Hysteresis Nonlinearity Research Articles

Model-free compensation learning control of asymmetric hysteretic systems with initial state learning

In this article, a model-free compensation learning control scheme is presented for asymmetric hysteretic systems to achieve high-precision output tracking, where the effects of asymmetric input hysteresis nonlinearities are denoted by the asymmetric Prandtl–Ishlinskii model (APIM). In the presented control scheme, the feedforward iterative learning technique is generalized to the control design of asymmetric hysteretic systems. To improve the robustness and dynamic performance of the existing feedforward learning control for hysteretic systems, both the feedback action and the differential term are utilized to design a discrete-time PD-P open-closed-loop learning control law for simultaneously compensating the asymmetric input hysteresis nonlinearities and the linear dynamics effects without constructing compensators based on their models. The initial state error of such a system is also considered, a modified initial state learning strategy is proposed to ensure the initial state error tends to a prescribed level with the increasing of iterations. By fully analyzing the properties of the APIM, the convergence conditions with respect to the input error, the state error, and the tracking error along the iteration domain are given. The simulation and experimental results are provided to demonstrate strong robustness and excellent tracking accuracy with the proposed model-free compensation learning control scheme.

Adaptive prescribed performance tracking control for uncertain nonlinear systems with unknown backlash-like hysteresis

In this paper, an adaptive prescribed performance tracking control(PPTC) problem of uncertain nonlinear systems with unknown hysteresis input is investigated. For the purpose of implementing the PPTC, a performance function and an error conversion function are introduced. Moreover, a backlash-like hysteresis model is adopted to describe the hysteresis nonlinearity, which makes the controller design feasible. Additionally, by converting the backlash-like hysteresis model into a linear model with bounded error, the difficulties caused by hysteresis behavior on controller design are settled. Thus, integrating multi-dimensional Taylor network(MTN) approximation technique into adaptive backstepping method, an adaptive control scheme for uncertain nonlinear systems is proposed. Apart from ensuring that all signals of the closed-loop system keep bounded, the proposed control scheme not only makes the tracking error converge to an arbitrarily small neighborhood around the origin, but also guarantees the tracking error trajectory within the limits set by PPTC. Ultimately, two simulations are applied to verify the validity of the proposed control scheme.

Data‐driven model‐free predictive control for microstage with coupling and hysteresis nonlinearities

SummaryThe precision motion control problem is investigated in this paper for microstages with cross‐axial coupling and hysteresis. Cross‐axis coupling generally results in stress‐stiffening effects, thereby causing time‐varying dynamics in the microstages. Additionally, when a microstage is driven by piezoelectric actuators (PEAs), the hysteresis effect of the actuator itself must also be considered. Modeling the microstages becomes complicated when both nonlinear characteristics, coupling and hysteresis, coexist. To address this challenge without the need for modeling, a novel data‐driven model‐free predictive control scheme called first‐order tensor‐vector product polynomial approximation based model‐free predictive control (TPPA ‐MFPC is proposed. TPPA ‐MFPC solely relies on the sampling input/output (I/O) data of the systems. The main concept behind TPPA ‐MFPC is to derive a linear approximation model using the I/O data collected during operation. This linear approximation model then serves as a nominal model in a predictive controller, enabling the control of the microstages. Finally, the effectiveness of the proposed TPPA ‐MFPC scheme and the performance improvement over existing model‐free schemes, for example, proportion integration differentiation control (PID), model‐free adaptive control (MFAC), model‐free adaptive predictive control (MFAPC), data‐dependent LMI (DDLMI), and data‐enabled predictive control (DeePC) are demonstrated in the simulation examples with a 2‐degree of freedom (DOF) multileaf spring‐based microstage driven by PEA.

