Simulink Control Design™ - MathWorks

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

For more information about the relative advantages of each method, see the Discrete PID

Controller block reference page.

When you update a PID Controller block or custom PID controller with tuned parameter

values, make sure the filter method matches.

Tunable: Yes

Dependencies

This parameter is enabled when the Time Domain is discrete-time and the controller

includes derivative action.

Programmatic Use

Block Parameter: FilterFormula

Type: character vector

Values: 'Forward Euler' | 'Backward Euler' | 'Trapezoidal'

Default: 'Forward Euler'

Target bandwidth (rad/sec) — Target crossover frequency of tuned response

1 (default) | positive scalar

The target bandwidth is the target value for the 0-dB gain crossover frequency of the

tuned open-loop response CP, where P is the plant response, and C is the controller

response. This crossover frequency roughly sets the control bandwidth. For a rise-time τ,

a good guess for the target bandwidth is 2/τ.

To perform PID tuning, the autotuner block measures frequency-response information up

to a frequency of 10 times the target bandwidth. To ensure that this frequency is less than

the Nyquist frequency, the target bandwidth, ωc, must satisfy ωcTs ≤ 0.3, where Ts is the

16 Blocks — Alphabetical List