1D Observer Form [A(v),B(v),C(v),F(v),H(v)]

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

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Libraries:
Aerospace Blockset / GNC / Control

Description

The 1D Observer Form [A(v),B(v),C(v),F(v),H(v)] block implements a gain-scheduled state-space controller as defined in Algorithms.

The output from this block is the actuator demand, which you can input to an actuator block. Use this block to implement a controller designed using H-infinity loop-shaping, one of the design methods supported by Robust Control Toolbox.

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.

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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-y_dem — Set-point error

vector

Set-point error, specified as a vector, that conforms to the dimensions of the state-space matrices.

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

u_meas — Measured actuator position

vector

Measured actuator position, specified as a vector.

Data Types: double

Output

u_dem — Actuator demands

vector

Actuator demands, specified as a vector.

Data Types: double

Parameters

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

A (default) | array

A-matrix of the state-space implementation. 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: 'A'

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

B (default) | array

B-matrix of the state-space implementation. 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: 'B'

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

C (default) | array

C-matrix of the state-space implementation. The C-matrix should have three dimensions, the last one corresponding to the scheduling variable v. Hence, 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: 'C'

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

F (default) | array

State-feedback matrix. The F-matrix should have three dimensions, the last one corresponding to the scheduling variable v. Hence, for example, if the F-matrix corresponding to the first entry of v is the identity matrix, then F(:,:,1) = [1 0;0 1];.

Programmatic Use

Block Parameter: F

Type: character vector

Values: vector

Default: 'F'

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

H (default) | array

Observer (output injection) matrix. The H-matrix should have three dimensions, the last one corresponding to the scheduling variable v. Hence, for example, if the H-matrix corresponding to the first entry of v is the identity matrix, then H(:,:,1) = [1 0;0 1];.

Programmatic Use

Block Parameter: H

Type: character vector

Values: vector

Default: 'H'

Scheduling variable breakpoints — Breakpoints for scheduling variable

v_vec (default) | vector

Breakpoints for the scheduling variable, specified as a vector. The length of v should be same as the size of the third dimension of A, B, C, F, and H.

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, i.e., initial values for the state vector, x, specified as a vector. 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 defined in the following observer form:

$$\begin{array}{l}\dot{x}=(A(v)+H(v)C(v))x+B(v)u_{meas}+H(v)(y-y_{dem})\\ u_{dem}=F(v)x\end{array}$$

References

[1] Hyde, R. A., "H-infinity Aerospace Control Design — A VSTOL Flight Application," Springer Verlag, Advances in Industrial Control Series, 1995.

Extended Capabilities

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

Version History

Introduced before R2006a