# Documentation

### This is machine translation

Translated by
Mouseover text to see original. Click the button below to return to the English verison of the page.

To view all translated materals including this page, select Japan from the country navigator on the bottom of this page.

# 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

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 defined in the following observer form:

`$\begin{array}{l}\stackrel{˙}{x}=\left(A\left(v\right)+H\left(v\right)C\left(v\right)\right)x+B\left(v\right){u}_{meas}+H\left(v\right)\left(y-{y}_{dem}\right)\\ {u}_{dem}=F\left(v\right)x\end{array}$`

The main application of this block is to implement a controller designed using H-infinity loop-shaping, one of the design methods supported by Robust Control Toolbox.

## Parameters

A-matrix(v)

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

B-matrix(v)

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

C-matrix(v)

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];`.

F-matrix(v)

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];`.

H-matrix(v)

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];`.

Scheduling variable breakpoints

Vector of the breakpoints for the scheduling variable. The length of v should be same as the size of the third dimension of A, B, C, F, and H.

Initial state, x_initial

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.

## Inputs and Outputs

InputDimension TypeDescription

First

Contains the set-point error.

Second

Contains the scheduling variable.

Third

Contains the measured actuator position.

OutputDimension TypeDescription

First

Contains the actuator demands.

## Assumptions and Limitations

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

## Examples

See H-Infinity Controller (1 Dimensional Scheduling) in `aeroblk_lib_HL20` for an example of this block.

## Reference

Hyde, R. A., "H-infinity Aerospace Control Design - A VSTOL Flight Application," Springer Verlag, Advances in Industrial Control Series, 1995. ISBN 3-540-19960-8. See Chapter 6.