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arxiv: 2601.01302 · v2 · submitted 2026-01-03 · 📡 eess.SY · cs.SY

Simple yet Effective Anti-windup Techniques for Amplitude and Rate Saturation: An Autonomous Underwater Vehicle Case Study

Pouria Sarhadi This is my paper

Pith reviewed 2026-05-16 17:21 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords anti-windupamplitude saturationrate saturationPID controlLQI controlAUVMPCyaw control
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0 comments X

The pith

Modifications to PID and LQI controllers handle both amplitude and rate saturation effectively in AUV yaw control while matching constrained MPC performance.

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

The paper proposes targeted modifications to classical PID and LQI controllers so they can manage actuator amplitude and rate saturation without windup. These changes are tested on the yaw control task for a REMUS autonomous underwater vehicle and directly compared with constrained model predictive control. Results indicate the modified classical methods deliver comparable tracking and stability for single-input single-output cases while using far simpler implementation and fewer tuning parameters. A reader would care because many practical systems already rely on PID or LQI structures, and the work suggests these can remain viable without switching to more complex modern anti-windup schemes.

Core claim

The paper shows that straightforward modifications to PID and LQI controllers can incorporate anti-windup compensation for both amplitude and rate saturation. When applied to the REMUS AUV yaw control problem, the resulting closed-loop behavior matches the performance of constrained MPC while requiring only one or a limited number of additional tuning parameters and remaining straightforward to implement.

What carries the argument

Modifications to PID and LQI controllers that add anti-windup compensation for simultaneous amplitude and rate saturation. The mechanism works by adjusting the integral term and controller output to prevent windup whenever the actuator hits either magnitude or speed limits.

Load-bearing premise

The modified controllers remain stable and effective for the nonlinear AUV dynamics and chosen saturation limits without needing extensive retuning or extra robustness checks.

What would settle it

A simulation run of the REMUS yaw control problem in which the modified PID or LQI controllers produce instability, large tracking errors, or clearly inferior performance to constrained MPC under the paper's amplitude and rate saturation conditions would falsify the central claim.

read the original abstract

Actuator amplitude and rate saturation (A\&RSat), together with their consequent windup problem, have long been recognised as challenges in control systems. Anti-windup (AW) solutions have been developed over the past decades, which can generally be categorised into two main groups: classical and modern anti-windup (CAW and MAW) approaches. Classical methods have provided simple and effective results, mainly addressing amplitude saturation. In contrast, modern approaches offer powerful and theoretically sound solutions capable of handling both amplitude and rate saturations. However, MAW's derivation process often imposes restrictive conditions and can be complex to apply in practical engineering problems. Nevertheless, the literature has paid limited attention (if not entirely ignored) to the potential of simple yet effective CAW schemes that can operate in the presence of both A\&RSat elements. This paper revisits this issue and proposes modifications to two well-known controllers: PID and LQI. The obtained results, benchmarked on the REMUS AUV yaw control problem and compared with constrained MPC, indicate that these classical techniques can still provide simple yet effective solutions with comparable performance, at least for SISO systems. These findings may stimulate further research into solutions that achieve comparable performance with only one (or a limited number of) additional tuning parameters and straightforward implementation.

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 proposes simple one-parameter modifications to classical PID and LQI controllers to address both amplitude and rate saturation in anti-windup schemes. It benchmarks these on the REMUS AUV yaw control problem and reports performance comparable to constrained MPC, concluding that such classical techniques remain simple yet effective for SISO systems.

Significance. If the results hold, the work is significant for control engineering practice because it shows that minimal extensions to well-known classical controllers can achieve performance on par with modern constrained optimization methods for systems subject to both amplitude and rate limits, using only straightforward implementation and a single extra tuning parameter. This could reduce the barrier to deploying anti-windup in real AUV and similar applications.

