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By Matthew Ellis, Jinfeng Liu, Panagiotis D. Christofides
This publication provides common equipment for the layout of monetary version predictive keep an eye on (EMPC) platforms for large periods of nonlinear platforms that handle key theoretical and useful issues together with recursive feasibility, closed-loop balance, closed-loop functionality, and computational potency. in particular, the ebook proposes:
- Lyapunov-based EMPC tools for nonlinear systems;
- two-tier EMPC architectures which are hugely computationally effective; and
- EMPC schemes dealing with explicitly uncertainty, time-varying rate services, time-delays and multiple-time-scale dynamics.
The proposed tools hire quite a few instruments starting from nonlinear platforms research, via Lyapunov-based keep watch over ideas to nonlinear dynamic optimization. The applicability and function of the proposed tools are validated via a couple of chemical technique examples.
The ebook offers state of the art equipment for the layout of monetary version predictive regulate structures for chemical processes.In addition to being mathematically rigorous, those tools accommodate key sensible concerns, for instance, direct optimization of technique economics, time-varying monetary fee features and computational potency. various reviews and feedback supplying primary knowing of the merging of technique economics and suggestions keep watch over right into a unmarried framework are incorporated. A keep an eye on engineer can simply tailor the various special examples of commercial relevance given in the textual content to a selected application.
The authors current a wealthy selection of new examine themes and references to major contemporary paintings making Economic version Predictive Control a huge resource of knowledge and thought for teachers and graduate scholars discovering the realm and for strategy engineers attracted to employing its ideas.
Read or Download Economic Model Predictive Control: Theory, Formulations and Chemical Process Applications PDF
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Additional resources for Economic Model Predictive Control: Theory, Formulations and Chemical Process Applications
Example text
F (0) = 0. If the origin is not the equilibrium point of interest, deviation variables may be introduced such that the origin of the shifted coordinate system is the equilibrium point. For example, consider the system x˙ = f (x) with an equilibrium xs = 0 ( f (xs ) = 0). 2) z˙ = f (z + xs ) =: g(z) where the equilibrium point of the shifted system is z = 0 and g(0) = 0. Within the context of the system of Eq. 1, stability of solutions is considered. In particular, the stability of the solution x ≡ 0 is considered using Lyapunov stability concepts.
17b) where x1 is the dimensionless reactant concentration, x2 is the dimensionless temperature, and A1 , A2 and x20 are constant parameters. 2. 5]. For this example, the production rate of the desired product is assumed to reflect the operating profit of the reactor, which is given by the following function: le (x, u) = k0 Cr2e f e−1/x2 x12 . , set u to u max for all time. A more interesting problem that may lead to a non-trivial solution is to determine the optimal input profile that maximizes the production rate subject to a constraint on the time-averaged amount of material that may fed to the reactor.
To achieve asymptotic stability of the origin of sampled-data system of Eq. 29, a stronger assumption is required. The following assumption and result are stated generally in the sense that no restrictions are placed on the state and input. 2 There exists a locally Lipschitz feedback controller u = h(x) with h(0) = 0 such that the vector field of the closed-loop system f (x, h(x), 0) is continuously differentiable on Rn . Furthermore, the origin of the nominal closedloop system of Eq. 18 (w ≡ 0) under the controller h(x) implemented continuously is locally exponentially stable and globally asymptotically stable.