We propose a new type of Proportional Integral (PI) state observer for a class of nonlinear systems in continuous time which ensures an asymptotic stable convergence of the state estimates. Approximations of nonlinearity are not necessary to obtain such results, but the functions must be, at least locally, of the Lipschitz type. The obtained state variables are exact and robust against noise. Naslin's damping criterion permits synthesizing gains in an algebraically simple and efficient way. Both the speed and damping of the observer response are controlled in this way. Model simulations based on a Sprott strange attractor are discussed as an example.
We propose a new observer where the model, decomposed in generalized canonical form of regulation described by Fliess, is dissociated from the part assuring error correction. The obtained stable exact estimates give direct access to state variables in the form of successive derivatives. The dynamic response of the observer converges exponentially, as long as the nonlinearities are locally of Lipschitz type. In this case, we demonstrate that a quadratic Lyapunov function provides a number of inequalities which guarantee at least local stability. A synthesis of gains is proposed, independent of the observation time scale. Simulations of a Düffing system and a Lorenz strange attractor illustrate theoretical developments.
The aim of this study was to increase the resistance to noise of an observer of a non-linear MISO system transformed into canonical regulation form of order n. For this, the principle idea was to add n observers on the output equations of the main observer. By adjusting the time scale of the output observers, the resistance to noise of the final estimates is considerably increased. The proposed method is illustrated by model simulations based on a non-linear Sludge Activation Model (SAM)
International audienceIn this study a new type of state observer for dynamic systems containing non-linear polynomials is proposed. The stability of the structure and also the uniform convergence of the state estimates are analyzed. The simple and efficient algebraic criteria of Naslin normal damping polynomials permit synthesis of the parameters. A series of simulations illustrates the proposed developments based on a Van der Pol equation
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