Automatic control matlab exam

University of technology and education Ho Chi Minh cityFaculty of international education Automatic control Matlab exam Teacher: Vu Van Phong Student: Tran Ngoc Xuan Thanh Student id: 20

University of technology and education Ho Chi Minh city

Faculty of international education

Automatic control

Matlab exam

Teacher: Vu Van Phong

Student: Tran Ngoc Xuan Thanh Student id: 20146280

TP HCM, Month 12 Year 2023

Question 1:

Student id: 20146280

 a=8 and b=1

-Code:

a) Define a function on Matlab

I have a=8 and b=1

After that using G(fuction of system)=tf([1],[1,2*a+b,(a+b)/2,0]) to enter a and

b and find G(s)

b) Draw a Numerical solution trajectory on Matlap

After that, I use rlocus to find a Numerical solution trajectory for a system on Matlab I have the graph:

c) Find Kgh?

d) Choose any K such that the system is stable then simulate the system in Simulink with the obtained value of K and an input signal as a step function

With K=0.3 the system is stable I simulate the system in Simulink I have a block diagram and the graph

+Block diagram

+The graph with K=0,3 and input step is 500 The system is stable:

Question 2:

Student id:20146280

=>a=8 and b=1

a)Draw a bode graph on Matlab

First, we I a G2=tf([100, 1800],conv([1 8],[1 11 1])) to enter a function(G2) on Matlab

I use a bode(G2) to draw a bode graph on Matlab and we have a graph:

b)Find a Phase and Magnitude

We can see a picture when I draw a bode graph on Matlab:

We have Phase(dự trữ Pha)=Pm and Magnitude(dự trữ biên)=Gm, so I have magnitude=infinity and phase=24,3degree(about 10,5 rad/s)

c)Comment on the stability of the system based on the Bode theory

-The system is stable When:

+with Gm(Magnitude): Gm>1(db) the system is stable

+with Pm(Phase margin): 30(degree)<Pm<60(degree) is the best Pm for the system stable

-I have Pm=24,3 degree and Gm=infinity

+With Gm=infinity the system is stable because Gm>1

+With Pm=24,3degree, Pm<30(degree) the system may be stable but the system will become sluggish with disturbances and the system may be have a risk of overshoot\

-Based on the given information, the system will be stable, but there is a possibility of overshoot

Question 3:

Student id: 20146280 so a=8 and b=1

-Code:

a)Draw a Nyquist graph on Matlab

I use G3=tf([8], conv([1 8], [1 11 1])) to enter the function on matlab

After that I use Nyquist(G3) to draw a Nyquist graph on Matlab:

b) Comment on the stability of the system based on the Nyquist theory -According to Nyquist, a system is stable if there is a loop on the Nyquist plot, but no point of the loop crosses the point -1 (1 + 0j); the system can still be stable

-We can see in picture, the circle don’t include the point(-1;0) so the system is stable(Nyquist theory)

Question 4:

-Code:

a) and b) Find a pole and zero of the system and draw on complex plane -We have a function G(s)=s2 1

+s+ 9 because the numerator of function is

=>we don’t have zero point

I use a pole(T4) and zero(T4) on Matlab to find a poles points and zero points

I use a pzplot(T4) to draw a pole point and zero point on complex plane