Disturbance rejection-based robust control for micropositioning of piezoelectric actuators

Precise control of piezoelectric actuators used in micropositioning applications is strongly under the effect of internal and external disturbances. Undesired external forces, unmodelled dynamics, parameter uncertainties, time variation of parameters and hysteresis are some sources of disturbances. These effects not only degrade the performance efficiency, but also may lead to closed-loop instability. Several works have investigated the positioning accuracy for constant and slow time-varying disturbances. The main concern is controlling performance and also the presence of time-varying perturbations. Considering unknown source and magnitude of disturbances, the estimation of the existing disturbances would be inevitable. In this paper, a compound disturbance observer-based robust control is developed to achieve precise positioning in the presence of time-varying disturbances. In addition, a modified disturbance observer is proposed to remedy the effect of switching behaviour in the case of slow time variations. A modified Prandtl–Ishlinskii (PI) operator and its inverse are utilized for both identification and real-time compensation of the hysteresis effect. Experimental results depict that the proposed approach achieves precise micropositioning in the presence of estimated disturbances.     

Adaptive trajectory tracking of magnetostrictive actuator based on preliminary hysteresis compensation and further adaptive filter controller

An adaptive dynamic surface control (DSC) scheme is proposed for the multi-input multi-output attitude control of near-space hypersonic vehicles (NHV). The proposed control strategy can improve the control performance of NHV despite uncertainties and external disturbances. The proposed controller combines dynamic surface control and radial basis function neural network (RBFNN) and is designed to control the longitudinal dynamics of NHV. The DSC technique is used to handle the problem of “explosion of complexity” inherent to the conventional backstepping method. RBFNN is used to approximate the unknown nonlinear function, and a robustness component is introduced in the controller to cancel the influence of compound disturbance and improve robustness and adaptation of the system. Simulation results show that the proposed strategy possesses good robustness and fast response.     

Precise tracking control of piezoelectric actuators based on a hysteresis observer

In this paper, a precise tracking control method for piezoelectric actuators based on a hysteresis observer is considered. A nonlinear observer to estimate the hysteretic nonlinearity in the piezoelectric actuator is designed, and then the hysteretic nonlinearity is compensated for by a feedforward control. The proposed observer is easy to design and has better performance compared to the previous work presented in the literature. A feedback controller is also designed to track reference signals. A numerical simulation is presented to verify the method proposed.     

Observer-based adaptive consensus tracking control for nonlinear multi-agent systems with actuator hysteresis

Nonlinear Dynamics - This paper addresses the consensus tracking problem of a class of nonlinear multi-agent systems by using observer-based control. The systems are in output-feedback form with...     

Dynamic modeling and trajectory tracking control method of segmented linkage cable-driven hyper-redundant robot

Nonlinear Dynamics - The dynamics modeling and trajectory optimization of a segmented linkage cable-driven hyper-redundant robot (SL-CDHRR) become more challenging, since there are multiple...     

Neural-network-based adaptive robust precision motion control of linear motors with asymptotic tracking performance

High precision motion control of permanent magnet linear motors (PMLMs) is limited by undesired nonlinear dynamics, parameter variations, and unstructured uncertainties. To tackle these problems, this paper presents a neural-network-based adaptive robust precision motion control scheme for PMLMs. The presented controller contains a robust feedback controller and an adaptive compensator. The robust controller is designed based on the robust integral of the sign of the error method, and the adaptive compensator consists of a neural network component and a parametric component. Moreover, a composite learning law is designed for the parameter adaption in the compensator to further enhance the control performance. Rigorous stability analysis is provided by using the Lyapunov theory, and asymptotic tracking is theoretically achieved. The effectiveness of the proposed method is verified by comparative simulations and experiments on a PMLM-driven motion stage.

     

Robust trajectory tracking control for a laboratory helicopter

This paper presents a robust nonlinear control strategy to deal with the trajectory tracking control problem for a laboratory helicopter. The helicopter model is considered as a nominal one with uncertainties such as unmodeled nonlinear dynamics, parametric uncertainties, and external disturbances. The proposed control approach incorporates the feedback linearization technique (FLT) and the signal compensation technique. The FLT is first applied to achieve the linearization of the nominal nonlinear model for reducing the conservation of the robust compensator design. A nominal controller based on the linear quadratic regulation method is designed for the linearized nominal system, whereas a robust compensator is introduced to restrain the influences of the uncertainties. It is shown that the trajectory tracking errors of the closed-loop system are ultimately bounded, and the boundaries can be specified by choosing the controller parameters. Simulation and experimental results on the lab helicopter verify the effectiveness of the proposed method.     

