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Self-Conditioned [A,B,C,D]

Implement state-space controller in self-conditioned form

  • Library:
  • Aerospace Blockset / GNC / Control

  • Self-Conditioned [A,B,C,D] block

Description

The Self-Conditioned [A,B,C,D] block can be used to implement the state-space controller defined by

[x˙=Ax+Beu=Cx+De]

in the self-conditioned form

z˙=(AHC)z+(BHD)e+Humeasudem=Cz+De

The input umeas is a vector of the achieved actuator positions, and the output udem is the vector of controller actuator demands. In the case that the actuators are not limited, then umeas=udem and substituting the output equation into the state equation returns the nominal controller. In the case that they are not equal, the dynamics of the controller are set by the poles of A-HC.

Hence H must be chosen to make the poles sufficiently fast to track umeas but at the same time not so fast that noise on e is propagated to udem. The matrix H is designed by a callback to the Control System Toolbox™ command place to place the poles at defined locations.

Limitations

This block requires the Control System Toolbox license.

Ports

Input

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Control error, specified as a vector.

Data Types: double

Achieved actuator positions, specified as a vector.

Data Types: double

Output

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Actuator demands, specified as a vector.

Data Types: double

Parameters

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A-matrix of the state-space implementation. 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];.

Programmatic Use

Block Parameter: Ak
Type: character vector
Values: vector
Default: '[-1 -0.2;0 -3]'

B-matrix of the state-space implementation, specified as a array. 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];.

Programmatic Use

Block Parameter: Bk
Type: character vector
Values: vector
Default: '[1;1]'

C-matrix of the state-space implementation, specified as a array. 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];.

Programmatic Use

Block Parameter: Ck
Type: character vector
Values: vector
Default: '[1 0]'

D-matrix of the state-space implementation. 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];.

Programmatic Use

Block Parameter: Dk
Type: character vector
Values: vector
Default: '0.02'

Initial states for the controller, that is, initial values for the state vector, z. It should have length equal to the size of the first dimension of A.

Programmatic Use

Block Parameter: x_initial
Type: character vector
Values: vector
Default: '0'

Desired poles of A-H*C, specified as a vector. Hence the number of pole locations defined should be equal to the dimension of the A-matrix.

Programmatic Use

Block Parameter: vec_w
Type: character vector
Values: vector
Default: '[-5 -2]'

More About

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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

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Introduced before R2006a