asymptotic magnitude bode plot for PI^alpha controller

how do i add the first three plot to get the forth plot

individual plot

a) for fractional zero

close all;hold off;alpha=0.8;Wcr=3.948;ki=3;w1=logspace(-2,log10(Wcr),1000);w2=logspace(log10(Wcr),2,1000);

Mag1= (20*log10(abs(ki)))*ones(1,numel(w1));Mag2=@(w2) 20*alpha*log10(w2);semilogx(w1,Mag1);hold on;

semilogx(w2,Mag2(w2));grid on;xlabel('Frequency');ylabel('Magnitude dB');

b)fractional pole at origin

clear all;hold off;alpha=0.8;Wcr=1;w1=logspace(-2,log10(Wcr),1000);w2=logspace(log10(Wcr),2,1000); Mag1= 0;Mag2=@(w2) -(20*alpha*log10(w2));

semilogx(w1,Mag1);hold on;semilogx(w2,Mag2(w2));grid on;xlabel('Frequency(rad/sec)');ylabel('Magnitude dB');

[darova]

Do you have better code and better picture? Hard to read

[Irshad Baruah]

[darova]

What about this?

[Irshad Baruah]

that is PI^alpha final equation,as per the above image they plot separately each plot 1)Kp, 2)s^alpha+ki and 3)1/s^alpha, from the PI^alpha equation and add the three plots to get the final plot

1) constant gain magnitude equation |T(jw)|= 20log|Kp|

2)fractional zero magnitude equation, a) w<Wcr,|T(jw)|= 20log|Ki|

b) w>Wcr,|T(jw)|= 20*alphalog*w

here Wcr=|Ki|^(1/alpha)

and 3) for fractional pole, 1/s^alpha,magnitude equation |T(jw)|=- 20*alphalog*w,here w=1

i plotted fractional zero and fractional pole separetly (as the code given above),as per the paper it says when you add the first three it result the final graph

Answer 1

[Ameer Hamza]

Try this

Kp = 1;
Ki = 2;
alpha = 1.5;

w_cr = abs(Ki)^(1/alpha);
w = logspace(-1, 3, 1000);
mask = w < w_cr;

term1 = 20*log(Kp)*ones(size(w));
term2 = mask.*(20*log(Ki)) + (~mask).*(20*alpha*log(w));
term3 = -20*alpha*log(w);
combined = term1 + term2 + term3;

subplot(4,1,1);
semilogx(w, term1)
subplot(4,1,2);
semilogx(w, term2)
subplot(4,1,3);
semilogx(w, term3)
subplot(4,1,4);
semilogx(w, combined)

[Irshad Baruah]

mask = w < Wcr only this condition is used

is w>Wcr condition in fractional zero not required???

[Ameer Hamza]

I also used inverted mask (~mask) which is is equivalent to w>Wcr.

[Irshad Baruah]

ok thanks

[Ameer Hamza]

Glad to be of help.