Model Predictive Control Toolbox    
mod format

The MPC mod format is a compact way to store the model of a linear system for subsequent use in the MPC Toolbox functions.

Description

Consider the process shown in the above block diagram. Its discrete-time LTI state-space representation is:

where x is a vector of n state variables, u represents the nu manipulated variables, d represents nd measured but freely-varying inputs (i.e., measured disturbances), w represents nw unmeasured disturbances, y is a vector of ny plant outputs, z is measurement noise, and , u, etc., are constant matrices of appropriate size. The variable (k) represents the plant output before the addition of measurement noise. Define:

           = [u d w]

    D = [Du Dud Dw]

In some cases one would like to include nym measured and nyu unmeasured outputs in y, where nym + nyu = ny. If so, the mod format assumes that the y vector and the C and D matrices are arranged such that the measured outputs come first, followed by the unmeasured outputs.

The mod format is a single matrix that contains the , , C, and D matrices, plus some additional information. Let M be the mod representation of the above system. Its overall dimensions are:

The minfo vector is the first seven elements of the first row in M. The elements of minfo are:

minfo (1)
T, the sampling period used to create the model.
(2)
n, the number of states.
(3)
nu, the number of manipulated variable inputs.
(4)
nd, the number of measured disturbances.
(5)
 nw, the number of unmeasured disturbances.
(6)
nym, the number of measured outputs.
(7)
nyu, the number of unmeasured outputs.

The remainder of M contains the discrete state-space matrices:

F in rows 2 to n + 1
columns 2 to n + 1
in rows 2 to n + 1
columns n + 2 to n + nu +nd + nw + 1
C in rows n + 2 to n + ny + 1
columns 2 to n + 1
D in rows n + 2 to n + ny + 1
columns n + 2 to n + nu +nd + nw + 1

Notes
Since the minfo vector requires seven columns, this is the minimum possible number of columns in the mod format, regardless of the dimensions of the state-space matrices.

Also, the first column is reserved for other uses by MPC Toolbox routines. Thus the state-space matrices start in column 2, as described above.

In order for the mpcinfo routine to recognize matrices in the MPC mod format, the (2,1) element is set to NaN (Not-a-Number).

Example
See ss2mod for a mod format example.

See Also
mod2ss, mod2step, step format, mpcinfo, ss2mod, step, tfd2mod, tf format, th2mod, theta format


mlr mod2frsp, varying format