Coulomb and Viscous Friction

Model discontinuity at zero, with linear gain elsewhere

Libraries:
Simulink / Discontinuities
HDL Coder / Discontinuities

Description

The Coulomb and Viscous Friction block models Coulomb (static) and viscous (dynamic) friction. The block models a discontinuity at zero and a linear gain otherwise.

The block output matches the MATLAB^® result for:

y = sign(x) .* (Gain .* abs(x) + Offset)

where y is the output, x is the input, Gain is the signal gain for nonzero input values, and Offset is the Coulomb friction.

The block accepts one input and generates one output. The input can be a scalar, vector, or matrix with real and complex elements.

For a scalar input, Gain and Offset can have dimensions that differ from the input. The output is a scalar, vector, or matrix depending on the dimensions of Gain and Offset.
For a vector or matrix input, Gain and Offset must be scalar or have the same dimensions as the input. The output is a vector or matrix of the same dimensions as the input.

Examples

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Scalar Expansion with the Coulomb and Viscous Friction Block

Open Model

This example shows a model that provides a scalar input to a Coulomb & Viscous Friction block. The Coulomb & Viscous Friction uses scalar expansion to produce a vector output.

Double click the Coulomb & Viscous Friction block to see the parameters. The Coefficient of viscous friction (Gain) parameter has a scalar value of 2, and the Coulomb friction value (Offset) parameter has a vector value of [1 3 2 0]. Because the dimensions of the input and the dimensions of the offset are different, the block uses element-wise scalar expansion to compute the output.

Each output is calculated using this formula.

$y = sign(x) .* (Gain .* abs(x) + Offset(idx))$

For example, this equation shows the calculation for the first offset, 1.

$y = - * ((2 * 5) + 1)$

$y = -11$

No scalar expansion is necessary if the input and offset have the same dimensions.

Ports

Input

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Port_1 — Input signal
scalar | vector | matrix

The input signal to the model of Coulomb and viscous friction.

Output

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Port_1 — Output signal
scalar | vector | matrix

The output signal calculated by applying the friction models to the input.

Parameters

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To edit the parameters for the Coulomb and Viscous Friction block, double-click the block icon.

Coulomb friction value — Static friction offset
`[1320]` (default) | real values

Specify the offset that applies to all input values.

Programmatic Use

Block Parameter: offset

Type: character vector

Value: real values

Default:

'[1 3 2
									0]'

Coefficient of viscous friction — Dynamic friction coefficient
`1` (default) | real values

Specify the signal gain for nonzero input values.

Programmatic Use

Block Parameter: gain

Type: character vector

Value: real values

Default: '1'

Block Characteristics

Data Types	`double` \| `fixed point` \| `integer` \| `single`
Direct Feedthrough	`yes`
Multidimensional Signals	`no`
Variable-Size Signals	`no`
Zero-Crossing Detection	`no`

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

HDL Code Generation
Generate VHDL, Verilog and SystemVerilog code for FPGA and ASIC designs using HDL Coder™.

HDL Coder™ provides additional configuration options that affect HDL implementation and synthesized logic.

HDL Architecture

This block has one default HDL architecture.

HDL Block Properties

ConstrainedOutputPipeline	Number of registers to place at the outputs by moving existing delays within your design. Distributed pipelining does not redistribute these registers. The default is `0`. For more details, see ConstrainedOutputPipeline (HDL Coder).
InputPipeline	Number of input pipeline stages to insert in the generated code. Distributed pipelining and constrained output pipelining can move these registers. The default is `0`. For more details, see InputPipeline (HDL Coder).
OutputPipeline	Number of output pipeline stages to insert in the generated code. Distributed pipelining and constrained output pipelining can move these registers. The default is `0`. For more details, see OutputPipeline (HDL Coder).

Restrictions

HDL code generation does not support complex input.

PLC Code Generation
Generate Structured Text code using Simulink® PLC Coder™.

Fixed-Point Conversion
Design and simulate fixed-point systems using Fixed-Point Designer™.

Version History

Introduced before R2006a

Coulomb and Viscous Friction

Description

Examples

Scalar Expansion with the Coulomb and Viscous Friction Block

Ports

Input

Port_1 — Input signal scalar | vector | matrix

Output

Port_1 — Output signal scalar | vector | matrix

Parameters

Coulomb friction value — Static friction offset [1320] (default) | real values

Programmatic Use

Coefficient of viscous friction — Dynamic friction coefficient 1 (default) | real values

Programmatic Use

Block Characteristics

Extended Capabilities

C/C++ Code Generation Generate C and C++ code using Simulink® Coder™.

HDL Code Generation Generate VHDL, Verilog and SystemVerilog code for FPGA and ASIC designs using HDL Coder™.

PLC Code Generation Generate Structured Text code using Simulink® PLC Coder™.

Fixed-Point Conversion Design and simulate fixed-point systems using Fixed-Point Designer™.

Version History

See Also

Port_1 — Input signal
scalar | vector | matrix

Port_1 — Output signal
scalar | vector | matrix

Coulomb friction value — Static friction offset
`[1320]` (default) | real values

Coefficient of viscous friction — Dynamic friction coefficient
`1` (default) | real values

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

HDL Code Generation
Generate VHDL, Verilog and SystemVerilog code for FPGA and ASIC designs using HDL Coder™.

PLC Code Generation
Generate Structured Text code using Simulink® PLC Coder™.

Fixed-Point Conversion
Design and simulate fixed-point systems using Fixed-Point Designer™.