Research on the Coupled Dynamic Response of Vibratory Roller-Unsaturated Subgrade under Different Compaction and Moisture Content States

The dynamic response between the vibratory roller and subgrade under vibratory compaction is essential to improve the compaction quality and optimize the construction technology. Considering the nonlinear hysteresis characteristics of the subgrade in vibratory compaction, a two-degree-of-freedom viscoelastic-plastic, vibratory roller-unsaturated subgrade coupling model, is established to evaluate the effect of compaction stage and moisture content on the vibratory roller-unsaturated subgrade coupling dynamic response. The dynamic resilient modulus semi-empirical model is established based on the dynamic resilient modulus experiment by considering the matrix suction of the unsaturated subgrade and it is the basis of the vibratory roller-unsaturated subgrade coupling model to consider the moisture content influence of compaction. In addition, a plasticity index was proposed to divide the selection of coupling models to consider the influence of compaction stages. The results show that the semi-empirical model takes into account the effect of moisture content by soil–water characteristic curve and it performs well in responding to the experiment results and other experimental data in the published literature. Based on this, the vibratory roller-unsaturated subgrade coupling dynamic response varied for different compaction stages and the moisture content of the unsaturated subgrade. The compaction quality gradually improved as the increase of compaction passes and the decrease of the moisture content. However, the compaction quality of the unsaturated subgrade is weakened by over compaction and excessive moisture content and should balance the compaction operation and quality assurance of the unsaturated subgrade. The results of the research will indicate the compaction mechanism of unsaturated subgrade and provide a theoretical basis for the development of intelligent compaction technology.

Adaptive backstepping controller based on a novel framework for dynamic solution of an ankle rehabilitation spherical parallel robot

AbstractThis research offers an adaptive model-based methodology for autonomous control of 3-RRR spherical parallel manipulator (RSPM) based on a novel modeling framework. RSPM is an overconstrained parallel mechanism that has a variety of applications in medical procedures such as ankle rehabilitation because of its precision and accuracy. However, obtaining a complete explicit dynamic model of these mechanisms for tracking purposes has been a problematic challenge due to their inherent singularities, coupling effects of the limbs, and redundant constraints imposed by the intermediate joints. This paper presents a novel algorithm to obtain the analytical kinematic solutions of RSPMs based on the closed-loop vector method, which includes constraint analysis. By incorporating constrained kinematics into the dynamic model, a comprehensive explicit dynamic solution of the non-overconstrained version 3-RCC of RSPM is developed in task space, based on screw theory and the linear homogeneous property of algebraic equations on the manipulator twist. Based on the proposed computational framework, a robust self-tuning backstepping control (STBC) strategy is applied to the robot to overcome the effect of external disturbances and time-varying uncertainties. Furthermore, an observer-based compensation (OBC) method is presented for dealing with the nonlinear hysteresis loops of the ankle during trajectory tracking purposes. The closed-loop stability of the whole system including STBC and OBC is theoretically performed by Lyapunov methods. The proposed methodologies are validated by realistic co-simulations in different scenarios. For instant, in the presence of external disturbances, the maximum tracking error norm of STBC is 37.5% less than the sliding mode approach.

Research on multi-scale hysteresis constitutive model of giant magnetostrictive materials considering multi-field coupling

The magnetization and magnetostrictive strain of giant magnetostrictive materials exhibit a complex nonlinear trend under the coupling of multiple fields, including magnetic field, temperature field, and prestress field. To enhance prediction accuracy, we propose a three-dimensional magnetic-thermal-force coupled nonlinear multi-scale hysteresis vector model. This model is derived from the principles of thermodynamics and continuum mechanics, taking into account the interactions among magnetic domains, grains, polycrystals, and macroscopic scales. It combines the volume-averaging principle of magnetic domain microscopy with the generalized Jiles-Atherton hysteresis model. The predicted hysteresis magnetization and magnetostrictive strain curves obtained from this model are in good agreement with experimental results. By analyzing the predicted hysteresis magnetization and magnetostrictive strain under different conditions, we demonstrate that our proposed model can comprehensively describe the effects of temperature and prestress on the multi-field coupled hysteresis behaviors of giant magnetostrictive materials. Moreover, it provides theoretical guidance for both macroscopic and microscopic optimization in designing active devices incorporating super magnetostrictive materials.

