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A backstepping-based fault compensation scheme for a class of Euler-Bernoulli beam-ODE cascade systems. (English) Zbl 1480.93109

Summary: This paper develops a fault compensation scheme for a class of Euler-Bernoulli beam-ODE cascade systems to deal with certain boundary input faults, using a model transform-based backstepping control design. A model transformation is introduced to convert the Euler-Bernoulli beam-ODE cascade system to a Schrödinger-ODE cascade system. The FTC law is designed to compensate boundary input faults for the Schrödinger-ODE cascade system by constructing a normal intermediate system and a new exponentially stable target system. The purposes of the two-step backstepping are to bring in a state feedback and to improve the system performance. The performance of the target system, intermediate system, and Schrödinger-ODE cascade system is analysed in the Riesz basis frame. The stability analysis of the original Euler-Bernoulli beam-ODE cascade system is further provided. Simulation results illustrate the effectiveness of the proposed fault compensation scheme.

MSC:

93B35 Sensitivity (robustness)
93C20 Control/observation systems governed by partial differential equations
93C15 Control/observation systems governed by ordinary differential equations
93B52 Feedback control
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