Generalized Prandtl Ishlinskii Research Articles

Modeling and parameter identification of rate-dependent hysteresis behavior based on modified-generalized Prandtl–Ishlinskii model

The intrinsic characteristic of piezoelectric actuators (PEA), known as hysteresis, has been demonstrated to diminish the capability and stability of the system significantly. This paper proposes a modified-generalized Prandtl–Ishlinskii (MGPI) model to describe the rate-dependent hysteresis in piezoelectric actuators. The developed model incorporates a voltage change rate function to replace the first part of the generalized Prandtl–Ishlinskii (GPI) model. Additionally, the model integrates the cubic polynomial into the envelope function, along with the dynamic thresholds and weights. When describing the hysteresis of the piezoelectric actuator (PEA), the model parameters are identified using the Improved Grey Wolf Optimizer (IGWO) algorithm. To prevent the algorithm from getting trapped in local optima, the cubic chaotic mapping is utilized for population initialization, as well as a nonlinear convergence factor, and the Levy flight strategy factor is introduced to update the Wolf pack’s position. The rate-dependent hysteresis behavior of a PEA under excitation in the 1–200 Hz frequency range was experimentally measured. The measured data were used to demonstrate the validity of the proposed MGPI model. The relative root-mean-square error and the relative maximum error of the MGPI model are 1.41% and 6.00%, respectively, which are lower than those of the GPI model, which are 3.15% and 10.58%. Under the composite frequency driving, the outputs of the GPI model and MGPI model were compared with the measured data of the PEA, the results suggest that the MGPI model and the IGWO algorithm can more accurately describe the rate-dependent hysteresis of the piezoelectric actuators.

Model predictive control for a bending pneumatic muscle based on an online modified generalized Prandtl–Ishlinskii model

Model predictive control for a bending pneumatic muscle based on an online modified generalized Prandtl–Ishlinskii model

Model-based linear control of nonlinear pneumatic soft bending actuators

Advanced model-based control techniques hold great promise for the precise control of pneumatic soft bending actuators (PSBAs) with strong nonlinearities. However, most previous controllers were designed in a cumbersome nonlinear form. Considering the simplicity of linear system theory, this paper presents a novel perspective on using model-based linear control to handle nonlinear PSBAs, and for the first time, summarizes two methodologies, global linearization and pseudo-linear construction. Derived from them, Koopman-based and hysteresis-based linear control approaches are proposed, respectively. For the former, a novel fusion prediction equation is developed to build a high-fidelity Koopman model, realizing global linearization, and then the linear model predictive control (MPC) is deployed. For the latter, the inverse of the generalized Prandtl–Ishlinskii (GPI) model cascades with the PSBA to construct a pseudo-linear system, eliminating the asymmetric hysteresis, which activates the linear proportional-integral-derivative (PID) control. It is worth noting that the above two are based on data-driven models adapted to various PSBAs with material and structural customization. Finally, the two model-based linear control approaches are verified and compared through a series of experiments. The results show that the proposed linear controls, with more concise designs, achieve comparable or even superior performance than nonlinear controls.

Development of a Modified Generalized Prandtl–Ishlinskii Modeling and Compensation Method for Complex Hysteresis Behaviors of the Flexible Ureteroscope

Development of a Modified Generalized Prandtl–Ishlinskii Modeling and Compensation Method for Complex Hysteresis Behaviors of the Flexible Ureteroscope

Wet clutch pressure hysteresis compensation control under variable oil temperatures for electro-hydraulic actuators

The hysteresis characteristics and oil temperatures of wet clutch electro-hydraulic actuators have a significant impact on clutch pressure tracking performance, thereby influencing the launch, shift, and mode transition performance of both fuel and hybrid electric vehicles. In this study, we introduce a novel compensator for wet clutch pressure hysteresis that effectively adapts to variations in oil temperature. Experimental investigations were conducted to examine the hysteresis characteristic of the electro-hydraulic actuator and its susceptibility to changes in oil temperature. Subsequently, a temperature-dependent modified generalized Prandtl–Ishlinskii (TDMGPI) hysteresis model that accounts for the influence of oil temperature was established. To mitigate the effects of oil temperature fluctuations on the controller, we developed a fuzzy proportional-integral-derivative (FPID) controller, which dynamically adjusts controller gain. Furthermore, a feedforward-feedback controller for clutch pressure was established, incorporating the inverse solution of the TDMGPI model as the feedforward component and the FPID controller as the feedback element. The experiments were conducted at various oil temperatures, revealing that the proposed controller significantly enhances response speed and pressure tracking accuracy, maintaining good control performance across the tested range of oil temperatures.

