Dead-zone Operator Research Articles

Discrete-Time Event-Triggered Type-2 fuzzy wavelet neural network control for Multi-Motor servo system

This paper investigates a discrete-time event-triggered adaptive neural network control scheme for a multi-motor servo system (MMSS) to realize a desired position tracking performance. First, a discrete-time model of the MMSS, including a dead-zone and a nonlinear friction, is established based on the Euler’s discretization. Then, a discrete-time adaptive neural network controller is designed by integrating a type-2 fuzzy wavelet neural network (T2FWNN) and the backstepping technology. The neural network is not only used to estimate uncertain nonlinearities, but also can handle the non-causal problem caused by the conventional backstepping method. Meanwhile, a fixed threshold event-triggered mechanism along with the incorporation of a dead-zone operator is superimposed into the actual controller thus saving communicational resources. Besides, stability analysis proves that all the signals in the closed MMSS are bounded, and the position tracking error converges to a small neighborhood of the origin. Finally, abundant simulation experience results demonstrate the effectiveness and robustness of the proposed scheme.

Event-Triggered Distributed Data-Driven Iterative Learning Bipartite Formation Control for Unknown Nonlinear Multiagent Systems.

In this study, we investigate the event-triggering time-varying trajectory bipartite formation tracking problem for a class of unknown nonaffine nonlinear discrete-time multiagent systems (MASs). We first obtain an equivalent linear data model with a dynamic parameter of each agent by employing the pseudo-partial-derivative technique. Then, we propose an event-triggered distributed model-free adaptive iterative learning bipartite formation control scheme by using the input/output data of MASs without employing either the plant structure or any knowledge of the dynamics. To improve the flexibility and network communication resource utilization, we construct an observer-based event-triggering mechanism with a dead-zone operator. Furthermore, we rigorously prove the convergence of the proposed algorithm, where each agent's time-varying trajectory bipartite formation tracking error is reduced to a small range around zero. Finally, four simulation studies further validate the designed control approach's effectiveness, demonstrating that the proposed scheme is also suitable for the homogeneous MASs to achieve time-varying trajectory bipartite formation tracking.

Saturated adaptive single-parameter backstepping design for underactuated MSVs tracking control with uncertain dynamics

For realizing the trajectory tracking of underactuated marine surface vehicles (MSVs) in the presence of model dynamic uncertainties, actuator saturation constraints, and time-varying uncertain disturbances, a saturated adaptive single-parameter backstepping control (SPBC) scheme is developed, which possesses the properties of being model-parameter free and single-parameter adaptive. A smooth dead-zone operator (SDZO) and dynamic compensation equations are designed to deal with the propulsion system saturation constraints problem. Then, desired velocities and an auxiliary combined velocity variable are introduced to solve the potential singular problem and stabilize the subsystem of kinematics. Following that, a single-parameter adaptive law is designed in surge and yaw channels to compensate compounded uncertainties, which further alleviate computational burdens. Theoretical analysis indicates that the proposed scheme can guarantee the boundedness of all closed-loop signals. Approach efficiency is validated by simulations and experiments.

A nonsingular fast terminal sliding mode predictive controller for underwater soft crawling robots with parameter uncertainty

Unknown disturbances and material properties affect the trajectory tracking of underwater soft clawing robots. A nonsingular fast terminal sliding mode predictive controller is proposed to eliminate these effects. To characterize hysteresis and creep in dielectric elastomer materials, a dynamic model incorporating an improved dead-zone operator algorithm is constructed. Meanwhile, a nonsingular fast terminal sliding mode predictive controller that combines the Lie derivative function and sliding mode controller surface is developed to improve the accuracy and robustness of trajectory tracking. Additionally, the dynamic response and convergence speed of the proposed control system are improved by using an adaptive nonlinear disturbance observer to estimate the disturbance and uncertainty terms. Finally, the superiority and effectiveness of the proposed control method are verified by numerical simulations and experiments.

