1D Controller [A(v),B(v),C(v),D(v)]

Implement gain-scheduled state-space controller depending on one scheduling parameter

• 

Libraries:
Aerospace Blockset / GNC / Control

Description

The 1D 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.

Examples

HL-20 with Flight Instrument Blocks and Visualization Using Unreal Engine

Model NASA HL-20 lifting body and controller modeled in Simulink^® and Aerospace Blockset™, using Unreal Engine^® for visualization.

• Open Live Script

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

v — Scheduling variable

vector

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(v) — A matrix of the state-space implementation

A1 (default) | array

A-matrix of the state-space implementation, specified as an array. In the case of 1-D scheduling, the A-matrix should have three dimensions, the last one corresponding to the scheduling variable v. For example, if the A-matrix corresponding to the first entry of v is the identity matrix, then A(:,:,1) = [1 0;0 1];.

Programmatic Use

Block Parameter: A

Type: character vector

Values: vector

Default: 'A1'

B-matrix(v) — B matrix of the state-space implementation

B1 (default) | array

B-matrix of the state-space implementation, specified as an array. In the case of 1-D scheduling, the B-matrix should have three dimensions, the last one corresponding to the scheduling variable v. For example, if the B-matrix corresponding to the first entry of v is the identity matrix, then B(:,:,1) = [1 0;0 1];.

Programmatic Use

Block Parameter: B

Type: character vector

Values: vector

Default: 'B1'

C-matrix(v) — C matrix of the state-space implementation

C1 (default) | array

C-matrix of the state-space implementation, specified as a vector. In the case of 1-D scheduling, the C-matrix should have three dimensions, the last one corresponding to the scheduling variable v. For example, if the C-matrix corresponding to the first entry of v is the identity matrix, then C(:,:,1) = [1 0;0 1];.

Programmatic Use

Block Parameter: C

Type: character vector

Values: vector

Default: 'C1'

D-matrix(v) — D

D1 (default) | array

D-matrix of the state-space implementation, specified as an array. In the case of 1-D scheduling, the D-matrix should have three dimensions, the last one corresponding to the scheduling variable v. For example, if the D-matrix corresponding to the first entry of v is the identity matrix, then D(:,:,1) = [1 0;0 1];.

Programmatic Use

Block Parameter: D

Type: character vector

Values: vector

Default: 'D1'

Scheduling variable breakpoints — Breakpoints for scheduling variable

v_vec (default) | vector

Breakpoints for the scheduling variable, specified as a vector. The length of v must be the 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: 'v_vec'

Initial state, x_initial — Initial states

0 (default) | vector

Initial states for the controller, such as initial values for the state vector, x, specified as a vector. The length of the vector must equal 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 parameter 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