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arxiv: 2606.07208 · v1 · pith:7PKS2AHHnew · submitted 2026-06-05 · 📡 eess.SY · cs.SY

Unlocking feedforward capabilities in Model Predictive Control algorithms to deal with measurable disturbances

Jos\'e Luis Guzm\'an , Igor Pataro , Juan D. Gil , Manuel Berenguel This is my paper

Pith reviewed 2026-06-27 21:22 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords model predictive controlfeedforward controldisturbance rejectiondynamic matrix controlgeneralized predictive controlreverse osmosis
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The pith

Model Predictive Control can achieve complete feedforward rejection of measurable disturbances by separating tracking and disturbance-rejection actions.

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

Standard MPC formulations penalize control effort in their cost function, preventing full compensation of measurable disturbances even when they can be measured in advance. This paper introduces a dual-control structure that computes a tracking-oriented action and a separate feedforward-oriented action without any penalty on the latter. The two actions are summed into one signal on which constraints are enforced. This allows MPC to match the performance of classical feedforward compensators for disturbance rejection while retaining its optimization and constraint-handling features. The approach is shown for several common MPC variants and tested on a reverse osmosis process.

Core claim

The paper claims that by formulating a feedforward-oriented control action without penalizing control effort and combining it with a tracking-oriented action into a single constrained signal, MPC can achieve full compensation of measurable disturbances.

What carries the argument

A dual-control structure that computes a tracking-oriented action addressing set-point tracking and robustness, and a feedforward-oriented action dedicated to disturbance rejection, then combines them.

If this is right

  • Full compensation of measurable disturbances becomes possible in MPC formulations.
  • The method works for Dynamic Matrix Control, Generalised Predictive Control, and state-space MPC.
  • Disturbance rejection improves compared to standard MPC while constraints are still handled.
  • Overall control performance is preserved alongside better disturbance handling.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar dual structures might extend to other predictive control methods beyond the three variants tested.
  • Stability guarantees would need separate analysis when the feedforward action is unconstrained in effort.
  • Application to real-time processes could reveal computational overhead from solving the dual optimizations.

Load-bearing premise

The two separate control actions can be added together into one signal while still enforcing all process constraints without losing the full disturbance compensation or stability.

What would settle it

A simulation or experiment where the proposed MPC is applied to a process with a known measurable disturbance, and the disturbance rejection performance is compared to a classical feedforward controller; if the rejection is not as complete, or if constraints are violated, the claim would be falsified.

Figures

Figures reproduced from arXiv: 2606.07208 by Igor Pataro, Jos\'e Luis Guzm\'an, Juan D. Gil, Manuel Berenguel.

Figure 1
Figure 1. Figure 1: Classical feedforward control scheme to deal with measurable disturbances. [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Comparative simulation results for the ideal measurable disturbance rejection [PITH_FULL_IMAGE:figures/full_fig_p026_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Comparative simulation results for the input-constrained feedforward compen [PITH_FULL_IMAGE:figures/full_fig_p029_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Comparative simulation results for the non-invertible feedforward compensation [PITH_FULL_IMAGE:figures/full_fig_p031_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Schematic diagram of the RO system. The nonlinear reverse-osmosis model used to simulate the plant is based on the classical solution–diffusion transport mechanism commonly employed in reverse-osmosis modelling. Similar dynamic formulations can be found in 33 [PITH_FULL_IMAGE:figures/full_fig_p033_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Comparison of the RO nonlinear case study under disturbance and reference [PITH_FULL_IMAGE:figures/full_fig_p036_6.png] view at source ↗
read the original abstract

Disturbance rejection is a central objective in process control, particularly when measurable disturbances can be exploited through feedforward action. Although Model Predictive Control (MPC) naturally incorporates disturbance models and prediction capabilities, standard formulations cannot achieve complete disturbance rejection since the cost function penalises control effort. This limitation prevents MPC from reproducing the behaviour of classical feedforward compensators. This work proposes a novel framework to embed true feedforward capabilities within MPC without removing the control effort penalty. The approach introduces a dual-control structure in which two control actions are computed simultaneously: a tracking-oriented action addressing set-point tracking and robustness, and a feedforward-oriented action dedicated to disturbance rejection. Both contributions are combined into a single control signal on which the process constraints are explicitly enforced. The feedforward-oriented action is formulated without penalising control effort, enabling full compensation of measurable disturbances. The methodology is developed for Dynamic Matrix Control (DMC), Generalised Predictive Control (GPC), and state-space MPC. Its effectiveness is demonstrated through simulation studies, including comparisons with standard MPC and classical feedforward schemes. A case study based on a reverse osmosis process shows that the proposed approach improves disturbance rejection while preserving constraint handling and overall control performance.

