Hybrid simulation of adaptive open loop control for parabolic systems

The “adaptive open loop control” is a compromise between the open loop and the closed loop controls. It consists in estimating the state of the system periodically in such a way that the control can be corrected, taking into account the estimated state, the final desired state and the criterion to be minimized. For a hybrid simulation, a linear parabolic system has been considered, with homogeneous boundary conditions and unknown initial condition. The purpose is to reach, in a finite time, a desired state profile, by minimising an energy criterion. The control is applied through a finite number of actuators (pointwise or by zones); the observation is made through a finite number of sensors. By using the eigenfunction method, it is possible to transform the original model into an infinite dimension set of decoupled ordinary differential equations. A hybrid simulation was carried out in real time, involving a truncated differential system simulated on the analog computer; the state estimation and the control being computed on the digital computer.