Adaptive identification and control of hysteresis in smart materials

Hysteresis hinders the effective use of smart materials in sensors and actuators. This paper addresses recursive identification and adaptive inverse control of hysteresis in smart material actuators, where hysteresis is modeled by a Preisach operator with a piecewise uniform density function. Two classes of identification schemes are proposed and compared, one based on the hysteresis output, the other based on the time-difference of the output. Conditions for parameter convergence are presented in terms of the input to the Preisach operator. An adaptive inverse control scheme is developed by updating the Preisach operator (and thus its inverse) with the output-based identification method. The asymptotic tracking property of this scheme is established, and for periodic reference trajectories, the parameter convergence behavior is characterized. Practical issues in the implementation of the adaptive identification and inverse control methods are also investigated. Simulation and experimental results based on a magnetostrictive actuator are provided to illustrate the proposed approach.     

Approximate inversion of the Preisach hysteresis operator with application to control of smart actuators

Hysteresis poses a challenge for control of smart actuators. A fundamental approach to hysteresis control is inverse compensation. For practical implementation, it is desirable for the input function generated via inversion to have regularity properties stronger than continuity. In this paper, we consider the problem of constructing right inverses for the Preisach model for hysteresis. Under mild conditions on the density function, we show the existence and weak-star continuity of the right-inverse, when the Preisach operator is considered to act on Holder continuous functions. Next, we introduce the concept of regularization to study the properties of approximate inverse schemes for the Preisach operator. Then, we present the fixed point and closest-match algorithms for approximately inverting the Preisach operator. The convergence and continuity properties of these two numerical schemes are studied. Finally, we present the results of an open-loop trajectory tracking experiment for a magnetostrictive actuator.     

具有Preisach类型磁滞输入的不确定非线性系统 自适应神经网络控制

本文针对一类执行器受Preisach磁滞约束的不确定非线性系统, 提出一种基于神经网络的直接自适应控制 方案, 旨在解决系统的预定精度轨迹跟踪问题. 由于Preisach算子与系统动态发生耦合, 导致算子输出信号不可测 量, 给磁滞的逆补偿造成了困难. 为解决此问题, 本文首先将Preisach模型进行分解, 以提取出控制命令信号用于 Backstepping递归设计, 并在此基础上融合一类降阶光滑函数与直接自适应神经网络控制策略, 形成对磁滞非线性 和被控对象非线性的强鲁棒性能, 且所设计方案仅包含一个需要在线更新的自适应参数, 同时可保证Lyapunov函数 时间导数的半负定性. 通过严格数学分析, 已证明该方案不仅保证闭环系统所有信号均有界, 而且输出跟踪误差随 时间渐近收敛到用户预定区间. 基于压电定位平台的半物理仿真实验进一步验证了所提出控制方案的有效性.     

Modeling and control of hysteresis in magnetostrictive actuators

A novel dynamic model is proposed for the hysteresis in magnetostrictive actuators by coupling a Preisach operator to an ordinary differential equation, and a parameter identification method is described. An efficient inversion algorithm for a class of Preisach operators with piecewise uniform density functions is then introduced, based upon which an inverse control scheme for the dynamic hysteresis model is presented. Finally the inversion error is quantified and l₁ control theory is applied to improve the robustness of inverse compensation. Simulation and experimental results based on a Terfenol-D actuator are provided.     

一类具有应力相关迟滞非线性智能结构的建模与跟踪控制研究

智能结构在变化的负载下产生的应力相关迟滞非线性严重影响了其在亚微米级跟踪控制中的应用. 因此, 本文提出了一种应力相关Preisach算子用以描述当输入信号与应力同时变化时, 智能结构所产生的迟滞非线性特性. 该应力相关Preisach算子是在经典Preisach算子的基础上, 通过将应力相关项引入密度函数所得到的. 此外, 为了实现逆补偿控制器的设计, 本文提出了应力相关Preisach算子的性质与基于模糊树方法的辨识方案. 继而, 本文设计了一种基于所提算子的前馈逆补偿与反馈控制器结合的复合控制方案, 并将其应用于一类超磁致伸缩智能结构的实时跟踪控制实验中. 实验证明, 与经典Preisach算子相比, 所提出的算子和相应的控制方案能够较好的消除应力相关迟滞非线性的影响并使控制效果显著提高.     

