By Matthew Ellis, Jinfeng Liu, Panagiotis D. Christofides
This ebook provides normal equipment for the layout of monetary version predictive keep an eye on (EMPC) structures for extensive sessions of nonlinear structures that tackle key theoretical and functional concerns together with recursive feasibility, closed-loop balance, closed-loop functionality, and computational potency. in particular, the ebook proposes:
- Lyapunov-based EMPC equipment for nonlinear systems;
- two-tier EMPC architectures which are hugely computationally effective; and
- EMPC schemes dealing with explicitly uncertainty, time-varying expense capabilities, time-delays and multiple-time-scale dynamics.
The proposed tools hire quite a few instruments starting from nonlinear structures research, via Lyapunov-based keep an eye on thoughts to nonlinear dynamic optimization. The applicability and function of the proposed tools are confirmed via a couple of chemical approach examples.
The publication provides cutting-edge tools for the layout of monetary version predictive keep an eye on platforms for chemical processes.In addition to being mathematically rigorous, those equipment accommodate key useful matters, for instance, direct optimization of approach economics, time-varying fiscal price services and computational potency. various reviews and comments offering primary figuring out of the merging of strategy economics and suggestions keep an eye on right into a unmarried framework are integrated. A keep watch over engineer can simply tailor the numerous particular examples of business relevance given in the textual content to a particular application.
The authors current a wealthy number of new learn issues and references to major contemporary paintings making Economic version Predictive Control a major resource of knowledge and idea for lecturers and graduate scholars discovering the world and for method engineers attracted to making use of its ideas.
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Extra resources for Economic Model Predictive Control: Theory, Formulations and Chemical Process Applications
4. 20 yields the best performance (Fig. 4). 30 percent better than the performance at the optimal steady-state. 96 achieve worse performance compared to that at steady-state. The state, input, and B T λ = b1T λ = λ1 + λ3 /τ trajectories are given in Fig. 5 over one period. From Fig. 5, the input trajectory satisfies the necessary condition of Eq. 26. From these results, timevarying operation is better than steady-state operation from an economical point of view for this example. If the average constraint of Eq.
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.
For every other interval, the proof is similar. If x(0) = 0, then Eq. 38 trivially holds (since x(t) = 0 for t ∈ [0, t1 )). Therefore, consider the case when x(0) = 0. The proof is made by contradiction. Suppose that there exists t ∈ [0, t1 ) with ∂ V (x(t)) q f (x(t), h(x(0)), 0) > − |x(t)|2 . ∂x 2 The case that x(t) is not defined for some t ∈ [0, t1 ) is also covered by this assumption. Define a := inf t ∈ [0, t1 ) : ∂ V (x(t)) q f (x(t), h(x(0)), 0) > − |x(t)|2 . ∂x 2 A standard continuity argument in conjunction with the fact that ∂ V (x(0)) q f (x(0), h(x(0)), 0) ≤ −μ|x(0)|2 < − |x(0)|2 ∂x 2 shows that a ∈ (0, t1 ) and that q ∂ V (x(t)) f (x(t), h(x(0)), 0) ≤ − |x(t)|2 ∂x 2 for all t ∈ [0, a] with (∂ V (x(a))/∂ x) f (x(a), h(x(0)), 0) = − q2 |x(a)|2 .
Economic Model Predictive Control: Theory, Formulations and Chemical Process Applications by Matthew Ellis, Jinfeng Liu, Panagiotis D. Christofides