lab sheet 6 (1)

8/10/2019 LAB SHEET 6 (1)

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SUBMISSION OF LAB SHEET 6

V.V.S.Prithvi(SC12B128)

ROLL.NO.=47

The parameters of the linear Elevon actuation system are:

KA=1;

KV=4*10^-5;

Kq=.8207;

wv=2*pi*150;

KC=3.92*10^-12; %flow pressure coefficient of servo valve Vo=1.063*10^-4;

Ap=20.44*10^-4;

Ba=20000; %viscous damping of the actuator Betae=9.81*10^8;

lm=.087;

wd1=2*pi*100;zeatad1=.707; %demodulator damping factor Kp=17.629;

K1=10*10^6; %actuator mounting structure stiffness Jcs=1.3;

Bcs=31.37;

zetav=1; %damping factor of servo valve spool w1=2*pi*150; zeta1=0.3;

1) The linear mathematical model of elevon actuation system

8/10/2019 LAB SHEET 6 (1)


Now the frequency response of uncompensated linear system open loop transfer function

Gpc(s) is found by giving open loop input after the compensator part and taking the output

at the feedback path.

The frequency response of uncompensated linear system open loop transfer function is

(2) A) Frequency response of linear compensated open loop transfer function:

Now the frequency response of compensated linear system open loop transfer function

Gpc(s) is obtained by giving open loop input after the compensator part and taking the

output at the feedback path.

On doing this simulation we get the frequency response as in the figure below:

8/10/2019 LAB SHEET 6 (1)


A) Frequency response of linear compensated closed loop transfer function:

Now the frequency response of compensated linear system closed loop transfer function Gpc(s) is

found by giving closed loop input after the compensator part and taking the output at the feedback

path.

On doing this simulation we get the frequency response as in the figure below:

Now from the above figure we can see that the frequency response value at -3 dB B.W is 6.7 Hz and

90 degrees B.W is 6.6 Hz which also match with the theoretical values which are given..

1) Gain margin:

8/10/2019 LAB SHEET 6 (1)


The gain margin is the amount of gain increase or decrease required to make the loop gain unity at

the frequency Wgm where the phase angle is –180° (modulo 360°). In other words, the gain margin

is 1/g if g is thegain at the –180° phase frequency.

2) Phase margin:

In electronic amplifiers, the phase margin (PM) is the difference between the phase, measured in

degrees, and 180°, for an amplifier's output signal (relative to its input), as a function of frequency.

The phase crossover frequency, wpc, is the frequency where phase shift is equal to -180o.

The gain crossover frequency, wgc, is the frequency where the amplitude ratio is 1, or when

log modulus is equal to 0.

So the values for closed loop compensated transfer function are:

1) Gain crossover frequency = 3.48 Hz.

2) Phase crossover frequency = 20 Hz.

3) Gain margin = -17.3 db.

4) Phase margin = 129 degrees.

INFERENCE:

1) Any stable system should have positive phase margin, for this compensated system phase

margin is found to be positive so we can say that given compensated system is stable

system.

2) Magnitude at the frequency where phase is -180\degree is less than zero ,so we can say

that system is stable.

lab sheet 6 (1)

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