考虑参数不确定性的转子系统瞬态动平衡研究

针对含不确定性参数的转子系统,提出了一种基于区间数学、泰勒展开和摄动理论的转子瞬态响应区间分析法.该方法求解不确定性问题时无需不确定参数的具体概率分布,适用于一般性工程分析.利用转子瞬态响应信息对一弹性支承双盘转子进行瞬态动平衡.将不确定性引入动平衡过程,分析了不同不确定性水平下不确定性参数对瞬态动平衡效率的影响.研究结果表明,该方法能有效分析转子不确定性瞬态响应,随着不确定水平增大,转子动平衡效率大幅降低.     

An efficient method for evaluating the natural frequencies of structures with uncertain-but-bounded parameters

Using interval theory and the second-order Taylor series, the eigenvalue problems of structures with multi-parameter can be transformed into those with single parameter. The epsilon-algorithm is used to accelerate the convergence of the Neumann series to obtain the bounds of eigenvalues of structures with single interval parameter, thus increasing the computing accuracy and reducing the computational effort. Finally, the effect of uncertain parameters on natural frequencies is evaluated. Two engineering examples show that the proposed method can give better results than those obtained by the first-order approximation, even if the uncertainties of parameters are fairly large.     

Pitch Angle Control of Unmanned Air Vehicle with Uncertain System Parameters

In this paper a new algorithm of trajectory tracking based on closest radius solution of the interval equations system is proposed. The design procedure is given and applied to the pitch angle control of unmanned testing rocket with uncertain parameters. The proposed algorithm gives a framework to design a control for a wide range of different linear time-invariant processes with uncertain parameters and can be implemented also in the case of non-convex problems. The algorithm gives the analytical way of finding the nearly optimal solution of model reference trajectory tracking in the case of general time-invariant systems with uncertain parameters and can be used when optimization method fails due to the complexity of the problem.     

基于鲁棒可靠性的不确定时滞系统最优H∞控制器设计

用区间变量描述控制系统参数的不确定性,提出了不确定时滞系统鲁棒H_∞控制的鲁棒可靠性方法,基于鲁棒可靠性的不确定时滞系统最优状态反馈H_∞控制器设计方法,将系统的最优控制器设计归结为基于线性矩阵不等式(LMI)的优化问题．所设计的控制器可以在满足对所有不确定性鲁棒可靠的前提条件下,具有最优的H_∞鲁棒性能,并能在控制系统的设计中综合考虑控制性能、控制代价和鲁棒可靠性．数值算例说明了所提方法的有效性和可行性．     

区间系数不确定性系统的鲁棒控制器设计

本文提出了一种方法用于设计区间系数不确定性系统的鲁棒镇定控制器，所考虑的区间系数可以是时变的，控制器的设计仅依赖于区间系数的上下界，而设计步骤具有迭代特征。虽然所提到的控制器是线性和确定性的，但能够承受所有容允不确定性。所提出的方法通过一个电力系统负荷频率控制例子加以说明。     

解最优控制问题结合同伦法的自适应拟谱方法

针对弱间断最优控制问题和Bang-Bang最优控制问题,提出一种结合同伦法的自适应拟谱方法.Chebyshev拟谱方法转换原问题成为非线性规划问题.基于同伦法思想,同伦参数改变路径约束的界限,得到一系列比较光滑的最优控制问题.通过解这些问题得到原问题的不光滑解.文中证明了弱间断情况下数值解的收敛性.依据这收敛性和同伦参数,误差指示量可以捕捉不光滑点.本文方法与其他方法在数值算例中的对比表明,本文方法在精度和效率上都有明显优势.     

Dynamical adaptive integral backstepping variable structure controller design for uncertain systems and experimental application

In this study, a dynamical adaptive integral backstepping variable structure control (DAIBVSC) system based on the Lyapunov stability theorem is proposed for the trajectory tracking control of a nonlinear uncertain mechatronic system with disturbances. In this control scheme, no prior knowledge is required on the uncertain parameters and disturbances because it is estimated by two types of dynamical adaptive laws. These adaptive laws are integrated into the dynamical adaptive integral backstepping control and variable structure control (VSC) parts of the DAIBVSC. The dynamical adaptive law in the dynamical adaptive integral backstepping control part updates parametric uncertainties, while the other in the VSC part adapts upper bounds of non‐parametric uncertainties and disturbances. In order to achieve a more robust output tracking and better parameter adaptation, the control system is extended by one integrator and sliding surface is augmented by an integral action. Experimental evaluation of the DAIBVSC is conducted with respect to performance and robustness to parametric uncertainties. Experimental results of the DAIBVSC are compared with those of a traditional VSC. The proposed DAIBVSC exhibits satisfactory output tracking performance, good estimation of the uncertain parameters and can reject disturbances with a chattering free control law. Copyright © 2017 John Wiley & Sons, Ltd.     

