2D Controller [A(v),B(v),C(v),D(v)]
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A linear switched state-space controller with two variable parameters (scheduling variable).
Description
Block 2D Controller [A(v),B(v),C(v),D(v)] implements a linear switched state-space controller with two variable parameters defined by Eq:
where is the scheduling variable, depending on which , , and are defined. This type of controller assumes that the matrices , , and vary smoothly depending on , which is common in the aerospace industry.
The output of this block produces a control signal that can be applied to the drive unit.
Limitations
If the input parameters of the block are outside the valid range, they are truncated. The state space matrices are not interpolated outside the valid range.
Ports
Input
#
y
—
measured values of the aircraft
vector
Details
A vector of measured aircraft quantities, meaning any measured quantities related to the state of the aircraft that are used to adjust control signals.
| Data types |
|
| Complex numbers support |
No |
#
v1
—
first planning variable
`vector
Details
The first planning variable, given as a vector that corresponds to the dimensions of the state-space matrices. This variable determines how the system should adapt its parameters in response to changing conditions.
| Data types |
|
| Complex numbers support |
No |
#
v2
—
second planning variable
`vector'
Details
A second planning variable given as a vector that corresponds to the dimensions of the state-space matrices. This variable determines how the system should adapt its parameters in response to changing conditions.
| Data types |
|
| Complex numbers support |
No |
Output
#
u
—
control signal
scalar | vector
Details
Control signal.
| Data types |
|
| Complex numbers support |
No |
Parameters
Parameters
# A-matrix(v1,v2): — matrix A of state space realisation
Details
A state-space realisation matrix. In the case of bivariate planning, the A-matrix must have four dimensions, the last two of which correspond to the planning variables v1 and v2. For example, if -matrix corresponding to the first element of v1 and the first element of v2 is a unit matrix, then A[:,::,1,1] = [1.0 0 0.0; 0.0 1.0].
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
# B-matrix(v1,v2): — matrix B of state space realisation
Details
State space realisation matrix. In the case of bivariate planning, -matrix must have four dimensions, the last two of which correspond to the planning variables v1 and v2. For example, if the -matrix corresponding to the first element of v1 and the first element of v2 is a unit matrix, then B[:,::,1,1] = [1.0 0 0.0; 0.0 1.0].
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
# C-matrix(v1,v2): — matrix C of state space realisation
Details
State space realisation matrix. In the case of bivariate planning, -matrix must have four dimensions, the last two of which correspond to the planning variables v1 and v2. For example, if the -matrix corresponding to the first element of v1 and the first element of v2 is a unit matrix, then C[:,::,1,1] = [1.0 0 0.0; 0.0 1.0].
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
# D-matrix(v1,v2): — matrix D of state space realisation
Details
State space realisation matrix. In the case of bivariate planning, -matrix must have four dimensions, the last two of which correspond to the planning variables v1 and v2. For example, if the -matrix corresponding to the first element of v1 and the first element of v2 is a unit matrix, then D[:,::,1,1] = [1.0 0 0.0; 0.0 1.0]
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
# First scheduling variable (v1) breakpoints: — control points of the first planning variable
Details
Control points of the first planning variable given as a vector. The length v1 must coincide with the size of the third dimension , , and .
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
# Second scheduling variable (v2) breakpoints: — control points of the second planning variable
Details
The control points of the second planning variable given as a vector. The length v2 must coincide with the size of the fourth dimension , , and .
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
# Initial state, x_initial: — initial states
Details
The initial states for the controller, such as the initial values of the state vector, x, are specified as a vector. The length of the vector must correspond to the size of the first dimension .
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |