The paper presents robust design methods for the automatic control of a dam±river system, where the action variable is the upstream¯ow rate and the controlled variable the downstream¯ow rate. The system is modeled with a linear model derived analytically from simpli®ed partial derivative equations describing open-channel¯ow dynamics. Two control methods (pole placement and Smith predictor) are compared in terms of performance and robustness. The pole placement is done on the sampled model, whereas the Smith predictor is based on the continuous model. Robustness is estimated with the use of margins and also with the use of a bound on multiplicative uncertainty taking into account the model errors, due to the nonlinear dynamics of the system. Simulations are carried out on a nonlinear model of the river and performance and robustness of both controllers are compared to the ones of a continuous-time PID controller.
An extension of the classical pandemic SIRD model is considered for the regional spread of COVID-19 in France under lockdown strategies. This compartment model divides the infected and the recovered individuals into undetected and detected compartments respectively. By fitting the extended model to the real detected data during the lockdown, an optimization algorithm is used to derive the optimal parameters, the initial condition and the epidemics start date of regions in France. Considering all the age classes together, a network model of the pandemic transport between regions in France is presented on the basis of the regional extended model and is simulated to reveal the transport effect of COVID-19 pandemic after lockdown. Using the measured values of displacement of people between cities, the pandemic network of all cities in France is simulated by using the same model and method as the pandemic network of regions. Finally, a discussion on an integro-differential equation is given and a new model for the network pandemic model of each age class is provided.
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