major comments (2)
  1. [Simulation results] Simulation results section: the comparison with constrained MPC is performed only on a single nominal REMUS AUV model with fixed hydrodynamic coefficients and saturation thresholds. No sensitivity analysis to parameter variations (e.g., added mass, damping, or saturation levels) is reported, leaving the claim that the modified PID/LQI remain effective and stable on the nonlinear dynamics unverified.
  2. [Method description] Method description (PID and LQI anti-windup modifications): the paper provides no stability analysis or Lyapunov-type argument for the closed-loop system under the combined amplitude/rate saturation and the nonlinear AUV yaw dynamics. The central claim of comparable performance therefore rests entirely on the nominal simulation without theoretical support.
minor comments (1)
  1. [Abstract] The abstract states that the techniques use 'one (or a limited number of) additional tuning parameters' but does not specify the exact count or the tuning procedure for the PID versus LQI cases; this should be stated explicitly in the introduction or method section.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and insightful comments on our manuscript. We address each major comment below with honest responses and indicate the revisions we will make to strengthen the paper.

read point-by-point responses

  1. Referee: [Simulation results] Simulation results section: the comparison with constrained MPC is performed only on a single nominal REMUS AUV model with fixed hydrodynamic coefficients and saturation thresholds. No sensitivity analysis to parameter variations (e.g., added mass, damping, or saturation levels) is reported, leaving the claim that the modified PID/LQI remain effective and stable on the nonlinear dynamics unverified.

    Authors: We agree that the simulations are limited to the nominal REMUS model and that a sensitivity analysis would provide stronger evidence of robustness. The manuscript focuses on demonstrating comparable performance under the standard nonlinear AUV dynamics with the given saturation limits. In the revised version, we will add a dedicated subsection with sensitivity analysis, perturbing parameters such as added mass, damping coefficients, and saturation thresholds by ±20% and reporting the resulting tracking errors and control effort for the modified PID, LQI, and MPC. This will directly address the verification concern for the nonlinear case. revision: yes

  2. Referee: [Method description] Method description (PID and LQI anti-windup modifications): the paper provides no stability analysis or Lyapunov-type argument for the closed-loop system under the combined amplitude/rate saturation and the nonlinear AUV yaw dynamics. The central claim of comparable performance therefore rests entirely on the nominal simulation without theoretical support.

    Authors: We acknowledge that no formal Lyapunov stability analysis is provided for the nonlinear closed-loop system with the proposed anti-windup modifications. Deriving such a proof is challenging due to the combined amplitude/rate saturation nonlinearities and the AUV hydrodynamics, and it was outside the practical scope of this SISO case study. The contribution centers on the simplicity and empirical effectiveness shown in simulations. In revision, we will add a discussion paragraph noting this limitation, explaining the practical evidence from the nonlinear simulations, and suggesting it as an avenue for future theoretical work, while preserving the manuscript's focus on implementable techniques. revision: partial

Circularity Check

0 steps flagged

No circularity: modifications to PID/LQI validated via external REMUS simulation benchmark

full rationale

The paper proposes explicit modifications to standard PID and LQI controllers to handle both amplitude and rate saturation, then evaluates them through simulation on the REMUS AUV yaw dynamics against an independent constrained MPC baseline. No equations reduce a claimed prediction to a fitted parameter defined by the same data, no self-definitional loops appear, and no load-bearing premises rest solely on self-citations. The central performance claim is tied to observable simulation outputs on a publicly referenced AUV model rather than internal redefinitions.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that the REMUS AUV yaw dynamics can be adequately represented by a linear model for controller design and that the saturation limits are known and fixed. No new entities are postulated.

free parameters (1)
  • anti-windup tuning parameters
    One or a limited number of additional parameters introduced for the modified PID and LQI to handle saturation; their specific values are chosen for the REMUS case.
axioms (1)
  • domain assumption The AUV yaw dynamics admit a linear approximation suitable for PID and LQI design
    Invoked when applying the modified controllers to the REMUS yaw control problem.

pith-pipeline@v0.9.0 · 5536 in / 1346 out tokens · 17734 ms · 2026-05-16T17:21:06.666455+00:00 · methodology

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Anti-Windup in PID Control: Review, Analysis, and New Tuning Directions

    eess.SY 2026-06 unverdicted novelty 5.0

    Proposes a hybrid conditional-integration plus dynamic back-calculation anti-windup method and systematic tuning rules for back-calculation tracking time constant derived from optimization on FOPDT processes.