2D Observer Form [A(v),B(v),C(v),F(v),H(v)]

Implement gain-scheduled state-space controller in observer form depending on two scheduling parameters

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Libraries:
Aerospace Blockset / GNC / Control

Description

The 2D 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.

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

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

A (default) | array

A-matrix of the state-space implementation. In the case of 2-D scheduling, the A-matrix should have four dimensions, the last two corresponding to scheduling variables v1 and v2. For example, if the A-matrix corresponding to the first entry of v1 and first entry of v2 is the identity matrix, then A(:,:,1,1) = [1 0;0 1];.

Programmatic Use

Block Parameter: A

Type: character vector

Values: vector

Default: 'A'

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

B (default) | array

B-matrix of the state-space implementation. In the case of 2-D scheduling, the B-matrix should have four dimensions, the last two corresponding to scheduling variables v1 and v2. For example, if the B-matrix corresponding to the first entry of v1 and first entry of v2 is the identity matrix, then B(:,:,1,1) = [1 0;0 1];.

Programmatic Use

Block Parameter: B

Type: character vector

Values: vector

Default: 'B'

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

C (default) | array

C-matrix of the state-space implementation. In the case of 2-D scheduling, the C-matrix should have four dimensions, the last two corresponding to scheduling variables v1 and v2. For example, if the C-matrix corresponding to the first entry of v1 and first entry of v2 is the identity matrix, then C(:,:,1,1) = [1 0;0 1];.

Programmatic Use

Block Parameter: C

Type: character vector

Values: vector

Default: 'C'

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

F (default) | array

State-feedback matrix. In the case of 2-D scheduling, the F-matrix should have four dimensions, the last two corresponding to scheduling variables v1 and v2. For example, if the F-matrix corresponding to the first entry of v1 and first entry of v2 is the identity matrix, then F(:,:,1,1) = [1 0;0 1];.

Programmatic Use

Block Parameter: F

Type: character vector

Values: vector

Default: 'F'

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

H (default) | array

Observer (output injection) matrix. In the case of 2-D scheduling, the H-matrix should have four dimensions, the last two corresponding to scheduling variables v1 and v2. For example, if the H-matrix corresponding to the first entry of v1 and first entry of v2 is the identity matrix, then H(:,:,1,1) = [1 0;0 1];.

Programmatic Use

Block Parameter: H

Type: character vector

Values: vector

Default: 'H'

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

v1_vec (default)

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, F, and H.

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 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, F, and H.

Programmatic Use

Block Parameter: Mach_vec

Type: character vector

Values: vector

Default: 'v2_vec'

Initial state, x_initial — Initial states

0 (default)

Vector of initial states for the controller,that is, 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 defined in the following observer form:

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

References

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

Extended Capabilities

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

Version History

Introduced before R2006a