Backlash
A model of the behaviour of a system with backlash.
Description
The Backlash block implements a system in which a change in the input signal causes the same change in the output signal, except when the sign of the change in the input signal changes (starts decreasing after increasing or vice versa). When this happens, in the first moment the change in the input signal does not affect the output signal. The amount of backlash in the system is called the Deadband width and is set by the Deadband width parameter. The Deadband width is symmetrical with respect to the output signal value. The figure below shows the initial state with the deadband width by default equal to 1 and the initial output value equal to 0.
The backlash system can be in one of three modes.
| Mode | Input | Output |
|---|---|---|
Disabled |
Inside the deadband. |
Remains constant. |
Positive direction |
Outside the deadband and increases. |
Equal to the value at the input minus half the width of the deadband. |
Negative direction |
Out of the deadband and decreasing. |
Equal to the value at the input plus half the width of the deadband. |
The Initial output parameter sets the initial centre of the deadband.
This table shows the output values under the following initial conditions: Deadband width = 2 and Initial output = 5.
| Output value | Condition |
|---|---|
5 |
4 <= input <= 6 |
input + 1 |
output < 4 |
input − 1 |
output > 6 |
For example, you can use the Backlash block to simulate the meshing of two gears on the input and output shafts of a simple gearbox: the input shaft drives the second shaft via a gear train. The gap between the teeth of the gears creates a backlash. The width of this gap determines the Deadband width. If the system is initially stationary, the value of the output signal is set by the Initial output parameter.
The figures below illustrate the operation of the unit, provided that the initial output value is within the deadband and the system starts from a stationary state.
When the input increases and reaches the end of the deadband, it turns on the output. The output remains at the same level.
After the input interacts with the output, the output changes by the same amount as the input.
If the input changes direction, it is disconnected from the output. The output remains constant until the input reaches the end of the deadband and triggers again.
Ports
Input
Port_1 - input signal
scalar | vector
Input signal for the backlash algorithm. The value of this signal is either in the deadband or turns on the output in the positive or negative direction.
Data types: Float16, Float32, Float64, Int8, Int16, Int32, Int64, UInt8, UInt16, UInt32, UInt64, Bool.
Parameters
Deadband width - deadband width
1 (by default) | scalar | vector
Sets the size of the deadband, centred relative to the output value. When the input signal is inside the deadband, a change in the input does not cause a change in the output. When the input signal is outside the deadband, the output signal changes as much as the input signal.
Block parameter |
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Values |
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* By default* |
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Initial output - initial output value
0 (By default) | scalar | vector
Sets the initial centre of the deadband. If the initial input value is within the deadband, the output value is Initial output. If the initial input value is outside the deadband, the output value is equal to the initial output plus or minus half the deadband width.
Block parameter |
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Values |
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* By default* |
|