Integral control by variable sampling based on steady-state data.

*(English)*Zbl 1016.93044The 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.

Reviewer: Svitlana P.Rogovchenko (Famagusta)

##### 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) |

##### Keywords:

sampled-data systems; integral control; adaptive sampling; infinite-dimensional control systems; steady-state gain matrix; step response data; robustness; diffusion equation
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\textit{N. Özdemir} and \textit{S. Townley}, Automatica 39, No. 1, 135--140 (2003; Zbl 1016.93044)

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