Underlying algorithms for designing multivariable
decoupling and multiloop PI/PID controllers
in a sequential fashion are addressed. A single-loop technique,
composed of biased relay
identification schemes and tuning formulae leading to the minimum
weighted integral of square
error, is developed to tune each loop in the predetermined sequence of
loop closing. The proposed
tuning technique is appropriate for a wide range of process dynamics in
a multivariable
environment. A method is then proposed to design decouplers to
compensate for the effect of
interactions and tune the resultant weakly interacting, single-loop
PI/PID controllers sequentially. The decouplers, together with the single-loop controllers,
constitute the multivariable
decoupling controller. If the interactions are not significant,
multiloop PI/PID controllers, which
do not incorporate decouplers, could be employed. Simulation and
comparative results are shown
for one 2 × 2 and one 3 × 3 multivariable system from the
literature. Despite its simplicity,
the proposed design method yields superior multivariable designs on the
basis of performance,
robust stability, and integrity.