Nonlinear adaptive tracking control of piezoelectric bimorph actuator using hybrid modeling approach

Piezoelectric bimorph actuator has the advantages of small size, fast response speed and high displacement accuracy, but its inherent hysteresis nonlinearity seriously affect the control accuracy and stability of the system. The dead-zone operator was incorporated into classical Prandtl–Ishlinskii model to enable the description of asymmetric hysteresis of piezoelectric bimorph actuator. A hybrid model approach was developed with neural network and improved Prandtl–Ishlinskii model, and it has the advantages of a neural network with ready-made training algorithms and improve the Prandtl–Ishlinskii (PI) model to describe the asymmetric hysteresis. The adaptive control method was derived from training algorithm of neural network, which can update the weight parameters of Play operator and Dead-zone operator in real time. Comparing the results without control, the RMSE of displacement error decreases by 61.35% with classic model, and decreases by 82.93% with hybrid model and proposed adaptive tracking control. Experimental results show that the proposed hybrid model and adaptive control approach can more effectively compensate the hysteresis of piezoelectric bimorph.

Design and disturbance rejection control of a piezoelectric nanopositioning stage

The article covers structural design and disturbance rejection control of a flexure-based compliant piezoelectric nanopositioning stage. The stage is devised using four-bar amplification mechanisms, auxiliary guiding mechanisms, and a compound parallelogram mechanism. Static and dynamic models of compliant mechanisms are analyzed based on a compliance matrix method. A modified Prandtl-Ishlinskii (PI) model with dead zone operators is used to describe the asymmetric hysteresis. Then, a global electromechanical dynamic model is built and identified. A comprehensive disturbance rejection controller (CDRC) combining a robust H∞ control and a disturbance observer-based (DOB) control is proposed for high trajectory tracking accuracy and anti-disturbance performance. The trajectory tracking accuracy of the stage can be up to 3 nm in experiments. As amplitudes of reference signals increases, relative tracking errors gradually decrease. System instability and oscillation caused by strong external disturbances are also reduced. Experimental results prove the effectiveness of the developed CDRC.

Data-Driven Event-Triggered Bipartite Consensus for Multi-Agent Systems Preventing DoS Attacks

This paper considers event-triggered bipartite consensus issues for discrete-time nonlinear networked multi-agent systems with antagonistic interactions and denial-of-service (DoS) attacks. Firstly, a pseudo partial derivative technology is applied to obtain an equivalent dynamic linearization model of the controlled system. The signed graph theory is employed to analyze the coopetition relationships among agents. Next, a distributed combined measurement error function is formulated to transform the bipartite consensus issue into a consensus issue. Then, an output predictive compensation scheme is proposed to offset the influence of DoS attacks. Furthermore, a dead-zone operator is designed to improve the flexibility of the proposed event-triggered mechanism. Additionally, a data-driven event-triggered resilient bipartite consensus scheme is formulated. Then, the convergence of the proposed method is strictly proved by using the Lyapunov theory and the contraction mapping principle, which indicates that the bipartite consensus error could be cut to a small region around zero. Finally, hardware tasks are conducted to verify the effectiveness of the proposed method.

Improved PI hysteresis model with one-sided dead-zone operator for soft joint actuator

Improved PI hysteresis model with one-sided dead-zone operator for soft joint actuator

A Modified Prandtl-Ishlinskii Hysteresis Model for Modeling and Compensating Asymmetric Hysteresis of Piezo-Actuated Flexure-Based Systems.

Piezo-actuated flexure-based systems are widely used in applications with high accuracy requirements, but the intrinsic hysteresis has a detrimental effect on the performance which should be compensated. Conventional models were presented to model this undesired effect using additional dead-zone operators. This paper presents a new approach using two sets of operators with a distributed compensator to model and compensate for the asymmetric system hysteresis based on inversion calculation with a simplified digitized representation. The experimental results validate the effectiveness of the proposed model in modeling and compensating the asymmetric system hysteresis.

