Pith. sign in

REVIEW 4 major objections 5 minor 175 references

Comparing Model-based Control Strategies for a Quadruple Tank System: Decentralized PID, LMPC, and NMPC

T0 review · 4 major / 5 minor · reviewed 2026-08-04 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read MPC’s advantage over a tuned PID lies in anticipating setpoints, not in rejecting disturbances.

desk verdict A solid, honest engineering comparison; the key claim that MPC's advantage over a SIMC-tuned PID is mostly anticipatory holds up, but the numeric magnitudes are tuning-dependent. read the letter →

arxiv 2509.11235 v1 pith:GP67EDML submitted 2025-09-14 math.OC cs.SYeess.SY

Anders H. D. Christensen , Tobias K. S. Ritschel , Jan Lorenz Svensen , Steen H{o}rsholt , Jakob Kj{o}bsted Huusom , John Bagterp J{o}rgensen This is my paper · ORCID
classification math.OCcs.SYeess.SY
keywords QuadrupletanksystemDecentralizedPIDLinearmodelpredictivecontrolNonlinearML-PEMparameterestimationSIMCtuningContinuous-discreteKalmanfilterAnticipatory
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper compares three control strategies on a physical quadruple tank system and in simulation: a decentralized PID tuned by SIMC rules, a linear MPC, and a nonlinear MPC. It finds that the MPCs track pre-announced time-varying setpoints far better than the PID, but only slightly better for disturbance rejection. The central claim is that the MPC advantage is mainly anticipatory: when future setpoint information is removed and only current setpoints are given, the PID actually achieves better tracking errors in simulation. The paper matters because it quantifies when the extra complexity of MPC pays off in a realistic benchmark.

What carries the argument

The comparison is carried by a common stochastic continuous-discrete-time model of the four-tank process, identified with a maximum-likelihood prediction-error method (ML-PEM). The NMPC uses the nonlinear model in its optimal control problem with a continuous-discrete extended Kalman filter (CD-EKF) for state and disturbance estimation; the LMPC uses the same model linearized, with a continuous-discrete Kalman filter (CD-KF). The PID is tuned from transfer functions of the same linearized model using SIMC rules. The decisive mechanism is the MPC prediction horizon: with a 13-minute horizon and pre-announced setpoints, the optimizer can move valves before the setpoint change arrives, which a

What would settle it

On the physical quadruple tank, run the same setpoint sequence with the LMPC and NMPC given only current setpoints (setpoint held constant over the prediction horizon); if either MPC still achieves lower NISE/NIAE than the SIMC-tuned PID, the claim that the primary MPC advantage is anticipatory is falsified.

Watch

Extended reading notes

Core claim

The paper claims that on the quadruple tank system, the performance gap between model predictive control and a well-tuned decentralized PID is driven by the MPC's ability to incorporate future setpoint information, not by superior feedback disturbance rejection. Experimentally, LMPC and NMPC achieve markedly lower tracking-error norms (NISE about 1.6 and 1.4 vs PID's 9.1) and much lower input movement (NISΔU about 12–29 vs PID's 249) on a preset setpoint sequence. In simulation, when the MPCs are only given current setpoints, the PID's tracking errors become smaller than the MPCs'. For large deterministic disturbances the MPCs are only slightly better, and for stochastic disturbances they ar

Load-bearing premise

The comparison's conclusions rest on the identified stochastic model being accurate enough that the simulated no-future-setpoint case faithfully represents real closed-loop behavior, yet that model depends on a manually inflated measurement noise covariance (factor 1000) whose correctness is untested.

Editorial extensions

If this is right

  • In industrial loops where setpoint changes are known in advance (batch transitions, grade changes, scheduled trajectories), MPC can deliver large reductions in both tracking error and valve wear compared with a well-tuned decentralized PID.
  • When disturbances are unmeasured and no future information exists, a SIMC-tuned decentralized PID with integral action is competitive with MPC; spending on MPC for pure regulatory control may yield little tracking benefit.
  • NMPC vs LMPC: nonlinearity pays only a small tracking dividend on this rig in the tested operating range, while roughly doubling the input movement; linear MPC may be the cost-effective choice for mildly nonlinear tank systems.
  • The large reduction in input rate of movement (NISΔU) with MPCs suggests that MPC can extend actuator life and reduce wear even when tracking gains over PID are modest.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The paper's logic suggests a testable general rule: for any well-modeled process, the tracking advantage of MPC over tuned PID scales with the amount and reliability of future setpoint information, not with model complexity; an optimization-based PID tuned on the same objective as the MPC would be a sharper baseline.
  • Because the simulation studies assume the controller and estimator know the true noise covariances, the 'no-future-information' result is an upper bound on PID competitiveness; with model mismatch, the PID's integral action may look even better, so the claim deserves a robustness test with perturbed plant parameters.
  • The manual 1000x inflation of upper-tank measurement noise variances in Section 4.2.2 is a fragile identification step; re-estimating the model with proper noise modeling (e.g., estimating separate sensor variances without inflation) and re-running the comparison would show whether the MPC advantage is sensitive to the identification procedure.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper compares a decentralized SIMC-tuned PID, an LMPC, and an NMPC on a quadruple tank system, using both physical experiments and simulations. The QTS is modeled as a stochastic nonlinear continuous-discrete-time system with parameters estimated by maximum-likelihood prediction-error methods. The central empirical claim is that the LMPC and NMPC outperform the decentralized PID for tracking pre-announced time-varying setpoints, that this advantage essentially disappears when future setpoint information is withheld from the MPCs, and that for disturbance rejection the MPCs provide only marginal improvements over the PID. The NMPC yields slightly better tracking than the LMPC at the cost of higher input activity. The paper also provides a structured comparison of the three controllers under identical setpoint sequences and discusses the tuning dependence of its conclusions.

Significance. If the claim holds, the paper provides a useful and fairly comprehensive benchmark: on a standard QTS, the measurable advantage of MPC over a well-tuned decentralized PID is primarily anticipatory, not regulatory. The study is valuable for its systematic experimental protocol, the use of the same identified model as the basis for all three controller designs, and the explicit acknowledgment of the limitations of the comparison. However, the strength of the central claim is currently limited by the use of one experimental run per controller, a single PID tuning, a manually manipulated measurement-noise covariance in the identification, and an ambiguity about the parameters used in the simulation plant.

major comments (4)
  1. [Sec. 6.1.2, Tables 4-5] The experimental comparison is based on one run per controller (Sec. 6.1.2). The headline NISE values in Table 4 (PID 9.063, LMPC 1.637, NMPC 1.423) are point estimates from single trajectories. Given the stochastic dynamics in (1) and the process disturbances, these differences could lie within run-to-run variability. The paper should provide repeated experiments or Monte Carlo simulations using the identified stochastic model, with confidence intervals for NISE, NIAE, and NISΔU. Without such an uncertainty analysis, the central claim rests on a single realization.
  2. [Secs. 5.1.1, 5.2, 5.3, 6.3.5] The PID is tuned once with SIMC using Tc=50, while the MPC weights (Q=10I, S=I) and horizon N=160 are chosen by trial-and-error. Section 6.3.5 itself concedes that different tunings could change the results and that the performance measures in Eq. (44) mirror the MPC cost. This makes the reported performance gap a property of the chosen tuning configurations rather than of the algorithms as such. The authors should add a sensitivity analysis over Tc and Q/S, or use optimization-based tuning of both designs under the same objective, before claiming that the MPCs 'perform better' than the PID. This is load-bearing for the paper's main conclusion.
  3. [Sec. 4.2.2, Table 3] The measurement noise covariance for the upper tanks is manually inflated by a factor 1000 (Sec. 4.2.2), and the subsequent ML-PEM estimation yields r_3^2 = r_4^2 = 1e-5, effectively giving zero weight to the upper-tank measurements. The estimated parameters A3, A4, and gamma1 differ substantially from the nominal values (Table 1). Since the same identified model is used to tune the PID and to design the MPCs and their state estimators, the controller comparison may be influenced by this ad hoc identification choice. Please validate the noise covariance on an independent steady-state data set, or demonstrate that the conclusions are invariant to a range of plausible R values.
  4. [Sec. 6.2] The text states that 'we apply the nominal parameters in Table 1 for all four simulation studies', while the controllers were designed using the estimated parameters in the same table. This plant-model mismatch is not discussed, and the claim in Sec. 6.2.1 that the CD-KF and CD-EKF have 'perfect knowledge about the systems' is misleading if the plant uses the nominal parameters. Specify explicitly which parameter set is used for the simulated plant and which is used in the controllers and estimators, and discuss the implications of any mismatch for the interpretation of Simulations 1-4.
minor comments (5)
  1. [Table 3] The units of r^2 are given as [m^2], but the measurement equation (1b) uses y in cm; the covariance units should be reconciled.
  2. [Eq. (44)] The measures are called 'normalized' NISE/NIAE, but the definitions are simple averages of squared/absolute errors; clarify the normalization or rename the quantities.
  3. [Sec. 4.2.2] The factor 1000 used to inflate the upper-tank measurement variances is introduced with only a qualitative turbulence argument; provide a quantitative justification or a sensitivity check.
  4. [Abstract / Sec. 5.1.1] The abstract describes the PID as 'well-tuned'; given the single SIMC tuning and the paper's own caveats, consider wording such as 'SIMC-tuned' to avoid overstatement.
  5. [Throughout] There are typographical issues (e.g., 'di fferent' in several places, 'Futhermore' in Sec. 6.3.4, 'tutotorial' in the Pannocchia reference). A careful proofread is recommended.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: empirical benchmark with independently validated models.