Adaptive Set-Membership Filter Based Discrete Sliding Mode Control for Pneumatic Artificial Muscle Systems With Hardware Experiments

Pneumatic artificial muscle (PAM), featuring good flexibility and safety, has been widely used in rehabilitation and bionic robots. However, the complex hysteretic nonlinearities and uncertainties of the PAM cause great difficulties and challenges to the accurate modeling and controller design, especially when confronted with unknown external disturbances in applications. This paper proposes a robust control strategy with disturbance compensation for the hysteresis compensation and trajectory tracking of PAMs. Considering the high hysteretic nonlinearity of the PAM, a modified Prandtl-Ishlinskii model is used as a feedforward hysteresis compensator. For the linearized system, adaptive set-membership filtering (ASMF) is used to estimate the nonlinear terms and external disturbances of the overall system. A sliding mode controller (SMC) with disturbance compensation is designed and cascaded to the feedforward hysteresis compensator in series. The stability of the closed-loop system is theoretically proved. The proposed method guarantees that the tracking error of the PAM system is bounded. Finally, the effectiveness and robustness of the proposed controller are verified via a series of experiments on an in-house built testbench for PAMs. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —With the increasing demand on human-robot interaction, the safety and compliance of robots have become one key requirement. PAM is a compliant actuator, exhibiting good flexibility, safety, and clean energy. PAM is widely used in rehabilitation robots, whereas its strong hysteresis nonlinearity and sensitivity to external disturbances affect its motion accuracy. This paper proposes an ASMF-based discrete SMC, which uses an inverse hysteresis model to compensate for the strong hysteresis of the PAM and uses ASMF to estimate the lumped disturbance of the system. Compared with the other filters, ASMF is unique in that its estimation error is bounded, which is very useful in the stability proof of the overall system. The effectiveness of the proposed controller is experimentally verified. Experimental results show that PAM’s hysteresis can be efficiently compensated, and the influence of external disturbances can be attenuated by the proposed controller, resulting in improved motion accuracy and robustness. In future work, efforts will be directed towards the modeling and control of PAMs in multi-DOF robots.

Model-based compensation of a concave nonlinear hysteresis in the displacement electro-hydraulic servo system

Abstract Nonlinearity exerts a profound influence on the displacement performance of actuators within electro-hydraulic servo systems, particularly in the context of hysteresis. This article analyses a specific hysteresis responsible for control instability, a consequence of the concave-hysteresis loop, giving rise to a notable peak phenomenon in displacement. The behavior of the concave-hysteresis loop is studied in the step load experiment of a triaxial apparatus. Subsequently, an accurately formulated mathematical model utilizing a mathematical function is derived. Notably, the article introduces an efficacious model-based compensation algorithm that integrates nonlinear iteration and fuzzy control. This strategic approach effectively addresses the issue associated with calculating the inverse model when the sensor is located in a nonlinear, hook-shaped domain. Simulation and experimentation verified the concave-hysteresis loop model and the compensation algorithm. The experiment demonstrated the elimination of peak phenomena and a decrease in sensor error from 3.7 mm to below 0.5 mm.

Precision positioning based on temperature dependence self-sensing magnetostrictive actuation mechanism

The self-sensing actuator that integrates both actuation and sensing functions is an effective way to simplify the structure of electromechanical systems. This paper proposes a temperature-dependent self-sensing actuation strategy based on a self-sensing giant magnetostrictive actuator (SSGMA) by sensing online stiffness. Utilizing the developed model considering temperature-dependent hysteresis nonlinearity, the self-sensing output characteristics of SSGMA are first evaluated. The self-sensing based control system is then designed in detail. The relationship between the self-sensing signal and the output displacement of SSGMA at different temperatures is constructed by General Regression Neural Network (GRNN) model for fast recognition by the controller. On this basis, a composite control scheme that takes into account rate-dependent asymmetric hysteresis nonlinearities and combines an adaptive feedforward controller with PID feedback controller is proposed for precision actuation of SSGMA. Finally, a temperature-controlled experimental platform is assembled for verification. Experimental results demonstrate that, based on the developed model, the SSGMA is capable of accurate self-sensing output at temperatures of 22 °C, 40 °C, and 70 °C, respectively. The SSGMA with the proposed control method enables the synchronous and precise self-sensing positioning of step and multiple-frequency sinusoidal expectations at different temperatures.

