Nonlinear Actuator Research Articles

Static and dynamic characteristics of electrostatically coupled MEMS beams under asymmetric actuation conditions

Abstract Electrostatically actuated microbeams have gained prominence due to their applications as micro-actuators and ultrasensitive sensors. In this study, we investigate the dynamic behavior of electrostatically coupled microbeams, specifically focusing on the effects of asymmetric actuation conditions. Our investigation encompasses both static and dynamic characteristics of the coupled microbeam system, considering various gap ratios between the beams and the fixed electrodes. Within the coupled system, two doubly clamped microbeams are positioned between two fixed electrodes. We develop a reduced-order model (ROM) to investigate static and dynamic responses of the coupled system. To validate the ROM, we rigorously compare its results with finite element (FE) simulations. Our findings reveal that the gap ratios play a pivotal role in shaping the system’s response. Notably, first two natural frequencies are important for design of micro-resonators and they exhibit complex variation with respect to the applied DC voltage. Moreover, we explore resonance frequency tunability and investigated interplay between geometric nonlinearity and nonlinear electrostatic actuation forces. These insights contribute significantly to the efficient design of MEMS resonators.

Robust flexible spacecraft attitude tracking under measurement errors, actuator nonlinearities, and faults

Reliable spacecraft attitude maneuver is one of the core research areas of the space industry due to the need for sustainable space exploration and advancements in the space technology. The paper presents an observer-based adaptive backstepping (OB-ABST) fault-tolerant control scheme for a flexible spacecraft attitude tracking under the effect of state measurement errors, inertial uncertainties, external disturbances, multiple actuator faults, and input nonlinear saturation (INS) while suppressing vibrations due to flexible modes. Initially, we design an adaptive backstepping controller to mitigate the system’s unwanted nonlinearities and observers to get estimates of the attitude dynamics in a recursive design framework. Later, the control structure incorporates a simple actuator saturation compensator to tackle input torque saturation in the system. The critical feature of the proposed OB-ABST control structure is to ensure precise attitude-tracking maneuvers and vibration suppression without intelligent materials such as shape memory alloys (SMA) and piezoelectric material (PZT). Lyapunov stability analysis proves practical finite-time convergence of the system state errors, observation errors, and actuator saturation compensators. Moreover, we provide specific conditions to tune design parameters. Finally, comparative simulation experiments validate the control performance of the proposed controller in the presence of multiple challenges.

Observer-Based Adaptive Fuzzy Control for Singular Systems with Nonlinear Perturbation and Actuator Saturation

Observer-Based Adaptive Fuzzy Control for Singular Systems with Nonlinear Perturbation and Actuator Saturation

Robust Fuzzy Adaptive Fault‐Tolerant Control for a Class of Second‐Order Nonlinear Systems

ABSTRACTIn this brief, an optimal active fuzzy fault‐tolerant control (OAFFTC) scheme is proposed for a class of unknown perturbed multi‐input multi‐output (MIMO) nonlinear systems with nonaffine nonlinear actuator faults and time‐varying sensor faults. The control strategy can handle automatically (online updating) with three additives (bias, drift, and loss of accuracy) along with one multiplicative (loss of effectiveness) sensor faults and nonlinear state‐dependent actuator faults. In order to deal with uncertain system dynamics, sensor and actuator faults, and external disturbances, fuzzy systems (FSs) and backstepping techniques were combined to provide the adaptive control term as well as a robust control term. Butterworth filter is used to get rid the algebraic loop problem. The suggested robust term, can deal with approximation errors of the fuzzy systems (FSs). To automatically optimize the adaptive parameters and the starting conditions, particle swarm optimization (PSO) approach is introduced. The Lyapunov approach is employed to demonstrate the closed‐loop system's stability. To assess the efficacy and correctness of the suggested scheme, quadrotor dynamic model is performed on the simulation part.

