Synthesis of linear, multivariable feedback control systems

A multivariable controlled process or plant is one in which there are
n
independent inputs and
m
outputs with
n > 1
and
m \leq n
. A control problem may exist for one or two principal reasons. 1) The plant parameters may vary or they may be only vaguely known, and the system response sensitivity to the parameter variation is to be reduced. 2) The system response to disturbances is to be reduced. A synthesis procedure for attaining these objectives and simultaneously realizing a desired set of system transmission functions is developed in this paper. The role of system configuration is considered. Design is broken up into two separate regions. In the significant system-response frequency region, there is straightforward synthesis in attaining the design objectives. In the higher frequency range, the loop transmission must be shaped so that the system is stable. The latter problem is considerably more difficult when there are substantial plant parameter variations. Some procedures are illustrated by two detailed examples (
n=m=2
in one example, and
n=3, m =2
in the second) in which there are large plant parameter variations.