Conditions for which MPC fails to converge to the correct target

Shead, Leo; Muske, Kenneth R.; Rossiter, J.A.

doi:10.3182/20080706-5-kr-1001.01181

Cited by 9 publications

(6 citation statements)

References 14 publications

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“…Thus, the problems regarding unreachable targets due to active constraints are not considered and nevertheless, these problems can be addressed by an on-line steady-state target calculator (e.g. L. Shead, Muske, and Rossiter (2008)) or soft-constraints (e.g. Zeilinger, Morari, and Jones (2014)).…”

Section: Constraint Formulations In Terms Of Perturbationsmentioning

confidence: 99%

Blade-Pitch Control for Wind Turbine Load Reductions

Lio

2018

Springer Theses

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Large wind turbines are subjected to the harmful loads that arise from the spatially uneven and temporally unsteady oncoming wind. Such loads are the known sources of fatigue damage that reduce the turbine operational lifetime, ultimately increasing the cost of wind energy to the end users. In recent years, a substantial amount of studies has focused on blade pitch control and the use of real-time wind measurements, with the aim of attenuating the structural loads on the turbine blades and rotor. I also would like to thank my colleagues for some interesting discussions that helped my

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Section: Constraint Formulations In Terms Of Perturbationsmentioning

confidence: 99%

Blade-Pitch Control for Wind Turbine Load Reductions

Lio

2018

Springer Theses

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“…A contractive constraint may be deployed to ensure convergence. (2) Persistent infeasibility or so called unreachable targets (Shead et al 2010, Rawlings et al 2008. In this case, the target cannot be reached, even asymptotically, without violating some constraints and thus an alternative parameterisation allowing changes to the target steady-state is needed, again along with a modified objective.…”

Section: Unreachable Targets and Advance Knowledgementioning

confidence: 99%

“…Assuming n c cannot be increased, an alternative algorithm is needed to maintain feasibility and convergence. A common proposal , Rossiter 2006, Limón et al 2008, Shead et al 2010) is to include extra d.o.f that capture changes in the steady state. A contractive constraint may be deployed to ensure convergence.…”

Section: Unreachable Targets and Advance Knowledgementioning

confidence: 99%

“…More recent work in the literature has focussed on issues linked to the interaction between set point changes and feasibility (Shead et al 2010, Ferramosca et al 2009, Limón et al 2008. Specifically, feasibility issues tend to apply most to dual-mode MPC approaches as these include a terminal constraint, that is, the predicted state n c steps into the future must be within a specified set in order to be sure that the predicted trajectories satisfy constraints.…”

Section: Introductionmentioning

confidence: 99%

“…A significant change in the target implies a significant change in the terminal constraint and it may not be possible to find a trajectory that satisfies this terminal constraint, as well as transient constraints; this is denoted as infeasibility. Infeasibility due to target changes can take two forms: (i) the target is infeasible only in transients , Rao and Rawlings 1999, Rossiter 2006, Limón et al 2008) and (ii) the target is permanently unreachable Rawlings et al (2008), Shead et al (2010).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Systematic and effective embedding of feedforward of target information into MPC

Dughman

Rossiter

2017

International Journal of Control

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Discussions on how to make effective use of advance information on target changes are discussed relatively rarely in the predictive control literature. While earlier work has indicated that the default solutions from conventional predictive control algorithms are often poor, very little work has proposed systematic alternatives. This paper proposes an embedding structure for utilising advance information on target changes within an optimum predictive control law. The proposed embedding is shown to be systematic and beneficial. Moreover, it allows for easy extension to deal with more challenging scenarios such as unreachable set points and guarantees of convergence/stability in the uncertain case.

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A robust least squares based approach to min‐max model predictive control

Jetto

Orsini

2020

Intl J Robust & Nonlinear

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SummaryThis article deals with the model predictive control (MPC) of linear, time‐invariant discrete‐time polytopic (LTIDP) systems. The 2‐fold aim is to simplify the treatment of complex issues like stability and feasibility analysis of MPC in the presence of parametric uncertainty as well as to reduce the complexity of the relative optimization procedure. The new approach is based on a two degrees of freedom (2DOF) control scheme, where the output r(k) of the feedforward input estimator (IE) is used as input forcing the closed‐loop system ∑f. ∑f is the feedback connection of an LTIDP plant ∑p with an LTI feedback controller ∑g. Both cases of plants with measurable and unmeasurable state are considered. The task of ∑g is to guarantee the quadratic stability of ∑f, as well as the fulfillment of hard constraints on some physical variables for any input r(k) satisfying an “a priori” determined admissibility condition. The input r(k) is computed by the feedforward IE through the on‐line minimization of a worst‐case finite‐horizon quadratic cost functional and is applied to ∑f according to the usual receding horizon strategy. The on‐line constrained optimization problem is here simplified, reducing the number of the involved constraints and decision variables. This is obtained modeling r(k) as a B‐spline function, which is known to admit a parsimonious parametric representation. This allows us to reformulate the minimization of the worst‐case cost functional as a box‐constrained robust least squares estimation problem, which can be efficiently solved using second‐order cone programming.

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Conditions for which MPC fails to converge to the correct target

Cited by 9 publications

References 14 publications

Blade-Pitch Control for Wind Turbine Load Reductions

Blade-Pitch Control for Wind Turbine Load Reductions

Systematic and effective embedding of feedforward of target information into MPC

A robust least squares based approach to min‐max model predictive control

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