Fully distributed practical fixed-time fault-tolerant consensus of nonlinear multiagent systems

In this article, the practical fixed-time fault-tolerant consensus problem of a class of first-order nonlinear multiagent systems with actuator faults is investigated. Owing to the existence of uncertain actuator failures (multiplicative faults and additive faults) and non-linearities, it is challenging to study the fixed-time consensus problem of such multiagent systems in a fully distributed approach. To get over this challenge, a fully distributed adaptive protocol that utilizes adaptive techniques is proposed. Under this control protocol, multiagent systems can achieve consensus, and by adjusting controller parameters, the consensus error can converge to the acceptable bounded region in a fixed time. In addition, due to the introduction of adaptive parameters, the design of the control protocol is not dependent on any global network topology information, which means the control protocol is fully distributed. Therefore, the proposed scheme has better scalability and wider applicability. Finally, the simulation results are proposed to validate the fault-tolerant ability and fully distributed characteristics of the presented scheme.

Adaptive neural chattering suppression pseudo inverse active control for a class of micromilling systems with multiaxis piezoelectric actuators

For a multi-axis nonlinear milling system with piezoelectric actuators, a pseudo inverse dynamic surface active control scheme with adaptive fuzzy output-feedback is developed. The main contributions can be characterized as following: (1) to overcome the hysteresis non-linearities in the piezoelectric actuators, the new hysteresis pseudo inverse compensators are established to replace the conventional hysteresis direct-inverse model construction, which is a very challenging or even impossible work. The hysteresis pseudo inverse means that the hysteresis direct-inverse model is no longer essential any more, instead, a search algorithm for the actual control signal from the designed hysteretic temporary control laws are proposed to alleviate the hysteresis nonlinearities effectively; (2) to realized high-precision tracking control and mitigate chattering suppression in the micromilling systems, the fuzzy logic systems, the novel dynamic surface control algorithms and the modified high-gain states observer are designed to approximise the unknown continuous functions of the micromilling systems, design the high performance controller and estimate the immeasurable states in the control system, respectively; (3) the hardware-in-loop simulation platform is constructed and the experiments of tracking control and chattering suppression are implemented to validate the effectivity of the developed control scheme.

Structure and properties of Er3+- modified (Bi0.5Na0.5)0.945Ba0.055TiO3-based lead-free ferroelectric ceramics

Er3+-modified (Bi0.5Na0.5)0.945Ba0.055Ti0.98(Fe0.5Sb0.5)0.02O3 (BNBT-FS) lead-free ferroelectric ceramics with large electrostrain and electrostrictive response were fabricated in our work. Results showed that Er3+-doping induced the destruction of ferroelectric order and significantly enhanced the field-induced strain. For 0.2 mol% modified sample, the unipolar strain reached 0.463 % under the electric field of 80 kV/cm, yielding a large normalized strain d33* (Smax/Emax) of 579 pm/V. For 0.4 mol% modified sample, high electrostrictive effect with temperature-insensitive electrostrictive coefficient Q33 (0.022–0.026 m4/C2 in the temperature range of 25–100°C) was obtained. The large electrostrain and electrostrictive response in the present materials show the great potential of the materials for nonlinear actuators applications.

Decreasing the non-linearity of hybrid reluctance actuators by air gap design

This paper presents an air gap design approach to improve the linearity of rotational Hybrid Reluctance Actuators (HRAs) used in fast steering mirrors. The approach involves modeling a one-degree-of-freedom HRA with a magnetic equivalent circuit to identify and analyze sources of non-linearities. On the basis of the verified model, solutions for an improved linear system behavior are analytically searched. Two linearized HRA designs are proposed, one with linear cross-section dependency and the other with hyperbolic air gap length dependency. Finite element method simulations are employed to evaluate the performance with respect to the linearity and the motor constant of these designs, showing factor 50 improved system linearity.

