3D Observer Form [A(v),B(v),C(v),F(v),H(v)]
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A linear switched state-space controller with three variable parameters (scheduling variable) with a state observer.
Description
Block 3D Observer Form [A(v),B(v),C(v),F(v),H(v)] implements a linear switched regulator in the state space with three variable parameters with a state observer 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-y_dem
—
control error
vector
Details
The control error given as a vector that corresponds to the dimensions of the state-space matrices.
| 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. It is a parameter that defines 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. It is a parameter that determines how the system should adapt its parameters in response to changing conditions.
| Data types |
|
| Complex numbers support |
No |
#
v3
—
third planning variable
`vector'
Details
A third planning variable given as a vector that corresponds to the dimensions of the state-space matrices. It is a parameter that determines how the system should adapt its parameters in response to changing conditions.
| Data types |
|
| Complex numbers support |
No |
#
u_meas
—
measured position of the actuator
``
Details
The measured position of the actuator, given as a vector. Helps to correct the state estimation by taking into account the actual behaviour of the actuator.
| Data types |
|
| Complex numbers support |
No |
Output
#
u_dem
—
control signal
scalar | vector
Details
Control signal to the actuator.
| Data types |
|
| Complex numbers support |
No |
Parameters
Parameters
# A-matrix(v1,v2,v3): — matrix A of state space realisation
Details
A state space realisation matrix. In the case of three-dimensional planning, the matrix should have five dimensions, the last three of which correspond to the planning variables v1,v2 and v3. For example, if -matrix corresponding to the first element of v1,the first element of v2 and the first element of v3 is a unit matrix, then A[:,::,1,1,1,1] = [1.0 0 0.0;0.0 1.0].
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
# B-matrix(v1,v2,v3): — matrix B of state space realisation
Details
State space realisation matrix. In the case of three-dimensional planning, the matrix should have five dimensions, the last three of which correspond to the planning variables v1,v2 and v3. For example, if -matrix corresponding to the first element of v1,the first element of v2 and the first element of v3 is a unit matrix, then B[:,::,1,1,1,1] = [1.0 0 0.0;0.0 1.0].
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
# C-matrix(v1,v2,v3): — matrix C of state space realisation
Details
State space realisation matrix. In the case of three-dimensional planning, the matrix should have five dimensions, the last three of which correspond to the planning variables v1,v2 and v3. For example, if -matrix corresponding to the first element of v1,the first element of v2 and the first element of v3 is a unit matrix, then C[:,::,1,1,1,1] = [1.0 0 0.0;0.0 1.0].
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
# F-matrix(v1,v2,v3): — matrix F of state space realisation
Details
The feedback matrix of the state observer. In the case of three-dimensional planning, the matrix should have five dimensions, the last three of which correspond to the planning variables v1,v2 and v3. For example, if -matrix corresponding to the first element of v1,the first element of v2 and the first element of v3 is a unit matrix, then F[:,::,1,1,1,1] = [1.0 0 0.0;0.0 1.0].
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
# H-matrix(v1,v2,v3): — state space realisation matrix H
Details
State Observer Matrix. In the case of three-dimensional planning, the matrix should have five dimensions, the last three of which correspond to the planning variables v1,v2 and v3. For example, if -matrix corresponding to the first element of v1,the first element of v2 and the first element of v3 is a unit matrix, then H[:,::,1,1,1,1] = [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 (v1)
Details
The control points of the first planning variable defined as a vector. The length of v1 must match 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 (v2)
Details
Control points of the second planning variable defined as a vector. The length of v2 must match the size of the fourth dimension , , , and .
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
# Third scheduling variable (v3) breakpoints: — control points of the third planning variable (v3)
Details
Control points of the third planning variable defined as a vector. The length of v3 must match the size of the fifth 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 |