full rationale

This paper is an experimental/computational benchmark, not a derivation chain whose conclusions are equivalent to its inputs. The QTS model is identified by ML-PEM on a separate estimation data set and checked against a validation data set (GOF 80.41%/74.20% vs 47.91%/57.28%, Table 2), so the model used by the MPCs is not constructed from the claimed comparison outcome. The PID, LMPC, and NMPC are distinct algorithms with explicit tunings (SIMC with Tc=50 for PID; Q=diag(10,10), S=diag(1,1), N=160 for both MPCs). The central tracking claim is supported by one physical run per controller plus simulations; no fitted parameter is renamed as a prediction. The anticipatory-advantage claim is tested by toggling future setpoint information in Simulation 1 vs Simulation 2, a controlled ablation rather than a tautology. Section 6.3.5 explicitly concedes that the performance measure (44) is aligned with MPC objectives and that tuning was not optimization-based; these are benchmarking limitations that affect robustness and fairness, not circular reasoning. The manual 1000x inflation of the measurement noise covariance (Sec. 4.2.2) is an identification assumption that may bias estimation, but it does not define the compared outcomes. Self-citations (Andersen et al. 2023a,b, and the group's NMPC application list) are contextual or software-description references and are not load-bearing for the comparison. Hence no circular step is identifiable from the paper's own equations or argument.

Assumptions & free parameters 8 free parameters · 5 assumptions · 1 invented entities

The paper rests on a standard grey-box model of the quadruple tank system, an integrated-white-noise disturbance model, and several tuning choices (SIMC Tc=50, MPC weights Q/S, horizons, augmented noise covariances). Most of these are explicitly stated. The manual inflation of measurement variances by 1000 is the most fragile choice.

free parameters (8)
  • Measurement noise covariance R (manual inflation and ML-PEM) = r1=1.44e-2, r2=1.34e-2, r3=1.00e-5, r4=1.00e-5
    Steady-state variances multiplied by 1000 by hand, then re-estimated via ML-PEM (Table 3).
  • Diffusion coefficients sigma_i = 10.07e-3, 13.09e-3, 12.50e-3, 16.62e-3 g/sqrt(s)
    Estimated by ML-PEM from estimation data (Table 1).
  • Disturbance diffusion coefficients sigma_d,i = 0.47, 3.08, 3.92, 3.42 g/sqrt(s)
    Estimated by ML-PEM for the augmented model (Table 3).
  • SIMC closed-loop time constant Tc = 50 s
    Chosen by hand for both PID loops (Section 5.1.1).
  • MPC weights Q and S = Q=diag([10,10]), S=diag([1,1])
    Tuned by trial-and-error (Section 5.2, 5.3).
  • Prediction horizon N = 160 steps (800 s)
    Chosen for both MPCs (Section 5.2).
  • PID filter constant N and windup time constant tau_t = N=5, tau_t=0.5*tau_i
    Chosen by hand (Section 5.1.1).
  • Simulation noise covariances = sigma_a=1.0, R=0.02 for simulations 1-3; sigma=20, sigma_a(d)=20 for simulation 4
    Assigned for the simulation studies (Section 6.2).
assumptions (5)
  • domain assumption Quadruple tank model: mass balances with Torricelli outflow, Eq. (2)-(4)
    The plant model assumes constant density, ideal valve splits, and square-root outflow laws.
  • domain assumption Unknown disturbances modeled as integrated white noise, Eq. (18)
    No prior information on disturbance dynamics; the paper uses Brownian motion integrators.
  • domain assumption Disturbances constant over the MPC prediction horizon, Eq. (35c) and (39c)
    Needed to keep the OCPs tractable; may be inaccurate for fast-varying disturbances.
  • domain assumption Linearized model at the operating point is adequate for LMPC and PID tuning, Eq. (9)
    The LMPC and SIMC transfer functions are derived from this linearization.
  • domain assumption Steady-state measurement distributions are representative for the noise covariance R
    Used as the starting point for R before manual inflation and ML-PEM re-estimation.
invented entities (1)
  • Augmented disturbance states d_i(t)
    purpose: Enable offset-free state and disturbance estimation in CD-KF and CD-EKF
    These unmeasured states are postulated to model plant-model mismatch; they have no falsifiable handle outside the paper.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Comparing Model-based Control Strategies for a Quadruple Tank System: Decentralized PID, LMPC, and NMPC." pith.science (2026). https://pith.science/paper/GP67EDML

@misc{pith2026250911235,
  author       = {Pith},
  title        = {Pith review of: Comparing Model-based Control Strategies for a Quadruple Tank System: Decentralized PID, LMPC, and NMPC},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GP67EDML}},
  note         = {Machine review of arXiv:2509.11235}
}
read the original abstract

This paper compares the performance of a decentralized proportional-integral-derivative (PID) controller, a linear model predictive controller (LMPC), and a nonlinear model predictive controller (NMPC) applied to a quadruple tank system (QTS). We present experimental data from a physical setup of the QTS as well as simulation results. The QTS is modeled as a stochastic nonlinear continuous-discrete-time system, with parameters estimated using a maximum-likelihood prediction-error-method (ML-PEM). The NMPC applies the stochastic nonlinear continuous-discrete-time model, while the LMPC uses a linearized version of the same model. We tune the decentralized PID controller using the simple internal model control (SIMC) rules. The SIMC rules require transfer functions of the process, and we obtain these from the linearized model. We compare the controller performances based on systematic tests using both the physical setup and the simulated QTS. We measure the performance in terms of tracking errors and rate of movement in the manipulated variables. The LMPC and the NMPC perform better than the decentralized PID control system for tracking pre-announced time-varying setpoints. For disturbance rejection, the MPCs perform only slightly better than the decentralized PID controller. The primary advantage of the MPCs is their ability to use the information of future setpoints. We demonstrate this by providing simulation results of the MPCs with and without such information. Finally, the NMPC achieves slightly improved tracking errors compared to the LMPC but at the expense of having a higher input rate of movement.

Figures

Figures reproduced from arXiv: 2509.11235 by the authors.

Figure 1
Figure 1. Squeeze and shift principle: Improving the nominal control system [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Illustration of the reactive and anticipatory behavior in control sys [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. The quadruple tank system. Finally, we present conclusions in Section 7. 2. Modeling the quadruple tank system We consider the QTS shown in [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (7 more)
Figure 4
Figure 4. Figure 4: Data used for estimation and simulations with nominal and estimated [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: Data used for validation and simulations with nominal and estimated [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]
Figure 6
Figure 6. Figure 6: Schematic diagram of the software framework used to implement the three control algorithms (PID, LMPC, NMPC) to the QTS. [PITH_FULL_IMAGE:figures/full_fig_p011_6.png]
Figure 7
Figure 7. Figure 7: Data for experiments of decentralized PID, LMPC, and NMPC on the physical QTS. [PITH_FULL_IMAGE:figures/full_fig_p011_7.png]
Figure 9
Figure 9. Figure 9: Simulation 1: Tracking predefined time-varying setpoints. The MPCs [PITH_FULL_IMAGE:figures/full_fig_p012_9.png]
Figure 10
Figure 10. Figure 10: Simulation 2: Tracking predefined time-varying setpoints. The [PITH_FULL_IMAGE:figures/full_fig_p013_10.png]
Figure 11
Figure 11. Figure 11: Simulation 3: Constant setpoints with large deterministic distur [PITH_FULL_IMAGE:figures/full_fig_p013_11.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

175 extracted references · 3 linked inside Pith

  1. [1]

    write newline

    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION word.in bbl.in ":" * " " * FUNCTION f...

