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This paper is concerned with the regulation control of a one-dimensionalreaction-diffusion equation in the presence of a state-delay in the reactionterm. The objective is to achieve the PI regulation of the right Dirichlettrace with a command selected as the left Dirichlet trace. The control designstrategy consists of the design of a PI controller on a finite dimensionaltruncated model obtained by spectral reduction. By an adequate selection of thenumber of modes of the original infinite-dimensional system, we show that theproposed control design procedure achieves both the exponential stabilizationof the original infinite-dimensional system as well as the setpoint regulationof the right Dirichlet trace.

Integral action for setpoint regulation control of a reaction-diffusion equation in the presence of a state delay