  In chemical process applications, model predictive control effectively deals
with input and state constraints during transient operations. However,
industrial PID controllers directly manipulates the actuators, so they play the
key role in small perturbation robustness. This paper considers the problem of
augmenting the commonplace PID with the constraint handling and optimization
functionalities of MPC. First, we review the MPC framework, which employs a
linear feedback gain in its unconstrained region. This linear gain can be any
preexisting multiloop PID design, or based on the two stabilizing PI or PID
designs for multivariable systems proposed in the paper. The resulting
controller is a feedforward PID mapping, a straightforward form without the
need of tuning PID to fit an optimal input. The parametrized solution of MPC
under constraints further leverages a familiar PID gain scheduling structure.
Steady state robustness is achieved along with the PID design so that
additional robustness analysis is avoided.
