3D Controller [A(v),B(v),C(v),D(v)]

Implement gain-scheduled state-space controller depending on three scheduling parameters

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Libraries:
Aerospace Blockset / GNC / Control

Description

The 3D Controller [A(v),B(v),C(v),D(v)] block implements a gain-scheduled state-space controller as described in Algorithms.

The output from this block is the actuator demand, which you can input to an actuator block.

Limitations

If the scheduling parameter inputs to the block go out of range, they are clipped. The state-space matrices are not interpolated out of range.

Ports

Input

y — Aircraft measurements

vector

Aircraft measurements, specified as a vector.

Data Types: double

v1 — First scheduling variable

vector

First scheduling variable, specified as a vector, that conforms to the dimensions of the state-space matrices.

Data Types: double

v2 — Second scheduling variable

vector

Second scheduling variable, specified as a vector, that conforms to the dimensions of the state-space matrices.

Data Types: double

v3 — Third scheduling variable

vector

Second scheduling variable, specified as a vector, that conforms to the dimensions of the state-space matrices.

Data Types: double

Output

u — Actuator demands

vector

Actuator demands, specified as a vector.

Data Types: double

Parameters

A-matrix(v1,v2,v3) — A matrix of the state-space implementation

A (default) | array

A-matrix of the state-space implementation. In the case of 3-D scheduling, the A-matrix should have five dimensions, the last three corresponding to scheduling variables v1, v2, and v3. For example, if the A-matrix corresponding to the first entry of v1, the first entry of v2, and the first entry of v3 is the identity matrix, then A(:,:,1,1,1) = [1 0;0 1];.

Programmatic Use

Block Parameter: A

Type: character vector

Values: vector

Default: 'A'

B-matrix(v1,v2,v3) — B matrix of the state-space implementation

B (default) | array

B-matrix of the state-space implementation. In the case of 3-D scheduling, the B-matrix should have five dimensions, the last three corresponding to scheduling variables v1, v2, and v3. For example, if the B-matrix corresponding to the first entry of v1, the first entry of v2, and the first entry of v3 is the identity matrix, then B(:,:,1,1,1) = [1 0;0 1];.

Programmatic Use

Block Parameter: B

Type: character vector

Values: vector

Default: 'B'

C-matrix(v1,v2,v3) — C matrix of the state-space implementation

C (default) | array

C-matrix of the state-space implementation. In the case of 3-D scheduling, the C-matrix should have five dimensions, the last three corresponding to scheduling variables v1, v2, and v3. For example, if the C-matrix corresponding to the first entry of v1, the first entry of v2, and the first entry of v3 is the identity matrix, then C(:,:,1,1,1) = [1 0;0 1];.

Programmatic Use

Block Parameter: C

Type: character vector

Values: vector

Default: 'C'

D-matrix(v1,v2,v3) — D matrix of the state-space implementation

D (default) | array

D-matrix of the state-space implementation. In the case of 3-D scheduling, the D-matrix should have five dimensions, the last three corresponding to scheduling variables v1, v2, and v3. For example, if the D-matrix corresponding to the first entry of v1, the first entry of v2, and the first entry of v3 is the identity matrix, then D(:,:,1,1,1) = [1 0;0 1];.

Programmatic Use

Block Parameter: D

Type: character vector

Values: vector

Default: 'D'

First scheduling variable (v1) breakpoints — Breakpoints for first scheduling variable

v1_vec (default) | vector

Vector of the breakpoints for the first scheduling variable. The length of v1 should be same as the size of the third dimension of A, B, C, and D.

Programmatic Use

Block Parameter: AoA_vec

Type: character vector

Values: vector

Default: 'v1_vec'

Second scheduling variable (v2) breakpoints — Breakpoints for second scheduling variable

v2_vec (default) | vector

Vector of the breakpoints for the second scheduling variable. The length of v2 should be same as the size of the fourth dimension of A, B, C, and D.

Programmatic Use

Block Parameter: AoS_vec

Type: character vector

Values: vector

Default: 'v2_vec'

Third scheduling variable (v3) breakpoints — Breakpoints for third scheduling variable

v3_vec (default) | vector

Vector of the breakpoints for the third scheduling variable. The length of v3 should be same as the size of the fifth dimension of A, B, C, and D.

Programmatic Use

Block Parameter: Mach_vec

Type: character vector

Values: vector

Default: 'v3_vec'

Initial state, x_initial — Initial states

0 (default) | vector

Vector of initial states for the controller, i.e., initial values for the state vector, x. It should have length equal to the size of the first dimension of A.

Programmatic Use

Block Parameter: x_initial

Type: character vector

Values: vector

Default: '0'

Algorithms

The block implements a gain-scheduled state-space controller as defined by this equation:

$$\begin{array}{l}\dot{x}=A(v)x+B(v)y\\ u=C(v)x+D(v)y\end{array}$$

where v is a vector of parameters over which A, B, C, and D are defined. This type of controller scheduling assumes that the matrices A, B, C, and D vary smoothly as a function of v, which is often the case in aerospace applications.

Extended Capabilities

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

Version History

Introduced before R2006a