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Abstract
The paper is devoted to the numerical performance evaluation of the speed-gradient algorithms, recently developed in (Orlov et al., 2018; Orlov et al., 2019) for controlling the energy of the sine-Gordon spatially distributed systems with several in-domain actuators. The influence of the level quantization of the state feedback control signal (possibly coupled to the time sampling) on the steady-state energy error and the closed loop system stability is investigated in the simulation study. The following types of quantization are taken into account: sampling-in-time control signal quantization, the level quantization for control, continuous in time; control signal quantization on level jointly with time sampling; control signal transmission over the binary communication channel with time-invariant first order coder; control signal transmission over the binary communication channel with first order coder and time-based zooming; control signal transmission over the binary communication channel with adaptive first order coder. A resulting impact on the closed-loop performance in question is concluded for each type of the quantization involved.
Highlights
During the last years the energy control problem of spatially distributed systems has been widely studied and proper solutions have been proposed and rigorously justified
The authors of [Orlov et al, 2017b] analyzed energy control problems for linear wave partial differential equation (PDE) and nonlinear sine-Gordon PDE where the distributed yet uniform over the space control was chosen
A step is made for clarifying some of the mentioned issues, namely the effect of level quantization separately, or jointly with a time sampling, is investigated for the control signal applied to the nonlinear chain with the state feedback control, developed in [Orlov et al, 2018]
Summary
During the last years the energy control problem of spatially distributed systems has been widely studied and proper solutions have been proposed and rigorously justified. The speedgradient method was generalized to the in-domain actuation such as in [Christofides, 2001; Fridman and Blighovsky, 2012; Fridman and Am, 2013; Pisano and Orlov, 2017] for the purpose of pump/dissipate the energy of the model to a desired level. This result has been extended to control via output feedback by means of developing the Luenberger-type spatial observer, which got measurement data from the sensors, placed within small spatial plant subdomains in [Orlov et al, 2019].
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