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1D Controller [A(v),B(v),C(v),D(v)]

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

GNC/Control

Description

The 1D Controller [A(v),B(v),C(v),D(v)] block implements a gain-scheduled state-space controller as defined by the equations

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

where v is a parameter 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.

Dialog Box

A-matrix(v)

A-matrix of the state-space implementation. In the case of 1-D scheduling, 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];.

B-matrix(v)

B-matrix of the state-space implementation. In the case of 1-D scheduling, 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];.

C-matrix(v)

C-matrix of the state-space implementation. In the case of 1-D scheduling, the C-matrix should have three dimensions, the last one corresponding to the scheduling variable v. For example, if the C-matrix corresponding to the first entry of v is the identity matrix, then C(:,:,1) = [1 0;0 1];.

D-matrix(v)

D-matrix of the state-space implementation. In the case of 1-D scheduling, the D-matrix should have three dimensions, the last one corresponding to the scheduling variable v. For example, if the D-matrix corresponding to the first entry of v is the identity matrix, then D(:,:,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, and D.

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

AnyContains the measurements.

Second

Contains the scheduling variable conforming to the dimensions of the state-space matrices.

OutputDimension TypeDescription

First

AnyContains 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 aeroblk_lib_HL20 for an example of this block.