1D Observer Form [A(v),B(v),C(v),F(v),H(v)] (Aerospace Blockset)

1D Observer Form [A(v),B(v),C(v),F(v),H(v)]

Implement a gain-scheduled state-space controller in an observer form depending on one scheduling parameter

Library

GNC

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 for:

The main application of this blocks is to implement a controller designed using H-infinity loop-shaping, one of the design methods supported by the -Analysis and Synthesis Toolbox.

Dialog Box

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

The first input is the set-point error.

The second input is the scheduling variable.

The third input is measured actuator position.

The output is the actuator demands.

Assumptions and Limitations

If the scheduling parameter input to the block goes out of range, then it is clipped; i.e., the state-space matrices are not interpolated out of range.

Examples

See the observer implementation within the aeroblk_HL20.mdl demo.

References

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.

1D Controller Blend u=(1-L).K1.y+L.K2.y

1D Self-Conditioned [A(v),B(v),C(v),D(v)]

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

3D Observer Form [A(v),B(v),C(v),F(v),H(v)]

1D Controller Blend u=(1-L).K1.y+L.K2.y 1D Self-Conditioned [A(v),B(v),C(v),D(v)]