Convert from One Model Type to Another

This example shows how to convert a numeric LTI model from one type (pid) to another type (tf).

In general, you can convert a model from one type to another type using the model-creation command for the target type. For example, you can use the tf command to convert an ss model to transfer function form, or use the ss command to convert a zpk model to state-space form.

Create a PID controller.

pid_sys = pid(1,1.5,3)

pid_sys =
 
             1          
  Kp + Ki * --- + Kd * s
             s          

  with Kp = 1, Ki = 1.5, Kd = 3
 
Continuous-time PID controller in parallel form.

Convert pid_sys to a transfer function model.

C = tf(pid_sys)

C =
 
  3 s^2 + s + 1.5
  ---------------
         s
 
Continuous-time transfer function.

C is a tf representation of pid_sys. C has the same dynamics as pid_sys, but stores the dynamic parameters as transfer-function numerator and denominator coefficients instead of proportional, integral, and derivative gains.

You can similarly convert transfer function models to pid models, provided the tf model object represents a parallel-form PID controller with $$T_f\ge 0$$.

In general, you can use the technique of this example to convert any type of model to another type of model. For more specific information about converting to a particular model type, see the reference page for that model type.