Robust Minimum Variance Lower Bound Estimation by Uncertainty Modeling Using Interval Type‐2 Fuzzy set

The Minimum Variance Lower Bound (MVLB) represents the best achievable controller capability in a variance sense. Estimation of the MVLB for nonlinear systems confronts some difficulties. If one simply ignores these nonlinearities, there is the danger of over‐estimating the performance of the control loop in rejecting uncertainties. Assuming that almost all models have uncertainties, in this paper, the MVLB has been estimated considering three types of uncertainties: structural, parametric, and algorithmic. To achieve accurate estimation of the MVLB an interval type‐2 fuzzy set has been utilized. This paper utilizes a strategy for modeling of symmetric interval type‐2 fuzzy sets using their uncertainty degrees. Then, based on this uncertainty measure, one method to construct interval type‐2 fuzzy set models using the uncertain interval data is introduced. Finally, simulation studies demonstrate the effectiveness of the proposed control scheme.     

Topology optimization of phononic crystals with uncertainties

Topology optimization of phononic crystals (PnCs) is generally based on deterministic models without considering effects of inherent uncertainties existed in PnCs. However, uncertainties presented in PnCs may significantly affect band gap characteristics. To address this, an interval Chebyshev surrogate model-based heuristic algorithm is proposed for topology optimization of PnCs with uncertainties. Firstly, the interval model is introduced to handle the uncertainties, and then the interval Chebyshev surrogate model (ICSM), in which the improved fast plane wave expansion method (IFPWEM) is used to calculate the integral points to construct the ICSM, is introduced for band structure analysis with uncertainties efficiently. After that, the sample data, which is randomly generated by the Monte Carlo method (MCM), is applied to the ICSM for predicting the interval bounds of the band structures. Finally, topology optimization of PnCs is conducted to generate the widest band gaps with uncertainties included by utilizing the genetic algorithm (GA) and the ICSM. Numerical results show the effectiveness and efficiency of the proposed method which has promising prospects in a range of engineering applications.     

Sum‐of‐Squares‐Based Finite‐Time Adaptive Sliding Mode Control of Uncertain Polynomial Systems With Input Nonlinearities

This paper proposes a novel adaptive sliding mode control (ASMC) for a class of polynomial systems comprising uncertain terms and input nonlinearities. In this approach, a new polynomial sliding surface is proposed and designed based on the sum‐of‐squares (SOS) decomposition. In the proposed method, an adaptive control law is derived such that the finite‐time reachability of the state trajectories in the presence of input nonlinearity and uncertainties is guaranteed. To do this, it is assumed that the uncertain terms are bounded and the input nonlinearities belong to sectors with positive slope parameters. However, the bound of the uncertain terms is unknown and adaptation law is proposed to effectively estimate the uncertainty bounds. Furthermore, based on a novel polynomial Lyapunov function, the finite‐time convergence of the sliding surface to a pre‐chosen small neighborhood of the origin is guaranteed. To eliminate the time derivatives of the polynomial terms in the stability analysis conditions, the SOS variables of the Lyapunov matrix are optimally selected. In order to show the merits and the robust performance of the proposed controller, chaotic Chen system is provided. Numerical simulation results demonstrate chattering reduction in the proposed approach and the high accuracy in estimating the unknown parameters.     

含区间参数多目标系统的微粒群优化算法

参数不确定优化问题是实践中经常遇到的复杂优化问题, 现有方法多针对单目标函数的情况. 本文利用微粒群优化算法解决含区间参数多目标优化问题, 提出一种基于概率支配的多目标微粒群优化算法. 该算法通过定义概率支配关系, 比较所得解的优劣; 基于 σ 区间值, 选择微粒的全局极值点, 并给出新的微粒个体极值点及外部储备集的更新策略. 与传统多目标微粒群优化算法比较, 仿真结果表明本文所提算法的有效性.     

动态区间系统的最优保性能控制--LMI方法

针对动态区间系统和一个给定的二次型性能指标,研究了其保性能控制问题,基于线性矩阵不等式(LMI)提出了最优保性能控制器设计方法,并将相关结果推广到参数不确定系统.利用功能强大的LMI工具,求解非常方便.所给实例表明,该方法用于设计动态区间系统与秩-1型参数不确定系统的最优保性能控制器,非常有效.     

