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arxiv: 2605.03489 · v1 · submitted 2026-05-05 · 📡 eess.SY · cs.SY

A simulation- and model-based approach to PI control pairing and tuning for the pyro process in a cement plant

Jan Lorenz Svensen , Steen H{\o}rsholt , Guruprasath Muralidharan , John Bagterp J{\o}rgensen This is my paper

Pith reviewed 2026-05-07 14:01 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords PI controlcement plantpyro processDAE modelrelative gain arrayinternal model controldecentralized controlprocess simulation
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The pith

A DAE model of the cement pyro process enables RGA-based pairing and IMC tuning of decentralized PI controllers that outperform manual tuning in closed-loop simulations.

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

The paper demonstrates that a novel differential algebraic equation model of the pyro-section can guide the design of control systems for cement production. Linearization of the model supplies the data needed to apply the relative gain array method for selecting which manipulated variables pair with which controlled variables. Simulated step responses then supply the process models used to tune single-loop PI controllers by the internal model control method. In closed-loop tests these model-derived parameters produce smoother and faster responses to disturbances than parameters tuned by hand. If the model represents the plant well, the approach replaces much of the trial-and-error tuning that currently occurs on the physical equipment.

Core claim

A novel DAE model of the pyro process is linearized to compute relative gain arrays that identify effective pairings between manipulated and controlled variables; step-response simulations of the same model then yield transfer-function approximations that are used to tune decentralized PI controllers via the internal model control procedure, and closed-loop simulations show that the resulting controllers respond more smoothly and quickly than manually tuned controllers.

What carries the argument

The novel differential algebraic equation (DAE) model of the pyro-section, which supplies both the linearizations for relative-gain-array pairing analysis and the step-response data for internal-model-control tuning of the PI controllers.

Load-bearing premise

The novel DAE model must accurately capture the dominant dynamics of the real pyro process so that linearizations and step-response simulations produce controller parameters that perform well on the physical plant.

What would settle it

Implement the IMC-tuned controllers on the actual cement-plant pyro section and measure the speed and smoothness of disturbance rejection; if the performance advantage over the manually tuned controllers disappears, the model-based design claim is falsified.

Figures

Figures reproduced from arXiv: 2605.03489 by Guruprasath Muralidharan, Jan Lorenz Svensen, John Bagterp J{\o}rgensen, Steen H{\o}rsholt.

Figure 1
Figure 1. Figure 1: a 5-stage pyro process with PI-control loops for view at source ↗
Figure 2
Figure 2. Figure 2: MV-CV step responses: simulated step responses of the simulator for 4 different step sizes (m1: -1%(blue), m2: view at source ↗
Figure 3
Figure 3. Figure 3: MV-CV normalized step responses for 4 differ view at source ↗
Figure 4
Figure 4. Figure 4: 50-hour closed-loop simulations using the IMC-PIs view at source ↗
Figure 6
Figure 6. Figure 6: Responsiveness of CVs to MVs. Maximum relative view at source ↗
read the original abstract

The operation of the pyro process in cement production significantly affects the energy efficiency and sustainability of the cement plant, especially for reductions in carbon dioxide emissions. Hence, pyro process control is essential to obtain efficient and sustainable operation of cement plants. In this paper, we demonstrate how simulations and models can be utilized to evaluate and design control strategies for the pyro section in cement plants. We apply a novel differential algebraic equation (DAE) model for dynamic simulation of the pyro-section in cement plants to design decentralized PI controllers for the pyro-section. We utilize the pyro-process model to evaluate the control structure design. Through linearization of the pyro-process model, we apply the Relative Gain Array (RGA) method to choose and evaluate the pairings of the manipulated variables (MVs) and the controlled variables (CVs). Using simulations of the pyro-section, we generate step responses to estimate transfer models and apply Internal Model Control (IMC) for the tuning of the individual decentralized single-input single-output (SISO) PI controllers. Closed-loop simulations of the PI controllers demonstrate that PI controllers with IMC parameters provide smoother and faster responses compared with manually tuned PI parameters.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper claims to demonstrate a simulation- and model-based approach for designing decentralized PI controllers for the pyro process in cement plants. It introduces a novel DAE model, uses linearization and the Relative Gain Array (RGA) to select MV-CV pairings, generates step responses to fit transfer-function models for Internal Model Control (IMC) tuning of the SISO PI controllers, and shows via closed-loop simulations that the IMC-tuned controllers yield smoother and faster responses than manually tuned parameters.