Data-Driven-Based Event-Triggered Control for Nonlinear CPSs Against Jamming Attacks.

This brief considers the security control problem for nonlinear cyber-physical systems (CPSs) against jamming attacks. First, a novel event-based model-free adaptive control (MFAC) framework is established. Second, a multistep predictive compensation algorithm (PCA) is developed to make compensation for the lost data caused by jamming attacks, even consecutive attacks. Then, an event-triggering mechanism with the dead-zone operator is introduced in the adaptive controller, which can effectively save communication resources and reduce the calculation burden of the controller without affecting the control performance of systems. Moreover, the boundedness of the tracking error is ensured in the mean-square sense, and only the input/output (I/O) data are used in the whole design process. Finally, simulation comparisons are provided to show the effectiveness of our method.

Dynamic modeling for soft dielectric elastomer actuator considering different input frequencies and external loads

A dynamic model for the soft dielectric elastomer actuator (SDEA) is developed in this paper to describe its intricately nonlinear behaviors considering different input frequencies and external loads. Firstly, the characteristics of the SDEA are observed by several groups of experiments. A phenomenological model is proposed to describe the asymmetric hysteresis behavior of the SDEA, which consists of a Prandtl-Ishlinskii model with one-side play operator and a dead-zone model with one-side dead-zone operator. Meanwhile, a mathematical model is built to depict the creep behavior of the SDEA. The dynamic model including a module and a linear system is proposed to further handle the rate-dependent and the stress-dependent hysteresis behaviors of the SDEA, in which the module is the superposition of the asymmetric hysteresis model and the creep model. To ensure that the inverse solution of the module is existing, as well as the linear system is controllable and observable, the constraint conditions of parameter values of the dynamic model are constructed. Next, the parameter identification is divided into two steps, and the differential evolution algorithm is employed in each step. Finally, the generalization of the proposed dynamics model is demonstrated by comparing the model output with the experimental data.

A Digitized Representation of the Modified Prandtl-Ishlinskii Hysteresis Model for Modeling and Compensating Piezoelectric Actuator Hysteresis.

Piezoelectric actuators are widely used in micromanipulation and miniature robots due to their rapid response and high repeatability. The piezoelectric actuators often have undesired hysteresis. The Prandtl–Ishlinskii (PI) hysteresis model is one of the most popular models for modeling and compensating the hysteresis behaviour. This paper presents an alternative digitized representation of the modified Prandtl–Ishlinskii with the dead-zone operators (MPI) hysteresis model to describe the asymmetric hysteresis behavior of piezoelectric actuators. Using a binary number with n digits to represent the classical Prandtl–Ishlinskii hysteresis model with n elementary operators, the inverse model can be easily constructed. A similar representation of the dead-zone operators is also described. With the proposed digitized representation, the model is more intuitive and the inversion calculation is avoided. An experiment with a piezoelectric stacked linear actuator is conducted to validate the proposed digitized MPI hysteresis model and it is shown that it has almost the same performance as compared to the classical representation.

Hysteresis modeling and feedforward compensation of a flexible structure actuated by macro fiber composites using bias bipolar Prandtl-Ishlinskii model

As a novel fiber-based piezoelectric composite material, macro fiber composites (MFC) affords notable advantages of good flexibility, high deformability, and large actuation ability. However, the intrinsic hysteresis behavior of the MFC decreases the positioning precision and performance of the flexible structure actuated by MFC actuators. A bias bipolar Prandtl-Ishlinskii (BBPI) model is presented to describe the bias bipolar hysteresis nonlinearity of a MFC-actuated flexible cantilever. The BBPI hysteresis model is composed of two parts: a superposition of the weighted play operators of the classical Prandtl-Ishlinskii (PI) model is employed to characterize the symmetric hysteresis. And a superposition of the weighted dead-zone operators is cascaded to deal with the bias bipolar behavior. Experimental identification results demonstrate that the presented BBPI model exhibits better modeling performance than the classical PI model. A feedforward compensation strategy based on the inverse BBPI hysteresis model is proposed. Experiments on trajectories tracking subject to a triangular wave, sinusoidal wave, and triangular wave with random amplitudes are carried out. Experimental results demonstrate the feasibility and effectiveness of the proposed BBPI model and the inverse feedforward compensator.

