Observer design for a class of parabolic PDE via sliding modes and backstepping

The observer design for partial differential equations has so far been an open problem. In this paper, an observer design for systems with distributed parameters using sliding modes theory and backstepping-like procedure in order to achieve exponential convergence is presented. Such an observer is built using the knowledge available within and throughout an integral transformation of Volterra with the output injection functions. The gains of the observer, which are attained by solving a partial differential equations system with output injection, will guarantee the exponential convergence of the observer. The design method is applied to an epidemic system to consider the sensitive population S.

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Guaranteed cost fuzzy state observer design for semilinear parabolic PDE systems under pointwise measurements

Automatica ◽

10.1016/j.automatica.2017.07.026 ◽

2017 ◽

Vol 85 ◽

pp. 53-60 ◽

Cited By ~ 16

Author(s):

Huai-Ning Wu ◽

Huan-Yu Zhu

Keyword(s):

State Observer ◽

Observer Design ◽

Guaranteed Cost ◽

Parabolic Pde ◽

Pde Systems ◽

Fuzzy State ◽

Semilinear Parabolic ◽

Fuzzy State Observer

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Efficient Sensorless Speed Estimation of Electrical Servo Drives Using a Full-Order Nonsingular Terminal Sliding Mode Observer

Mathematical Problems in Engineering ◽

10.1155/2021/8175848 ◽

2021 ◽

Vol 2021 ◽

pp. 1-8

Author(s):

Tan-No Nguyen ◽

Thanh-Binh Pham ◽

Van-Trong Hoang ◽

Tan-Tien Nguyen ◽

Viet-Long Nguyen ◽

...

Keyword(s):

Sliding Mode ◽

Motor Drives ◽

Sliding Mode Observer ◽

Observer Design ◽

Speed Estimation ◽

Sliding Modes ◽

Terminal Sliding Mode ◽

Nonsingular Terminal Sliding Mode ◽

Dc Motor Drives ◽

Servo Drives

This paper proposes an efficient sensorless speed estimation approach for electric servo drives based on the full-order nonsingular terminal sliding mode observer (FONTSM) with the application of DC motor drives. In this method, a specific full-order terminal sliding mode manifold is utilised for the observer design which results in the elimination of the chattering and avoiding the singularity phenomenon of conventional and terminal sliding modes. Here, speed and armature back emf can be directly estimated from the relevant observer’s inputs which are continuous instead of being discontinuous high-frequency “switching” signals. The efficiencies and advantages of this approach have been proven and validated in both simulation and experimental results.

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