In this paper, a new model based nonlinear control technique, called PID
(Proportional-Integral-Derivative) type sliding surface based sliding mode
control is designed using improved reaching law. To improve the performance of
the second order nonlinear differential equations with unknown parameters
modified particle swarm intelligent optimization (MPSO) is used for the
optimized parameters. This paper throws light on the sliding surface design, on
the proposed power rate exponential reaching law, parameters optimization using
modified particle swarm optimization and highlights the important features of
adding an integral term in the sliding mode such as robustness and higher
convergence, through extensive mathematical modeling. Siding mode control law
is derived using Lyapunov stability approach and its asymptotic stability is
proved mathematically and simulations showing its validity. MPSO PID-type
Sliding mode control will stabilize the highly nonlinear systems, will
compensate disturbances and uncertainty and reduces tracking errors.
Simulations and experimental application is done on the non-linear systems and
are presented to make a quantitative comparison.Comment: arXiv admin note: substantial text overlap with arXiv:2207.1112