This paper presents the novelty on a nonlinear proportional
integral
derivative (NPID) controller developed from the gain values obtained
using the Lyapunov-based nonlinear model predictive controller (LyNMPC).
The tuning parameters of the proposed controller are taken from the
dynamics of the nonlinear system, and these parmeters are dynamic
with their value varying according to the error in the system. In
this article, the authors have considered two highly nonlinear systems,
namely, batch polymerization reactor and quadrotor unmanned aerial
vehicle systems. The nonlinear mathematical modeling of the batch
reactor as well as the quadrotor system considered from the past literature
of authors. The acrylamide polymerization reaction under consideration
is an exothermic reaction, thereby making the temperature profile
tracking and control a challenging task. The primary aim of this article
is to develop the NPID controller based on the LyNMPC algorithm and
to validate the NPID on a batch reactor bench-scale plant and on an
hardware-in-the-loop platform for the quadrotor hardware. A comparative
study of trajectory tracking and control capabilities of LyNMPC on
derived non-linear models of the batch reactor and quadrotor system
is presented. The system mathematical models are obtained with the
help of the first-principle energy balance equation for the batch
reactor and with the nonlinear dynamics of the quadrotor which is
derived based on Newton–Euler formulations. With LyNMPC, the
stability of the nonlinear systems can be improved because the error
sensitivity is considered in the cost function.