Safety-Critical Control Systems [About this Issue

This issue of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">IEEE Control Systems</i> includes one feature and one lecture note. In the feature, “Runtime Assurance for Safety-Critical Systems: An Introduction to Safety Filtering Approaches for Complex Control Systems” <xref ref-type="list-item" rid="list-itemA1" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[A1]</xref> , authors Kerianne L. Hobbs, Mark L. Mote, Matthew C.L. Abate, Samuel D. Coogan, and Eric M. Feron provide an introductory tutorial of runtime assurance (RTA) concepts and their role in ensuring safety of complex control systems. Assuming an undergraduate-level understanding of control theory and state-space concepts, this article provides theory and examples for RTA architectures, four types of RTA approaches, and a number of systems engineering and practical considerations for employing RTA in safety-critical, cyberphysical systems. In the “Lecture Notes” column, “The Prandtl-Ishlinskii Hysteresis Model: Fundamentals of the Model and Its Inverse Compensator,” <xref ref-type="list-item" rid="list-itemA2" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[A2]</xref> Mohammad Al Janaideh, Mohammad Al Saaideh, and Xiaobo Tan introduce the mathematical formulations of the Prandtl–Ishlinskii (PI) and Generalized PI (GPI) hysteresis models as well as their analytical inverses. These models can effectively characterize hysteresis nonlinearities in various systems, especially smart-material actuators, and their inverses can be used in feedforward compensation to mitigate the effect of hysteresis. Numerical examples of the PI and GPI models as well as their analytical inverses are also included in the article. The intended audience includes graduate students and researchers from academia and industry interested in hysteresis modeling and compensation.

Accurate Position Tracking Control of SMAAs Based on Low-Complexity Self-Sensing Model and Compound Control Strategy

Shape memory alloy actuators (SMAAs) exhibit high strain, high power-to-weight ratio, and self-sensing ability, which are promising characteristics for application in micro-actuator systems. However, the complex self-sensing and nonlinear hysteresis characteristics of shape memory alloy (SMA) seriously affect the position tracking accuracy of SMAAs. In order to realize the accurate position tracking of the SMAAs without sensors, this article proposes a low-complexity self-sensing of modeling methods, which does not require complex mechanical structure, specific prestress, and complex mathematical models. Furthermore, a compound control strategy of generalized Prandtl–Ishlinskii (GPI) inverse model and fuzzy-proportional–integral derivative (PID) was presented to compensate the nonlinear hysteresis and time-varying characteristics of SMAAs. First, macroscopic and microcosmic characteristics of SMA were analyzed to explain the negative effect of the rhombohedral ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${R}$ </tex-math></inline-formula> ) phase on the self-sensing characteristics of SMA. Second, a NiTi-based SMA wire without <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${R}$ </tex-math></inline-formula> phase was selected as a self-sensing modeling object by comparative evaluation experiments, which has similar linear self-sensing properties under various pretension force conditions, a self-sensing model containing only quadratic polynomials is constructed by an offline identification. Third, a fuzzy-PID controller is designed based on the transfer function obtained from the SMAA’s system identification, further, a nonlinear hysteresis feedforward compensation controller is designed based on the GPI model. Finally, comparative experiments with the compound controller and fuzzy-PID controller for multistep and sinusoidal position tracking responses were performed, and the experimental results show that the proposed compound controller has a faster response and higher control accuracy in position tracking control.

Modeling and identification of rate-dependent and asymmetric hysteresis of soft bending pneumatic actuator based on evolutionary firefly algorithm

Soft-bending pneumatic actuators (SBPA) have shown great potential in various applications owing to their intrinsic compliance. However, motion control is still challenging because of the complicated hysteresis of the elastic material and pneumatic system, which unlike the general hysteresis found in the rigid body mechanism, is rate-dependent and asymmetric. A precise hysteresis model is crucial for improving the performance of SBPA. This study proposed a rate-dependent modified generalized Prandtl–Ishlinskii (RMGPI) model for a vulcanized silicone rubber-based fast pneu-net soft bending pneumatic actuator (fp-SBPA) to describe complicated hysteresis characteristics. A visual feedback system obtained the bending angle in real time. With the increase in the number of operators, the identification of the proposed model parameters became more complicated and time-consuming; thus, an evolutionary firefly algorithm (EFA) was developed to improve identification efficiency. A series of experiments and comparison studies were conducted to verify the effectiveness of the proposed model and identification method.

