Download Assessment and Future Directions of Nonlinear Model by Eduardo F. Camacho, Carlos Bordons (auth.), Dr.-Ing. Rolf PDF

By Eduardo F. Camacho, Carlos Bordons (auth.), Dr.-Ing. Rolf Findeisen, Prof. Dr. Frank Allgöwer, Prof. Dr. Lorenz T. Biegler (eds.)

Thepastthree decadeshaveseenrapiddevelopmentin the areaofmodelpred- tive keep watch over with appreciate to either theoretical and alertness points. Over those 30 years, version predictive keep watch over for linear platforms has been greatly utilized, particularly within the sector of method regulate. although, today’s purposes usually require using the method over a large zone and shut to the limits of - erability, whereas enjoyable constraints and attaining near-optimal functionality. for that reason, the appliance of linear regulate equipment doesn't continually bring about passable functionality, and right here nonlinear equipment has to be hired. this is often one of many the explanation why nonlinear version predictive keep an eye on (NMPC) has - joyed signi?cant realization during the last years,with a few contemporary advances on either the theoretical and alertness frontier. also, the common availability and gradually expanding energy of today’s desktops, in addition to the advance of especially adapted numerical resolution equipment for NMPC, convey thepracticalapplicabilityofNMPCwithinreachevenforveryfastsystems.This has ended in a sequence of recent, interesting advancements, in addition to new demanding situations within the quarter of NMPC.

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Extra resources for Assessment and Future Directions of Nonlinear Model Predictive Control

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It may be best to choose them from a range and that range possibly depends on the system and the other MPC related design parameters such as , g, and N . In the logic case, Hybrid MPC: Open-Minded but Not Easily Swayed 29 it is in general not trivial to obtain functions V q , but it is true that a larger µ will yield more robustness to measurement error, or at least it will not degrade robustness. However, the larger µ, the longer it may take for the closed loop to converge to the desired attractor.

F (x, u) = φ(T ) where φ(·) is the solution of x˙ = F (x, vu (x)) starting at φ(0) = x. We can now use MPC to decide the swing-up strategy. We construct the stage cost for standard MPC by adding the kinetic and potential energy of the pendulum. We also include a term in the stage cost that penalizes the control law during the continuous-time horizon to avoid large control efforts. The cost function is periodic in x1 with period 2π and therefore, there exists a surface on the state space x1 − x2 where on one side the algorithm tries to reach the upright position rotating the pendulum clockwise and on the other side rotating the pendulum counterclockwise.

Where α ¯ := maxq {αq }. Therefore if we adopt V (x, q) := V q (x) as the Lyapunov function for our closed loop generated by the logic algorithm we can write ¯ |e| V (f (x, κθ(x+e, q) (x + e)), θ(x + e, q)) − V (x, q) ≤ −σ(x)/2 + α for all x and q. Roughly speaking, the strength of robustness of the compound closed loop will be no less than that of the “weakest” individual system, provided that the buffer gain µ is high enough. Figure 2 depicts the level sets of two Lyapunov functions with minima at two distinct target points.

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