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arxiv: 1907.02314 · v1 · pith:67FHPWZ3new · submitted 2019-07-04 · 📡 eess.SY · cs.SY

A novel passivity based controller for a piezoelectric beam

Krishna Chaitanya Kosaraju , Matthijs C. de Jong , Jacquelien M.A. Scherpen This is my paper

Pith reviewed 2026-05-25 09:17 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords passivity-based controlpiezoelectric beamdistributed parameter systemsintegrable port variablesPI controllerenergy-based controlvibration control
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The pith

A new passivity property for distributed piezoelectric devices with integrable port-variables enables two PI-like control methodologies.

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

The paper establishes a new passivity property for piezoelectric beams where the port variables are integrable. By using this property, it derives two control strategies that take the form of proportional-integral controllers. A reader would care because this provides a systematic energy-based approach to controlling distributed systems like beams, which are common in smart structures and actuators. The work includes simulations that show how the gains affect transient response and steady-state performance.

Core claim

The paper presents a new passivity property for distributed piezoelectric devices with integrable port-variables. It exploits this integrability to develop two new control methodologies whose controllers have a Proportional-Integral like structure, and validates them through simulations with analysis of tuning gains.

What carries the argument

The integrability property of the port-variables, which underpins the new passivity property and allows construction of the PI-like controllers.

If this is right

  • The derived controllers can be applied to regulate the behavior of the piezoelectric beam.
  • Analysis of tuning gains explains the transient and steady-state behaviors of the closed-loop system.
  • The approach applies to other distributed piezoelectric devices with similar integrable ports.
  • Passivity-based design ensures stability properties for the system.

Where Pith is reading between the lines

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

  • This method could be tested on physical piezoelectric beam setups to verify real-world performance beyond simulations.
  • Similar integrability assumptions might apply to other distributed parameter systems in control engineering, such as flexible structures.
  • The PI structure might allow for easier implementation using standard industrial controllers.

Load-bearing premise

The port variables of the distributed piezoelectric beam model are integrable.

What would settle it

A derivation showing that the claimed passivity inequality fails to hold when the port variables do not meet the integrability condition.

Figures

Figures reproduced from arXiv: 1907.02314 by Jacquelien M.A. Scherpen, Krishna Chaitanya Kosaraju, Matthijs C. de Jong.

Figure 1
Figure 1. Figure 1: Piezoelectric beam. allows straightforward interconnection with other open sys￾tems, such as controllers and mechanical structures, where the latter is of interest for ongoing research. Furthermore, applying this structure to the system help us discover new passivity properties, that is otherwise not evident. Moreover, this helps us in using the structure preserving spatial dis￾cretization method presented… view at source ↗
Figure 2
Figure 2. Figure 2: Closed-loop response through the output shaping. - [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: Closed-loop response for tuned controllers - Left: [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
read the original abstract

This paper presents a new passivity property for distributed piezoelectric devices with integrable port-variables. We present two new control methodologies by exploiting the integrability property of the port-variables. The derived controllers have a Proportional-Integral (PI) like structure. Finally, we present the simulation results and in-depth analysis on the tuning gains explaining their transient and steady-state behaviors.

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

3 major / 2 minor

Summary. The paper claims a new passivity property for distributed piezoelectric devices whose port variables (voltage and conjugate output) are integrable. It derives two new controllers with PI-like structure by exploiting this integrability and presents simulation results together with an analysis of the effect of the tuning gains on transient and steady-state behavior.

