Compensation of input delay that depends on delayed input

• Autores: Mamadou Diagne, Nikolaos Bekiaris Liberis, Miroslav Krstić
• Localización: Automatica: A journal of IFAC the International Federation of Automatic Control, ISSN 0005-1098, Vol. 85, 2017, págs. 362-373
• Idioma: inglés
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• Resumen

  • Abstract For nonlinear systems, we develop a PDE-based predictor-feedback control design, which compensates actuator dynamics, governed by a transport PDE with outlet boundary-value-dependent propagation velocity. Global asymptotic stability under the predictor-feedback control law is established assuming spatially uniform strictly positive transport velocity. The stability proof is based on a Lyapunov-like argument and employs an infinite-dimensional backstepping transformation that is introduced. An equivalent representation of the transport PDE/nonlinear ODE cascade via a nonlinear system with an input delay that is defined implicitly through an integral of the past input is also provided and the equivalent predictor-feedback control design for the delay system is presented. The validity of the proposed controller is illustrated applying a predictor-feedback “bang–bang” boundary control law to a PDE model of a production system with a queue. Consistent simulation results are provided that support the theoretical developments.