SOUTHAMPTON SOLENT UNIVERSITY
WSMSE
(AUTOMATION & CONTROL LABORATORY)
CONTROL SYSTEM ANALYSIS USING MATLAB & SIMULINK
(SIMLAB1)
Aims:
· To use MATLAB & Simulink to assist in the process of analysing an example of a control system.
· In so doing, to become familiar with some of the basic functions of MATLAB & Simulink as applicable to control system analysis.
Objectives:
· Given a Control System Block Diagram, reduce to a single block, hence obtaining the associated closed-loop transfer function of the system.
· Use Routh-Hurwitz analysis to find a range of values of the system gain constant K for which the system is stable, and, after selecting a value of K in the region of stability identified, confirm the system’s stability using MATLAB.
· Use Simulink to find the time-domain transient behaviour of the system in response to a unit step input.
· Use MATLAB to find the time-domain equation of the system output in response to a unit step input, and confirm this by taking the Inverse Laplace transformation of the s-plane system output equation.
· Find the frequency-domain response of the system from the transfer function.
· Use MATLAB to create a Bode plot for the system transfer function.
· Comment on whether the system’s time-domain response, given a unit step input, represents an over, under or critically damped system.
Method, Results & Analysis:
The following is an example of a control system block diagram:
The block diagram reduces to the following single block system:
Task 1: Confirm the above by ca
ying out the block diagram reduction yourself.
Task 2: Given the following functions for G1(s) , G2(s) , and G3(s) find the transfer function of the system:
G1(s) = s
G2(s) = K
G3(s) = s + 2
You should a
ive at the following transfer function:
Task 3: Use Routh-Hurwitz analysis to find a range of values of the system gain constant K for which the system is stable.
You should find that the system is stable for: K ≥ 0.
Let: K = 1/3 ; Hence:
Task 4: Confirm the system’s stability using MATLAB, by entering the above transfer function into MATLAB and using the following commands:
num=[4 0]
%Sets up a row vector co
esponding to the coefficients of s in the numerator of the transfer function.
den=[1 6 3]
%Sets up a row vector co
esponding to the coefficients of s in the denominator of the transfer function.
F=tf(num,den)
%Sets up the transfer function.
zplane(num,den)
%Gives a pole-zero plot of the system.
Task 5: Use Simulink to find the time-domain transient behaviour of the system output in response to a unit step input by doing the following:
Set up a system schematic as follows:
Click the simulate button, and save the result.
With a unit step input the s-plane equation for the output of the system is given by:
Task 6: Use MATLAB to find the time-domain equation of the system output in response to a unit step input, by inputting the following commands:
s=sym('s')
%Sets up a variable ‘s’.
F=4/((s^2)+(6*s)+3)
%Sets up the s-plane output equation of the system in an appropriate format.
f=ilaplace(F)
%Finds the inverse Laplace transform and hence the co
esponding time-domain equation of the system.
Task 7 (Optional): Confirm the above by taking the Inverse Laplace transformation of the s-plane system output equation.
Task 8: Find the frequency-domain response of the system from the transfer function.
Task 9: Use MATLAB to create a Bode plot for the system transfer function, by entering the following commands:
F=tf(num,den)
%Re-initialises transfer function in appropriate format.
ode(F)
%Generates a Bode plot of the system frequency response.
Conclusions:
Comment on whether the system’s time-domain response, given a unit step input, represents an over, under or critically damped system.
SSI&CSIMLAB119/01/12r.2