Neimark D-partition method

[pcwortex]

Neimark D-partition method and PI regulator

Hi everybody. Recently I read two articles about Neimark D-partition method. It is interesting method, because you could unstable system make stable and with desirable phase margin My to read articles is:
http://www.nt.ntnu.no/users/skoge/p...trol_conference_2010/pdf/22_Osusky_Vesely.pdf
http://www.nt.ntnu.no/users/skoge/p...l_conference_2010/pdf/46_Hypiusova_Osusky.pdf
And I tried to make PID regulator using Neimark D-partition. My transfer function is:
**broken link removed**
there:

Perform compute:

I separate real piece from imag piece:


Using Matlab program and draw D-partition curve k_i(k). Matlab code:

w=(0:0.1:200);
rad=65*3.14/180;

k=(w.^2*cos(rad)+3998*cos(rad)-2.418.*w*sin(rad))./18400;
k_i=((2.418.*w*cos(rad)+w.^2*sin(rad)+3998*sin(rad)).*-w)./(18400);

plot(k,k_i)
grid on;

I give this curve:
**broken link removed**
In article show this curve:
**broken link removed**
I don't undestand why this curve is different. Maybe you see my mistake?

 

[mgate]

Hi,
I'm also new to this, I'll try to help anyway...

you missed the w in the equation k= .... -2.418*W*sin(phi);

As I understood your are not making the right calculations..

1st step

using equation (7) (I think)
- Calculate k1 and Kd from PD PLOT (similar calculations as you did for PI)


from the plot 3:

k1 = 10 and kd = 0.05, the poles of the charateristic equations with this PD controller are -633.39 and -284.18

2nd step
- Calculate k2 and Ki from the PI PLOT considering the transfer function of the initial system controlled by a PD with the constants calculated in the step1,

using equation (7) (I think)

"The PID controller design consists of two steps: in the first step, PD controller can be designed
and in the second step, PI controller design can by applied for the plant with the PD controller."

Jakub Osuský and Vojtech Veselý - MODIFICATION OF NEIMARK D-PARTITION METHOD FOR
DESIRED PHASE MARGIN

so, I think you need to find the new transfer function before go to the second step