PS Lookup Table (3D)

Approximate three-dimensional function using specified lookup method

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Libraries:
Simscape / Foundation Library / Physical Signals / Lookup Tables

Description

The PS Lookup Table (3D) block computes an approximation to some function f=f(x1,x2,x3) by interpolating the input query point coordinates against a three-dimensional lookup table.

You define the lookup table by specifying the Table grid vector 1 parameter (vector of data points along the first axis), the Table grid vector 2 parameter (vector of data points along the second axis), the Table grid vector 3 parameter (vector of data points along the third axis), and the 3D array of table values parameter (array of output values).

The table grid data vectors must be strictly monotonic, either increasing or decreasing. The array size of the tabulated function values must match the dimensions defined by the data vectors. That is, if the three data vectors have sizes 1-by-m, 1-by-n, and 1-by-p, respectively, supply an m-by-n-by-p array of the output function values.

The three inputs and the output of the block are physical signals of matching size. The block generates the output based on the input query and the table grid lookup, using the selected interpolation and extrapolation methods. You have a choice of two interpolation methods and two extrapolation methods. You also have an option for the block to issue an error if any of the input signal values is outside the respective table grid vector range.

Ports

Input

x1 — Input query point or N-D array of query points along the first axis, untyped

physical signal

Input query point or points along the first axis. The signal size is either a scalar, for a single query point, or an N-D array that represents the coordinates of the query points along the first axis.

x2 — Input query point or N-D array of query points along the second axis, untyped

physical signal

Input query point or points along the second axis. The signal size must match the signal size along the first axis.

x3 — Input query point or N-D array of query points along the third axis, untyped

physical signal

Input query point or points along the third axis. The signal size must match the signal size along the first axis.

Output

f — Output function value, untyped

physical signal

Output function value, based on applying the lookup table to the three input values. The output signal size matches the input signal size along the first axis. The output signal unit is determined by the unit of the 3D array of table values parameter.

Parameters

Table grid vector 1 — Vector of data values along the first axis

[1, 2, 3] 1 (default)

Specify the vector of data values along the first axis as a 1-by-m array. The vector must be strictly monotonic, either increasing or decreasing. The values can be nonuniformly spaced. For smooth interpolation, the vector must contain at least three values. For linear interpolation, two values are sufficient.

Parameter unit must be commensurate with the unit of the input signal at port x1. By default, the unit is 1 (unitless). You can select a different unit from the drop-down list or type the desired unit name, such as rpm, or a valid expression, such as rad/s. For more information and a list of unit abbreviations, see How to Specify Units in Block Dialogs and Unit Definitions.

Table grid vector 2 — Vector of data values along the second axis

[1, 2, 3, 4] 1 (default)

Specify the vector of data values along the second axis as a 1-by-n array. The vector must be strictly monotonic, either increasing or decreasing. The values can be nonuniformly spaced. For smooth interpolation, the vector must contain at least three values. For linear interpolation, two values are sufficient.

Parameter unit must be commensurate with the unit of the input signal at port x2. By default, the unit is 1 (unitless). You can select a different unit from the drop-down list or type the desired unit name, such as rpm, or a valid expression, such as rad/s. For more information and a list of unit abbreviations, see How to Specify Units in Block Dialogs and Unit Definitions.

Table grid vector 3 — Vector of data values along the third axis

[1, 2, 3] 1 (default)

Specify the vector of data values along the third axis as a 1-by-p array. The vector must be strictly monotonic, either increasing or decreasing. The values can be nonuniformly spaced. For smooth interpolation, the vector must contain at least three values. For linear interpolation, two values are sufficient.

Parameter unit must be commensurate with the unit of the input signal at port x3. By default, the unit is 1 (unitless). You can select a different unit from the drop-down list or type the desired unit name, such as rpm, or a valid expression, such as rad/s. For more information and a list of unit abbreviations, see How to Specify Units in Block Dialogs and Unit Definitions.

3D array of table values — Three-dimensional array of function values at table grid vertices

ones(3, 4, 3) 1 (default)

Specify the output values as an m-by-n-by-p array, defining the function values at the data grid vertices. The array size must match the dimensions defined by the data vectors.

Parameter unit determines the unit of the output signal at port f. By default, the unit is 1 (unitless). You can select a different unit from the drop-down list or type the desired unit name, such as rpm, or a valid expression, such as rad/s. For more information and a list of unit abbreviations, see How to Specify Units in Block Dialogs and Unit Definitions.

Interpolation method — Select the interpolation method

Linear (default) | Smooth

Select one of the following interpolation methods for approximating the output value when the input value is between two consecutive grid points:

• Linear — Uses an extension of linear algorithm for multidimensional interpolation. The method performs linear interpolation first in x1-direction, then in x2-direction, and then in x3-direction. Select this option to get the best performance.

• Smooth — Uses a modified Akima interpolation algorithm. For details, see tablelookup. Select this option to produce a continuous surface with continuous first-order derivatives.

Extrapolation method — Select the extrapolation method

Linear (default) | Nearest | Error

Select one of the following extrapolation methods for determining the output value when the input value is outside the range specified in the argument list:

• Linear — Extends from the edge of the interpolation region linearly. The slope of the linear extrapolation is equal to the slope of the interpolated surface at the edge of the interpolation region.

• Nearest — Extends from the edge of the interpolation region as a constant. The value of the nearest extrapolation is equal to the value of the interpolated surface at the edge of the interpolation region. Select this option to produce an extrapolation that does not go above the highest point in the data or below the lowest point in the data.

• Error — Issues an error if any of the input signals is outside the range of the table. Select this option to avoid going into the extrapolation mode when you want your data to be within the table range.

Extended Capabilities

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

Version History

Introduced in R2016a

R2019a: Unit Propagation

Prior to R2019a, this block did not propagate physical units.

If your model contains legacy blocks without unit propagation, use the Upgrade Advisor to upgrade your blocks to the latest version. For more information, see Upgrading Models with Legacy Physical Signal Blocks.