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Backlash

Model behavior of system with play

  • Library:
  • Simulink / Discontinuities

Description

The Backlash block implements a system in which a change in input causes an equal change in output, except when the input changes direction. When the input changes direction, the initial change in input has no effect on the output. The amount of side-to-side play in the system is referred to as the deadband. The deadband is centered about the output. This figure shows an initial state, with the default deadband width of 1 and initial output of 0.

A system with play can be in one of three modes.

ModeInputOutput
DisengagedInside deadband zone.Remains constant.
Engaged-positive directionOutside deadband zone and increasing.Equals input minus half of deadband width.
Engaged-negative directionOutside deadband zone and decreasing.Equals input plus half of deadband width.

The Initial output parameter value defines the initial center of the deadband zone.

This table shows output values when initial conditions are: Deadband width = 2 and Initial output = 5.

Output ValueCondition
5

4 < input < 6

input + 1input < 4
input - 1input > 6

For example, you can use the Backlash block to model the meshing of two gears. The input and output are both shafts with a gear on one end, and the input shaft drives the output shaft. Extra space between the gear teeth introduces play. The width of this spacing is the Deadband width parameter. If the system is disengaged initially, the Initial output parameter defines the output.

These figures illustrate operation when the initial input is within the deadband and the system begins in disengaged mode.

When the input increases and reaches the end of the deadband, it engages the output. The output remains at its previous value.

After the input engages the output, the output changes by the same amount as the input.

If the input reverses direction, it disengages from the output. The output remains constant until the input reaches the end of the deadband and engages again.

Ports

Input

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Input signal to the backlash algorithm. The value of this signal is either in the deadband or engaging the output in a positive or negative direction.

Data Types: double | single | int8 | int16 | int32 | uint8 | uint16 | uint32

Output

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Output signal after the backlash algorithm is applied to the input signal. When the input is in the deadband, then the output remains unchanged. If the input is engaged with the output, then the output changes an equal amount as the input.

Data Types: double | single | int8 | int16 | int32 | uint8 | uint16 | uint32

Parameters

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Specify the size of the deadband zone centered on the output value. When the input signal is inside the deadband, then a change in input does not cause a change in output. When the input signal is outside of the deadband, then the output changes an equal amount as the input.

Programmatic Use

Block Parameter: BacklashWidth
Type: character vector
Values: real scalar or vector
Default: '1'

Specify the initial center of the deadband zone. If the initial input value is in the deadband zone, then the output value is equal to Initial output. If the initial input value is outside of the deadband zone, then the output value is Initial output plus or minus half of the deadzone width.

Programmatic Use

Block Parameter: InitialOutput
Type: character vector
Values: real scalar or vector
Default: '0'

Specify whether the block performs sample- or frame-based processing:

  • Columns as channels (frame based) — Treat each column of the input as a separate channel (frame-based processing).

    Note

    Frame-based processing requires a DSP System Toolbox™ license.

    For more information, see Sample- and Frame-Based Concepts (DSP System Toolbox).

  • Elements as channels (sample based) — Treat each element of the input as a separate channel (sample-based processing).

Use Input processing to specify whether the block performs sample- or frame-based processing. The block accepts frame-based signals for the input u. All other input signals must be sample-based.

Input Signal uInput Processing ModeBlock Works?
Sample basedSample basedYes
Frame basedNo, produces an error
Sample basedFrame basedYes
Frame basedYes
Sample basedInheritedYes
Frame basedYes

For more information about these two processing modes, see Sample- and Frame-Based Concepts (DSP System Toolbox).

Programmatic Use

Block Parameter: InputProcessing
Type: character vector
Values: 'Columns as channels (frame based)' | 'Elements as channels (sample based)'
Default: 'Elements as channels (sample based)'

Select to enable zero-crossing detection. For more information, see Zero-Crossing Detection.

Programmatic Use

Block Parameter: ZeroCross
Type: character vector, string
Values: 'off' | 'on'
Default: 'on'

Block Characteristics

Data Types

double | single | base integer

Direct Feedthrough

No

Multidimensional Signals

No

Variable-Size Signals

No

Zero-Crossing Detection

Yes

Extended Capabilities

See Also

Introduced before R2006a