FSM状态间逻辑条件检验的算法研究

有限状态机(FSM)是VLSI控制结构的一种映射,它的自动综合成为设计自动化的一个十分重要的环节和途径。本文讨论在FSM自动综合中输入阶段的状态间逻辑条件检验的问题,研究分析状态间逻辑条件检验的相互关系及影响,并提出了FSM状态间逻辑条件检验的优化算法,从而使时间复杂度降低,实现更加简便。最后,本文给出了优化算法的流程和一些实验结果,结果令人满意。     

Activation dynamics in the optimization of targeted movements

Human movements, and their underlying muscular recruitment strategies, can be studied in several ways. In order to increase the understanding of human movement planning strategies, the movement problem is here seen as a boundary value problem for a mechanism with prescribed initial and final configurations. The time variations of a set of control actuator forces are supposed to fulfil some optimality criterion while creating this motion. The boundary value problem is discretized by temporal finite element interpolation, where the discrete variables are seen in an optimization context. The present work focusses on the introduction of the activation dynamics of the actuators, introducing a delay in the force production from the stimulation variables. The choice of interpolations of the variables is discussed in the light of the optimization setting. Examples show aspects of the results obtained for different assumptions. It is concluded that the formulation gives a good basis for further improvement of muscular force production models in an optimal movement setting.     

SVD‐Based Accurate Identification and Compensation of the Coupling Hysteresis and Creep Dynamics in Piezoelectric Actuators

In this paper, the coupling hysteresis and creep in piezoelectric actuators are identified and compensated for accurate tracking. First, we present the coupling hysteresis and creep model in smart actuators. Next, a complete identification strategy is designed according to the properties of the Preisach model. Then, an approach for parameter updating of the coupling model is provided. With the identified hysteresis and creep, the model‐based inversion compensation is designed. Finally, we apply the model identification and compensation to a piezoelectric stage to demonstrate the effectiveness of the proposed approaches. Significant reduction of the tracking error is achieved with the model‐based inversion feedforward compensator in which the relative errors at 10 Hz and 50 Hz are reduced to 1.85% and 4.53%, respectively. In addition, the model‐based feedforward is augmented with an integral feedback controller. With the composite controller, the relative errors at 10 Hz and 50 Hz are reduced to 0.42% and 3.04%, respectively.     

Trigonometric approximation of optimal periodic control problems for distributed-parameter systems

The optimal periodic control problem for a system described by first order partial differential equations is approximated by a sequence of discretized optimization problems. Trigonometric polynomials in two variables are used in the latter problems to approximate the state trajectory, the control and functions appearing in differential equations and in the criterion of the basic problem. The state equations and the instantaneous constraints on the state and the control are taken into account by the mixed exterior-interior penalty function. Sufficient conditions are given for the convergence of solutions of discretized problems to the optimal solution of the basic problem. The possibility of applying the method to a class of optimal periodic control problems in chemical engineering is emphasized.     

Approximations for optimal stopping of a piecewise-deterministic process

This paper deals with approximation techniques for the optimal stopping of a piecewise-deterministic Markov process (P.D.P.). Such processes consist of a mixture of deterministic motion and random jumps. In the first part of the paper (Section 3) we study the optimal stopping problem with lower semianalytic gain function; our main result is the construction of ε-optimal stopping times. In the second part (Section 4) we consider a P.D.P. satisfying some smoothness conditions, and forN integer we construct a discretized P.D.P. which retains the main characteristics of the original process. By iterations of the single jump operator from ℝ ^N to ℝ ^N , each iteration consisting ofN one-dimensional minimizations, we can calculate the payoff function of the discretized process. We demonstrate the convergence of the payoff functions, and for the case when the state space is compact we construct ε-optimal stopping times for the original problem using the payoff function of the discretized problem. A numerical example is presented.     