  2. [2]

    , year 2015

    author Abramovitch, D.Y. , year 2015 . title A unified framework for analog and digital PID controllers , in: booktitle 2015 IEEE Conference on Control Applications (CCA) , pp. pages 1492--1497

    2015

  3. [3]

    , author Andersson, S

    author Abramovitch, D.Y. , author Andersson, S. , author Leang, K.K. , author Nagel, W. , author Ruben, S. , year 2023 . title A tutorial on real-time computing issues for control systems , in: booktitle 2023 American Control Conference , pp. pages 3751--3768

    2023

  4. [4]

    , author Limon, D

    author Alvarado, I. , author Limon, D. , author Muñoz de la Peña , D. , author Maestre, J.M. , author Ridao, M.A. , author Scheu, H. , author Marquardt, W. , author Negenborn, R.R. , author De Schutter , B. , author Valencia, F. , author Espinosa, J. , year 2011 . title A comparative analysis of distributed MPC techniques applied to the HD-MPC four-tank b...

    2011

  5. [5]

    , author Ritschel, T.K.S

    author Andersen, A.H.D. , author Ritschel, T.K.S. , author Hørsholt, S. , author Huusom, J.K. , author Jørgensen, J.B. , year 2023 a. title M odel-based control algorithms for the quadruple tank system: A n experimental comparison , in: booktitle Foundations of Computer Aided Process Operations / Chemical Process Control (FOCAPO / CPC) , address San Anton...

    2023

  6. [6]

    , author Zhang, Z

    author Andersen, A.H.D. , author Zhang, Z. , author Hørsholt, S. , author Ritschel, T.K.S. , author Jørgensen, J.B. , year 2023 b. title Software principles and concepts applied in the implementation of cyber-physical systems for real-time advanced process control , in: booktitle 2023 European Control Conference (ECC) , address Bucharest, Romania

    2023

  7. [7]

    , author Gillis, J

    author Andersson, J.A.E. , author Gillis, J. , author Horn, G. , author Rawlings, J.B. , author Diehl, M. , year 2019 . title CasADi -- A software framework for nonlinear optimization and optimal control . journal Mathematical Programming Computation volume 11 , pages 1--36

    2019

  8. [8]

    , author J rgensen, J.B

    author Azam, S.N.M. , author J rgensen, J.B. , year 2018 . title U nconstrained and constrained model predictive control for a modified quadruple tank system , in: booktitle IEEE Conference on Systems, Process and Control (ICSPC 2018) , address Melaka, Malaysia . pp. pages 147--152

    2018

Show all 175 references
  1. [9]

    , author Qin, S.J

    author Badgwell, T.A. , author Qin, S.J. , year 2021 . title Model predictive control in practice , in: editor Baillieul, J. , editor Samad, T. (Eds.), booktitle Encyclopedia of Systems and Control . publisher Springer International Publishing , pp. pages 1239--1252

    2021

  2. [10]

    , author Craig, I.K

    author Bauer, M. , author Craig, I.K. , year 2008 . title Economic assessment of advanced process control – A survey and framework . journal Journal of Process Control volume 18 , pages 2--18

    2008

  3. [11]

    , year 2003

    author Bequette, B.W. , year 2003 . title Process control: modeling, design, and simulation . publisher Prentice Hall

    2003

  4. [12]

    , author Blank, L

    author Binder, T. , author Blank, L. , author Bock, H.G. , author Bulirsch, R. , author Dahmen, W. , author Diehl, M. , author Kronsender, T. , author Marquardt, W. , author Schlöder, J.P. , author von Stryk , O. , year 2001 . title Introduction to model based optimization of ...

    2001

  5. [13]

    , year 2015

    author Bindlish, R. , year 2015 . title Nonlinear model predictive control of an industrial polymerization process . journal Computers and Chemical Engineering volume 73 , pages 43--48

    2015

  6. [14]

    , author Gevers, M

    author Bitmead, R.R. , author Gevers, M. , author Wertz, V. , year 1990 . title Adaptive optimal control: The thinking man's GPC . publisher Prentice-Hall

    1990

  7. [15]

    , author Chevrel, P

    author Blaud, P.C. , author Chevrel, P. , author Claveau, F. , author Haurant, P. , author Mouraud, A. , year 2022 . title Four MPC implementations compared on the quadruple tank process benchmark: pros and cons of neural MPC . journal IFAC-PapersOnLine volume 55 , pages 344--349

    2022

  8. [16]

    , author Plitt, K.J

    author Bock, H.G. , author Plitt, K.J. , year 1984 . title A multiple shooting algorithm for direct solution of optimal control problems . journal IFAC Proceedings Volumes volume 17 , pages 1603--1608

    1984

  9. [17]

    , year 2009

    author Boiroux, D. , year 2009 . title Nonlinear Model Predictive Control for an Artificial Pancreas . Master's thesis. Technical University of Denmark

    2009

  10. [18]

    , year 2013

    author Boiroux, D. , year 2013 . title Model Predictive Control Algorithms for Pen and Pump Insulin Administration . Ph.D. thesis. Technical University of Denmark

    2013

  11. [19]

    , author Finan, D.A

    author Boiroux, D. , author Finan, D.A. , author J rgensen, J.B. , author Poulsen, N.K. , author Madsen, H. , year 2010 a. title Nonlinear model predictive control for an artificial -cell , in: editor Diehl, M. , editor Glineur, F. , editor Jarlebring, E. , editor Michiels, W....

    2010

  12. [20]

    , author Finan, D.A

    author Boiroux, D. , author Finan, D.A. , author Jørgensen, J.B. , author Poulsen, N.K. , author Madsen, H. , year 2010 b. title Meal estimation in nonlinear model predictive control for type 1 diabetes . journal IFAC PapersOnLine volume 43-14 , pages 1052--1057

    2010

  13. [21]

    , author Finan, D.A

    author Boiroux, D. , author Finan, D.A. , author Jørgensen, J.B. , author Poulsen, N.K. , author Madsen, H. , year 2010 c. title Optimal insulin administration for people with type 1 diabetes . journal IFAC Proceedings Volume volume 43-5 , pages 248--253

    2010

  14. [22]

    , author Hagdrup, M

    author Boiroux, D. , author Hagdrup, M. , author Mahmoudi, Z. , author Poulsen, N.K. , author Madsen, H. , author Jørgensen, J.B. , year 2016 a. title An ensemble nonlinear model predictive control algorithm in an artificial pancreas for people with type 1 diabetes , in: bookt...

    2016

  15. [23]

    , author Juhl, R

    author Boiroux, D. , author Juhl, R. , author Madsen, H. , author Jørgensen, J.B. , year 2016 b. title An efficient UD -based algorithm for the computation of maximum likelihood sensitivity of continuous-discrete systems , in: booktitle 2016 IEEE 55th Conference on Decision an...

    2016

  16. [24]

    , author Jørgensen, J.B

    author Boiroux, D. , author Jørgensen, J.B. , year 2017 . title C code generation applied to nonlinear model predictive control for an artificial pancreas , in: booktitle 2017 21st International Conference on Process Control (PC) , publisher IEEE . pp. pages 327--332

    2017

  17. [25]

    , author Jørgensen, J.B

    author Boiroux, D. , author Jørgensen, J.B. , year 2018 a. title Nonlinear model predictive control and artificial pancreas technologies , in: booktitle 2018 IEEE Conference on Decision and Control (CDC) , pp. pages 284--290

    2018

  18. [26]

    , author Jørgensen, J.B

    author Boiroux, D. , author Jørgensen, J.B. , year 2018 b. title A nonlinear model predictive control strategy for glucose control in people with type 1 diabetes . journal IFAC PapersOnLine volume 51-27 , pages 192--197

    2018

  19. [27]

    , author Mahmoudi, Z

    author Boiroux, D. , author Mahmoudi, Z. , author Jørgensen, J.B. , year 2019 a. title Parameter estimation in type 1 diabetes models for model-based control applications , in: booktitle 2019 American Control Conference (ACC) , pp. pages 4112--4117

    2019

  20. [28]

    , author Ritschel, T.K.S

    author Boiroux, D. , author Ritschel, T.K.S. , author Poulsen, N.K. , author Madsen, H. , author Jørgensen, J.B. , year 2019 b. title Efficient computation of the continuous-discrete extended kalman filter sensitivities applied to maximum likelihood estimation , in: booktitle ...

