d2c PID-Conversion

Hi,

I'm trying to convert a discrete-time PID-controller to a continuous-time PID using the d2c function.

c_discrete = pid(4.406,0.0114,0.0112,0,0.0050) %Kp, Ki, Kd, Tf, Ts
c_continuous = d2c(c_discrete) 

But I keep getting the following Error:

Error using DynamicSystem/d2c (line 108)

The "d2c" conversion failed because the result cannot be expressed as a PID controller.

Does anyone have an Idea, where my mistake is?

Answer 1

[Walter Roberson]

That error is given when Tf < Ts, and apparently exists in order to avoid getting complex-valued outputs.

Your Tf is 0, certainly less than Ts.

Example with Tf > Ts

c_discrete = pid(4.406,0.0114,0.0112,0+0.01,0.0050) %Kp, Ki, Kd, Tf, Ts

c_discrete =
 
              Ts               1     
  Kp + Ki * ------ + Kd * -----------
              z-1         Tf+Ts/(z-1)

  with Kp = 4.41, Ki = 0.0114, Kd = 0.0112, Tf = 0.01, Ts = 0.005
 
Sample time: 0.005 seconds
Discrete-time PIDF controller in parallel form.

c_continuous = d2c(c_discrete) 

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

  with Kp = 4.41, Ki = 0.0114, Kd = 0.00808, Tf = 0.00721
 
Continuous-time PIDF controller in parallel form.

[Walter Roberson]

c_discrete = pid(4.406,0.0114,0.0112,0,0.0050) %Kp, Ki, Kd, Tf, Ts

c_discrete =
 
              Ts            z-1 
  Kp + Ki * ------ + Kd * ------
              z-1           Ts  

  with Kp = 4.41, Ki = 0.0114, Kd = 0.0112, Ts = 0.005
 
Sample time: 0.005 seconds
Discrete-time PID controller in parallel form.

c_continuous = d2c(c_discrete, d2cOptions(method='matched')) 

Error using DynamicSystem/d2c (line 108)
The "matched" method of the "d2c" command cannot be used for models with negative real zeros with odd multiplicity.