WOLFRAM SYSTEM MODELER
StateSpaceDiscrete-time State Space block |
SystemModel["Modelica_Synchronous.RealSignals.Periodic.StateSpace"]
This block defines the state space representation of a discrete-time block with input vector u, output vector y and state vector x:
x = A * previous(x) + B * u y = C * previous(x) + D * u
where previous(x) is the value of the clocked state x at the previous clock tick. The input is a vector of length nu, the output is a vector of length ny and nx is the number of states. Accordingly
A has the dimension: A(nx,nx), B has the dimension: B(nx,nu), C has the dimension: C(ny,nx), D has the dimension: D(ny,nu)
Example:
parameter: A = [0.12, 2;3, 1.5] parameter: B = [2, 7;3, 1] parameter: C = [0.1, 2] parameter: D = zeros(ny,nu) results in the following equations: [x[1]] [0.12 2.00] [previous(x[1])] [2.0 7.0] [u[1]] [ ] = [ ]*[ ] + [ ]*[ ] [x[2]] [3.00 1.50] [previous(x[2])] [0.1 2.0] [u[2]] [previous(x[1])] [u[1]] y[1] = [0.1 2.0] * [ ] + [0 0] * [ ] [previous(x[2])] [u[2]]
nin |
Value: size(B, 2) Type: Integer Description: Number of inputs |
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nout |
Value: size(C, 1) Type: Integer Description: Number of outputs |
A |
Value: Type: Real[:,size(A, 1)] Description: Matrix A of state space model |
B |
Value: Type: Real[size(A, 1),:] Description: Matrix B of state space model |
C |
Value: Type: Real[:,size(A, 1)] Description: Matrix C of state space model |
D |
Value: zeros(size(C, 1), size(B, 2)) Type: Real[size(C, 1),size(B, 2)] Description: Matrix D of state space model |
x |
Type: Real[size(A, 1)] Description: State vector |
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u |
Type: RealInput[nin] Description: Connector of clocked, Real input signals |
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y |
Type: RealOutput[nout] Description: Connector of clocked, Real output signals |
Modelica_Synchronous.WorkInProgress.Tests |
Release Notes: