I am having trouble with PID controller design Non minimum phase system

Hello I am trying to develop a PI controller for peak current control of boost converter. When I plot the Bode plot of the system, I am having the phase starting at 180 at 10rad/sec. And when I am trying to develop a PI controller using SISO tool, I do not get to design it. Is it because of the Phase that I am not able to get the controller to work ? The TF is

        3e-09 s^2 + 3.76e-05 s - 10.83
  ----------------------------------------------
  9.727e-15 s^3 + 3.826e-09 s^2 + 0.001503 s + 1
This includes the high frequency term 
Thanks!

[Sandip Kumar]

I used the same TF, and using "sisotool", I was able to get a stable closed loop with a PI controller.

C = -96.929 x (1 + 0.00045 s)/s

what version of MATLAB are you on?

Answer 1

[Sam Chak]

The pidtune() command from the Control System Toolbox can be applied to this problem.

%% Plant
s   = tf('s');
Gp  = (3e-09*s^2 + 3.76e-05*s - 10.83)/(9.727e-15*s^3 + 3.826e-09*s^2 + 0.001503*s + 1);
Gp  = minreal(Gp)

Gp =
 
     3.084e05 s^2 + 3.866e09 s - 1.113e15
  ------------------------------------------
  s^3 + 3.933e05 s^2 + 1.545e11 s + 1.028e14
 
Continuous-time transfer function.

zP  = zero(Gp)

zP = 2×1

1.0e+04 * -6.6676 5.4143

step(Gp), grid on

%% PIDF controller
Gc1 = pidtune(Gp, 'PIDF')

Gc1 =
 
             1            s    
  Kp + Ki * --- + Kd * --------
             s          Tf*s+1 

  with Kp = -0.121, Ki = -157, Kd = 8.64e-06, Tf = 0.000156
 
Continuous-time PIDF controller in parallel form.

%% PI controller
Gc2 = pidtune(Gp, 'PI')

Gc2 =
 
             1 
  Kp + Ki * ---
             s 

  with Kp = -0.0956, Ki = -188
 
Continuous-time PI controller in parallel form.

%% Plot results
Gcl1= feedback(Gc1*Gp, 1);
Gcl2= feedback(Gc2*Gp, 1);
step(Gcl1), hold on
step(Gcl2), grid on, hold off
legend('PIDF controller', 'PI controller', 'location', 'east')

margin(Gc1*Gp), grid on

margin(Gc2*Gp), grid on