Adaptive neural tracking control of strict-feedback nonlinear systems with event-triggered state measurement

This paper investigates the adaptive neural tracking control of the strict-feedback nonlinear systems, where the states are measured in an event-triggered manner so as to save the communication resources. As the neural networks (NNs) account for the unknown dynamics of the system, the minimum learning parameters (MLPs) are extracted from the weights of the NNs and the upper bounds of the disturbances. The estimates of the MLPs are updated in an event-triggered manner to ensure the approximation ability of the NNs and the stability of the closed-loop system. An adaptive neural model is established to substitute for the original strict-feedback system and direct the design of the backstepping-based control laws. The states of this adaptive model are reset to the measured states of the original system when the triggering condition is violated. The triggering condition is constructed in the compound form and with the adaptive threshold. The dead-zone operator is involved to avoid the accumulation of triggering instants. In this paper, we notice the problem of “jumps of virtual control laws” for the event-triggered control (ETC) in the backstepping frame, and a detailed formulaic definition is given in section 2.2. To solve this problem, the first-order filters are fabricated to provide the continuous substitutes for virtual control laws. In addition, the “complexity explosion” generated by direct differentiating of virtual control laws can be averted. Through the proposed scheme, the closed-loop system can be viewed as an impulsive dynamic system, and the semi-globally uniformly ultimate boundedness (SGUUB) of all the errors is proved. Finally, two examples validate the feasibility of the proposed control scheme.

Modeling of the dynamic hysteresis in DEAP actuator using an empirical mode decomposition based long-short term memory network

As a smart material-based actuator, the dielectric electro-active polymer (DEAP) actuator is widely considered to be a potential driving mechanism for many applications, especially in intelligent bio-inspired robotics. However, the DEAP actuator demonstrates rate-dependent and asymmetrical hysteresis phenomenon which leads to great tracking inaccuracy and even oscillatory response, severely limiting its further development. Feedforward Neural Network (FNN) model has already become a widely used method to describe this kind of strong hysteresis nonlinearity in recent years. However, the FNN has no ability to remember the historical state of long period of time which is also a very important factor to restrict hysteresis phenomenon. In this paper, a novel hybrid model, Long-Short Term Memory (LSTM) network combined with Empirical Mode Decomposition (EMD), is proposed to model the dynamic hysteresis nonlinearity in DEAP actuator. At first, the original control signal sequence is preprocessed into a series of sub-sequence by the EMD method and is reshaped by one-sided dead-zone operator. Then the input space of LSTM is conducted using the original control signal, the sub-sequence, and reshaped signal. Finally, the input space and the displacement signal are applied to train the long-short term memory network. In order to verify the performance of the proposed model, the traditional artificial back propagation neural network (BPNN) model, rate-dependent Prandtl-Ishlinskii (RPI) model, and nonlinear electromechanical (NEM) model are compared from prediction accuracy. The results demonstrate that: (1) the proposed model has a higher prediction accuracy than the traditional artificial BPNN, RPI, and NEM model; and (2) the prediction accuracy of LSTM network is significantly improved by using EMD. Therefore, the long-short term memory network combined with empirical mode decomposition is a competitive method compared to the existing state-of-the-art approach.

Modified adaptive filter for digital subdivision of a four-frequency differential laser gyro.

