xsort
Syntax
Description
sorts
the xsys
= xsort(sys
)x
or q
vector based on the state partition.
Signal-based connections and physical interfaces between model components gives rise to
differential algebraic equation (DAE) models where some internal signals and forces become
extra states. The StateInfo
property of sparss
and
mechss
model
objects keeps track of the state partition into sub-components, interface variables, and
signal variables.
Examples
Sparse Second-Order Model in a Feedback Loop
For this example, consider sparseSOSignal.mat
that contains a sparse second-order model. Define an actuator, sensor, and controller and connect them together with the plant in a feedback loop.
Load the sparse matrices and create the mechss
object.
load sparseSOSignal.mat plant = mechss(M,C,K,B,F,[],[],'Name','Plant');
Next, create an actuator and sensor using transfer functions.
act = tf(1,[1 0.5 3],'Name','Actuator'); sen = tf(1,[0.02 7],'Name','Sensor');
Create a PID controller object for the plant.
con = pid(1,1,0.1,0.01,'Name','Controller');
Use the feedback
command to connect the plant, sensor, actuator, and controller in a feedback loop.
sys = feedback(sen*plant*act*con,1)
Sparse continuous-time second-order model with 1 outputs, 1 inputs, and 7111 degrees of freedom. Use "spy" and "showStateInfo" to inspect model structure. Type "help mechssOptions" for available solver options for this model.
The resultant system sys
is a mechss
object since mechss
objects take precedence over all other model object types.
Use showStateInfo
to view the component and signal groups.
showStateInfo(sys)
The state groups are: Type Name Size ------------------------------- Component Sensor 1 Component Plant 7102 Signal 1 Component Actuator 2 Signal 1 Component Controller 2 Signal 1 Signal 1
Use xsort
to sort the components and signals, and then view the component and signal groups.
sysSort = xsort(sys); showStateInfo(sysSort)
The state groups are: Type Name Size ------------------------------- Component Sensor 1 Component Plant 7102 Component Actuator 2 Component Controller 2 Signal 4
Observe that the components are now ordered before the signal partition. The signals are now sorted and grouped together in a single partition.
You can also visualize the sparsity pattern of the resultant system using spy
.
spy(sysSort)
Physical Connections Between Components in Sparse Second-Order Model
For this example, consider a structural model that consists of two square plates connected with pillars at each vertex as depicted in the figure below. The lower plate is attached rigidly to the ground while the pillars are attached rigidly to each vertex of the square plate.
Load the finite element model matrices contained in platePillarModel.mat
and create the sparse second-order model representing the above system.
load('platePillarModel.mat') model = ... mechss(M1,[],K1,B1,F1,'Name','Plate1') + ... mechss(M2,[],K2,B2,F2,'Name','Plate2') + ... mechss(Mp,[],Kp,Bp,Fp,'Name','Pillar3') + ... mechss(Mp,[],Kp,Bp,Fp,'Name','Pillar4') + ... mechss(Mp,[],Kp,Bp,Fp,'Name','Pillar5') + ... mechss(Mp,[],Kp,Bp,Fp,'Name','Pillar6'); sys = model;
Use showStateInfo
to examine the components of the mechss
model object.
showStateInfo(sys)
The state groups are: Type Name Size ---------------------------- Component Plate1 2646 Component Plate2 2646 Component Pillar3 132 Component Pillar4 132 Component Pillar5 132 Component Pillar6 132
Now, load the interfaced degree of freedom (DOF) index data from dofData.mat
and use interface
to create the physical connections between the two plates and the four pillars. dofs
is a 6x7
cell array where the first two rows contain DOF index data for the first and second plates while the remaining four rows contain index data for the four pillars. By default, the function uses dual-assembly method of physical coupling.
load('dofData.mat','dofs') for i=3:6 sys = interface(sys,"Plate1",dofs{1,i},"Pillar"+i,dofs{i,1}); sys = interface(sys,"Plate2",dofs{2,i},"Pillar"+i,dofs{i,2}); end
Specify connection between the bottom plate and the ground.
sysConDual = interface(sys,"Plate2",dofs{2,7});
Use showStateInfo
to confirm the physical interfaces.
showStateInfo(sysConDual)
The state groups are: Type Name Size ----------------------------------- Component Plate1 2646 Component Plate2 2646 Component Pillar3 132 Component Pillar4 132 Component Pillar5 132 Component Pillar6 132 Interface Plate1-Pillar3 12 Interface Plate2-Pillar3 12 Interface Plate1-Pillar4 12 Interface Plate2-Pillar4 12 Interface Plate1-Pillar5 12 Interface Plate2-Pillar5 12 Interface Plate1-Pillar6 12 Interface Plate2-Pillar6 12 Interface Plate2-Ground 6
You can use spy
to visualize the sparse matrices in the final model.
spy(sysConDual)
Now, specify physical connections using the primal-assembly method.
sys = model; for i=3:6 sys = interface(sys,"Plate1",dofs{1,i},"Pillar"+i,dofs{i,1},'primal'); sys = interface(sys,"Plate2",dofs{2,i},"Pillar"+i,dofs{i,2},'primal'); end sysConPrimal = interface(sys,"Plate2",dofs{2,7},'primal');
Use showStateInfo
to confirm the physical interfaces.
showStateInfo(sysConPrimal)
The state groups are: Type Name Size ---------------------------- Component Plate1 2646 Component Plate2 2640 Component Pillar3 108 Component Pillar4 108 Component Pillar5 108 Component Pillar6 108
Primal assembly eliminates half of the redundant DOFs associated with the shared set of DOFs in the global finite element mesh.
You can use spy
to visualize the sparse matrices in the final model.
spy(sysConPrimal)
The data set for this example was provided by Victor Dolk from ASML.
Input Arguments
Output Arguments
xsys
— Sparse state-space model with sorted components
sparss
model object | mechss
model object
Sparse state-space model with sorted components, returned as a sparss
or
mechss
model object. In the sorted xsys
, all components appear first,
followed by the interfaces, and then followed by a single group of all internal signals.
The matrices and have the following block arrow structure:
Here, each diagonal block is a sub-component of sys
. The last
row and column combines the Interface
and Signal
groups to capture all couplings and connections between components.
Version History
Introduced in R2020b
See Also
sparss
| mechss
| interface
| showStateInfo
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