Sensitivity-Based Economic NMPC with a Path-Following Approach

Suwartadi, Eka; Kungurtsev, Vyacheslav; Jäschke, Johannes

doi:10.3390/pr5010008

Cited by 19 publications

(20 citation statements)

References 26 publications

(28 reference statements)

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“…Using the Real-Time Iteration scheme, the real-time application of the NMPC algorithm extended the DMOC based NMPC applied to the swing-up and stabilization task of a double pendulum on a cart with limited rail length to show its capability for controlling nonlinear dynamical systems with input and state constraints [51]. Suwartadi et al presented a sensitivity-based predictor-corrector path-following algorithm for fast nonlinear model predictive control (NMPC) and demonstrated it on a large case study with an economic cost function solving a sequence of quadratic programs to trace the optimal nonlinear model's predictive control solution along a parameter change incorporating strongly-active inequality constraints included as equality constraints in the quadratic programs, while the weakly-active constraints are left as inequalities [52].…”

Section: Introductionmentioning

confidence: 99%

Comparison and Interpretation Methods for Predictive Control of Mechanics

Sands

2019

Algorithms

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Objects that possess mass (e.g., automobiles, manufactured items, etc.) translationally accelerate in direct proportion to the force applied scaled by the object’s mass in accordance with Newton’s Law, while the rotational companion is Euler’s moment equations relating angular acceleration of objects that possess mass moments of inertia. Michel Chasles’s theorem allows us to simply invoke Newton and Euler’s equations to fully describe the six degrees of freedom of mechanical motion. Many options are available to control the motion of objects by controlling the applied force and moment. A long, distinguished list of references has matured the field of controlling a mechanical motion, which culminates in the burgeoning field of deterministic artificial intelligence as a natural progression of the laudable goal of adaptive and/or model predictive controllers that can be proven to be optimal subsequent to their development. Deterministic A.I. uses Chasle’s claim to assert Newton’s and Euler’s relations as deterministic self-awareness statements that are optimal with respect to state errors. Predictive controllers (both continuous and sampled-data) derived from the outset to be optimal by first solving an optimization problem with the governing dynamic equations of motion lead to several controllers (including a controller that twice invokes optimization to formulate robust, predictive control). These controllers are compared to each other with noise and modeling errors, and the many figures of merit are used: tracking error and rate error deviations and means, in addition to total mean cost. Robustness is evaluated using Monte Carlo analysis where plant parameters are randomly assumed to be incorrectly modeled. Six instances of controllers are compared against these methods and interpretations, which allow engineers to select a tailored control for their given circumstances. Novel versions of the ubiquitous classical proportional-derivative, “PD” controller, is developed from the optimization statement at the outset by using a novel re-parameterization of the optimal results from time-to-state parameterization. Furthermore, time-optimal controllers, continuous predictive controllers, and sampled-data predictive controllers, as well as combined feedforward plus feedback controllers, and the two degree of freedom controllers (i.e., 2DOF). The context of the term “feedforward” used in this study is the context of deterministic artificial intelligence, where analytic self-awareness statements are strictly determined by the governing physics (of mechanics in this case, e.g., Chasle, Newton, and Euler). When feedforward is combined with feedback per the previously mentioned method (provenance foremost in optimization), the combination is referred to as “2DOF” or two degrees of freedom to indicate the twice invocation of optimization at the genesis of the feedforward and the feedback, respectively. The feedforward plus feedback case is augmented by an online (real time) comparison to the optimal case. This manuscript compares these many optional control strategies against each other. Nominal plants are used, but the addition of plant noise reveals the robustness of each controller, even without optimally rejecting assumed-Gaussian noise (e.g., via the Kalman filter). In other words, noise terms are intentionally left unaddressed in the problem formulation to evaluate the robustness of the proposed method when the real-world noise is added. Lastly, mismodeled plants controlled by each strategy reveal relative performance. Well-anticipated results include the lowest cost, which is achieved by the optimal controller (with very poor robustness), while low mean errors and deviations are achieved by the classical controllers (at the highest cost). Both continuous predictive control and sampled-data predictive control perform well at both cost as well as errors and deviations, while the 2DOF controller performance was the best overall.