Modeling and vibration suppression for overhead crane in planar space with nonlinear time-varying actuator faults and uncertain control directions

Modeling and vibration suppression for overhead crane in planar space with nonlinear time-varying actuator faults and uncertain control directions

Deformation theory and nonlinear dynamic behavior of PVC gel actuators

Polyvinyl chloride (PVC) gel generates complex nonlinear vibration behavior under an alternating current voltage excitation, which has potential application as a dynamic electromechanical actuator. However, there are few studies on the deformation theory of PVC gel actuators, especially the dynamic nonlinear response theory. In this paper, a complex dynamic model is established according to the electrodeformation mechanism of PVC film, and the nonlinear dynamic behavior of the actuator is numerically studied by a differential equation. The effects of applied voltage amplitude, voltage frequency, dibutyl adipate content, mechanical tension, and bias voltage on the dynamic properties of PVC film were analyzed under the condition of equal biaxial tension. The variation of amplitude and the generation and disappearance of the beat frequency during vibration are analyzed by using time-domain characteristics. The degree of PVC actuator nonlinearity as well as vibration stability and periodicity is also reflected based on the phase path and Poincare map. Finally, the law of influence of external condition parameters on the dynamic response of the PVC actuator is obtained.

Temperature gradient for improving the output non-linearity in shape memory alloy actuators

The non-linearity of shape memory alloy’s (SMA) input vs. output relationship has been a significant barrier to their broader application for actuators. In this article, we introduce a novel activation approach with the objective of improving the output nonlinearity in SMA actuators by using a liquid temperature gradient for activation. This gradient, with a narrow inflection point, selectively activates and deactivates different portions of the SMA, allowing control of the overall actuator’s output by adjusting the inflection point’s position. Two prototypes with the proposed concept were constructed and tested for force and displacement output. Their inner shape design facilitates the creation of a temperature gradient, whose inflection point is adjusted by varying the mix ratio of the inlet of hot and cold water. The performance of the prototypes was evaluated, including their ability to generate a temperature gradient, output linearity, activation dead time and time constant, and compatibility with a linear controller. The output linearity, activation dead time, and time constant were also compared with traditional wet activation. Our findings suggest that this technique significantly enhances the performance and predictability of SMA-based actuators and is compatible with PID controllers without additional feedforward or modeling techniques, offering a practical solution to a long-standing challenge in the field.

Numerical algorithm for nonlinearity compensation of hardly constrained actuation for trajectory tracking control of deadzone-included dynamic systems

This paper addresses the control of a nonlinear system affected by deadzone effects, using a constrained actuator. The system itself incorporates a second-order oscillatory dynamic actuator, with an unknown nonlinear input-output relationship. The proposed algorithm not only accommodates the deadzone constraints on control inputs but also considers the actuator's saturation limits in control input calculations. It introduces a trajectory tracking mechanism that, instead of directly following the primary trajectory, adheres to an alternative trajectory capable of stable tracking, gradually converging to the main trajectory while accounting for operational constraints. In practical control systems, the actuator's input-output relationship is often nonlinear and unknown, requiring inversion for model-based control. This paper employs an offline-trained neural network trained on synthetic data to identify and approximate the actuator's behavior. To optimize the control system's performance and ensure stability during sudden error changes, the control input operates in two modes: position and velocity control. This dual-mode control allows for continuous switching between the two, facilitated by an innovative optimization technique based on the gradient descent method with a variable step size. Simulation results validate the effectiveness of the proposed algorithm in controlling systems constrained by hard limits and featuring nonlinear oscillatory actuators, providing a valuable contribution to the field of control systems.

Dynamical sensitivity on thermal fluctuations of torsional homogeneous and nonhomogeneous microsystems under the influence of Casimir and electrostatic torques: Nonlinear actuation towards chaotic motion

