Nonlinear Displacement Control and Force Estimation in a Piezoelectric Robotic Manipulator

Mechanics Electrical Engineering Mechanical Engineering Engineering Information Science Automation Physics
piezoelectric manipulator nonlinear control force estimation viscoelastic deformation robotic systems

Academic Background

In the fields of engineering and materials science, precise control of robotic manipulator displacement and force is crucial for studying the mechanical properties of materials, especially when dealing with objects exhibiting nonlinear viscoelastic deformation. For instance, in textiles, aerospace, medical, and energy production industries, the mechanical behavior of textiles significantly impacts design and performance. Traditional tensile/compression machines typically measure force by controlling deformation velocity, but this method cannot directly observe critical deformation points such as the elastic limit, plastic deformation, and break point. To overcome this limitation, robotic systems have recently been employed for position/deformation-controlled object characterization. However, industrial robots face limitations when handling micro-forces and deformations, while piezoelectric robotic manipulators, with their high resolution and bandwidth, have emerged as ideal candidates. Nevertheless, the strong hysteresis nonlinearity of piezoelectric actuators poses challenges for precise control. This paper aims to address this issue by proposing a novel control strategy that combines hysteresis models and state observers to achieve precise displacement control and force estimation for piezoelectric robotic manipulators, thereby offering a new approach for characterizing the mechanical properties of objects.

Source of the Paper

This paper is authored by Gerardo Flores and Micky Rakotondrabe, affiliated with the Raptor Lab at Texas A&M International University and the Laboratoire Génie de Production at the University of Technology of Tarbes, respectively. The paper was accepted on February 17, 2025, and published in the journal Nonlinear Dynamics, with DOI 10.1007/s11071-025-11019-0.

Research Process

1. Problem Modeling and Objectives

The research focuses on a piezoelectric robotic manipulator designed to characterize objects with nonlinear viscoelastic deformation. The authors use the classical Bouc-Wen hysteresis model to approximate the manipulator’s nonlinear dynamics, capturing its inherent hysteretic behavior. The primary objective is to design an output feedback control law to ensure accurate position reference tracking for the manipulator and to estimate its states and interaction forces with the deformable object through state observers. By combining the estimated interaction force with controlled position data, the force-deformation characteristics of the object are analyzed, providing insights for identifying its model parameters.

2. Controller and Observer Design

Two observers are proposed: one for estimating the total disturbance (including hysteresis state and external force) and another for estimating the hysteresis state. The specific steps are as follows: - Total Disturbance Observer: Based on the first-order dynamics of the system, an extended observer is designed to estimate the total disturbance Δ(t). This observer ensures global uniform boundedness (GUB) of the estimation error by introducing a correction term μ. - Hysteresis State Observer: Based on the Bouc-Wen model, an exponential observer is designed to estimate the hysteresis state h. This observer ensures global exponential stability of the estimation error by solving a Riccati-like equation. - Force Estimation: Using the estimated values of the total disturbance and hysteresis state, the external force f is derived, providing data support for characterizing the mechanical properties of the object.

3. Output Feedback Control Law

Based on the estimation results from the observers, an output feedback control law is designed to ensure that the manipulator’s displacement y tracks the desired reference signal yd. The control law introduces a control gain k to ensure global uniform boundedness of the tracking error.

4. Simulation Validation

To validate the effectiveness of the proposed control strategy and observers, the authors conducted two sets of simulation experiments: - First Simulation: Without an object model, the force f is treated as an external disturbance to validate the performance of the control technique and observers. The simulation results demonstrate that the control law and observers effectively track the desired reference signal and estimate the total disturbance. - Second Simulation: The force f is connected to an object model (e.g., the viscoelastic model of flax fiber fabric) to validate the effectiveness of the control technique and force observer in object characterization. The simulation results show that the force-deformation characteristics obtained through the control law and observers are consistent with the natural behavior of the object model, proving the effectiveness of the method.

Main Results

  1. Observer Performance: Both the total disturbance observer and the hysteresis state observer exhibit excellent estimation performance, with estimation errors rapidly converging in the simulations, demonstrating the effectiveness of the observers.
  2. Control Performance: The output feedback control law ensures precise tracking of the desired reference signal by the manipulator’s displacement, with tracking errors remaining within a small range even in the presence of external disturbances.
  3. Object Characterization: Through simulation experiments, the authors validate that the proposed control strategy and force observer can accurately characterize the force-deformation properties of objects, providing reliable data for identifying object model parameters.

Conclusion and Significance

This paper proposes a novel control strategy that combines the Bouc-Wen hysteresis model with state observers to achieve precise displacement control and force estimation for piezoelectric robotic manipulators. The method not only effectively compensates for the hysteresis nonlinearity of piezoelectric actuators but also accurately estimates the mechanical properties of objects without requiring prior knowledge of the object model. This research provides a new approach for precise control of micro-forces and deformations, with broad application prospects, particularly in textiles, medical, and micro/nano-manipulation fields.

Research Highlights

  1. Innovative Control Strategy: This paper is the first to combine the Bouc-Wen hysteresis model with state observers, proposing a novel output feedback control law that effectively addresses the hysteresis nonlinearity of piezoelectric actuators.
  2. No Object Model Required: The proposed control strategy and force observer do not require prior knowledge of the object, making it applicable to characterizing the mechanical properties of various objects.
  3. High Precision and Robustness: Simulation experiments demonstrate that the method maintains high-precision displacement control and force estimation even in the presence of external disturbances and noise.

Other Valuable Information

The simulation files and code from this paper are publicly available on GitHub for other researchers to download and use, further advancing research and applications in related fields. Additionally, part of this work was presented at the American Control Conference held in Toronto, Canada, in July 2024.