Squaring down plant model and I/O grouping strategies for a dynamic decoupling of left-invertible MIMO plants

Abstract

Abstract.In the paper problems with dynamic decoupling of the left-invertible multi-input multi-output dynamic (MIMO) linear time invariant plants using a squaring down technique are considered. The procedure of squaring down the plant model and grouping of plant inputs and outputs are discussed. The final part of the paper includes a few examples of different strategies of synthesis of a decoupled system along with conclusions and final remarks.

Canonical Structure Transitions of System Pencils

“…By neglecting this redundant input, we get a non-square system with one more output than inputs (m < p) that cannot be diagonally decoupled. However, (as we will see) the perturbed systems are all left invertible so they may (but not for sure) be block decoupled [14,30]. Notably, all nodes in Figure 2 with one L 0 block correspond to a system with one redundant input.…”

“…To illustrate how the stratification can be used we consider a decoupling example with input failure taken from [14]. Our intention of studying this example is not to solve the problem of decoupling.…”

“…Both these systems are controllable and can be block decoupled; they belong to the bundle L 3 ⊕L 2 ⊕L 0 in Figure 3. Failure in the third input results in a system that is still left invertible with the canonical form L 0 ⊕L T 3 ⊕2N 2 (codimension 12 in Figure 2), but it is uncontrollable with the canonical form 2L 2 ⊕ L 0 ⊕ J 1 (−1) and thus it is not possible to decouple the system [14].…”

Effective Use of MPC for Dynamic Decoupling of MIMO Systems

“…u N  sampling times, respectively. The plant model (13) has been discretized with the sampling time equal to 1 second.…”