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

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

The 2D Self-Conditioned [A(v),B(v),C(v),D(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.

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.

This block requires the Control System Toolbox™ license.

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. This
block implements 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.

[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.

1D Self-Conditioned [A(v),B(v),C(v),D(v)] | 2D Controller [A(v),B(v),C(v),D(v)] | 2D Controller Blend | 2D Observer Form [A(v),B(v),C(v),F(v),H(v)] | 3D Self-Conditioned [A(v),B(v),C(v),D(v)] | Linear Second-Order Actuator | Nonlinear Second-Order Actuator