    2019

  21. [29]

    , author Bemporad, A

    author Borrelli, F. , author Bemporad, A. , author Morari, M. , year 2017 . title Predictive Control for Linear and Hybrid Systems . publisher Cambridge University Press

    2017

  22. [30]

    , author Madsen, H

    author Brok, N.L. , author Madsen, H. , author Jørgensen, J.B. , year 2018 . title Nonlinear model predictive control for stochastic differential equation systems . journal IFAC-PapersOnLine volume 51 , pages 430--435

    2018

  23. [31]

    , author Joseph, B

    author Brosilow, C. , author Joseph, B. , year 2002 . title Techniques of Model-Based Control . publisher Prentice Hall

    2002

  24. [32]

    , author Wellings, A

    author Burns, A. , author Wellings, A. , year 2009 . title Real-Time Systems and Programming Languages. Ada, Real-Time Java and C/Real-Time POSIX . edition Fourth ed., publisher Addison Wesley

    2009

  25. [33]

    , author Bordons, C

    author Camacho, E.F. , author Bordons, C. , year 1995 . title Model predictive control in the process industry . publisher Springer-Verlag London

    1995

  26. [34]

    , author Jørgensen, J.B

    author Capolei, A. , author Jørgensen, J.B. , year 2012 . title Solution of constrained optimal control using multiple shooting and ESDIRK methods , in: booktitle 2012 American Control Conference (ACC) , pp. pages 295--300

    2012

  27. [35]

    , author Jørgensen, J.B

    author Christensen, A.H.D. , author Jørgensen, J.B. , year 2024 . title A comparative study of sensitivity computations in ESDIRK -based optimal control problems . journal European Journal of Control volume 80 , pages 101064

    2024

  28. [36]

    , author Mohtadi, C

    author Clarke, D.W. , author Mohtadi, C. , year 1989 . title Properties of generalized predictive control . journal Automatica volume 25-6 , pages 859--875

    1989

  29. [37]

    , author Mohtadi, C

    author Clarke, D.W. , author Mohtadi, C. , author Tuffs, P.S. , year 1987 a. title Generalized predictive control. 1. the basic algorithm . journal Automatica volume 23-2 , pages 137--148

    1987

  30. [38]

    , author Mohtadi, C

    author Clarke, D.W. , author Mohtadi, C. , author Tuffs, P.S. , year 1987 b. title Generalized predictive control. 2. extensions and interpretations . journal Automatica volume 23-2 , pages 149--160

    1987

  31. [39]

    , year 2021

    author Darby, M.L. , year 2021 . title Industrial MPC of continuous processes , in: editor Baillieul, J. , editor Samad, T. (Eds.), booktitle Encyclopedia of Systems and Control . publisher Springer International Publishing , pp. pages 985--993

    2021

  32. [40]

    , author Ferreau, H.J

    author Diehl, M. , author Ferreau, H.J. , author Haverbeke, N. , year 2009 . title Efficient numerical methods for nonlinear MPC and moving horizon estimation , in: editor Magni, L. , editor Raimondo, D.M. , editor Allgöwer, F. (Eds.), booktitle Nonlinear Model Predictive Cont...

    2009

  33. [41]

    , author Troutman, K

    author Doyle III , F. , author Troutman, K. , author Meadows, E. , author Gatzke, E. , author Vadigepalli, R. , author Mahadevan, K. , author Whitmyre, G. , author Stoole, G. , author Rickards, P. , year 2000 . title Innovative control education using a 4-tank experiment and t...

    2000

  34. [42]

    , author Gatzke, E.P

    author Doyle III , F.J. , author Gatzke, E.P. , author Parker, R.S. , year 1999 . title Process Control Modules. A Software Laboratory for Control Design . publisher Prentice Hall

    1999

  35. [43]

    , author Ritschel, T.K.S

    author Drejer, A. , author Ritschel, T.K.S. , author Jørgensen, S.B. , author Jørgensen, J.B. , year 2017 . title Economic optimizing control for single-cell protein production in a U-Loop reactor . journal Computer Aided Chemical Engineering volume 40 , pages 1759--1764

    2017

  36. [44]

    , author Sokoler, L.E

    author Edlund, K. , author Sokoler, L.E. , author Jørgensen, J.B. , year 2009 . title A primal-dual interior-point linear programming algorithm for MPC , in: booktitle Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference , pp. pages 351--356

    2009

  37. [45]

    , author Karg, B

    author Fiedler, F. , author Karg, B. , author Lüken, L. , author Brander, D. , author Heinlein, M. , author Brabender, F. , author Lucia, S. , year 2023 . title do-mpc : T owards FAIR nonlinear and robust predictive control . journal Control Engineering Practice volume 40 , pa...

    2023

  38. [46]

    , author Patwardhan, R.S

    author Forbes, M.G. , author Patwardhan, R.S. , author Hamadah, H. , author Gopaluni, R.B. , year 2015 . title Model predictive control in industry: Challenges and opportunities . journal IFAC-PapersOnLine volume 48-8 , pages 531--538

    2015

  39. [47]

    , author Powell, J.D

    author Franklin, G.F. , author Powell, J.D. , author Workmann, M.L. , year 1997 . title Digital Control of Dynamic Systems . edition 3rd ed., publisher Addison-Wesley

    1997

  40. [48]

    , year 2016

    author Frison, G. , year 2016 . title Algorithms and Methods for High-Performance Model Predictive Control . Ph.D. thesis. Technical University of Denmark

    2016

  41. [49]

    , author Diehl, M

    author Frison, G. , author Diehl, M. , year 2020 . title HPIPM : a high-performance quadratic programming framework for model predictive control . journal IFAC-PapersOnLine volume 53-2 , pages 6563--6569

    2020

  42. [50]

    , author Jørgensen, J.B

    author Frison, G. , author Jørgensen, J.B. , year 2013 a. title Efficient implementation of the R iccati recursion for solving linear-quadratic control problems , in: booktitle 2013 IEEE Multi-conference on Systems and Control Applications , pp. pages 1117--1122

    2013

  43. [51]

    , author Jørgensen, J.B

    author Frison, G. , author Jørgensen, J.B. , year 2013 b. title A fast condensing method for solution of linear-quadratic control problems , in: booktitle 52nd IEEE Conference on Decision and Control , pp. pages 7715--7720

    2013

  44. [52]

    , author Kouzoupis, D

    author Frison, G. , author Kouzoupis, D. , author Jørgensen, J.B. , author Diehl, M. , year 2016 . title An efficient implementation of partial condensing for nonlinear model predictive control , in: booktitle 2016 IEEE 55th Conference on Decision and Control (CDC) , pp. pages...

    2016

  45. [53]

    , author Kouzoupis, D

    author Frison, G. , author Kouzoupis, D. , author Sartor, T. , author Zanelli, A. , author Diehl, M. , year 2018 . title BLASFEO : Basic linear algebra subroutines for embedded optimization . journal ACM Transactions on Mathematical Software (TOMS) volume 44-4 , pages 1--30

    2018

  46. [54]

    , author Kufoalor, D.K.M

    author Frison, G. , author Kufoalor, D.K.M. , author Imsland, L. , author Jørgensen, J.B. , year 2014 a. title Efficient implementation of solvers for linear model predictive control on embedded devices , in: booktitle 2014 IEEE Conference on Control Application (CCA) , pp. pa...

