FB_SecondOrderPlant (Function Block)

Simulates a second-order linear plant using the Tustin (bilinear) discretisation with frequency pre-warping to preserve the natural frequency Wn exactly.

The continuous-time transfer function is:

\[G(s) = \frac{K \omega_n^2}{s^2 + 2 \zeta \omega_n s + \omega_n^2}\]

where \(K\) is Gain, \(\omega_n\) is Wn, and \(\zeta\) is Zeta.

Note

The block is FINAL and must be instantiated, not extended. Use FB_init to set fGain, fWn, and fZeta at declaration time.

Extends: FB_SisoComponent

Properties

Gain

Type: LREAL

Gets or sets the steady-state gain.

This is the factor by which a constant input is scaled to produce the output once the plant has fully settled. For example, a gain of 2 with a constant input of 5 will eventually produce an output of 10.

Wn

Type: LREAL

Gets or sets the natural frequency in rad/s.

This controls the speed of the plant’s response. A higher value means a faster response. To convert from Hz, multiply by 2π.

Zeta

Type: LREAL

Gets or sets the damping ratio.

This controls the shape of the response.

A value below 1 produces an oscillating response that overshoots before settling.
A value of exactly 1 (critically damped) settles as fast as possible without any overshoot.
A value above 1 settles more slowly with no overshoot.

Methods

FB_init

Inputs

Name	Type	Description
`bInitRetains`	`BOOL`	if TRUE, the retain variables are initialized (warm start / cold start)
`bInCopyCode`	`BOOL`	if TRUE, the instance afterwards gets moved into the copy code (online change)
`fGain`	`LREAL`	Steady-state gain (K). Ratio of output to input once the plant has fully settled.
`fWn`	`LREAL`	Natural frequency in rad/s. Controls how fast the plant responds.
`fZeta`	`LREAL`	Damping ratio. Less than 1 gives overshoot, 1 is critically damped, greater than 1 is overdamped.

Run

Advances the plant by one time step.

Note

Must be called once per cycle on a single PLC task. This is because on the first call, the cycle time is measured and stored for use in all subsequent calls.

If the cycle time is zero or Wn is zero, the method returns early without updating the output.