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 / 2 minor

Summary. The paper proposes a dual-action MPC framework for DMC, GPC, and state-space formulations. A tracking-oriented action handles set-point tracking and robustness while a separate feedforward-oriented action (formulated with zero penalty on control effort) handles measurable disturbance rejection; the two are summed and the combined input is projected onto the feasible set to enforce constraints. The central claim is that this structure achieves full (unpenalized) disturbance compensation while retaining standard MPC constraint handling and stability properties. Effectiveness is illustrated via simulation studies and a reverse-osmosis case study.

Significance. If the invariance property under active constraints can be established, the result would allow MPC to recover the exact compensation behavior of classical feedforward controllers without sacrificing the ability to optimize tracking or enforce input/output bounds. This would be a meaningful advance for process-control applications where measurable disturbances are common and constraint satisfaction is mandatory.

major comments (2)
  1. [Methodology (dual-action combination and constraint enforcement)] The manuscript states that constraints are enforced on the combined control signal, yet provides no explicit invariance, decomposition, or proof that the feedforward component remains unaltered when the quadratic program projects the sum onto the feasible set. Because the feedforward action is defined with zero weight on control effort, any active constraint that modifies this component reintroduces an implicit penalty and can leave a residual disturbance error. This point is load-bearing for the central claim of “full compensation.”
  2. [Stability analysis] The stability argument for the closed-loop system under the dual structure is not shown to hold when the feedforward term is non-zero and constraints become active; the standard MPC stability proofs rely on a single optimized input sequence whose cost includes control effort. An explicit Lyapunov or terminal-set argument that accounts for the unpenalized feedforward contribution is required.
minor comments (2)
  1. [Notation] Notation for the two actions (tracking vs. feedforward) should be introduced with distinct symbols and kept consistent across the DMC, GPC, and state-space sections.
  2. [Simulation results] The simulation figures would benefit from an additional panel or table quantifying the residual disturbance error when constraints are active, to directly support the “full compensation” claim.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. The two major comments identify substantive gaps in the current presentation of the dual-action framework. We respond to each point below and commit to revisions that strengthen the manuscript without altering its core claims.

read point-by-point responses

  1. Referee: [Methodology (dual-action combination and constraint enforcement)] The manuscript states that constraints are enforced on the combined control signal, yet provides no explicit invariance, decomposition, or proof that the feedforward component remains unaltered when the quadratic program projects the sum onto the feasible set. Because the feedforward action is defined with zero weight on control effort, any active constraint that modifies this component reintroduces an implicit penalty and can leave a residual disturbance error. This point is load-bearing for the central claim of “full compensation.”

    Authors: We acknowledge that the manuscript currently lacks an explicit invariance argument. The feedforward action is computed independently with zero effort weight and added to the tracking action before projection; however, the projection step can in principle alter the effective feedforward contribution. In the revision we will insert a new subsection that decomposes the QP solution into tracking and feedforward components and proves that, because the feedforward term carries no quadratic penalty, any feasible adjustment required by the projection can be absorbed entirely by the penalized tracking component without residual disturbance error, provided the tracking action remains within its own feasible region. This decomposition will be stated formally for the DMC, GPC and state-space cases. revision: yes

  2. Referee: [Stability analysis] The stability argument for the closed-loop system under the dual structure is not shown to hold when the feedforward term is non-zero and constraints become active; the standard MPC stability proofs rely on a single optimized input sequence whose cost includes control effort. An explicit Lyapunov or terminal-set argument that accounts for the unpenalized feedforward contribution is required.

    Authors: The referee is correct that standard terminal-cost or terminal-set arguments assume a single penalized input sequence. We will augment the stability section with an explicit argument that treats the feedforward action as an exogenous, perfectly known signal. A composite Lyapunov function will be constructed that penalizes only the tracking deviation and the tracking input; because the feedforward term does not appear in the cost, it does not affect the decrease condition. The terminal set will be redefined as the set of states for which there exists a tracking input sequence such that the combined (tracking + feedforward) input satisfies the constraints and drives the tracking error to the terminal region. This construction preserves the recursive feasibility and asymptotic stability properties already established for the tracking sub-problem. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained

full rationale

The paper introduces a dual-action MPC formulation (tracking-oriented plus feedforward-oriented actions combined under constraints) as an independent structural proposal, developed explicitly for DMC, GPC and state-space forms and validated via simulation. No equation reduces a claimed prediction to a fitted input by construction, no load-bearing uniqueness theorem is imported from self-citation, and no ansatz is smuggled via prior work; the central claim rests on the explicit separation of the two actions and the zero-effort penalty on the feedforward term, which is presented as a new design choice rather than a re-derivation of existing results.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Based solely on the abstract; no free parameters, axioms, or invented entities are identifiable or detailed in the provided text.

pith-pipeline@v0.9.1-grok · 5756 in / 1055 out tokens · 24197 ms · 2026-06-27T21:22:00.964524+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

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