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Backlash

Model behavior of system with play

Discontinuities

Description

The Backlash block implements a system in which a change in input causes an equal change in output. However, when the input changes direction, an 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 the block's 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:

• Disengaged — In this mode, the input does not drive the output and the output remains constant.

• Engaged in a positive direction — In this mode, the input is increasing (has a positive slope) and the output is equal to the input minus half the deadband width.

• Engaged in a negative direction — In this mode, the input is decreasing (has a negative slope) and the output is equal to the input plus half the deadband width.

If the initial input is outside the deadband, the Initial output parameter value determines whether the block is engaged in a positive or negative direction, and the output at the start of the simulation is the input plus or minus half the deadband width.

For example, the Backlash block can be used to model the meshing of two gears. The input and output are both shafts with a gear on one end, and the output shaft is driven by the input 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 output (the position of the driven gear) is defined by the Initial output parameter.

The following figures illustrate the block's operation when the initial input is within the deadband. The first figure shows the relationship between the input and the output while the system is in disengaged mode (and the default parameter values are not changed).

The next figure shows the state of the block when the input has reached the end of the deadband and engaged the output. The output remains at its previous value.

The final figure shows how a change in input affects the output while they are engaged.

If the input reverses its direction, it disengages from the output. The output remains constant until the input either reaches the opposite end of the deadband or reverses its direction again and engages at the same end of the deadband. Now, as before, movement in the input causes equal movement in the output.

For example, if the deadband width is 2 and the initial output is 5, the output, y, at the start of the simulation is as follows:

• 5 if the input, u, is between 4 and 6

• u + 1 if u < 4

• u – 1 if u > 6

Data Type Support

The Backlash block accepts and outputs real values of single, double, and built-in integer data types.

Parameters and Dialog Box

Specify the width of the deadband. The default is 1.

Initial output

Specify the initial output value. The default value is 0. This parameter is tunable. Simulink® does not allow the initial output of this block to be inf or NaN.

Input processing

Specify whether the block performs sample- or frame-based processing. You can select one of the following options:

• Elements as channels (sample based) — Treat each element of the input as a separate channel (sample-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 in the DSP System Toolbox documentation.
• Inherited — Inherit the processing mode from the input signal and delay the input accordingly. You can identify whether the input signal is sample or frame based by looking at the signal line. Simulink represents sample-based signals with a single line and frame-based signals with a double line.

 Note:   When you choose the Inherited option for the Input processing parameter, and the input signal is frame-based, Simulink will generate a warning or error in future releases.

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 in the DSP System Toolbox documentation.

Enable zero-crossing detection

Sample time (-1 for inherited)

Specify the time interval between samples. To inherit the sample time, set this parameter to -1. See Specify Sample Time in the Simulink documentation.

Examples

The following modelmodel shows the effect of a sine wave passing through a Backlash block.

The Backlash block uses default parameter values: the deadband width is 1 and the initial output is 0. The following plot shows that the Backlash block output is zero until the input reaches the end of the deadband (at 0.5). Now the input and output are engaged and the output moves as the input does until the input changes direction (at 1.0). When the input reaches 0, it again engages the output at the opposite end of the deadband.

Characteristics

 Direct Feedthrough Yes Sample Time Specified in the Sample time parameter Scalar Expansion Yes Dimensionalized Yes Zero-Crossing Detection Yes, if enabled