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29 Sep 2022
Skill-Lync
A lookup table is an array of data that maps input values to output values, thereby resembling a mathematical function. A lookup operation retrieves the corresponding output values from the table if there is a given set of input values. In other words, a lookup table computes an approximation to some mathematical function y=f(x), given data vectors x and y. We can define the lookup table by specifying a vector of output values parameter as a 1-by-n vector. The lookup table block in Simulink generates an output based on the input values using one of the methods selected from the Look-up method parameter list. If the lookup table does not define the input values, the block estimates the output values based on a nearby table
Below are the common methods used:
If we go to Simulink and type a lookup table, this is how it appears (image below). You can go to the library browser.
There are several lookup tables available in the Lookup table block library with different functions.
The following example illustrates a one-dimensional lookup table that approximates the function y = x^3
The lookup table defines its output (y) data discretely over the input (x) range [-2, 2].
The lookup table defines its output (y) data discretely over the input (x) range [-2, 2].
The above figure shows the breakpoints of the function when plotted in the XY axis
Interpolation-Extrapolation- -This is the default method used to plot the breakpoints. it performs linear interpolation and extrapolation of the inputs.
When the lookup table block encounters an input that does not match any of the table's x values, it can interpolate or extrapolate the answer. For instance, the lookup table does not define an input value of -1.5; however, the block can linearly interpolate the nearest adjacent data points. For example, given these two points:
Similarly, although the lookup table does not include data for x values beyond the range of [-2, 2], the block can extrapolate values using a pair of data points at either end of the table.
If an input falls between breakpoint values or outside the range of a breakpoint data set and you do not specify interpolation or extrapolation, the block rounds the value to an adjacent breakpoint and returns the corresponding output value. If you explore the Lookup Table Dynamic block, it lets you select any of the rounding methods
Click on the drop-down for rounding options:
Here is an example of the rounding method in Simulink
This example shows how to use the Lookup Table Dynamic block to approximate the sinh function. The breakpoint data is given by the vector [-5:5] and the vector sinh gives the table data ([-5:5]). The input x is provided by the Constant block with a vector 1.4
The simulation time was given as 10s. Three constant blocks were used for giving the input values and the lookup table dynamic block is used to map the output. The rounding method option for the nearest input value was given. So the lookup table uses the value for sinh (1.0) which is near to 1.4.value given in the input. You can analyse the results by changing the option in the Lookup dynamic block and giving different input values.
Here is a simple example of a 1D Lookup table in Simulink
The input is taken as a Repeating stair sequence and the values given are 6 2.5 4 with a sample time of 1. The lookup table is configured as shown below.
Parameter estimation
Table and Breakpoints
Breakpoints: Feed the x values of the function
Breakpoint Specification: Specify whether to enter data as explicit breakpoints or as parameters that generate evenly spaced breakpoints.
Table Data: Enter the table of output values (Here, Feed the Y values of the function)
Data Specification: Specify the table data and breakpoints
Number of Table Dimensions: Enter the number of dimensions of the lookup table ( Here it is 1 (because we use a 1D lookup table))
The values given here are such that the output will give twice the value of the input .; y=2x
The algorithm was set to Linear point-slope for the Interpolation method, and by default, the option for Linear will be set for the Extrapolation method.
Data types were kept as default
Results
The simulation is carried out for 3s because we have given only three values at the input side (repeating sequence stair). We have defined a mathematical function y=2x using a lookup table in this article
From the scope, you can see that the Lookup table plot gives values which are double the input values from repeating sequence stairs. Likewise, you can define a mathematical function with one variable. You can use a 2D lookup table for defining two variables.
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Navin Baskar
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Skill-Lync
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