Model predictive control-based robust stabilization of a chemical reactor

The paper addresses an approach to robust stabilization of chemical continuous stirred tank reactors. State feedback was used for the stabilization and the feedback controller was designed using the robust model-based predictive control algorithm in which the symmetric constraints on input and output variables are taken into account. The known strategy was modified by adding integral action to the controller. Parameters of robust feedback controllers with and without integral action were found as solutions of a constrained optimization problem solved on the infinite prediction horizon. The possibility to stabilize chemical reactors with uncertainty using the robust model-based predictive control has been verified by simulations and compared with the optimal linear quadratic control and the model-based predictive control. The obtained results confirm that the robust model-based predictive control provides better results than other approaches.     

Essential oil composition of Cachrys cristata--a rare and endangered species in the flora of Serbia

Cachrys cristata DC. (Apiaceace) is a rare and critically endangered species in the flora of Serbia. Essential oil isolated by hydrodistillation from the aerial parts and fruits of this species was analyzed using combined GC and GC/MS. The oil from the aerial parts was rich in sesquiterpenes (45.7%) and oxygenated sesquiterpenes (32.9%), while the fruit oil consisted of a higher percentage of sesquiterpenes (48.3%) and oxygenated sesquiterpenes (36.7%). The dominant constituents in the oil from aerial parts were phytol (13.1%) and germacrene D (12.9%), while in the fruit oil suberosin (19.7%) and germacrene D (12.3%) were the most abundant.     

Orthogonal Polynomials for Modified Chebyshev Measure of the First Kind

Given numbers \({n,s \in \mathbb{N}}\), \({n \geq 2}\), and the \({n}\)th-degree monic Chebyshev polynomial of the first kind \({\widehat T_n(x)}\), the polynomial system “induced” by \({\widehat T_n(x)}\) is the system of orthogonal polynomials \({\{p_{k}^{n,s} \}}\) corresponding to the modified measure \({d \sigma^{n,s}(x)=\widehat T^{2s}_n(x) d\sigma(x)}\), where \({d\sigma(x)=1/\sqrt{1-x^{2}}dx}\) is the Chebyshev measure of the first kind. Here we are concerned with the problem of determining the coefficients in the three-term recurrence relation for the polynomials \({p^{n,s}_{k}}\). The desired coefficients are obtained analytically in a closed form.