Aerospace Blockset

Interpolate Matrix(x,y,z)

Return an interpolated matrix for given inputs x, y, and z

Library

GNC

Description

The Interpolate Matrix(x,y,z) block interpolates a three-dimensional array of matrices.

This three-dimensional case assumes the matrix is defined as a function of three independent variables, x = [ x₁ x₂ x₃ ... x_i x_i+1 ... x_n ], y = [ y₁ y₂ y₃ ... y_j y_j+1 ... y_m], and z = [ z₁ z₂ z₃ ... z_k z_k+1 ... z_p ]. For given values of x, y, and z, eight matrices are interpolated. Then for x_i < x < x_i+1, y_j < y < y_j+1 and z_k < z < z_k+1, the output matrix is given by

where the three interpolation fractions are denoted by

In the three-dimensional case, the interpolation is carried out first on x, then y, and finally z.

Dialog Box and Parameters

Matrix to interpolate

Matrix to be interpolated. It should be five dimensional, the first two dimensions corresponding to the matrix at each value of x, y, and z. For example, if you have eight matrices A, B, C, D, E, F, G, and H defined at the following values of x, y, and z, then the corresponding input matrix is given by

(x = 0.0,y = 1.0,z = 0.1)	matrix(:,:,1,1,1) = A;
(x = 0.0,y = 1.0,z = 0.5)	matrix(:,:,1,1,2) = B;
(x = 0.0,y = 3.0,z = 0.1)	matrix(:,:,1,2,1) = C;
(x = 0.0,y = 3.0,z = 0.5)	matrix(:,:,1,2,2) = D;
(x = 1.0,y = 1.0,z = 0.1)	matrix(:,:,2,1,1) = E;
(x = 1.0,y = 1.0,z = 0.5)	matrix(:,:,2,1,2) = F;
(x = 1.0,y = 3.0,z = 0.1)	matrix(:,:,2,2,1) = G;
(x = 1.0,y = 3.0,z = 0.5)	matrix(:,:,2,2,2) = H;

Inputs and Outputs

The first input is the first independent variable.

The second input is the second independent variable.

The third input is the third independent variable.

The output is the interpolated matrix.

Assumptions and Limitations

This block must be driven from the Simulink PreLookup Index Search block.

Examples

See the following Aerospace Blockset blocks: 3D Controller [A(v),B(v),C(v),D(v)], 3D Observer Form [A(v),B(v),C(v),F(v),H(v)], and 3D Self-Conditioned [A(v),B(v),C(v),D(v)].

See Also
Interpolate Matrix(x)

Interpolate Matrix(x,y)

Interpolate Matrix(x,y)

ISA Atmosphere Model