Sinusodial Wave for PID controller

need help on finding a sinusodial wave for a PID controller = 410.39*[(s^2+3.24+1.136)/1]

Answer 1

[Sam Chak]

Hi @Juan Barragan

After simplifying the expression, what does mean?

If you want to simulate the system in transfer functions, you can try the following.

s  = tf('s');

% Plant
Gp = 410.39/(s^2 + 4.376)

Gp =
 
     410.4
  -----------
  s^2 + 4.376
 
Continuous-time transfer function.

step(Gp, 20)

% PID controller
kp  = - 0.0026657569;
ki  =   0.0053315139;
kd  =   0.0025512318;
Tf  =   0.5;
Gc  = pid(kp, ki, kd, Tf)

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

  with Kp = -0.00267, Ki = 0.00533, Kd = 0.00255, Tf = 0.5
 
Continuous-time PIDF controller in parallel form.

% Closed-loop transfer function
Gcl = minreal(feedback(Gc*Gp, 1))

Gcl =
 
          s^2 + 4.104e-08 s + 4.376
  -----------------------------------------
  s^4 + 2 s^3 + 5.376 s^2 + 8.752 s + 4.376
 
Continuous-time transfer function.

step(Gcl, 20)