Noninteracting Control I: Basic Principles

Abstract

Consider a multivariable system whose scalar outputs z _ij have been grouped in disjoint subsets, each having a physical significance to distinguish it from the remaining subsets. Represent the output subsets by vectors

$${z_i} = col(zi1,...,{z_{ipi}}),i \in k$$

For instance, with k = 3 and each p _i = 2, z _i could represent angular position and velocity of a rigid body relative to the ith axis of rotation. Next, suppose the system is controlled by scalar inputs u₁, …, u _m , where m ≥ k. In many applications it is desirable to partition the input set into k disjoint subsets U₁, …, U _k , such that for each i ∊ k the inputs of U _i control the output vector z _i completely, without affecting the behavior of the remaining z _j , j ≠ i. Such a control action is noninteracting, and the system is decoupled. From an input-output viewpoint decoupling splits the system into k independent subsystems. Considerable advantages may result of simplicity and reliability, especially if control is partially to be executed by a human operator.