A novel health indicator based on hysteresis loop for health prediction of flight control systems

For the high-demand operating safety and flight safety, the hysteresis dead-zone as a health indicator (HI) related to backlash abrasion is proposed for health monitoring and prediction of aircraft mechanical control systems (MCSs). First, a multi-backlash mass-damper-spring (MDS) model is built for MCSs degradation simulation to demonstrate the HI’s validity. Then, by comparing with Prandtl-Ishlinskii (PI), generalized PI (GPI), and Preisach model, the Backlash-like-PSO model gets the best results on criteria of correlation index (R2) and root mean square error (RMSE). The Backlash-like-PSO model is innovatively adopted for HI extraction. Finally, compared with several generally used approaches, the Gaussian process regression (GPR) approach is designated for the MCSs degradation prediction based on HI, depending on its better prediction accuracy and smoother degradation trend by performance estimation on RMSE, R2, etc. The effectiveness and feasibility of the proposed method are validated by the practical flight data.

Stress-dependent generalized Prandtl–Ishlinskii hysteresis model of a NiTi wire with superelastic behavior

The extremely useful superelastic behavior of NiTi has been poorly explored because of the limited number of models that can describe the complete hysteretic behavior of NiTi, including a superelastic condition that strongly depends on the applied stress. This paper presents the development of a stress-dependent phenomenological model of NiTi by modifying the existing generalized Prandtl–Ishlinskii (GPI) model. The parameters of the envelop function of the GPI model’s play operator are reformulated as quadratic functions of the applied stress. The stress-dependent GPI model can satisfactorily predict the output strain of a NiTi #6 wire under temperature and stress variation.

Modeling and compensation of asymmetric rate-dependent hysteresis of a miniature pneumatic artificial muscle-based catheter

Hysteresis phenomenon limits the effective use of pneumatic artificial muscles in numerous driving applications. Experimental results show widening hysteresis loops and lowering displacement amplitudes by increasing excitation frequency. In this study, a feedforward controller is proposed to compensate for this hysteretic behavior. This proposed controller is based on a rate-dependent Prandtl–Ishlinskii model. In order to avoid analytical calculation of inverse model, a direct inverse model is proposed. To identify unknown parameters of a direct inverse rate-dependent model, an inverse model of the rate-independent Generalized Prandtl-Ishlinskii (GPI) is used. The inverse GPI model can provide a fairly accurate output to diminish the hysteresis effect at a single-frequency hysteresis. The genetic algorithm combined with an interior-point method as a gradient-based optimization, is proposed to estimate the parameters of the proposed controller quickly. Simulation and experimental results show that the proposed feedforward controller that is identified along this new approach is able to compensate for the hysteresis in the PAM-driven catheter successfully. The identification procedure to optimize the parameters takes less than five minutes and is thus very convenient in use. It should be noted that while demonstrated on a single PAM, the approach is believed to be general and hence also applicable to other actuators that possess the complex hysteresis behavior.

Adaptive dynamic surface control of a class of pure feedback systems preceded by generalized P‐I hysteresis

AbstractIn this paper, an adaptive dynamic surface control is proposed for a class of completely non‐affine nonlinear systems preceded by the generalized Prandtl–Ishlinskii (P‐I) hysteresis, in which the hysteresis input function is also non‐affine with respect to the control input. Instead of the mean value theorem widely used in existing literature, new nonlinear functions are introduced, leading to the removal of the assumption caused by the mean value theorem. Moreover, no constraint is imposed on the bound of the P‐I hysteresis density function. Then, the filtered signals are constructed to address the algebraic loop problem and the complexity explosion inherent in backstepping method. Based on the filtered signals, the adaptive dynamic surface control is developed, which can ensure the transient tracking performance.

