# 3D Self-Conditioned [A(v),B(v),C(v),D(v)]

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

**Library:**Aerospace Blockset / GNC / Control

## Description

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

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

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

## Limitations

This block requires the Control System Toolbox™ license.

## Ports

### Input

### Output

## Parameters

## Algorithms

The block implements a gain-scheduled state-space controller as defined by the equations:

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

in the self-conditioned form

$$\begin{array}{l}\dot{z}=\left(A(v)-H(v)C(v)\right)z+\left(B(v)-H(v)D(v)\right)e+H(v){u}_{meas}\\ {u}_{dem}=C(v)z+D(v)e\end{array}$$

For the rationale behind this self-conditioned implementation, refer to the Self-Conditioned [A,B,C,D] block reference. These
blocks implement a gain-scheduled version of the Self-Conditioned [A,B,C,D] block,
*v* being the 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.

## References

[1] Kautsky, Nichols, and Van Dooren.
"Robust Pole Assignment in Linear State Feedback." *International Journal of
Control*, Vol. 41, Number 5, 1985, pp. 1129-1155.

## Extended Capabilities

## Version History

**Introduced before R2006a**