Modified Backstepping Algorithm and its Application to Control of Distillation Column

Abstract

A novel robust algorithm is proposed for control of plants under parametric and structural uncertainties, as well as, external bounded disturbances. The algorithm design is based on the modified backstepping approach that allows to compensate mismatched disturbances under presence of nonlinearities. The obtained results are extended to control of network systems with nonlinear agents and with nonlinear links in the presence of mismatched disturbances. Effectiveness of the proposed algorithm is demonstrated on control of a distillation column which is described by parametric and structurally uncertain differential equation in presence of external bounded disturbances. It is assumed that only scalar input and output of the distillation column are available for measurement, but not their derivatives. The developed algorithm provides output tracking of a smooth bounded reference signal with a required accuracy at a finite time. The synthesis of control algorithm is separated into ρ steps, where ρ is an upper bound of the relative degree of the distillation column model. Therefore, the dynamical order of the proposed algorithm is equal to ρ. The sufficient conditions of the closed-loop stability is formulated and proved by using methods of stability of singular perturbed differential equations and Lyapunov functions. The simulations illustrate effectiveness of the proposed algorithm and confirm analytical results.