This study represents a modified adaptive filter to suppress the beat noise of four-frequency differential laser gyro (FFDLG), which greatly affects the result of the eightfold digital subdivision. By constructing the demodulated signal model of FFDLG, the influence of beat noise to digital subdivision is analyzed. Based on the least mean square adaptive algorithm, a process of signal reconstruction and dead-zone operator of error are adopted in the modified adaptive algorithm. When implemented on a field-programmable gate array chip, the filter replaces the multiplication with 2:1 multiplexer to reduce the complexity of algorithm and resources in circuit. This circuit effectively suppresses the beat noise of the demodulated signal without changing the optical structure of the FFDLG and increases the signal-to-noise ratio from 20 dB to about 40 dB, which is conducive to improving the performance of the FFDLG.

Asymmetric Hysteresis Modeling Approach Featuring "Inertial System + Shape Function" for Magnetostrictive Actuators.

Hysteresis of the actuators based on magnetostrictive materials influences the control performance of the application systems. It is of importance and significance to establish an effective hysteresis model for the magnetostrictive actuators for precision engineering. In this paper, based on the analysis of the Duhem model, a first-order inertial system with hysteresis characteristic under harmonic input is used to describe the hysteresis caused by the inertia of the magnetic domains of magnetostrictive materials. Shape function is employed to describe the pinning of domain walls, the interactions of different magnetic domains of magnetostrictive materials, and the saturation properties of the hysteresis. Specifically, under an architecture of “inertial system + shape function” (ISSF-Duhem model), firstly a new hysteresis model is proposed for magnetostrictive actuators. The formulation of the inertial system is constructed based on its general expression, which is capable of describing the hysteresis characteristics of magnetostrictive actuators. Then, the developed models with a Grompertz function-based shape function, a modified hyperbolic tangent function-based shape function employing an exponential function as an offset function, a one-sided dead-zone operator-based shape function are compared with each other, and further compared with the classic modified Prandtl–Ishlinskii model with a one-sided dead-zone operator. Sequentially, feasibility and capability of the proposed hysteresis model are verified and evaluated by describing and predicting the hysteresis characteristics of a commercial magnetostrictive actuator.

Hardware-in-the-Loop Multiobjective Extremum-Seeking Control of Mineral Grinding

In this article, a model-free extremum-seeking control (ESC) design is proposed for the operational control of mineral grinding, where both operational indices regulation and throughput maximization are considered. Operational indices regulation and throughput maximization, as two conflicting objectives, are balanced through assigning weighting matrices to obtain a specific choice from the Pareto frontier of the multiobjective optimization problem. To deal with the input constraints, due to the physical limitations and operational constraints, a saturation function is imposed on each input and an extra penalty function is introduced to punish the inputs outside the feasible regions. The integrators and the additive perturbation signals in the ESC are swapped such that dead-zone operators can be added in between and imposed on the estimated gradients to attenuate the oscillation caused by modulating signals. The stability analysis of the proposed control design is provided in the absence of dead-zone operators. A Hardware-in-the-Loop simulation experiment is carried out to show the effectiveness of the proposed ESC.

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.

Decentralized Event-Triggered Adaptive Control of Discrete-Time Nonzero-Sum Games Over Wireless Sensor-Actuator Networks With Input Constraints.

This article studies an event-triggered communication and adaptive dynamic programming (ADP) co-design control method for the multiplayer nonzero-sum (NZS) games of a class of nonlinear discrete-time wireless sensor-actuator network (WSAN) systems subject to input constraints. By virtue of the ADP algorithm, the critic and actor networks are established to attain the approximate Nash equilibrium point solution in the context of the constrained control mechanism. Simultaneously, as the sensors and actuators are physically distributed, a decentralized event-triggered communication protocol is presented, accompanied by a dead-zone operation which avoids the unnecessary events. By predefining the triggering thresholds and compensation values, a novel adaptive triggering condition is derived to guarantee the stability of the event-based closed-loop control system. Then resorting to the Lyapunov theory, the system states and the critic/actor network weight estimation errors are proven to be ultimately bounded. Moreover, an explicit analysis on the nontriviality of the interevent times is also provided. Finally, two numerical examples are conducted to validate the effectiveness of the proposed method.