Remarks on the paper “Optimal control of a class of linear multivariable systems with integral quadratic energy constraint ”

An optimal periodic control problem for a system described by differential equations is considered. Control units are assumed to generate control actions with the square-integrable derivative. The above problem is approximated by a sequence of discretized problems containing trigonometric polynomials, which approximate the state and control variables, and the functions in the criterion and differential equations. The conditions for a sequence of optimal solutions to discretized problems, which are to be a generalized minimizing sequence for the basic problem, are given. Extensions to more general problem formulations are presented. The possibility of application is illustrated by the example of an optimal periodic control problem for a chemical reactor.     

Modeling hysteresis in piezoelectric actuators using NARMAX models

This paper presents a non-linear moving average model with exogenous inputs (NMAX) and a non-linear auto-regressive moving average model with exogenous inputs (NARMAX) respectively to model static and dynamic hysteresis inherent in piezoelectric actuators. The modeling approach is based on the expanded input space that transforms the multi-valued mapping of hysteresis into a one-to-one mapping. In the expanded input space, a simple hysteretic operator is proposed to be used as one of the coordinates to specify the moving feature of hysteresis. Both the modified Akaike's information criterion (MAIC) and the recursive least squares (RLS) algorithm are employed to estimate the appropriate orders and coefficients of the models. The advantage of the proposed approach is in the systematic design procedure which can on-line update the model parameters so as to accommodate to the change of operation environment compared with the classical Preisach model. Moreover, the obtained model is non-linear in variables but linear in parameters so that it can avoid the problem of sticking in local minima which the neural network based models usually have. The results of the experiments have shown that the proposed models can accurately describe static and dynamic behavior of hysteresis in piezoelectric actuators.     

On optimal control of a class of partially observed discrete event systems

We are interested in a new class of optimal control problems for discrete event systems. We adopt the formalism of supervisory control theory (Proc. IEEE 77(1) (1989) 81) and model the system as a finite state machine (FSM). Our control problem is characterized by the presence of uncontrollable as well as unobservable events, the notion of occurrence and control costs for events and a worst-case objective function. We first derive an observer for the partially unobservable FSM, which allows us to construct an approximation of the unobservable trajectory costs. We then define the performance measure on this observer rather than on the original FSM itself. We then use the algorithm presented in Sengupta and Lafortune (SIAM J. Control Optim. 36(2) (1998)) to synthesize an optimal submachine of the C-observer. This submachine leads to the desired supervisor for the system.     

基于形状记忆合金驱动器的微纳定位系统鲁棒自适应控制

针对基于智能材料驱动器串联驱动的微纳定位系统,本文主要探讨了此类高精定位系统的控制设计策略.其控制设计的主要任务是消除驱动器中未知回滞特性对系统性能所造成的负面影响.本文重点以形状记忆合金驱动器为例,采用基于广义play算子的广义Prandtl-Ishlinskii回滞模型来表征形状记忆合金驱动器中的未知饱和回滞非线性,并在此基础上提出了一种鲁棒自适应控制设计方法来消除前置回滞存在的影响.设计的控制器在保证全局稳定性的基础上能实现理想的跟踪精度,仿真结果验证了控制策略的有效性和正确性.     