Vibration control of giant electrorheological damper combining nonlinear fractional-order controller and extended state observer

As a typical smart material, giant electrorheological fluid (GERF) has a greater yield stress than electrorheological fluid for vibration isolation. However, as rheological material, the modeling precision is severely degraded by its innate rate-dependent hysteretic nonlinearity and uncertainty. In this paper, a novel control method is proposed, which requires little information about the damper based on GERF. The proposed method combines nonlinear fractional-order control (FC) and extended state observer (ESO) by constructing damper as a second-order disturbance-based structure to handle hysteretic nonlinearities, dynamic uncertainties and unknown disturbances. In contrast to the prevalent model-free control (MFC) that neglects hysteresis nonlinearity, the proposed control algorithm considers it as a general disturbance and eliminates it. In addition, compared with linear FC with complex fractional-order ESO, where the order needs to be known in advance, nonlinear FC has improved robustness for uncertain fractional-order systems only via pure ESO. Simulations and experimental results demonstrate that the nonlinear controller outperforms the linear counterpart and the proposed method exhibits superior control performance compared to the existing MFC, with an improvement of 26.9%.

Modeling, identification, and high-speed compensation study of dynamic hysteresis nonlinearity for piezoelectric actuator

Hysteresis nonlinearity widely exists in the piezoelectric actuator (PEA), and the hysteresis nonlinearity has strong dynamic characteristics that lead to deterioration of tracking performance. To decrease the positioning error caused by hysteresis nonlinearity, a generalized Bouc-Wen (GBW) hysteresis model and its compensation method are proposed in this paper. First, based on the Bouc-Wen hysteresis model, two asymmetric terms and a second-order IIR filter are applied to describe the asymmetric hysteresis and high-frequency phase lag characteristics of PEA. Then, the model parameters with strong relevance to frequency variation are modified as frequency-dependent parameters. Meanwhile, based on the particle swarm optimization (PSO) algorithm, a novel parameter identification algorithm is designed for identifying the parameters of GBW hysteresis model. Then, an inverse feedforward controller is constructed based on the GBW hysteresis model, and a composite compensation control algorithm combining PID controller and repetitive controller is developed to reduce the unmodeled dynamics errors and unknown external disturbances. Finally, the comparison experiment results show that the accuracy and performance of the GBW model proposed in this paper are much better than the classical Bouc-Wen (CBW) model and the enhanced Bouc-Wen (EBW) model, and the developed compensation controller has excellent control performance and robustness.

High-Precision Position Tracking Control with a Hysteresis Observer Based on the Bouc–Wen Model for Smart Material-Actuated Systems

The Bouc–Wen model has been widely adopted to describe hysteresis nonlinearity in many smart material-actuated systems, such as piezoelectric actuators, shape memory alloy actuators, and magnetorheological dampers. For effective control design, it is of interest to estimate the hysteresis state that is not measurable. In this paper, the design of a state observer for the Bouc–Wen model is presented. It is shown that, with sufficiently high observer gains, the state estimate error, including that for the hysteresis state, converges to zero exponentially fast. The utility of the proposed hysteresis observer is illustrated in the design of a high precision output-feedback position tracking controller, and the resulting tracking error is shown to decay exponentially via Lyapunov analysis. Simulation and experimental results show that the proposed hysteresis observer and the high precision position tracking controller outperform a traditional extended state observer and the corresponding tracking controller, respectively.

Nonlinear motion characteristics of the high-temperature superconducting levitation system with boundary crack

High-temperature superconducting levitation systems have nonlinear behaviors, such as the period-doubling bifurcation and chaotic vibration under external excitation, in connection with the nonlinear hysteresis interaction between the high-temperature superconductors (HTSC) and permanent magnet. The HTSC is a non-ideal type II superconductor in which the fracture is generated internally during manufacturing, and the material properties are brittle. The HTSC tends to crack under a strong magnetic field and electromagnetic force, and its internal defects are likely to cause structural damage with the variable Lorentz force. The fracture performance of the superconducting magnetic levitation system will affect the temperature variation of HTSC, in which the temperature is coupled with the internal electromagnetic force. In this paper, we analyze the fracture characteristics of the HTSC in nonlinear vibration with thermal effect. A superconducting magnetic levitation system model with boundary cracks is applied to study the coupling of multiple physical fields in dynamic processes. The Maxwell equation and superconducting electromagnetic constitutive equation are used to obtain the superconductor’s current density, and the temperature is calculated through the heat conduction equation. The superconducting magnetic flux flow and creep model is applied to analyze the magnetic flux motion inside the superconductors. We compare the superconducting levitation system’s electromagnetic force, temperature, and current density with four critical current densities. The numerical results show that the critical current density of superconductors significantly impacts bifurcation motion, and the temperature of the crack tip of the superconductors varies greatly during vibration, causing the superconductor to lose its superconductivity.

