.Modelica.Clocked.RealSignals.Periodic.StateSpace

Information

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]]

Revisions

Release Notes:

• August 13, 2012 by Bernhard Thiele:
  Used the code from Blocks.Discrete.StateSpace and converted it into the Modelica 3.3 clocked equation style.