    2014

  47. [55]

    , author Sokoler, L.E

    author Frison, G. , author Sokoler, L.E. , author Jørgensen, J.B. , year 2014 b. title A family of high-performance solvers for linear model predictive control , in: booktitle IFAC Proceedings Volumes , pp. pages 3074--3079

    2014

  48. [56]

    , author Sørensen, H.H.B

    author Frison, G. , author Sørensen, H.H.B. , author Dammann, B. , author Jørgensen, J.B. , year 2014 c. title High-performance small-scale solvers for linear model predictive control , in: booktitle 2014 European Control Conference , pp. pages 128--133

    2014

  49. [57]

    , author Meadows, E.S

    author Gatzke, E.P. , author Meadows, E.S. , author Wang, C. , author Doyle III , F.J. , year 2000 . title Model based control of a four-tank system . journal Computers and Chemical Engineering volume 24 , pages 1503--1509

    2000

  50. [58]

    , author Johansen, T.A

    author Grancharova, A. , author Johansen, T.A. , year 2018 . title Distributed quasi-nonlinear model predictive control with contractive constraint . journal IFAC-PapersOnLine volume 51 , pages 41--47

    2018

  51. [59]

    , author Chaudhari, V

    author Gurjar, B. , author Chaudhari, V. , author Kurode, S. , year 2021 . title Parameter estimation based robust liquid level control of quadruple tank system - S econd order sliding mode approach . journal Journal of Process Control volume 104 , pages 1--10

    2021

  52. [60]

    , author Hägglund, T

    author Guzmán, J.L. , author Hägglund, T. , year 2024 . title Feedforward Control . publisher De Gruyter

    2024

  53. [61]

    , author Boiroux, D

    author Hagdrup, M. , author Boiroux, D. , author Mahmoudi, Z. , author Madsen, H. , author Poulsen, N.K. , author Poulsen, B. , author Jørgensen, J.B. , year 2016 . title On the significance of the noise model for the performance of a linear MPC in closed-loop operation . jour...

    2016

  54. [62]

    , author Shishavan, R.A

    author Hedengren, J.D. , author Shishavan, R.A. , author Powell, K.M. , author Edgar, T.F. , year 2014 . title Nonlinear modeling, estimation and predictive control in APMonitor . journal Computers and Chemical Engineering volume 70 , pages 133--148

    2014

  55. [63]

    , author Jannerup, O

    author Hendricks, E. , author Jannerup, O. , author Sørensen, P.H. , year 2008 . title Linear Systems Control. Deterministic and Stochastic Methods . publisher Springer

    2008

  56. [64]

    , year 1998

    author Henson, M.A. , year 1998 . title Nonlinear model predictive control: current status and future directions . journal Computers and Chemical Engineering volume 23 , pages 187--202

    1998

  57. [65]

    , author Riggs, J.B

    author Huang, H. , author Riggs, J.B. , year 2002 . title Comparison of PI and MPC for control of a gas recovery unit . journal Journal of Process Control volume 12 , pages 163--173

    2002

  58. [66]

    , author Poulsen, N.K

    author Huusom, J.K. , author Poulsen, N.K. , author Jørgensen, S.B. , author Jørgensen, J.B. , year 2010 . title Tuning of methods for offset free MPC based on ARX model representations , in: booktitle 2010 American Control Conference , pp. pages 2355--2369

    2010

  59. [67]

    , author Poulsen, N.K

    author Huusom, J.K. , author Poulsen, N.K. , author Jørgensen, S.B. , author Jørgensen, J.B. , year 2011 a. title Adaptive disturbance estimation for offset-free SISO model predictive control , in: booktitle 2011 American Control Conference , pp. pages 2417--2422

    2011

  60. [68]

    , author Poulsen, N.K

    author Huusom, J.K. , author Poulsen, N.K. , author Jørgensen, S.B. , author Jørgensen, J.B. , year 2011 b. title Noise modelling and MPC tuning for systems with infrequent step disturbances . journal IFAC Proceedings Volumes volume 44-1 , pages 11226--11232

    2011

  61. [69]

    , author Poulsen, N.K

    author Huusom, J.K. , author Poulsen, N.K. , author Jørgensen, S.B. , author Jørgensen, J.B. , year 2012 . title Tuning SISO offset-free model predictive control based on ARX models . journal Journal of Process Control volume 22-10 , pages 1997--2007

    2012

  62. [70]

    , author Santacoloma, P.A

    author Huusom, J.K. , author Santacoloma, P.A. , author Poulsen, N.K. , author Jørgensen, S.B. , year 2007 . title D ata driven tuning of inventory controllers , in: booktitle 46th IEEE Conference on Decision and Control , pp. pages 4191--4196

    2007

  63. [71]

    , author Christiansen, L.H

    author Hørsholt, A. , author Christiansen, L.H. , author Ritschel, T.K.S. , author Meyer, K. , author Huusom, J.K. , author Jørgensen, J.B. , year 2019 . title State and input estimation of nonlinear chromatographic processes , in: booktitle 2019 IEEE Conference on Control Tec...

    2019

  64. [72]

    , author Maxim, A

    author Ionescu, C.M. , author Maxim, A. , author Copot, C. , author Keyser, R.D. , year 2016 . title Robust PID auto-tuning for the quadruple tank system . journal IFAC-PapersOnLine volume 49 , pages 919--924

    2016

  65. [73]

    , year 2000

    author Johansson, K.H. , year 2000 . title T he quadruple-tank process: A multivariable laboratory process with an adjustable zero . journal IEEE Transactions on Control Systems Technology volume 8 , pages 456--465

    2000

  66. [74]

    , year 2004

    author Jørgensen, J.B. , year 2004 . title Moving Horizon Estimation and Control . Ph.D. thesis. Technical University of Denmark

    2004

  67. [75]

    , year 2007 a

    author Jørgensen, J.B. , year 2007 a. title Adjoint sensitivity results for predictive control, state- and parameter-estimation with nonlinear models , in: booktitle 2007 European Control Conference (ECC) , pp. pages 3649--3656

    2007

  68. [76]

    , year 2007 b

    author Jørgensen, J.B. , year 2007 b. title A critical discussion of the continuous-discrete extended K alman filter , in: booktitle European Congress of Chemical Engineering-6 , address Copenhagen, Denmark

    2007

  69. [77]

    , author Frison, G

    author Jørgensen, J.B. , author Frison, G. , author Gade-Nielsen, N.F. , author Damman, B. , year 2012 . title Numerical methods for solution of the extended linear quadratic control problem . journal IFAC Proceedings Volume volume 45-17 , pages 187--193

    2012

  70. [78]

    , author Jørgensen, S.B

    author Jørgensen, J.B. , author Jørgensen, S.B. , year 2007 a. title Comparison of prediction-error-modelling criteria , in: booktitle American Control Conference (ACC) , address New York City, USA . pp. pages 140--146

    2007

  71. [79]

    , author Jørgensen, S.B

    author Jørgensen, J.B. , author Jørgensen, S.B. , year 2007 b. title MPC -relevant prediction-error identification , in: booktitle American Control Conference (ACC) , address New York City, USA . pp. pages 128--133

    2007

  72. [80]

    , author Kristensen, M.R

    author Jørgensen, J.B. , author Kristensen, M.R. , author Thomsen, P.G. , year 2018 . title a family of ESDIRK integration methods . journal arXiv.org , pages arXiv:1803.01613

    2018 arXiv

  73. [81]

    , author Kristensen, M.R

    author Jørgensen, J.B. , author Kristensen, M.R. , author Thomsen, P.G. , author Madsen, H. , year 2007 a. title New extended K alman filter algorithms for stochastic differential equations , in: editor Findeisen, R. , editor Allgöwer, F. , editor Biegler, L.T. (Eds.), booktit...

    2007

  74. [82]

    , author Kristensen, M.R

    author Jørgensen, J.B. , author Kristensen, M.R. , author Thomsen, P.G. , author Madsen, H. , year 2007 b. title A numerically robust ESDIRK -based implementation of the continuous-discrete extended K alman filter , in: booktitle European Control Conference 2007 , pp. pages 2859--2866

    2007

  75. [83]

    , author Rawlings, J.B

    author Jørgensen, J.B. , author Rawlings, J.B. , author Jørgensen, S.B. , year 2004 . title Numerical methods for large scale moving horizon estimation and control . journal IFAC Proceedings Volumes volume 37-9 , pages 895--900

    2004

  76. [84]

    , author Ritschel, T.K.S

    author Jørgensen, J.B. , author Ritschel, T.K.S. , author Boiroux, D. , author Schroll-Fleischer, E. , author Wahlgreen, M.R. , author Nielsen, M.K. , author Wu, H. , author Huusom, J.K. , year 2020 . title Simulation of NMPC for a laboratory adiabatic CSTR with an exothermic ...

