Control of Homogeneous Reaction Systems using Extent-Based LPV Models

Constrained Control and Estimation of Homogeneous Reaction Systems Using Extent-Based Linear Parameter Varying Models

“…However, in this paper, we make use of the diagonal structure of the A matrix, and the physical interpretation of the parameter θ to solve eq 10. To this end, the parametric state feedback and feedforward proposed by Marquez-Ruiz et al 23 for the extentbased LPV systems is used, and this stated in the following theorem.…”

“…The proof of the Theorem 2 can be found in the work of Marquez-Ruiz et al 23 Remark 2. Note that, if γ ≠ 0, the rank(B) = p + 1, then B † = B −1 = K, where † is the Moore−Penrose pseudoinverse.…”

“…Then, if γ ≠ 0, there exist a parametric feedback gain , and a feedforward gain such that u = K­(θ)­x + v + K d d, and the closed-loop representation of the system described by eq has an equivalent LTI representation given by where ϑ are the constant desired poles of the closed-loop system, and v ∈ are the new input variable of the system. K­(θ) and K d are given by The proof of the Theorem 2 can be found in the work of Marquez-Ruiz et al…”

“…One of the key features of the extent transformation is that it allows the development of an LPV representation with a diagonal state matrix. 23 In this paper, the aforementioned LPV representation is used to propose a new MPC strategy for nonlinear homogeneous reaction systems. Given the time-varying nature of the parameter in the LPV formulation, parametric state-feedback and feed-forward laws are designed.…”

“…The extent-based representation of the process presents many advantages, such as model reduction, identification of reaction systems from measured data, parametric sensitivity analysis, model-based control, etc. One of the key features of the extent transformation is that it allows the development of an LPV representation with a diagonal state matrix …”