Significance. If the integrability property is shown to follow directly from the underlying distributed-parameter model (Euler-Bernoulli or Timoshenko beam with piezoelectric coupling) and the resulting controllers are shown to be stabilizing, the work would supply a new passivity-based design route for distributed piezoelectric actuators. The simulation study of gain tuning is a modest but useful addition.

major comments (3)
  1. [Abstract / model derivation] Abstract and model section: the integrability of the port variables is stated as the foundation for the new passivity property and the subsequent controller derivations, yet no explicit substitution of the beam PDEs and boundary conditions is provided to verify that one port variable is the time-integral of the other (up to boundary terms). This step is load-bearing for the central claim.
  2. [Controller design] Controller derivation: the two PI-like controllers are asserted to follow from the new storage function and supply rate, but the manuscript supplies neither the explicit storage function nor the passivity inequality that would confirm the closed-loop dissipation property.
  3. [Numerical results] Simulation section: the reported closed-loop responses are shown only for the proposed controllers; no comparison against standard collocated or non-collocated passivity-based designs is given, so the practical advantage of the new structure cannot be assessed.
minor comments (2)
  1. [Notation] Notation for the distributed port variables should be introduced once and used consistently; the abstract refers to “integrable port-variables” without defining the pair (u,y) that satisfies the integrability condition.
  2. [Abstract / simulations] The phrase “in-depth analysis on the tuning gains” in the abstract is not matched by quantitative statements (e.g., ranges of gains that guarantee stability or explicit trade-off curves) in the simulation discussion.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. We address each major comment below and will revise the paper accordingly where the points identify gaps in the presentation of the core claims.

read point-by-point responses

  1. Referee: [Abstract / model derivation] Abstract and model section: the integrability of the port variables is stated as the foundation for the new passivity property and the subsequent controller derivations, yet no explicit substitution of the beam PDEs and boundary conditions is provided to verify that one port variable is the time-integral of the other (up to boundary terms). This step is load-bearing for the central claim.

    Authors: We agree that an explicit verification step would make the foundation clearer. In the revised manuscript we will add the substitution of the Euler-Bernoulli PDEs together with the piezoelectric boundary conditions to show that the voltage and its conjugate output satisfy the integrability relation up to boundary terms. revision: yes

  2. Referee: [Controller design] Controller derivation: the two PI-like controllers are asserted to follow from the new storage function and supply rate, but the manuscript supplies neither the explicit storage function nor the passivity inequality that would confirm the closed-loop dissipation property.

    Authors: This is a valid observation on the presentation. The revised version will explicitly define the storage function constructed from the integrable port variables and derive the closed-loop passivity inequality that establishes the dissipation property for both controllers. revision: yes

  3. Referee: [Numerical results] Simulation section: the reported closed-loop responses are shown only for the proposed controllers; no comparison against standard collocated or non-collocated passivity-based designs is given, so the practical advantage of the new structure cannot be assessed.

    Authors: The manuscript's contribution centers on the new passivity property arising from integrability and the resulting PI-like controllers, together with the tuning-gain analysis. The simulations are intended to illustrate the closed-loop behavior under the new design rather than to benchmark against existing passivity-based methods. We therefore do not plan to add comparative simulations, as they would shift the paper's focus. revision: no

Circularity Check

0 steps flagged

No significant circularity; passivity property presented as independent modeling observation

full rationale

The abstract and provided excerpts frame the integrability of port-variables as a modeling property of the piezoelectric beam that enables the new passivity result and PI-like controllers. No equations, self-citations, or fitting steps are quoted that reduce the claimed property or controllers back to their own inputs by construction. The derivation chain is presented as starting from the stated integrability assumption rather than deriving it tautologically from the target controllers or prior self-citations. This is the common case of an independent modeling claim; external verification against the PDE would be a correctness question, not circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Review performed on abstract only; integrability of port variables is the key unverified modeling assumption required for the passivity property and controller synthesis. No free parameters or invented entities are visible in the abstract.

axioms (1)
  • domain assumption Port variables of the distributed piezoelectric device are integrable.
    Stated in abstract as the property that enables the new passivity and the two control methodologies.

pith-pipeline@v0.9.0 · 5587 in / 1138 out tokens · 16573 ms · 2026-05-25T09:17:53.384958+00:00 · methodology

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Reference graph

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