Feedback linearization and equivalent-disturbance compensation control strategy for piezoelectric stage

Piezoelectric stages use piezoelectric actuators and flexure hinges as driving and amplifying mechanisms, respectively. These systems have high positioning accuracy and high-frequency responses, and they are widely used in various precision/ultra-precision positioning fields. However, the main challenge with these devices is the inherent hysteresis nonlinearity of piezoelectric actuators, which seriously affects the tracking accuracy of a piezoelectric stage. Inspired by this challenge, in this work, we developed a Hammerstein model to describe the hysteresis nonlinearity of a piezoelectric stage. In particular, in our proposed scheme, a feedback-linearization algorithm is used to eliminate the static hysteresis nonlinearity. In addition, a composite controller based on equivalent-disturbance compensation was designed to counteract model uncertainties and external disturbances. An analysis of the stability of a closed-loop system based on this feedback-linearization algorithm and composite controller was performed, and this was followed by extensive comparative experiments using a piezoelectric stage developed in the laboratory. The experimental results confirmed that the feedback-linearization algorithm and the composite controller offer improved linearization and trajectory-tracking performance.

Proxy-Based Sliding Mode Force Control for Compliant Grinding via Diagonal Recurrent Neural Network and Prandtl-Ishlinskii Hysteresis Compensation Model

Traditional industrial robots often face challenges in achieving a perfectly polished surface on a workpiece because of their high mechanical rigidity. The active compliance force control device installed at the robotic arm’s end enables high-precision contact force control between the grinding tool and the workpiece. However, the complex hysteresis nonlinearity between cylinder air pressure and output force, as well as various random disturbances during the grinding process, can affect the accuracy of the contact force and potentially impact the grinding effect of the workpiece, even causing irreversible damage to the surface of the workpiece. Given the complex random variation of cylinder output force in the actual grinding process, a rate-dependent hysteresis model based on diagonal recurrent neural network and Pradtl–Ishlinskii models named dRNN-PI is designed to compensate for the complex nonlinear hysteresis of the cylinder and calculate the desired air pressure to maintain a steady contact force on the workpiece. The proxy-based sliding mode control (PSMC) is utilized to quickly track the desired air pressure without overshooting. This paper also proves the controller’s stability using the Lyapunov-based methods. Finally, the accuracy of the proposed hysteresis compensation model and the effectiveness and robustness of the PSMC are verified by experiment results.

Driving torque model of the bionic soft arm’s hyperelastic bellows

ABSTRACT The technology of soft continuum robots represents an advance in the field of robotics to benefit a wide range of industries such as healthcare, manufacturing or environmental exploration. Soft continuum robots can be driven pneumatically by bellows as the soft continuum manipulator presented in this article. A driving torque model of the bellows considering hyperelastic material properties, friction and restoring torques is derived, whose purpose is suitability for model-based control design and subsequent trajectory generation. Hence, the driving torque model must be real-time capable. This is realized by an iterative algorithm calculating the bellows’ torque transmission by assuming a two-dimensional no-slip membrane contact. Nonlinear strain behaviours and hysteresis effects of the bellows are considered by the Ogden material model. The driving torque model’s performance is validated experimentally by measuring the external torques of the bellows.

Modeling and Control of a Linear Piezoelectric Actuator

To improve the output displacement of piezoelectric actuators, a linear piezoelectric actuator based on a multistage amplifying mechanism with a small volume, large thrust, high resolution, high precision, and fast response speed is proposed. However, inherent nonlinear characteristics, such as hysteresis and creep, significantly affect the output accuracy of piezoelectric actuators and may cause system instability. Therefore, a complex nonlinear hysteresis mathematical model with a high degree of fit was established. A Play operator was introduced into the backpropagation neural network, and a genetic algorithm (GA) was used to reduce the probability of the fitting of the neural network model falling into a local minimum. Moreover, simulation and experimental test platforms were constructed. The results showed that the maximum displacement of the actuator was 558.3 μm under a driving voltage of 150 V and a driving frequency of 1 Hz. The complex GA-BP neural network model of the piezoelectric actuator not only exhibited high modeling accuracy but also solved the problems of strong randomness and slow convergence. Compared with other control algorithms, the GA-BP fuzzy PID control exhibited higher control precision.

