Aerospace Blockset

2D Controller Blend

Implement a 2-D vector of state-space controllers by linear interpolation of their outputs

Library

GNC

Description

The 2D Controller Blend block implements an array of state-space controller designs. The controllers are run in parallel, and their outputs interpolated according to the current flight condition or operating point. The advantage of this implementation approach is that the state-space matrices A, B, C, and D for the individual controller designs do not need to vary smoothly from one design point to the next.

For the 2D Controller Blend block, at any given instant in time, nine controller designs are updated.

As the value of the scheduling parameter varies and the index of the controllers that need to be run changes, the states of the oncoming controller are initialized by using the self-conditioned form as defined for the Self-Conditioned [A,B,C,D] block.

Dialog Box

A-matrix(v1,v2)

A-matrix of the state-space implementation. In the case of 2D blending, the A-matrix should have four dimensions, the last two corresponding to scheduling variables v1 and v2. Hence, for example, if the A-matrix corresponding to the first entry of v1 and first entry of v2 is the identity matrix, then A(:,:,1,1) = [1 0;0 1];.

B-matrix(v1,v2)

B-matrix of the state-space implementation.

C-matrix(v1,v2)

C-matrix of the state-space implementation.

D-matrix(v1,v2)

D-matrix of the state-space implementation.

First scheduling variable (v1) breakpoints

Vector of the breakpoints for the first scheduling variable. The length of v1 should be same as the size of the third dimension of A, B, C, and D.

Second scheduling variable (v2) breakpoints

Vector of the breakpoints for the second scheduling variable. The length of v2 should be same as the size of the fourth 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.

Poles of A(v)-H(v)*C(v)

For oncoming controllers, an observer-like structure is used to ensure that the controller output tracks the current block output, u. The poles of the observer are defined in this dialog box as a vector, the number of poles being equal to the dimension of the A-matrix. Poles that are too fast result in sensor noise propagation, and poles that are too slow result in the failure of the controller output to track u.

Inputs and Outputs

The first input is the measurements.

The second and third inputs are the scheduling variables ordered conforming to the dimensions of the state-space matrices.

The output is the actuator demands.

Assumptions and Limitations

This block requires the Control Systems Toolbox.

Examples

See the autopilot in the aeroblk_HL20.mdl demo for an example of this block in use.

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 5.

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

2D Controller [A(v),B(v),C(v),D(v)]

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

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

2D Controller [A(v),B(v),C(v),D(v)]

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