showStateInfo
State vector map for sparse model
Syntax
Description
showStateInfo( prints a state vector map
of the sys)x or q vectors, that is, how they are
partitioned into components, interfaces, and signals.
For sparss models,
showStateInfo maps the content of the state vector x
back to individual components and internal signals. Here, Component
refers to the sub-components or sub-structures that were combined into
sys. The Signal group includes all signals flowing
between components, for example, in series or feedback connections.
For mechss models,
showStateInfo maps the content of the vector q of
generalized degrees of freedom in terms of components, interfaces, and signals. The
Interface group includes all DAE variables arising from physical
couplings between components (see interface).
Examples
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. Model Properties 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)
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
Version History
Introduced in R2020b