Delay-range-dependent local adaptive and robust adaptive synchronization approaches for time-delay chaotic systems

Nonlinear Dynamics - This paper studies the local adaptive and robust adaptive control methodologies for the synchronization of the chaotic drive and the response systems with finite time lags,...     

Adaptive fixed-time trajectory tracking control for Mars entry vehicle

Nonlinear Dynamics - This paper develops a fixed-time trajectory tracking control scheme for Mars entry vehicle under uncertainty. First, a novel fixed-time nonsingular terminal sliding mode...     

A unified framework for modeling hysteresis in ferroic materials

This paper addresses the development of a unified framework for quantifying hysteresis and constitutive nonlinearities inherent to ferroelectric, ferromagnetic and ferroelastic materials. Because the mechanisms which produce hysteresis vary substantially at the microscopic level, it is more natural to initiate model development at the mesoscopic, or lattice, level where the materials share common energy properties along with analogous domain structures. In the first step of the model development, Helmholtz and Gibbs energy relations are combined with Boltzmann theory to construct mesoscopic models which quantify the local average polarization, magnetization and strains in ferroelectric, ferromagnetic and ferroelastic materials. In the second step of the development, stochastic homogenization techniques are invoked to construct unified macroscopic models for nonhomogeneous, polycrystalline compounds exhibiting nonuniform effective fields. The combination of energy analysis and homogenization techniques produces low-order models in which a number of parameters can be correlated with physical attributes of measured data. Furthermore, the development of a unified modeling framework applicable to a broad range of ferroic compounds facilitates material characterization, transducer development, and model-based control design. Attributes of the models are illustrated through comparison with piezoceramic, magnetostrictive and shape memory alloy data and prediction of material behavior.     

非线性轨迹优化问题的保辛自适应求解方法

非线性轨迹优化问题一般是一个非线性最优控制问题。将非线性系统的最优控制问题导入到哈密顿体系的辛几何空间当中,基于对偶变量变分原理提出了求解非线性最优控制问题的一种保辛自适应方法。以时间区段两端协态作为独立变量,在时间区段内采用拉格朗日插值近似状态和协态变量,并利用对偶变量变分原理将非线性最优控制问题转化为非线性方程组的求解,保持了哈密顿系统的辛几何结构。并进一步,提出了基于多层次迭代的自适应算法,提高了非线性最优控制问题的求解效率。数值实验验证了该算法在求解非线性轨迹优化问题中的有效性。     

Efficient and robust constitutive integrators for single-crystal plasticity modeling

Small-scale deformation phenomena such as subgrain formation, development of texture, and grain boundary sliding require simulations with a high degree of spatial resolution. When we consider finite-element simulation of metal deformation, this equates to thousands or hundreds of thousands of finite elements. Simulations of the dynamic deformations of metal samples require elastic–plastic constitutive updates of the material behavior to be performed over a small time step between updates, as dictated by the Courant condition. Further, numerical integration of physically-based equations is inherently sensitive to the step in time taken; they return different predictions as the time step is reduced, eventually approaching a stationary solution. Depending on the deformation conditions, this converged time step becomes short (10⁻⁹ s or less). If an implicit constitutive update is applied to this class of simulation, the benefit of the implicit update (i.e., the ability to evaluate over a relatively large time step) is negated, and the integration is prohibitively slow. The present work recasts an implicit update algorithm into an explicit form, for which each update step is five to six times faster, and the compute time required for a plastic update approaches that needed for a fully-elastic update. For dynamic loading conditions, the explicit model is found to perform an entire simulation up to 50 times faster than the implicit model. The performance of the explicit model is enhanced by adding a subcycling algorithm to the explicit model, by which the maximum time step between constitutive updates is increased an order of magnitude. These model improvements do not significantly change the predictions of the model from the implicit form, and provide overall computation times significantly faster than the implicit form over finite-element meshes. These modifications are also applied to polycrystals via Taylor averaging, where we also see improved model performance.     