Significance. If the DAE model is validated against plant data, the work offers a systematic, reproducible methodology for control-structure selection and tuning in a high-impact industrial process, potentially supporting energy-efficiency gains and CO2 reductions in cement production. The integration of standard tools (RGA, IMC) with process simulation is a clear strength, providing a template that could be applied to other complex DAE-governed systems.

major comments (2)
  1. [Abstract and model-description sections] Abstract and model-description sections: the novel DAE model is the sole basis for RGA pairing, transfer-function identification, IMC tuning, and all closed-loop performance claims, yet the manuscript supplies no quantitative validation (steady-state matching, dynamic response errors, or comparison to logged plant measurements). This is load-bearing because controller parameters are derived directly from the model; without evidence that the model captures the dominant gains and time constants of the physical pyro process, the transfer of the reported IMC superiority to the real plant remains untested.
  2. [Closed-loop simulation results] Closed-loop simulation results: the claim that IMC-tuned PIs provide smoother and faster responses is supported only by qualitative description of step-response trajectories; no quantitative metrics (settling time, overshoot, IAE, or robustness margins) or error bars are reported, weakening the comparison to manual tuning.
minor comments (1)
  1. Figure captions and axis labels should explicitly state the simulation conditions (e.g., which disturbances are applied) and the exact transfer-function forms fitted for IMC design.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed feedback, which highlights important aspects of model credibility and result quantification. We address each major comment below and outline revisions to strengthen the manuscript while preserving its focus on the simulation-based methodology.

read point-by-point responses

  1. Referee: [Abstract and model-description sections] Abstract and model-description sections: the novel DAE model is the sole basis for RGA pairing, transfer-function identification, IMC tuning, and all closed-loop performance claims, yet the manuscript supplies no quantitative validation (steady-state matching, dynamic response errors, or comparison to logged plant measurements). This is load-bearing because controller parameters are derived directly from the model; without evidence that the model captures the dominant gains and time constants of the physical pyro process, the transfer of the reported IMC superiority to the real plant remains untested.

    Authors: We agree that the absence of quantitative validation against plant data is a limitation for claims of direct applicability to the physical pyro process. The manuscript's core contribution is the demonstration of a reproducible, simulation-driven workflow (linearization, RGA, step-response identification, and IMC tuning) using the novel DAE model; all performance comparisons are therefore model-internal. The paper does not assert that the IMC parameters have been deployed or validated on the real plant. In the revision we will (i) add an explicit limitations subsection clarifying that results are simulation-based and that plant validation remains necessary for industrial transfer, (ii) include any available steady-state gain comparisons derivable from the model equations, and (iii) rephrase the abstract and introduction to emphasize the methodological rather than plant-validated nature of the study. This constitutes a partial revision. revision: partial

  2. Referee: [Closed-loop simulation results] Closed-loop simulation results: the claim that IMC-tuned PIs provide smoother and faster responses is supported only by qualitative description of step-response trajectories; no quantitative metrics (settling time, overshoot, IAE, or robustness margins) or error bars are reported, weakening the comparison to manual tuning.

    Authors: We concur that quantitative metrics would make the comparison more rigorous and reproducible. In the revised manuscript we will augment the closed-loop results section with explicit numerical values for settling time (to 5 % and 2 % bands), percentage overshoot, integral absolute error (IAE), and robustness margins (gain margin, phase margin, and sensitivity peak) for both the IMC-tuned and manually tuned controllers. Where multiple simulation runs are feasible, we will also report variability or error bars. These additions will be presented in a new table and referenced in the text, directly addressing the qualitative-only limitation. revision: yes

Circularity Check

0 steps flagged

No circularity; model-based RGA/IMC design and closed-loop simulation form an independent evaluation chain.

full rationale

The paper linearizes its DAE model, applies standard RGA for pairing, generates step-response data to fit SISO transfer functions, applies IMC tuning formulas, and compares closed-loop behavior against manually tuned parameters via simulation on the same model. None of these steps reduce by construction to their inputs: the performance difference is an emergent simulation outcome rather than a fitted or self-defined quantity. No self-citation chains, uniqueness theorems, or ansatzes are invoked to force the result. The central claim remains a demonstration within the model, with transfer to the physical plant treated as an external assumption rather than a tautology.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the existence and fidelity of a novel DAE model whose detailed equations and validation are not supplied in the abstract; standard linearization and IMC assumptions are invoked without further justification.

axioms (2)
  • domain assumption The pyro process dynamics can be represented by a system of differential-algebraic equations that remain valid after linearization around a nominal operating point.
    Invoked when the authors linearize the model to obtain transfer functions for RGA and IMC.
  • domain assumption Step-response data generated from the simulator are sufficient to identify first-order-plus-dead-time models accurate enough for IMC tuning.
    Used to generate the transfer models for each SISO loop.

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