First Order Hold

Implement linearly extrapolated first order hold on input signal

Libraries:
Simulink / Continuous

Description

The First Order Hold block generates a continuous piecewise linear approximation of the input signal. Use the First Order Hold block to convert a sampled discrete signal to a continuous signal without triggering a solver reset.

You can also use the First Order Hold block to break algebraic loops in your model.

Ports

Input

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Port 1 — Input signal
scalar | vector | matrix

Input signal, specified as a real scalar, vector, or matrix.

Data Types: double

Output

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Port 1 — Linearly approximated output signal
scalar | vector | matrix

Piecewise linear approximation of the input signal.

Data Types: double

Parameters

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Initial output — Initial output
`0` (default) | scalar | vector

Specify the output that the block generates until the simulation time exceeds the first sample hit time of the discrete input.

Dependencies

The initial output of this block cannot be inf or NaN.
A Run-to-run tunable parameter cannot be changed during simulation run time. However, changing it before a simulation begins does not cause Accelerator or Rapid Accelerator to regenerate code.

Programmatic Use

Block Parameter: InitialOutput

Type: character vector, string

Values: scalar | vector

Default: '0'

Output algorithm — Output signal approximation technique
`Slow (Avoid Overshoot)` (default) | `Fast (Minimize Error)`

Specify the approximation technique used to generate the output signal. The slow, low pass algorithm avoids overshooting the input signal. The fast, high pass algorithm minimizes error in the approximated output but can overshoot the input signal.

Programmatic Use

Block Parameter: OutputAlgorithm

Type: character vector, string

Values: Slow (Avoid Overshoot)|

Fast (Minimize
									Error)

Default: 'Slow (Avoid Overshoot)'

Reset if relative extrapolation error exceeds — Error tolerance for solver reset
`inf` (default) | non-negative real scalar

Specify the tolerance level for the extrapolation error of the output algorithm. Extrapolation error greater than the specified value causes Simulink^® to reset the solver for the model.

Tip

Enabling the Allow continuous input parameter when this parameter is set to inf can lead to numerical inaccuracies in simulation.

Programmatic Use

Block Parameter: ErrorTolerance

Type: character vector, string

Values: scalar

Default: 'inf'

Allow continuous input — Apply hold on continuous signals
`off` (default) | `on`

Select this parameter to enable the block to accept continuous signals as input. Enabling this parameter creates a delay between the input and output continuous signals.

Note

Enable this parameter when using this block to break an algebraic loop.

Programmatic Use

Block Parameter: AllowContinuousInput

Type: character vector, string

Values: 'off'| 'on'

Default: 'off'

Block Characteristics

Data Types	`double`
Direct Feedthrough	`no`
Multidimensional Signals	`no`
Variable-Size Signals	`no`
Zero-Crossing Detection	`no`

Algorithms

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Slow (Avoid overshoot)

The linear extrapolation performed by the slow or low pass algorithm can be described as:

$y (t) = M_{k} (t - T_{k}) + C_{k} \forall T_{k} \leq t < t_{k + 1}$

where:

T_k is the time at the kth major step.
U_k is the input at the kth major step.
C_k and M_k are the linear extrapolation coefficients.
y_k is the continuous output at time T_k.

The coefficients, or slope M_k and y-intercept C_k, are calculated as follows

$\begin{array}{l} H_{k} = T_{k} - T_{k - 1} \\ M_{k + 1} = \frac{U_{k} - U_{k - 1}}{H_{k}} \\ C_{k} = y_{k} \end{array}$

Fast (Minimize Error)

The linear extrapolation performed by the fast, or high pass, algorithm can be described as:

$y (t) = N_{k} (t - T_{k}) + C_{k} \forall T_{k} \leq t < T_{k + 1}$

where:

T_k is the time at k^th major step.
U_k is the input at k^th major step.
$\hat{U}$ is the predicted value of the input at (k+1)^th major step.
(C_k and N_k are the linear extrapolation coefficients.
y_k is the continuous output at time T_k.

The coefficients, or slope N_k and y-intercept C_k, are calculated as follows

$\begin{array}{l} H_{k} = T_{k} - T_{k - 1} \\ M_{k + 1} = \frac{U_{k} - U_{k - 1}}{H_{k}} \\ \hat{U} = U_{k} + M_{k + 1} (H_{K}) \\ N_{k + 1} = \frac{\hat{U} - y_{k}}{H_{K}} \\ C_{k} = y_{k} \end{array}$

The fast algorithm minimizes error by attempting to predict the next input during the update method of the block. This error reduction in predicted output of the block is traded off against a tendency to overshoot the input signal.

Extended Capabilities

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

Not recommended for production code generation.

Consider discretizing your model.

Version History

Introduced in R2019b

First Order Hold

Description

Ports

Input

Port 1 — Input signal scalar | vector | matrix

Output

Port 1 — Linearly approximated output signal scalar | vector | matrix

Parameters

Initial output — Initial output 0 (default) | scalar | vector

Dependencies

Programmatic Use

Output algorithm — Output signal approximation technique Slow (Avoid Overshoot) (default) | Fast (Minimize Error)

Programmatic Use

Reset if relative extrapolation error exceeds — Error tolerance for solver reset inf (default) | non-negative real scalar

Programmatic Use

Allow continuous input — Apply hold on continuous signals off (default) | on

Programmatic Use

Block Characteristics

Algorithms

Slow (Avoid overshoot)

Fast (Minimize Error)

Extended Capabilities

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

Version History

See Also

Port 1 — Input signal
scalar | vector | matrix

Port 1 — Linearly approximated output signal
scalar | vector | matrix

Initial output — Initial output
`0` (default) | scalar | vector

Output algorithm — Output signal approximation technique
`Slow (Avoid Overshoot)` (default) | `Fast (Minimize Error)`

Reset if relative extrapolation error exceeds — Error tolerance for solver reset
`inf` (default) | non-negative real scalar

Allow continuous input — Apply hold on continuous signals
`off` (default) | `on`

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