Fractional integral sliding modes for robust tracking of nonlinear systems

Memory and heritage of differintegral operators require knowledge of the error manifold derivative at the initial time to sustain a sliding motion for any initial condition. Moreover, when the system is subject to (unknown) disturbances, such initial condition is unknown; thus, the enforcement of an integral sliding motion has been elusive with a chatter-less controller. In this paper, a novel fractional-order integral sliding mode (FISM) is proposed to maintain an invariant sliding mode due to an exact estimation of disturbances at first step. Our scheme is continuous after initial condition, avoiding chattering effects thanks to the topological properties of differintegral operators. In contrast to other FISM approaches, the proposed scheme induces a fractional-order reaching dynamics of order \((1+\nu )\in (1,2)\) to enforce an integral sliding mode for any initial condition, even in the presence of Hölder (continuous but not necessarily differentiable) disturbances and model uncertainties. Simulations show the reliability of the proposed scheme.     

Analytical modeling of sandwich beam for piezoelectric bender elements

Piezoelectric bender elements are widely used as electromechanical sensors and actuators.An analytical sandwich beam model for piezoelectric bender elements was developed based on the first-order shear deformation theory(FSDT),which assumes a single rotation angle for the whole cross-section and a quadratic distribution function for coupled electric potential in piezoelectric layers,and corrects the effect of transverse shear strain on the electric displacement integration.Free vibration analysis of simply- supported bender elements was carried out and the numerical results showed that,solu- tions of the present model for various thickness-to-length ratios are compared well with the exact two-dimensional solutions,which presents an efficient and accurate model for analyzing dynamic electromechanical responses of bender elements.     

Dual input–output pairs for modeling hysteresis inspired by mem-models

We call attention to a dual-pair concept for modeling hysteresis involving instantaneous switching: Specifically, there are two input–output pairs for each hysteresis model under one specific input, namely a differential pair and an integral pair. Currently in engineering mechanics, only one pair is being recognized and utilized, not the other. Whereas this dual-pair concept is inherent in the differential and algebraic forms of memristors and memcapacitors, the concept has not been carried over to memristive system theory, nor to memcapacitive system theory. We show that the “zero-crossing” feature in memristors, memcapacitors, and memristive/memcapacitive models (i.e., the “mem-models”) is also a feature of the differential pairs of well-known non-mem-models, examples of which are Ramberg–Osgood, Bouc–Wen, bilinear hysteresis, and classical Preisach. The dual-pair concept thus connects mem-models and non-mem-models, thereby facilitating the modeling of hysteresis, and raising a set of scientific questions for further studies that might not otherwise come to awareness.     

Geometric finite-time inner-outer loop trajectory tracking control strategy for quadrotor slung-load transportation

Nonlinear Dynamics - This paper presents a geometric finite-time inner-outer loop control strategy for slung payload transportation using a quadrotor. The underactuated nature of the quadrotor in...     

导弹编队协同攻击分布式鲁棒自适应控制

在有向通信拓扑下研究了导弹编队的鲁棒自适应协同跟踪控制问题。针对导弹编队系统中队形跟踪、外部扰动和模型不确定性的情况,通过选取包含位置跟踪误差和速度跟踪误差的辅助变量,提出了一种基于有向通信拓扑的鲁棒自适应编队控制策略。提出了自适应律对未知参数进行估计,并且利用Lyapunov稳定性理论分析了闭环系统的渐近稳定性。进一步,对于通信时滞的情况,给出了系统渐近稳定所需要满足的条件。与滑模控制等传统鲁棒控制不同,所设计的鲁棒自适应控制器是连续的,更便于导弹编队系统的实现。数值仿真结果表明,队形跟踪误差小于0.03 m,队形保持误差小于0.07 m,所设计的控制器能实现高精度的编队跟踪控制。     

Ferroelectric and ferroelastic piezoceramics – modeling of electromechanical hysteresis phenomena

Received December 18, 2000 / Published online: June 1, 2001     

Experimental evaluation and constitutive modeling of non-proportional deformation for asymmetric steels

Recently non-proportional deformation has received increased attention from researchers working in the area of experimental and computational modeling of metal deformation. However, most of them are numerical in nature with limited experimental data available, making it further difficult to model non-proportional deformation. In the present work, two-stage uniaxial tests, along with uniaxial cyclic and biaxial tests for different stress ratios, have been performed to evaluate deformation behavior of ultra-low carbon high strength automotive steel. Behaviors like cross-effect and hardening stagnation, which are attributed to the evolution of complex dislocation structures, were observed in this steel. It was also noticed that this steel exhibits tension-compression asymmetry. As for constitutive modeling, a modified asymmetric yield function is proposed to be used with a combined isotropic-kinematic hardening model. Also methods to account for the hardening stagnation during reverse loading and the cross-effect during two-stage deformation are proposed. The resulting constitutive model showed reasonably good agreement with experimental results.