Adaptive almost disturbance decoupling for a class of nonlinear differential-algabraic equation systems

Abstract

A class of engineering systems is modeled by Differential Algebraic Equations (DAEs), which are also known as singular, descriptor, semistate and generalized systems. In the chemical engineering processes, the differential equations are constituted by the dynamic balances of mass and energy, while the thermodynamic equilibrium relations, empirical correlations, and pseudo-steady-state conditions build the algebraic equations. The robotic systems with kinematic constraints are also modeled by DAE systems. Physical and complex plants are exposed to extraneous noises and signals such as sensor measurement noise, structural vibration and environmental disturbances. For example, the external disturbance of a wind gust on an aircraft affects its control system. The challenge of almost disturbance decoupling is to design a controller to attenuate the effect of disturbances on the output to an arbitrary degree of accuracy in the L2 gain sense. It is worth noting that some parameters of the real plants are naturally unknown due to the difficulty of measurement. For example, the damping, stiffness and friction coefficients in the dynamic equations of a constrained robotic system are difficult to measure. In this work, the problem of adaptive almost disturbance decoupling for a class of nonlinear DAE systems is investigated. The DAE system is converted to equivalent lower triangular structure by regularization and standardization algorithms and an adaptive almost disturbance decoupling controller is constructed based on adaptive backstepping technique. At the end, an application of the design procedure to a physical model is shown and the results are discussed.