Feedforward Plus Feedback Control of an Electro-Hydraulic Valve System Using a Proportional Control Valve

The output feedback signal of the electro-hydraulic valve system (EHVS) affects the activation of its right or left envelope function; thus, even weak measurement noise can cause high-frequency switching between the two envelope functions, leading to chattering in the control input. Consequently, feedforward and feedback controllers in a cascaded configuration generate undesirable chattering in the output signal. We propose a practical and reliable control approach for an EHVS actuated by a proportional control valve. The proposed controller has a parallel structure comprising an inverse generalized Prandtl–Ishlinskii (P–I) model-based feedforward controller, with both hydraulic dead-zone and flow saturation limits, for compensating asymmetric hysteretic behavior. Further, the proposed controller comprises a robust proportional-integral-derivative (PID) feedback controller for achieving robustness against disturbances and noises. The proposed parallel structure is independent of the output feedback of the EHVS. Moreover, the proposed robust PID feedback controller guarantees EHVS stability by precisely selecting the cutoff frequency for the sensitivity and complementary sensitivity functions based on the amplitude spectrum of the inverse-model-based feedforward compensation error. The results verify the high reliability of the proposed EHVS control scheme for the precise control of an EHVS actuated by a proportional control valve in practice.

The hysteresis modeling of pneumatic artificial muscles using least squares support vector machine approach

Reducing the modeling errors of hysteresis model is of great significance for improving the control accuracy of pneumatic artificial muscles. However, the asymmetry and complexity of its hysteresis loops limit the effect of existing modeling approach, especially for the irregular loops. This article extends the least squares support vector machine approach to the domain of asymmetric and irregular hysteresis characterization for pneumatic artificial muscles. Compared with the established hysteresis models, the significance of this approach is that it does not depend on the shapes of hysteresis loops and possess the advantages of both few identification parameters and high accuracy. The effectiveness and advantage of the presented model is compared with modified symmetric generalized Prandtl–Ishlinskii model. In addition, the length–pressure hysteresis experiment and modeling comparison on both of Festo commercial and self-made pneumatic artificial muscles are presented. The modeling errors of least squares support vector machine model for both loops are suppressed to a negligible level, and are not affected by the shape and complexity of hysteresis loops, which validates the effectiveness of this approach.

A modified asymmetric generalized Prandtl–Ishlinskii model for characterizing the irregular asymmetric hysteresis of self-made pneumatic muscle actuators

Reducing the errors of hysteresis models is of great significance for improving the accuracy of controlling pneumatic muscle actuators (PMAs). However, the irregularity and asymmetry of the hysteresis loops of PMAs limit the modeling accuracy of existing models. This paper proposes a modified asymmetric generalized Prandtl–Ishlinskii (MAGPI) model for the irregular asymmetric hysteresis characterization of PMAs, which adopts cascading operators. The first element in the cascade is the superposition of two weighted generalized play operators with different parameters; the second element is the superposition of weighted dead-zone operators. The effectiveness of the proposed approach is validated by experimental testing using Festo commercial and self-made PMAs, where its capacity to capture the irregular asymmetric hysteresis relationship between length and pressure parameters has been examined by generating different input pressure signals. The experimental results prove that the modeling capacity of the MAGPI model is better to characterize the complex hysteresis loops of PMAs, and this strength is more apparent when the hysteresis loops become irregular. Meanwhile, a crosswise comparative study on three envelope functions investigating modeling accuracy reveals that the newly introduced arc tangent function exhibits better performance than the traditional exponential and hyperbolic tangent functions.

A method for the length-pressure hysteresis modeling of pneumatic artificial muscles

This paper presents a method for the length-pressure hysteresis modeling of pneumatic artificial muscles (PAMs) by using a modified generalized Prandtl-Ishlinskii (GPI) model. Different from the approaches for establishing the GPI models by replacing the linear envelope functions of operators with hyperbolic tangent and exponential envelop functions, the proposed model is derived by modifying the envelope functions of operators into arc tangent functions, which shows an improvement in the modeling accuracy. The effectiveness of the proposed model is verified by the experimental data of a PAM. Furthermore, its capacity in capturing the hysteresis relationship between length and pressure is testified by giving different input pressure signals. With regard to the computational efficiency, the influence of the number of operators on the modeling accuracy is discussed. Furthermore, the inversion of the GPI model is derived. Its capability of compensating the hysteresis nonlinearities is confirmed via the simulation and experimental study.

