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Integral control by variable sampling based on steady-state data. (English) Zbl 1016.93044
The authors are concerned with the continuous-time, infinite-dimensional $$m$$-input, $$m$$-output system $\dot{x}(t)=Ax(t)+Bu(t),\quad x(0)\in X,\qquad y(t)=Cx(t),$ where $$A$$ is the generator of an exponentially stable semigroup $$T(t),$$ the input operator $$B$$ is potentially unbounded, but it is assumed that $$A^{-1}B$$ is bounded, and the output operator $$C$$ is bounded. A sampled-data integral control approach with fixed integrator gain and convergent adaptive sampling is used. Using the sampling period as a parameter for adaptation, the authors determine appropriate integrator gains based on knowledge of step response data. They investigate robustness of the choice of the integrator gain $$K$$ with respect to uncertainty in experimental measurement of the steady-state gain and show how to select the gain robustly. The results are illustrated by a simple two-input, two-output example of a diffusion equation with point actuators and spatially distributed sensors.

##### MSC:
 93C57 Sampled-data control/observation systems 93C25 Control/observation systems in abstract spaces 93C20 Control/observation systems governed by partial differential equations 93C40 Adaptive control/observation systems 93B35 Sensitivity (robustness)
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