Nonlinear Reduced-Order Observer Design for State and Disturbance Estimation

A new systematic framework for nonlinear reduced-order observer design that allows the concurrent estimation of the process state variables, together with key unknown process or sensor disturbances is proposed. From a mathematical standpoint, the problem under consideration reduces to solving a set of first-order singular PDEs along with a set of algebraic equations for which a rather general set of solvability conditions is derived. On the basis of the solution of the set of singular PDEs, a nonlinear reduced-order observer can then be designed so that both state and disturbance estimation errors converge to zero with assignable rates. The convergence properties of the proposed nonlinear reduced-order observer are tested through simulation studies in an illustrative example involving state and sensing error estimation in a biochemical reactor