Identification of hysteresis models using real-coded genetic algorithms

Finding an accurate model to present the hysteresis nonlinearities behavior of the smart actuator has attracted the attention of the researchers in recent years, since an accurate model has an essential role in the position control application of these actuators. Different models have been developed to describe the hysteresis nonlinearities, the generalized Prandtl-Ishlinskii (GPI) model is one of the most popular used models. This model uses the play operators represented by the threshold values and weights integrated with the odd envelope functions to characterize the hysteresis nonlinearities of smart actuators. The contribution of this paper proposes three different approaches using the Real-Coded Genetic Algorithm (RCGA) for the parameters identification of the Generalized Prandtl-Ishlinskii (GPI) model. In Approach 1, the thresholds and the values of the weights are calculated based on the proposed formulas with the unknown parameters to be identified using RCGA. In Approach 2, the thresholds values are calculated based on the proposed formula with the unknown parameters to be identified using RCGA and the values of the weights are identified directly using RCGA. In Approach 3, the thresholds and the values of the weights are identified directly using RCGA. Also, RCGA was used to identify the values of the coefficients of the envelope functions for all approaches. All approaches are tested through four different examples. Two examples are simulated examples that have linear and tangent hyperbolic envelope functions. Moreover, the other two examples represent experimental data obtained for a piezoelectric actuator and a shape alloy memory (SMA) actuator. The simulation results are carried through by the statistical and convergence analysis of the proposed approaches. The comparison and analysis show that three different approaches can be employed for modeling hysteresis nonlinearities with minimum differences between them.

Modeling and compensation of hysteresis for pneumatic artificial muscles based on Gaussian mixture models

This paper presents a new data-driven model of length-pressure hysteresis of pneumatic artificial muscles (PAMs) based on Gaussian mixture models (GMMs). By ignoring the high-order dynamics, the hysteresis of PAMs is modeled as a first-order nonlinear dynamical system based on GMMs, and inversion of the model is subsequently derived. Several verification experiments are conducted. Firstly, parameters of the model are identified under low-frequency triangle-wave pressure excitations. Then, pressure signals with different amplitudes, shapes and frequencies are applied to the PAM to test the prediction performance of the model. The proposed model shows advantages in identification efficiency and prediction precision compared with a generalized Prandtl–Ishlinskii (GPI) model and a modified generalized Prandtl–Ishlinskii (MGPI) model. Finally, the effectiveness of the inverse model is demonstrated by implementing the feedforward hysteresis compensation in trajectory tracking experiments.

Robust adaptive neural control for pure-feedback stochastic nonlinear systems with Prandtl–Ishlinskii hysteresis

Abstract This work considers robust adaptive neural-based control of pure-feedback stochastic nonlinear systems with the generalized Prandtl–Ishlinskii hysteresis. The mean-value theorem is employed to handle the non-affine difficulties from the generalized Prandtl–Ishlinskii hysteresis and the pure-feedback systems. By using the radial basis function (RBF) neural networks’ universal approximation capability and backstepping technique, an adaptive neural control scheme with minimum adaptive parameter is developed. The presented controller can guarantee the semi-global boundedness in fourth-moment of all signals of the resulting closed-loop system. Furthermore, the system output is ensured to converge to a small domain of the given trajectories. Simulation results are presented to demonstrate the effectiveness of the scheme.

Modeling and compensation of asymmetric hysteresis for pneumatic artificial muscles with a modified generalized Prandtl–Ishlinskii model

This paper presents a modified generalized Prandtl–Ishlinskii (MGPI) model for the asymmetric hysteresis characterization of pneumatic artificial muscles (PAMs), which can be considered as a cascade of the superposition of weighted generalized play operators and the superposition of weighted dead-zone operators. Compared with the established hysteresis models, the significance of the MGPI model is that it has a simple expression including a small number of parameters to be identified. Besides, the analytical form of its inverse model is easy to be obtained, which can be applied to the compensation of asymmetric hysteresis of the PAM in real-time. The wiping-out and congruency properties of the proposed model are verified by simulations. Meanwhile, by carrying out the experimental study on length–pressure hysteresis of a PAM, the parameters in the MGPI model are identified from measured data using the Levenberg–Marquardt method. Then, a feedforward hysteresis compensator based on the inverse MGPI model is designed for trajectory tracking control of the PAM. The simulation and experimental results indicate that the proposed model and its inversion are effective to characterize and compensate the length–pressure hysteresis of the PAM.