⚙

Backlash

Discontinuous

Models mechanical backlash (play/speling). The output stays constant until the input moves more than half the deadband width away from the current output position. Used for modeling gears, linkages, and other mechanical systems with play.

Mathematical Model

y = \begin{cases} u - D/2, & \text{if } u > y_{\text{prev}} + D/2 \\ u + D/2, & \text{if } u < y_{\text{prev}} - D/2 \\ y_{\text{prev}}, & \text{otherwise} \end{cases}

where u is the input, y the output, y_prev the previous output, and D the deadband width.

Inputs & Outputs

Direction	ID	Label	Type	Status
→ In	`in`	In	number	Required
← Out	`out`	Out	number	Output

Parameters

Parameters	Label	Type	Default	Description
`deadbandWidth`	Deadband Width	number	`1`
`initialOutput`	Initial Output	number	`0`

Usage Examples

Zie de ingebouwde voorbeelden in de handleiding voor een demonstratie van dit blok.

Remarks & Best Practices

Direction-dependent: Backlash output trajectory depends on whether the input is increasing or decreasing
Initial condition: The initialOutput parameter should match the physical system's rest position
Deadband symmetry: The deadband is centred around the current output; total play equals deadbandWidth
Cascading: Multiple backlash blocks in series model complex mechanical drivetrains
Numerical stability: Small deadband widths relative to signal amplitude may cause chattering

Related Components

DeadZone: Zero output within band, no state memory
Relay: Hysteresis switching between two values