National Polytechnic School of Constantine Module: Electrical and Electronics Measurements
Department of EEA 3rd year of Automation
Year: 2024/2025
Lab 03:
Closed-loop performances
1. Objective:
The objective of this lab is to cover the main aspects of closed-loop system performance. One of
the most important characteristics in closed-loop performance is the steady-state specification, which
is defined by the error between the desired input and the system’s response. In the case of a unit step
input, the error is called position error (denoted by �� ), and when the input is a ramp signal, the
error is called velocity error (denoted by �� ). In the case of a parabolic input, the error is called
acceleration error (denoted by �� )
2. Materials:
Computer included a MATLAB software with Word editor to prepare the final report.
3. Part A (Steady state error):
MATLAB commands needed: (see the code below)
clear all
clc
gf=tf([4],[1 2,10]); % the open-loop transfer function (feedforward)
gc=feedback(gf,1);% the closed-loop transfer function for a unity
feedback
t=0:0.01:20; % simulation time
%%%%%% If the input is a unit step you can use step(gc) or you can
use the following commands)
u=ones(size(t));% the input is a unit step
lsim(gc,u,t);% plot the unit step response of the closed-loop
system
%%%% If the input is ramp%%%%%%
u=t;
lsim(gc,u,t);
%%%% If the input is a parabolic%%%%
u=t.^2;
lsim(gc,u,t);
1. Determine graphically the steady-state error for a unit step input, unit ramp input and unit
parabolic input for the control system described by the following transfer function:
1 N. ZERARI
National Polytechnic School of Constantine Module: Electrical and Electronics Measurements
Department of EEA 3rd year of Automation
Year: 2024/2025
5 (� + 1)
� � = 2
� + 4� + 10
2. For the following control system determine graphically the steady-state error for the inputs:
5�(�), 5��(�), and 5�2 �(�).
3. For the control system described by the following feed forward transfer function determine the
steady-state error for the input 15�2 �(�)
10 (� + 20)(� + 30)
� � =
�2 (� + 25)(� + 50)
4. Design the following control system by selecting a value of � graphically such that there is a
10% steady state error for a unit ramp input. Use the Routh-Hurwitz criterion to confirm that the
system is stable at the value of � selected.
4. Part B (Stability and Transient response performances):
1. Find the values of � that make the system instable based on a simple MATLAB code of the
following system.
2 N. ZERARI
National Polytechnic School of Constantine Module: Electrical and Electronics Measurements
Department of EEA 3rd year of Automation
Year: 2024/2025
Hint: you must construct a vector that contains many values (for example K=[1:1500]) and replace it
in the characteristic equation and check the stability. You can use Routh array to find the stability
range.
2. Consider the closed-loop system defined by
�(�) �2�
=
�(�) �2 +2��� �+�2�
Using a “for loop,” write a MATLAB program to obtain unit-step response of this system for the
following four cases:
First case: �� = 1; � = 0.3
Second case: �� = 2; � = 0.5
Third case: �� = 4; � = 0.7
Fourth case: �� = 6; � = 0.8
3. For the following block diagram:
Find the closed-loop transfer function.
Tune the pole P and the gain k to meet the following specifications (use stepinfo(g) to
confirm your choice):
-Percentage overshoot ≤ 5%
-settling time �� ≤ 4�
3 N. ZERARI