We have studied how the mechanical Casimir torque between the components of a torsional double beam microdevice under the influence of thermal fluctuations could play significant role on the dynamics of the device, and under what conditions can even lead to chaotic behavior. The influence of thermal fluctuations on the dynamical behavior of torsional microsystems, whether homogeneous or nonhomogeneous, has been revealed through bifurcation and phase diagrams, and Poincare maps. For nonhomogeneous microsystems, the device with low conductivity reveals significant sensitivity to thermal fluctuations. Moreover, it is shown the significant dependence of the optimal voltage distribution, which leads to a significant increase in the stable operation range of the device, on the ambient temperature conditions and the optical properties of the constituent materials. For nonconservative torsional microsystem, the use of the Melnikov method and Poincaré plots have shown how thermal effects increase the probability of chaotic behavior. This is because different temperature enhances the effective Casimir torque and the possibility of chaotic motion. Furthermore, it is illustrated how the use of the optimal voltage distribution, by taking into consideration thermal fluctuations and optical properties, can keep the device away from chaotic behavior. This is because by dividing the electrostatic torques the influence of the effective Casimir torque is reduced. Finally, it is demonstrated that by transforming a homogeneous system into a heterogeneous one, the response of the system to thermal fluctuations is reduced making it possible to avoid to increase the possibility for chaotic behavior by changing the temperature.

Modeling and analysis of hysteresis using the Maxwell-slip model for variable stiffness actuators

Hysteresis non-linearity in variable stiffness actuators (VSAs) causes significant torque errors and reduces the stability of the actuators, leading to poor human–computer interaction performance. At present, fewer hysteresis compensation models have been developed for compliant drives, so it is necessary to establish a suitable hysteresis model for compliant actuators. In this work, a new model with a combination of the Maxwell-slip model and virtual deformation is proposed and applied to an elbow compliant actuator. The method divides the periodic variation of the actuator into three parts: an ascending phase, a descending phase, and a transition phase. Based on the concept of virtual deformation, the nonlinear hysteresis curve is transformed into a polyline, and the output torque is estimated using the revised Maxwell-slip model. The simulation results are compared with the experimental data. Its torque error is controlled within 0.2Nm, which validates the model. An inverse model is finally established to calculate the deformation deflection angle for hysteresis compensation. The results show that the inverse model has high accuracy, and the deformation deflection is less than 0.15 rad.

An improved dynamic Prandtl–Ishlinskii hysteresis model and a PID-type adaptive sliding mode controller for piezoelectric micro-motion platform

Piezoelectric actuators are widely used in the field of micro-nano driving due to their advantages of fast frequency response, high displacement resolution, large stiffness, small size, and low heat generation. However, the hysteresis non-linearity of piezoelectric actuators severely affects their positioning accuracy during operation. Therefore, the study of hysteresis model and compensation control for piezoelectric actuators has always been a hot topic in the field of micro-nano driving. However, existing hysteresis models and control methods cannot well describe the dynamic hysteresis curve of piezoelectric actuators and track the desired trajectory. To address this issue, this paper proposes an improved dynamic Prandtl–Ishlinskii (IDPI) model and a finite-time trajectory tracking adaptive sliding mode control method based on PID-type. Firstly, this paper introduces the construction and parameter identification method of the IDPI model. Secondly, the accuracy of the IDPI model in describing hysteresis curves under different input signals is verified through experiments, and the effectiveness of the feedforward controller based on the IDPI model is validated experimentally. Then, considering the modeling uncertainty, unmodeled internal dynamics, and external environmental disturbances of the piezoelectric micro-motion platform, a finite-time trajectory tracking adaptive sliding mode controller based on PID-type is designed to suppress the non-linear characteristics of the piezoelectric micro-motion platform. Finally, the performance of the compensator is verified through simulation experiments.

