G)
title('Impulse Response of G(s)')
grid on

Explanation

In control systems, the step response and impulse response are important tools used to analyze system dynamics. The transfer function provided is G(s) = 1.5 / (1 + s)^3, which represents a third-order system with repeated poles at s = -1. This means the system is stable and behaves in a smooth, overdamped manner.

To analyze this system in MATLAB, we first define the transfer function using the tf command. Here, the numerator is simply 1.5, and the denominator is (1 + s)^3, which is expanded by MATLAB automatically.

The step command is then used to plot the system’s response to a unit step input. This type of response tells us how the system reacts when a sudden change from zero to one occurs in the input. The stepinfo command provides key performance indicators like rise time, settling time, peak response, and steady-state value.

The impulse command is used to determine how the system responds to an idealized instantaneous pulse input. The impulse response shows the system’s natural dynamics without a sustained input.

From the results, you will observe that the step response gradually increases toward a steady value due to the system’s integrative effect. Since the system has three identical time constants, the response is relatively slow and smooth.

The impulse response will show a peak and then decay toward zero, reflecting how energy introduced instantly into the system dissipates over time.

This analysis helps in understanding how the process behaves under different inputs and is essential for controller design and system tuning.

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