Unreachable Setpoints in Model Predictive Control

Rawlings, James B.; Bonné, Dennis; Jørgensen, John Bagterp; Venkat, Aswin N.; Jørgensen, Sten Bay

doi:10.1109/tac.2008.928125

Cited by 146 publications

(107 citation statements)

References 12 publications

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“…Remark 1: From [14], we know that the steerable set X N is convex and that 0 ∈ X N . We also denote by u * (x) the optimal solution to (2) with initial conditionx and σ(H) the smallest eigenvalue to H.…”

Section: Algorithm 1: Accelerated Gradient Algorithmmentioning

confidence: 99%

Execution time certification for gradient-based optimization in model predictive control

Giselsson

2012

2012 IEEE 51st IEEE Conference on Decision and Control (CDC)

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Abstract-We consider model predictive control (MPC) problems with linear dynamics, polytopic constraints, and quadratic objective. The resulting optimization problem is solved by applying an accelerated gradient method to the dual problem. The focus of this paper is to provide bounds on the number of iterations needed in the algorithm to guarantee a prespecified accuracy of the dual function value and the primal variables as well as guaranteeing a prespecified maximal constraint violation. The provided numerical example shows that the iteration bounds are tight enough to be useful in an inverted pendulum application.

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Section: Algorithm 1: Accelerated Gradient Algorithmmentioning

confidence: 99%

Execution time certification for gradient-based optimization in model predictive control

Giselsson

2012

2012 IEEE 51st IEEE Conference on Decision and Control (CDC)

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“…The use of unreachable setpoints is analyzed in [7] for linear MPC, and conditions for stability and convergence are established. Moreover, [7] compares MPC using unreachable setpoints to a standard two-layer structure with a target-tracking cost function in two examples, and considerable cost improvements are achieved under certain disturbance scenarios.…”

Section: Unreachable Setpointsmentioning

confidence: 99%

“…Moreover, [7] compares MPC using unreachable setpoints to a standard two-layer structure with a target-tracking cost function in two examples, and considerable cost improvements are achieved under certain disturbance scenarios.…”

Section: Unreachable Setpointsmentioning

confidence: 99%

“…However, cost functions using unreachable setpoints are unbounded on infinite horizons, and thus standard analysis of stability and convergence employing cost functions as Lyapunov functions can no longer be used. This has been a subject of recent research, and is for linear MPC analysis provided in [7], while results towards nonlinear systems can be found in [14].…”

Section: Unreachable Setpointsmentioning

confidence: 99%

“…It is assumed (with little loss of generality) that the production optimization objective can be cast as maximization of one (or more) of the controlled variables. Two methods are studied: the use of unreachable setpoints [7], and infeasible softconstraints (see also [8]). To the authors' knowledge, the use of the latter approach in an economic optimization setting is new.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Short-term Production Optimization of Offshore Oil and Gas Production Using Nonlinear Model Predictive Control

Willersrud

Imsland

Hauger

et al. 2011

IFAC Proceedings Volumes

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The topic of this paper is the application of nonlinear model predictive control (NMPC) for optimizing control of an offshore oil and gas production facility. Of particular interest is the use of NMPC for direct short-term production optimization, where two methods for (one-layer) production optimization in NMPC are investigated. The first method is the unreachable setpoints method where an unreachable setpoint is used in order to maximize oil production. The ideas from this method are combined with the exact penalty function for soft constraints in a second method, named infeasible soft-constraints. Both methods can be implemented within standard NMPC software tools.The case-study first looks into the use of NMPC for "conventional" pressure control, where disturbance rejection of time-varying disturbances (caused, e.g., by the 'slugging' phenomenon) is an issue. Then the above two methods for production optimization are employed, where both methods find the economically optimal operating point. Two different types of reservoir models are studied, using rate-independent and rate-dependent gas/oil ratios. These models lead to different types of optimums. The relative merits of the two methods for production optimization, and advantages of the two one-layer approaches compared to a two-layer structure, are discussed.

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A multistage H‐infinity–based controller for adjusting voltage and frequency and improving power quality in islanded microgrids

Sedhom

El‐Saadawi

Hatata

et al. 2019

Int Trans Electr Energ Syst

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Summary This paper proposes a novel methodology for controlling voltage and frequency of islanded microgrids and meanwhile improving the system power quality. The proposed methodology is based on applying a multi‐stage H‐Infinity (H∞) controller with different control loops to restore the nominal values of voltage and frequency after any load variation. These control loops include power control, current control, and voltage control loops. The H∞ is also applied with an LCL filter to enhance the system power quality. The proposed controller is applied to a test system under three different loading conditions and the obtained results are compared with that obtained by applying the model predictive control (MPC) method. The results are compared with that obtained by applying a proposed traditional control method in the same test system. A comparison between the droop controller and the proposed controller, MPC is performed based on fitness value, controller response time, and maximum frequency deviation. In addition, the system stability is analysed using root locus, system step response, singular value decomposition, and bode diagram. The results prove the effectiveness and the efficiency of the proposed method in restoring voltage and frequency and improving the system power quality.

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Unreachable Setpoints in Model Predictive Control

Cited by 146 publications

References 12 publications

Execution time certification for gradient-based optimization in model predictive control

Execution time certification for gradient-based optimization in model predictive control

Short-term Production Optimization of Offshore Oil and Gas Production Using Nonlinear Model Predictive Control

A multistage H‐infinity–based controller for adjusting voltage and frequency and improving power quality in islanded microgrids

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