Robust Compensation of Delay and Diffusive Actuator Dynamics Without Distributed Feedback

[EN] This paper deals with robust observer-based output-feedback stabilization of systems whose actuator dynamics can be described in terms of partial differential equations (PDEs). More specifically, delay dynamics (first-order hyperbolic PDE) and diffusive dynamics (parabolic PDE) are considered. The proposed controllers have a PDE observer-based structure. The main novelty is that stabilization for an arbitrarily large delay or diffusion domain length is achieved, while distributed integral terms in the control law are avoided. The exponential stability of the closed loop in both cases is proved using Lyapunov functionals, even in the presence of small uncertainties in the time delay or the diffusion coefficient. The feasibility of this approach is illustrated in simulations using a second-order plant with an exponentially unstable mode.This work was supported in part by Project TIN2017-86520-C3-1-R, Ministerio de Economia y Competitividad, in part by the 16/17 UPV Mobility Award, and in part by the FPI-UPV 2014 Ph.D. Grant, Universitat Politecnica de Valencia, Spain.Sanz Diaz, R.; García Gil, PJ.; Krstic, M. (2019). Robust Compensation of Delay and Diffusive Actuator Dynamics Without Distributed Feedback. IEEE Transactions on Automatic Control. 64(9):3663-3675. https://doi.org/10.1109/TAC.2018.2887148S3663367564