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Section: Introductionmentioning

confidence: 99%

Comparison and Interpretation Methods for Predictive Control of Mechanics

Sands

2019

Algorithms

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“…Ideally, the trajectory is updated instantaneously right after measuring the actual state of the aircraft at each time sample. In practical applications, however, solving the NLP problem may take significant time, leading to potential stability issues and degrading the performance of the operation [6]. In order to reduce the execution time, educated simplifications in the models can be used [7], at the expense of reducing the accuracy of the solution.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, the SbNMPC strategy is implemented to guide aircraft during a CDOs subject to CTAs, and several descents are simulated with intentional errors in the parameters used by the FMS to describe the wind profile. Then, the performance of SbNMPC in terms of fuel consumption and ability to satisfy operational constraints is compared with those of the openloop solution and the ideal NMPC (INMPC) [6], which ideally updates the optimal descent trajectory without delay.…”

Section: Introductionmentioning

confidence: 99%

Fast sensitivity-based optimal trajectory updates for descent operations subject to time constraints

Dalmau

Prats

Baxley

2018

2018 IEEE/AIAA 37th Digital Avionics Systems Conference (DASC)

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The ability to meet a controlled time of arrival while also flying a continuous descent operation will enable environmentally friendly and fuel efficient descent operations while simultaneously maintaining airport throughput. Previous work showed that guidance strategies based on a frequent recalculation of the optimal trajectory during the descent result in excellent environmental impact mitigation figures while meeting operational constraints in the presence of modelling errors. However, the time lag of recalculating the trajectory using traditional optimisation algorithms could lead to performance degradation and stability issues. This paper proposes an alternative strategy, which allows for fast updates of the optimal trajectory based on parametric sensitivities. Promising results show that the performance of this method is comparable to that of instantaneously recalculating the optimal descent trajectory at each time sample.

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“…In this method, the NLP problem is solved in advance with respect to a predicted initial state. Then, as soon as the new state measurements (or estimates) are available, the NLP solution is updated using a fast sensitivityupdate step and the IPOPT solver [39][40][41]. Successful implementations have been documented in the literature, in particular for large-scale processes [42,43].…”

Section: Introductionmentioning

confidence: 99%

Computationally efficient NMPC for batch and semi-batch processes using parsimonious input parameterization

Aydın

Bonvin

Sundmacher

2018

Journal of Process Control

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The trend towards high-quality, low-volume chemical production has put more emphasis on batch and semi-batch processing due to its increased operational flexibility. The transient behavior of these processes makes their real-time optimization very challenging. In particular, the large prediction horizons required in shrinking-horizon NMPC increase the real-time computational effort due to expensive matrix factorizations. The computational delay associated with advanced control methods is usually underestimated in theoretical studies. However, this delay may contribute to suboptimal or, worse, infeasible operation in real-life applications. This study proposes to combine a tailored parsimonious input parameterization with shrinking-horizon NMPC to reduce the real-time computational effort. Models of the optimal solution are used to suggest parsimonious parameterizations (especially for sensitivity-seeking arcs) that lead to computationally efficient optimization. The proposed approach is illustrated in simulation on two case studies in the presence of uncertainty, namely a batch binary distillation column and a semi-batch reactor for the hydroformylation of 1-dodecene. The results show that the tailored parsimonious shrinking-horizon NMPC (i) performs very similarly to the standard shrinking-horizon NMPC in terms of cost, (ii) is computationally much more efficient than the standard shrinking-horizon NMPC especially at the beginning of the batch, (iii) is robust to plant-model mismatch.

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Sensitivity-Based Economic NMPC with a Path-Following Approach

Cited by 19 publications

References 26 publications

Comparison and Interpretation Methods for Predictive Control of Mechanics

Comparison and Interpretation Methods for Predictive Control of Mechanics

Fast sensitivity-based optimal trajectory updates for descent operations subject to time constraints

Computationally efficient NMPC for batch and semi-batch processes using parsimonious input parameterization

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