Simulink Control Design™ - MathWorks

When you update a PID Controller block or custom PID controller with tuned parameter
values, make sure the integrator method matches.

Tunable: Yes

Dependencies

This parameter is enabled when the Time Domain is discrete-time and the controller
includes integral action.

Programmatic Use
Block Parameter: IntegratorFormula
Type: character vector
Values: 'Forward Euler' | 'Backward Euler' | 'Trapezoidal'
Default: 'Forward Euler'

Filter method — Discrete integration formula for derivative filter term
Forward Euler (default) | Backward Euler | Trapezoidal

Specify the discrete integration formula for the derivative filter term in your controller. In
discrete time, the PID controller transfer function assumed by the block is:

C=P+FizI+

D

N+Fdz

,

in parallel form, or in ideal form,

C=P1+

Fiz

I +

D

D/N+Fdz.

For a controller sample time Ts, the Filter method parameter determines the formula
Fd as follows:

Filter method Fd

Forward Euler Ts

z− 1

Backward Euler Tsz

z− 1

Trapezoidal Ts

2

z+1

z− 1

Closed-Loop PID Autotuner