Lookup Table 2D — Control Systems/Lookup Tables

2-D Lookup Table

Control Systems / Lookup Tables

Maps a pair of inputs through a rectangular table: y = table(u1, u2). The two axes are searched independently and the surrounding table entries are blended – which for the Linear rule is ordinary bilinear interpolation.

u1 runs down the rows and u2 across the columns, so a table written [1 -2 0.5; 3 0.25 -1; -0.5 2 1.5] is read the way it looks on the page. That is Simulink's dimension order too.

Ports

• Input u1 – the row coordinate, a scalar.
• Input u2 – the column coordinate, a scalar.
• Output – the table's value y, a scalar.

Unlike the 1-D table this block does not run elementwise: a pair of matrix inputs has no single sensible reading, so all three ports are scalar.

Parameters

• Row Breakpoints – the first axis, indexing the table's rows. A row or column vector; both spell the same list. At least two strictly increasing values.
• Column Breakpoints – the second axis, indexing the columns, under the same rules.
• Table Data – the table itself, a matrix with one row per row breakpoint and one column per column breakpoint. A table whose shape disagrees with the two axes is reported and the run stopped.
• Interpolation Method – what the table says between the points.
  • Linear point-slope – bilinear across the surrounding four entries.
  • Flat – the entry at the breakpoint at or below each input, on both axes independently.
  • Nearest – the entry at the nearer breakpoint on each axis. An exact tie takes the higher one.
• Extrapolation Method – what the table says outside its own range.
  • Linear – continue the surface off the edge, along the slopes of the edge cell. Off a corner both axes extrapolate at once.
  • Clip – hold each input inside its own axis, so an input off an edge reads the edge and one off a corner reads the corner entry.
  Consulted only by Linear point-slope. Flat and Nearest never form a slope, so this parameter changes nothing for them – as in Simulink.
• Sampling Time (s) – zero or less inherits the solver's rate; a positive value runs the block at that period.

Code export

All ten targets: Python, MATLAB, Java, Rust, C, C++, VHDL, Verilog, SystemVerilog and PLC Structured Text. The table and both rules are baked into the arithmetic at export time rather than exposed as tunable parameters, and they have to be: the table's shape decides the size of the generated code, which is an outer chain of comparisons picking the row, an inner one picking the column, and one expression per cell.

The three HDL targets are not simulation-only. Each cell's four coefficients fold both axes' widths in at export time, so a cell is three multiplies and three adds and no divider is emitted. The caveat is range – a signal is carried in Q16.16 there, so a breakpoint or table value outside ±32767 cannot be represented, and the bilinear cross term is the one place a large table value meets a large coordinate.

Simulink bridge

Import and export, mapped to simulink/Lookup Tables/2-D Lookup Table. "Row Breakpoints" to BreakpointsForDimension1, "Column Breakpoints" to BreakpointsForDimension2, "Table Data" to Table, "Interpolation Method" to InterpMethod and "Extrapolation Method" to ExtrapMethod – those values are Simulink's own strings, so the mappings are 1:1 and lossless both ways. The block always writes NumberOfTableDimensions = 2, which is what having two input ports means. "Sampling Time (s)" goes to SampleTime, as on every block.

Simulink's three further interpolation methods – Linear Lagrange, Cubic spline and Akima spline – have no counterpart here, and a model importing one is reported rather than silently mapped onto a bilinear blend.

Notes

• Algebraic, with no state.
• Not linear, and so deliberately carries no state space – model reduction reports it as unmergeable.
• See 1-D Lookup Table for one axis and n-D Lookup Table for more than two.