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Adsorption equilibrium is a fundamental concept in the adsorption science and relates the equilibrium between the quantity of the adsorbed material and its concentration in the bulk phase. Several models have been proposed for prediction of adsorption equilibrium and all models depend on parameters whose values must be estimated from available experimental data. Although linear parameter estimation procedures can be used for model fitting, through transformation of available experimental data and model parameters, non-linear parameter estimation procedures lead to more reliable results and allow for direct comparison of results obtained with different adsorption equilibrium models. The main objective of this work is to present and compare different non-linear procedures for parameter estimation of adsorption equilibrium models, based on theoretical arguments and also on the numerical estimation of adsorption equilibrium parameters, using available experimental data for adsorption of methylene blue onto activated carbon. The results obtained indicate that the best parameter estimation procedure is the one that relies on available equilibrium concentrations in the bulk phase as a function of the fluid volume, adsorbent mass and initial concentrations in the bulk phase, without transformation of measured experimental values and model parameters. Besides, it is shown that parameter estimates should be obtained through proper minimization of weighted least-squares objective function, in accordance with maximum likelihood procedures.

This manuscript addresses a novel output model predictive controller design for a representative model of continuous stirred-tank reactor (CSTR) and axial dispersion reactor with recycle. The underlying model takes the form of ODE-PDE in series and it is operated at an unstable point. The model predictive controller (MPC) design is explored to achieve optimal closed-loop system stabilization and to account for naturally present input and state constraints. The discrete representation of the system is obtained by application of the structure properties (stability, controllability and observability) preserving Cayley-Tustin discretization to the coupled system. The design of a discrete Luenberger observer is also considered to accomplish the output feedback MPC realization. Finally, the simulations demonstrate the performance of the controller, indicating proper stabilization and constraints satisfaction in the closed loop.

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This manuscript addresses the regulator design in the discrete-time setting for the unstable linearized Saint–Venant–Exner model, which describes the dynamics of a sediment-filled water canal. The proposed regulator ensures the closed-loop stability and proper tracking of polynomial and periodic reference signals using output feedback in a sample-data setting. To design this regulator, the system discrete representation is achieved by the application of the structure-preserving Cayley-Tustin time discretization and the direct relation with the regulator in the continuous-time setting is shown. The regulator design in the continuous-time setting is developed using the backstepping methodology ensuring the closed-loop stability and the observer design, while the Sylvester equations are solved to achieve proper tracking. Finally, the numerical simulation results are presented to show the performance of the regulator.