    2020

  77. [85]

    , author Thomsen, P.G

    author Jørgensen, J.B. , author Thomsen, P.G. , author Madsen, H. , author Kristensen, M.R. , year 2007 c. title A computationally efficient and robust implementation of the continuous-discrete extended K alman filter , in: booktitle American Control Conference 2007 , pp. page...

    2007

  78. [86]

    , author Burri, M

    author Kamel, M. , author Burri, M. , author Siegwart, R. , year 2017 . title Linear vs nonlinear MPC for trajectory tracking applied to rotary wing micro aerial vehicles , in: booktitle IFAC PapersOnLine , pp. pages 3463--3469

    2017

  79. [87]

    , year 2023

    author Kaysfeld, M.W. , year 2023 . title Economic Nonlinear Model Predictive Control for Integrated and Optimized Non-stationary Operation of Biotechnological Processes . Ph.D. thesis. Technical University of Denmark

    2023

  80. [88]

    , author Zanon, M

    author Kaysfeld, M.W. , author Zanon, M. , author Jørgensen, J.B. , year 2023 . title Performance quantification of a nonlinear model predictive controller by parallel Monte Carlo simulations of a closed-loop system , in: booktitle 2023 European Control Conference (ECC) , addr...

    2023

  81. [89]

    , author Jørgensen, J.B

    author Kristensen, M.R. , author Jørgensen, J.B. , author Thomsen, P.G. , author Jørgensen, S.B. , year 2004 a. title Efficient sensitivity computation for nonlinear model predictive control . journal IFAC Proceedings Volumes volume 37-13 , pages 567--572

    2004

  82. [90]

    , author Jørgensen, J.B

    author Kristensen, M.R. , author Jørgensen, J.B. , author Thomsen, P.G. , author Jørgensen, S.B. , year 2004 b. title An ESDIRK method with sensitivity analysis capabilities . journal Computers and Chemical Engineering volume 28-12 , pages 2695--2707

    2004

  83. [91]

    , author Jørgensen, J.B

    author Kristensen, M.R. , author Jørgensen, J.B. , author Thomsen, P.G. , author Michelsen, M.L. , author Jørgensen, S.B. , year 2005 . title Sensitivity analysis in index-1 differential equations by ESDIRK methods . journal IFAC Proceedings Volumes volume 38-1 , pages 212--217

    2005

  84. [92]

    , author Madsen, H

    author Kristensen, N.R. , author Madsen, H. , author J rgensen, S.B. , year 2004 c. title Parameter estimation in stochastic grey-box models . journal Automatica volume 40 , pages 225--237

    2004

  85. [93]

    , year 2011

    author Kucera, V. , year 2011 . title A method to teach the parameterization of all stabilizing controllers , in: booktitle 18th IFAC World Congress , pp. pages 6355--6360

    2011

  86. [94]

    , author Jeyabharathi, R

    author Kumar, B.A. , author Jeyabharathi, R. , author Surendhar, S. , author Senthilrani, S. , author Gayathri, S. , year 2019 . title Control of four tank system using model predictive controller , in: booktitle 2019 IEEE International Conference on System, Computation, Autom...

    2019

  87. [95]

    , author Rawlings, J.B

    author Kuntz, S.J. , author Rawlings, J.B. , year 2024 . title Offset-free model predictive control: satbility under plant-model mismatch . journal arXiv:2412.08104

    2024 arXiv

  88. [96]

    , author Laugesen, C

    author Lindkvist, E.B. , author Laugesen, C. , author Reenberg, A.T. , author Ritschel, T.K.S. , author Svensson, J. , author Jørgensen, J.B. , author Nørgaard, K. , author Ranjan, A.G. , year 2023 . title Performance of a dual-hormone closed-loop system versus insulin-only cl...

    2023

  89. [97]

    , author Tatuleau-Codrean, A

    author Lucia, S. , author Tatuleau-Codrean, A. , author Schoppmeyer, C. , author Engell, S. , year 2017 . title Rapid development of modular and sustainable nonlinear model predictive control solutions . journal Control Engineering Practice volume 60 , pages 51--62

    2017

  90. [98]

    , year 2002

    author Maciejowski, J.M. , year 2002 . title Predictive control with constraints . publisher Prentice Hall

    2002

  91. [99]

    , author Morari, M

    author Maeder, U. , author Morari, M. , year 2010 . title Offset-free reference tracking with model predictive control . journal Automatica volume 46 , pages 1469--1476

    2010

  92. [100]

    , author Navas, F

    author Mahtout, I. , author Navas, F. , author Milanes, V. , author Nashashibi, F. , year 2020 . title Advances in the Youla-Kucera parametrization: A review . journal Annual Reviews in Control volume 49 , pages 81--94

    2020

  93. [101]

    , year 2000

    author Marlin, T.E. , year 2000 . title Process Control. Designing Processes and Control Systems for Dynamic Performance . edition 2nd ed., publisher McGraw-Hill

    2000

  94. [102]

    , author Doyle, F.J

    author Mercangöz, M. , author Doyle, F.J. , year 2007 . title Distributed model predictive control of an experimental four-tank system . journal Journal of Process Control volume 17 , pages 297--308

    2007

  95. [103]

    , author Maeder, U

    author Morari, M. , author Maeder, U. , year 2012 . title Nonlinear offset-free model predictive control . journal Automatica volume 48 , pages 2059--2067

    2012

  96. [104]

    , author Zafiriou, E

    author Morari, M. , author Zafiriou, E. , year 1989 . title Robust Process Control . publisher Prentice Hall

    1989

  97. [105]

    , author Badgwell, T.A

    author Muske, K.R. , author Badgwell, T.A. , year 2002 . title Disturbance modeling for offset-free linear model predictive control . journal Journal of Process Control volume 12 , pages 617--632

    2002

  98. [106]

    , author Guiver, J

    author Naidoo, K. , author Guiver, J. , author Turner, P. , author Keenan, M. , author Harmse, M. , year 2007 . title Experiences with nonlinear MPC in polymer manufacturing , in: editor Findeisen, R. , editor Allgöwer, F. , editor Biegler, L. (Eds.), booktitle Assessment and ...

    2007

  99. [107]

    , year 2023

    author Nielsen, M.K. , year 2023 . title Economic Optimizing Control for a U-loop Reactor. Modelling, Estimation, and Economic Nonlinear Model Predictive Control . Ph.D. thesis. Technical University of Denmark

    2023

  100. [108]

    , author Abirami, B.V

    author Nirmala, S. , author Abirami, B.V. , author Manamalli, D. , year 2011 . title Design of model predictive controller for a four-tank process using linear state space model and performance study for reference tracking under disturbances , in: booktitle 2011 International ...

    2011

  101. [109]

    , author Xiao, D

    author Niu, S.S. , author Xiao, D. , year 2022 . title Process Control. Engineering Analyses and Best Practices . publisher Springer

    2022

  102. [110]

    , author Rawlings, J.B

    author Odelson, B.J. , author Rawlings, J.B. , year 2003 . title Online monitoring of MPC disturbance models using closed-loop data , in: booktitle American Control Conference (ACC) , address Colorado, USA . pp. pages 2714--2719

    2003

  103. [111]

    , author Ray, W.H

    author Ogunnaike, B.A. , author Ray, W.H. , year 1994 . title Process Dynamics, Modeling, and Control . publisher Oxford University Press

    1994

  104. [112]

    , author Huusom, J.K

    author Olesen, D.H. , author Huusom, J.K. , author Jørgensen, J.B. , year 2013 a. title A tuning procedure for ARX -based MPC , in: booktitle 2013 IEEE Multi-conference on Systems and Control , pp. pages 188--193

    2013

  105. [113]

    , author Huusom, J.K

    author Olesen, D.H. , author Huusom, J.K. , author Jørgensen, J.B. , year 2013 b. title A tuning procedure for ARX -based MPC of multivariate processes , in: booktitle 2013 American Control Conference , pp. pages 1721--1726

    2013

  106. [114]

    , year 2015

    author Pannocchia, G. , year 2015 . title Offset-free tracking MPC : A tutotorial review and comparison of different formulations , in: booktitle 2015 European Control Conference (ECC) , pp. pages 527--532

    2015

  107. [115]

    , author Laachi, N

    author Pannocchia, G. , author Laachi, N. , author Rawlings, J.B. , year 2005 . title A candidate to replace PID control: SISO -constrained LQ control . journal AIChE Journal volume 51 , pages 1178--1189

    2005

  108. [116]