Actuation Force Modeling and Identification for Piezoelectric Actuator With Neural Network Compensator and Nonlinear Hysteresis

Actuation Force Modeling and Identification for Piezoelectric Actuator With Neural Network Compensator and Nonlinear Hysteresis

Research on energy-saving optimization method for central air conditioning system based on multi-strategy improved sparrow search algorithm

Aiming at the problem of high energy consumption caused by the nonlinear, strong coupling, and large hysteresis characteristics of central air conditioning (CAC) system, an energy-saving optimization method based on WTD–CNN–LSTM and multi-strategy improved sparrow search algorithm (MISSA) is proposed, which works to minimize the total energy consumption during the operation of the CAC system. Firstly, minimize the sum of energy consumption of chillers, freezing pumps, cooling pumps, and cooling towers as the objective function, and use the range of operating parameters of each equipment as the basic constraint conditions to establish an energy-saving optimization model for the CAC system. Then, WTD–CNN–-LSTM is used to predict the future cooling load, and the predicted results are used as key constraint condition to achieve on-demand cooling. Finally, MISSA is proposed to improve the initialization, update and convergence stages of the CAC system operation parameter optimization process, accurately obtaining the optimal operating parameters. Compared with manual experience, MISSA reduces energy consumption by 15.32 % and improves energy efficiency ratio by 20.76 %. Meanwhile, compared with other optimization algorithms, MISSA reduces energy consumption by 4.85–13.26 % and improves energy efficiency ratio by 6.53–16.33 % after optimizing the CAC system. The experiment verifies that MISSA is more energy efficient when applied to the CAC system and has the advantages of accuracy, fast convergence, strong global search capability, and the ability to jump out of local optimization.

Numerical Investigation on the Evolution Process of Different Vortex Structures and Distributed Blowing Control for Dynamic Stall Suppression of Rotor Airfoils

The influencing characteristic for the evolution mechanism of a dynamic stall vortex structure and distributed blowing control on rotor airfoils was investigated. Based on the moving-embedded grid method, the finite volume scheme, and Roe’s FDS scheme, a simulation method for the unsteady flow field of a pitch-oscillating airfoil was established. The flow field of the NACA63-218 airfoil was calculated using Reynolds-averaged Navier–Stokes equations. The evolution processes of different vortex structures during dynamic stall and the principal controlled vortex mechanism affecting aerodynamic nonlinearity were analyzed based on the pressure contours Cp and Q of the flow field structure and the spatiotemporal evolution characteristics of the wall pressure distribution. The research indicated that dynamic stall vortices (DSVs) and shear layer vortices (SLVs) were the major sources of the increase in aerodynamic coefficients and the onset of nonlinear hysteresis. Building upon these findings, the concept of distributed blowing control for DSVs and shear layer vortices (SLVs) was introduced. A comparative analysis was conducted to assess the control effectiveness of dynamic stall with different blowing locations and blowing coefficients. The results indicated that distributed blowing control effectively inhibited the formation of DSVs and reduced the intensity of SLVs. This led to a significant decrease in the peak values of the drag and pitch moment coefficients and the disappearance of secondary peaks in the aerodynamic coefficients. Furthermore, an optimal blowing coefficient existed. When the suction coefficient Cμ exceeded 0.03, the effectiveness of the blowing control no longer showed a significant improvement. Finally, with a specific focus on the crucial motion parameters in dynamic stall, the characteristics of dynamic stall controlled by air blowing were investigated. The results showed that distributed air blowing control significantly reduced the peak pitching moment coefficient and drag coefficient. The peak pitching moment coefficient was reduced by 72%, the peak drag coefficient was reduced by 70%, and the lift coefficient hysteresis loop area decreased by 46%. Distributed blowing jet control effectively suppressed the dynamic stall characteristics of the airfoil, making the unsteady load changes gentler.