迭代粒子群算法及其在间歇过程鲁棒优化中的应用

针对无状态独立约束和终端约束的间歇过程鲁棒优化问题，将迭代方法与粒子群优化算法相结合，提出了迭代粒子群算法．对于该算法，首先将控制变量离散化，用标准粒子群优化算法搜索离散控制变量的最优解．然后在随后的迭代过程中将基准移到刚解得的最优值处，同时收缩控制变量的搜索域，使优化性能指标和控制轨线在迭代过程中不断趋于最优解．算法简洁、可行、高效，避免了求解大规模微分方程组的问题．对一个间歇过程的仿真结果证明了迭代粒子群算法可以有效地解决无状态独立约束和终端约束的间歇过程鲁棒优化问题．     

A priori error estimates for the finite element discretization of optimal distributed control problems governed by the biharmonic operator

In this article a priori error estimates are derived for the finite element discretization of optimal distributed control problems governed by the biharmonic operator. The state equation is discretized in primal mixed form using continuous piecewise biquadratic finite elements, while piecewise constant approximations are used for the control. The error estimates derived for the state variable as well as that for the control are order-optimal on general unstructured meshes. However, on uniform meshes not all error estimates are optimal due to the low-order control approximation. All theoretical results are confirmed by numerical tests.     

Regularized trigonometric approximation of optimal periodic control problems

The optimal periodic control problem with the main and the additional optimality criterion for a system described by differential equations is investigated. The energy and raw material consumption are considered as the additional criteria. The problem characterized is approximated by a sequence of discretized optimization problems using trigonometric polynomials and penalty functions. Sufficient conditions are given for the convergence of solutions of discretized problems to the regular optimal solution, which minimizes the additional criterion over the set of solutions minimizing the main criterion. Strong convergence in the case where the energy consumption is the additional criterion is proven.     

Augmented Lagrangian method applied to American option pricing

The American option pricing problem is originally formulated as a stochastic optimal stopping time problem. It is also equivalent to a variational inequality problem or a complementarity problem involving the Black-Scholes partial differential operator. In this paper, the corresponding variational inequality problem is discretized by using a fitted finite volume method. Based on the discretized form, an algorithm is developed by applying augmented Lagrangian method (ALM) to the valuation of the American option. Convergence properties of ALM are considered. By empirical numerical experiments, we conclude that ALM is more effective than penalty method and Lagrangian method, and comparable with the projected successive overrelaxation method (PSOR). Furthermore, numerical results show that ALM is more robust in terms of computation time under changes in market parameters: interest rate and volatility.     

FAULT TOLERANT CONTROL OF FLEXIBLE SMART STRUCTURES USING ROBUST DECENTRALIZED FAST OUTPUT SAMPLING FEEDBACK TECHNIQUE

This paper presents the modeling, design and simulation of a Robust Decentralized Fast Output Sampling (RDFOS) feedback controller for the vibration control of a smart structure (flexible cantilever beam) when there is actuator failure. The beam is divided into 8 finite elements and the sensors / actuators are placed at finite element positions 2, 4, 6, and 8 as collocated pairs. The smart structure is modeled using the concepts of piezoelectric theory, Euler‐Bernoulli beam theory, Finite Element Method (FEM) techniques and the state space techniques. Four multi‐variable state‐space models of the smart structure plant are obtained when there is a failure of one of the four actuators to function. The effect of failure of one of the piezo actuators to function during the vibration of the beam is observed. The tip displacements, open and closed loop responses with and without the controller are observed. For all of these models, a common stabilizing state feedback gain F is obtained. A robust decentralized fast output sampling feedback gain L which realizes this state feedback gain is obtained using the LMI approach. In this designed control law, the control inputs to each actuator of the multi‐model representation of the smart structure is a function of the output of that corresponding sensor only and the gain matrix has got all off‐diagonal terms zero and this makes the control design a robust decentralized one. Then, the performance of the designed smart system is evaluated for Active Vibration Control (AVC). The robust decentralized FOS controller obtained by the designed method requires only constant gains and hence may be easier to implement in real time.     

On the complexity of generating optimal test sequences

The authors investigate whether maximal overlapping of protocol test subsequences can be achieved in polynomial time. They review the concepts related to FSM (finite state machine)-based test sequence generation and then define the optimal test sequence generation (OTSG) problem. It is proved that the OTSG problem is NP-complete. Therefore an efficient solution to the problem should not be expected in the general case