    , author Rawlings, J.B

    author Pannocchia, G. , author Rawlings, J.B. , year 2003 . title Disturbance models for offset-free model predictive control . journal AIChE Journal volume 49 , pages 426--437

    2003

  109. [117]

    , year 2016

    author Petersen, L.N. , year 2016 . title Economic Model Predictive Control for Spray Drying Plants . Ph.D. thesis. Technical University of Denmark

    2016

  110. [118]

    , author Poulsen, N.K

    author Petersen, L.N. , author Poulsen, N.K. , author Niemann, H.H. , author Utzen, C. , author Jørgensen, J.B. , year 2017 . title Comparison of three control strategies for optimization of spray dryer operation . journal Journal of Process Control volume 57 , pages 1--14

    2017

  111. [119]

    , author Zhang, W

    author Pulsipher, J.L. , author Zhang, W. , author Hongisto, T.J. , author Zavala, V.M. , year 2022 . title A unifying modeling abstraction for infinite-dimensional optimization . journal Computers and Chemical Engineering volume 156 , pages 107567

    2022

  112. [120]

    , author Badgwell, T.A

    author Qin, S.J. , author Badgwell, T.A. , year 2000 . title An overview of nonlinear model predictive control applications , in: editor Allgöwer, F. , editor Zheng, A. (Eds.), booktitle Nonlinear Model Predictive Control . publisher Birkhäuser , pp. pages 369--392

    2000

  113. [121]

    , author Badgwell, T.A

    author Qin, S.J. , author Badgwell, T.A. , year 2003 . title A survey of industrial model predictive control technology . journal Control Engineering Practice volume 11 , pages 733--764

    2003

  114. [122]

    , author Huber, S

    author Raff, T. , author Huber, S. , author Nagy, Z.K. , author Allgöwer, F. , year 2006 . title Nonlinear model predictive control of a four tank system: An experimental stability study , in: booktitle Proceeding of the 2006 IEEE International Conference on Control Applicatio...

    2006

  115. [123]

    , author Mayne, D.Q

    author Rawlings, J.B. , author Mayne, D.Q. , author Diehl, M. , year 2022 . title Model predictive control: theory, computation, and design . edition Second ed., publisher Nob Hill Publishing

    2022

  116. [124]

    , year 2023

    author Reenberg, A.T. , year 2023 . title Systematic Mathematical Modeling for Agile Development of Model Based Medical Control Systems . Ph.D. thesis. Technical University of Denmark

    2023

  117. [125]

    , author Ritschel, T.K.S

    author Reenberg, A.T. , author Ritschel, T.K.S. , author Lindkvist, E.B. , author Laugesen, C. , author Svensson, J. , author Ranjan, A.G. , author Nørgaard, K. , author Jørgensen, J.B. , year 2022 . title Nonlinear model predictive control and system identification for a dual...

    2022

  118. [126]

    , year 2018

    author Ritschel, T.K.S. , year 2018 . title Nonlinear Model Predictive Control for Oil Reservoirs . Ph.D. thesis. Technical University of Denmark

    2018

  119. [127]

    , author Boiroux, D

    author Ritschel, T.K.S. , author Boiroux, D. , author Nielsen, M.K. , author Huusom, J.K. , author Jørgensen, S.B. , author Jørgensen, J.B. , year 2019 a. title Economic optimal control of a U-loop bioreactor using simultaneous collocation-based approaches , in: booktitle 2019...

    2019

  120. [128]

    , author Boiroux, D

    author Ritschel, T.K.S. , author Boiroux, D. , author Nielsen, M.K. , author Huusom, J.K. , author Jørgensen, S.B. , author Jørgensen, J.B. , year 2019 b. title The extended kalman filter for nonlinear state estimation in a U-loop bioreactor , in: booktitle 2019 IEEE Conferenc...

    2019

  121. [129]

    , author Boiroux, D

    author Ritschel, T.K.S. , author Boiroux, D. , author Nielsen, M.K. , author Huusom, J.K. , author Jørgensen, S.B. , author Jørgensen, J.B. , year 2020 . title Economic nonlinear model predictive control of a U -loop bioreactor , in: booktitle 2020 European Control Conference ...

    2020

  122. [130]

    , author Capolei, A

    author Ritschel, T.K.S. , author Capolei, A. , author Gaspar, J. , author Jørgensen, J.B. , year 2018 . title An algorithm for gradient-based dynamic optimization of UV flash processes . journal Computers and Chemical Engineering volume 114 , pages 281--295

    2018

  123. [131]

    , author Jørgensen, J.B

    author Ritschel, T.K.S. , author Jørgensen, J.B. , year 2018 a. title The extended kalman filter for state estimation of dynamic UV flash processes . journal IFAC-PapersOnLine volume 51-8 , pages 164--169

    2018

  124. [132]

    , author Jørgensen, J.B

    author Ritschel, T.K.S. , author Jørgensen, J.B. , year 2018 b. title Nonlinear filters for state estimation of UV flash processes , in: booktitle 2018 IEEE Conference on Control Technology and Applications (CCTA) , pp. pages 1753--1760

    2018

  125. [133]

    , author Jørgensen, J.B

    author Ritschel, T.K.S. , author Jørgensen, J.B. , year 2019 . title Nonlinear model predictive control for disturbance rejection in isoenergetic-isochoric flash processes . journal IFAC-PapersOnLine volume 52 , pages 796--801

    2019

  126. [134]

    , author Morari, M

    author Rivera, D.E. , author Morari, M. , author Skogestad, S. , year 1986 . title Internal model control: PID controller design . journal Industrial & Engineering Chemistry Process Design and Development volume 25 , pages 252--265

    1986

  127. [135]

    , author Limon, D

    author Santos, T.L.M. , author Limon, D. , author Normey-Rico, J.E. , author Alamo, T. , year 2012 . title On the explicit dead-time compensation for robust model predictive control . journal Journal of Process Control volume 22 , pages 236--246

    2012

  128. [136]

    , author Jørgensen, J.B

    author Schytt, M.J. , author Jørgensen, J.B. , year 2024 . title Numerical methods for optimal boundary control of advection-diffusion-reaction systems . journal arXiv.org , pages arXiv:2404.07674

    2024 arXiv

  129. [137]

    , author Edgar, T.F

    author Seborg, D.E. , author Edgar, T.F. , author Mellichamp, D.A. , author Doyle, F.J. , year 2011 . title Process dynamics and control . edition Third ed., publisher John Wiley & Sons, Inc

    2011

  130. [138]

    , author Puig, V

    author Segovia, P. , author Puig, V. , author Duviella, E. , author Etienne, L. , year 2021 . title Distributed model predictive control using optimality condition decomposition and community detection . journal Journal of Process Control volume 99 , pages 54--68

    2021

  131. [139]

    , author Rajaoarisoa, L

    author Segovia, P. , author Rajaoarisoa, L. , author Nejjari, F. , author Duviella, E. , author Puig, V. , year 2019 . title A communication-based distributed model predictive control approach for large-scale systems , in: booktitle 58th IEEE Conference on Decision and Control...

    2019

  132. [140]

    , author Patel, D.M

    author Shaha, D.H. , author Patel, D.M. , year 2019 . title Design of sliding mode control for quadruple-tank MIMO process with time delay compensation . journal Journal of Process Control volume 76 , pages 46--61

    2019

  133. [141]

    , year 2003

    author Skogestad, S. , year 2003 . title Simple analytic rules for model reduction and PID controller tuning . journal Journal of Process Control volume 13 , pages 291--309

    2003

  134. [142]

    , year 2023

    author Skogestad, S. , year 2023 . title Advanced control using decomposition and simple elements . journal Annual Reviews in Control volume 56 , pages 100903

    2023

  135. [143]

    , author Postlethwaite, I

    author Skogestad, S. , author Postlethwaite, I. , year 2005 . title Multivariable feedback control: analysis and design . edition Second ed., publisher John Wiley & Sons, Inc

    2005

  136. [144]

    , author Josefsson, F

    author Skålén, S. , author Josefsson, F. , author Ihrström, J. , year 2016 . title Nonlinear MPC for grade transitions in an industrial LDPE tubular reactor . journal IFAC-PapersOnLine volume 49-7 , pages 562--567

    2016

  137. [145]

    , author Li, W

    author Slotine, J.J.E. , author Li, W. , year 1991 . title Applied nonlinear control . publisher Prentice Hall Internatioal Inc. , address Upper Saddle River, New Jersey

    1991

  138. [146]

    , author Frison, G

    author Sokoler, L.E. , author Frison, G. , author Edlund, K. , author Skajaa, A. , author Jørgensen, J.B. , year 2013 a. title A R iccati based homogeneous and self-dual interior-point method for linear economic model predictive control , in: booktitle 2013 IEEE Multi-Conferen...