Incremental fully actuated system approach-based prescribed-time fault-tolerant formation control of helicopters under multiple faults

Helicopter formation is characterized by intricate dynamics, complex mechanics, and challenging scenarios, raising the necessity for agile, robust, and convenient controller design. This paper explores the prescribed-time fault-tolerant formation control of multiple helicopters through the incremental fully actuated system approach, which addresses multiple faults in sensors and swash plate struts. First, the helicopter model encompassing aerodynamic, flapping dynamic, swash plate dynamic, actuator faults, and sensor faults is established and further partitioned into attitude and position subsystems. Then, in the attitude subsystem, a prescribed-time attitude controller based on the incremental fully actuated system approach is proposed to track the desired attitude with robustness against actuator faults, aerodynamic drags, inter-axis coupling, and non-linearity. Next, in the position subsystem, the faults of velocity and position sensors are estimated and compensated through the prescribed-time fault-estimation observer, and a prescribed-time formation controller through the incremental fully actuated system approach is designed to achieve distributed leader-follower formation control. A Task-Fault dual-driven scheduling mechanism of the parameters of the prescribed-time technique is developed to promptly activate the prescribed-time function, and the control scheme is proven to be prescribed-time convergent via Lyapunov stability theory. Finally, numerical simulations are conducted to illustrate the efficiency of the algorithm.

Development and Validation of Robotic Ankle Exoskeleton With Parallel Nonlinear Elastic Actuator

Abstract This paper presents the development of a robotic ankle exoskeleton for human walking assistance. First, the biomechanical properties of a human ankle joint during walking are presented. Next, design of the robotic ankle exoskeleton is introduced. The exoskeleton is actuated by a novel parallel nonlinear elastic actuator. The cam-spring mechanism in the actuator can function as a parallel nonlinear spring with an adjustable stiffness, and the design of the cam profile curve is described. Additionally, an adaptive controller is proposed for the exoskeleton to generate a desired assistive torque according to the wearer's total weight. Finally, experiments are conducted to validate the effectiveness of the developed robotic ankle exoskeleton. The experimental results demonstrate that during a gait cycle, reductions of 42.7% and 40.1% of the peak and average currents of the driving motor in the actuator are observed, respectively, with the designed cam-spring mechanism. A peak assistive torque of 23.9 Nm can be provided for the wearers by the exoskeleton during walking. With the assistance provided by the exoskeleton, the average and peak soleus activities of the wearers during a gait cycle are decreased by 25.42% and 31.94%, respectively.

Adaptive Tracking Control for Tethered Aircraft Systems With Actuator Nonlinearities and Output Constraints

Adaptive Tracking Control for Tethered Aircraft Systems With Actuator Nonlinearities and Output Constraints

Cross-Medium Time-Delay active vibration isolation method based on Voltage-Force hysteresis model

Micro-vibration significantly impacts spacecraft precision equipment operations, which can be resolved by using a piezoelectric actuator. The voltage-displacement relationship is the primary focus of current research on the hysteresis nonlinearity of piezoelectric actuators. Nevertheless, when tracking and controlling the acceleration/force signals of micro-vibration, control method based on the voltage-displacement introduces needless errors. In this paper, a cross-medium active vibration isolation control method based on voltage-force hysteresis model that can be utilised to track micro-vibration acceleration signals with high accuracy is proposed. The method exploits the slow transmission speed of vibration waves in a rubber medium to design a hybrid actuator mechanism containing a slow buffer medium and a piezoelectric actuator, and adopts a sliding mode control method to achieve accurate force control. Experiments demonstrated that compared with the vibration isolation control method based on voltage-displacement hysteresis model, the vibration isolation accuracy of the proposed method can be improved by 23.4%

Event-triggered consensus tracking control of flexible manipulators with nonlinear time-varying fault-tolerant actuators and input constraint

This paper introduces a novel event-triggered consensus control strategy for a multi-agent system composed of underactuated flexible manipulators. Most existing research on consensus tracking control assumes that the model targeted is fully actuated, the control signal is continuous, and that both time-varying actuator failures and input constraints are managed separately. These challenges were tackled in this study within the context of multi-agent systems, addressing input constraints and nonlinear time-varying actuator failures simultaneously. Moreover, an event-triggered mechanism is proposed to reduce signal communication. A double closed-loop consensus tracking method is designed based on the multi-agent topology, enabling all flexible manipulators to track the angle and angular velocity of the leader and an adaptive control law is designed to solve actuator faults. Finally, the simulation results demonstrate the effectiveness of the proposed control scheme.