    2013

  139. [147]

    , author Frison, G

    author Sokoler, L.E. , author Frison, G. , author Skajaa, A. , author Halvgaard, R. , author Jørgensen, J.B. , year 2016 . title A homogeneous and self-dual interior-point linear programming algorithm for economic model predictive control . journal IEEE Transactions on Automat...

    2016

  140. [148]

    , author Skajaa, A

    author Sokoler, L.E. , author Skajaa, A. , author Frison, G. , author Halvgaard, R. , author Jørgensen, J.B. , year 2013 b. title A warm-started homogeneous and self-dual interior-point method for linear economic model predictive control , in: booktitle 52nd IEEE Conference on...

    2013

  141. [149]

    , author Muske, K.R

    author Soroush, M. , author Muske, K.R. , year 2000 . title Analytical model predictive control , in: editor Allgöver, F. , editor Zheng, A. (Eds.), booktitle Progress in Systems and Control Theory . publisher Birkhäuser Verlag , address Basel, Switzerland , pp. pages 163--179

    2000

  142. [150]

    , year 1984

    author Stephanopoulos, G. , year 1984 . title Chemical Process Control: An Introduction to Theory and Practice . publisher Prentice Hall International

    1984

  143. [151]

    , year 2025

    author Stephanopoulos, G. , year 2025 . title Chemical and Biological Process Dynamics and Control . publisher Tetractýs Editions

    2025

  144. [152]

    , author Solin, A

    author Särkkä, S. , author Solin, A. , year 2019 . title Applied Stochastic Differential Equations . publisher Cambridge

    2019

  145. [153]

    , author Mareels, I

    author Tay, T.T. , author Mareels, I. , author Moore, J.B. , year 1998 . title High Performance Control . publisher Springer Science+Business Media

    1998

  146. [154]

    , author Sorensen, C.D

    author Taysom, B.S. , author Sorensen, C.D. , author Hedengren, J.D. , year 2017 . title A comparison of model predictive control and PID temperature control in friction stir welding . journal Journal of Manufacturing Processes volume 29 , pages 232--241

    2017

  147. [155]

    , author Skogestad, S

    author Turan, E.M. , author Skogestad, S. , author Jäschke, J. , year 2024 . title Model predictive control for bottleneck isolation with unmeasured faults . journal 12th IFAC International Symposium on Advanced Control of Chemical Processes (ADCHEM) , pages 770--777

    2024

  148. [156]

    , author Frison, G

    author Verschueren, R. , author Frison, G. , author Kouzoupis, D. , author Frey, J. , author van Duijkeren , N. , author Zanelli, A. , author Novoselnik, B. , author Albin, T. , author Quirynen, R. , author Diehl, M. , year 2022 . title acados - a modular open-source framework...

    2022

  149. [157]

    , year 2006

    author Visioli, A. , year 2006 . title Practical PID control . publisher Springer-Verlag London

    2006

  150. [158]

    , author Reenberg, A.T

    author Wahlgreen, M.R. , author Reenberg, A.T. , author Nielsen, M.K. , author Rydahl, A. , author Ritschel, T.K.S. , author Dammann, B. , author Jørgensen, J.B. , year 2021 . title A high-performance monte carlo simulation toolbox for uncertainty quantification of closed-loop...

    2021

  151. [159]

    , author Schroll-Fleischer, E

    author Wahlgreen, M.R. , author Schroll-Fleischer, E. , author Boiroux, D. , author Ritschel, T.K.S. , author Wu, H. , author Huusom, J.K. , author Jørgensen, J.B. , year 2020 . title Nonlinear model predictive control for an exothermic reaction in an adiabatic CSTR . journal ...

    2020

  152. [160]

    , author Jørgensen, J.B

    author Waschl, H. , author Jørgensen, J.B. , author Huusom, J.K. , author del Re, L. , year 2014 . title A tuning approach for offset-free MPC with conditional reference adaptation , in: booktitle 19th IFAC World Congress , address Cape Town, South Africa . pp. pages 3062--3067

    2014

  153. [161]

    , author Jørgensen, J.B

    author Waschl, H. , author Jørgensen, J.B. , author Huusom, J.K. , author del Re, L. , year 2015 . title A novel tuning approach for offset-free MPC , in: booktitle 2015 European Control Conference , pp. pages 545--550

    2015

  154. [162]

    , year 2006

    author Williams, R. , year 2006 . title Real-Time Systems Development . publisher Butterworth-Heinemann (Elsevier)

    2006

  155. [163]

    , author Biegler, L

    author Wächter, A. , author Biegler, L. , year 2006 . title On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming . journal Mathematical Programming volume 106 , pages 25--57

    2006

  156. [164]

    , author Wang, Y

    author Yu, S. , author Wang, Y. , author Wang, J. , author Chen, H. , year 2016 . title Constrained output feedback H _ control of a four-tank system , in: booktitle Proceedings of 2016 IEEE International Conference on Mechatronics and Automation , publisher IEEE , address Har...

    2016

  157. [165]

    , author Biegler, L.T

    author Zavala, V.M. , author Biegler, L.T. , year 2009 . title Nonlinear programming strategies for state estimation and model predictive control , in: editor Magni, L. , editor Raimondo, D.M. , editor Allgöwer, F. (Eds.), booktitle Nonlinear Model Predictive Control. Toward N...

    2009

  158. [166]

    , year 2024

    author Zhang, Z. , year 2024 . title Model Predictive Control for Zero Emission Industrial Processes . Ph.D. thesis. Technical University of Denmark

    2024

  159. [167]

    , author Christensen, A.H.D

    author Zhang, Z. , author Christensen, A.H.D. , author Svensen, J.L. , author Hørsholt, S. , author Jørgensen, J.B. , year 2025 a. title Linear-quadratic model predictive control for continuous-time systems with time delays and piecewise constant inputs , in: booktitle 14th IF...

    2025

  160. [168]

    , author Hørsholt, S

    author Zhang, Z. , author Hørsholt, S. , author Jørgensen, J.B. , year 2024 a. title Numerical discretization methods for linear quadratic control problems with time delays . journal IFAC-PapersOnLine volume 58 , pages 874--880

    2024

  161. [169]

    , author Svensen, J.L

    author Zhang, Z. , author Svensen, J.L. , author Hørsholt, S. , author Jørgensen, J.B. , year 2025 b. title Numerical discretization methods for the discounted linear quadratic control problem , in: booktitle 2025 European Control Conference (ECC)

    2025

  162. [170]

    , author Svensen, J.L

    author Zhang, Z. , author Svensen, J.L. , author Kaysfeld, M.W. , author Christensen, A.H.D. , author Hørsholt, S. , author Jørgensen, J.B. , year 2024 b. title Numerical discretization methods for the extended linear quadratic control problem , in: booktitle 2024 European Con...

    2024

  163. [171]

    , author Yang, Z

    author Zong, X. , author Yang, Z. , author Yuan, D. , year 2010 . title Nonlinear modeling and predictive control of the four-tank system , in: booktitle The 2nd International Conference on Software Engineering and Data Mining , publisher IEEE

    2010

  164. [172]

    , year 1980

    author Åström, K.J. , year 1980 . title Maximum likelihood and prediction error methods . journal Automatica volume 16 , pages 551--574

    1980

  165. [173]

    , author Hägglund, T

    author Åström, K.J. , author Hägglund, T. , year 1995 . title PID controllers: theory, design, and tuning . edition Second ed., publisher Instrument Society of America

    1995

  166. [174]

    , author Murray, R.M

    author Åström, K.J. , author Murray, R.M. , year 2009 . title Feedback Systems: A n Introduction for Scientists and Engineers . edition v2.10b ed., publisher Princeton University Press

    2009

  167. [175]

    , author Wittenmark, B

    author Åström, K.J. , author Wittenmark, B. , year 2011 . title Computer-controlled systems: T heory and design . edition Third ed., publisher Dover Publications Inc

    2011

Pith tools

Reviewed August 4, 2026 · model on record in the stance chip above.