Discrete modelling of uncertain continuous systems having an interval structure using higher-order integrators

In this paper, a higher-order integrator approach is proposed to obtain an approximate discrete-time transfer function for uncertain continuous systems having interval uncertainties. Because of the simple algebraic operations of this approach, the resulting discrete model is a rational function of the uncertain parameters. The problem of non-linearly coupled coefficients with exponential nature occurring in the exact discretetime transfer function is therefore circumvented. Furthermore, the interval structure of the uncertain continuous-time system is preserved in the resulting discrete model by using this approach. Formulae to obtain the lower and upper bounds for the coefficients of the discrete interval system are derived, so that digital simulation and design for the uncertain continuous systems can be performed by using the available robustness results in the discrete-time domain.     

Interval Mathematical Library Based on Chebyshev and Taylor Series Expansion

In this paper, we present a mathematical library designed for use in interval solvers of nonlinear systems of equations. The library computes the validated upper and lower bounds of ranges of values of elementary mathematical functions on an interval, which are optimal in most cases. Computation of elementary functions is based on their expansion in Chebyshev and Taylor series and uses the rounded directions setting mechanism. Some original techniques developed by the authors are applied in order to provide high speed and accuracy of the computation.     

Interval-model-based global optimization framework for robust stability and performance of PID controllers

PID controller structure is regarded as a standard in the control-engineering community and is supported by a vast range of automation hardware. Therefore, PID controllers are widely used in industrial practice. However, the problem of tuning the controller parameters has to be tackled by the control engineer and this is often not dealt with in an optimal way, resulting in poor control performance and even compromised safety. The paper proposes a framework, which involves using an interval model for describing the uncertain or variable dynamics of the process. The framework employs a particle swarm optimization algorithm for obtaining the best performing PID controller with regard to several possible criteria, but at the same time taking into account the complementary sensitivity function constraints, which ensure robustness within the bounds of the uncertain parameters’ intervals. Hence, the presented approach enables a simple, computationally tractable and efficient constrained optimization solution for tuning the parameters of the controller, while considering the eventual gain, pole, zero and time-delay uncertainties defined using an interval model of the controlled process. The results provide good control performance while assuring stability within the prescribed uncertainty constraints. Furthermore, the controller performance is adequate only if the relative system perturbations are considered, as proposed in the paper. The proposed approach has been tested on various examples. The results suggest that it is a useful framework for obtaining adequate controller parameters, which ensure robust stability and favorable control performance of the closed-loop, even when considerable process uncertainties are expected.     

Successive Chebyshev pseudospectral convex optimization method for nonlinear optimal control problems

This article aims at proposing a successive Chebyshev pseudospectral convex optimization method for solving general nonlinear optimal control problems (OCPs). First, Chebyshev pseudospectral discrete scheme is used to discretize a general nonlinear OCP. At the same time, a convex subproblem is formulated by using the first-order Taylor expansion to convexify the discretized nonlinear dynamic constraints. Second, a trust-region penalty term is added to the performance index of the subproblem, and a successive convex optimization algorithm is proposed to solve the subproblem iteratively. Noted that the trust-region penalty parameters can be adjusted according to the linearization error in iterative process, which improves convergence rate. Third, the Karush–Kuhn–Tucker conditions of the subproblem are derived, and furthermore, a proof is given to show that the algorithm will iteratively converge to the subproblem. Additionally, the global convergence of the algorithm is analyzed and proved, which is based on three key lemmas. Finally, the orbit transfer problem of spacecraft is used to test the performance of the proposed method. The simulation results demonstrate the optimal control is bang-bang form, which is consistent with the result of theoretical proof. Also, the algorithm is of efficiency, fast convergence rate, and high accuracy. Therefore, the proposed method provides a new approach for solving nonlinear OCPs online and has great potential in engineering practice.     

Robust fusion steady‐state filtering for multisensor networked systems with one‐step random delay,missing measurements,and uncertain‐variance multiplicative and additive white noises

The robust fusion steady‐state filtering problem is investigated for a class of multisensor networked systems with mixed uncertainties including multiplicative noises, one‐step random delay, missing measurements, and uncertain noise variances, the phenomena of one‐step random delay and missing measurements occur in a random way, and are described by two Bernoulli distributed random variables with known conditional probabilities. Using a model transformation approach, which consists of augmented approach, derandomization approach, and fictitious noise approach, the original multisensor system under study is converted into a multimodel multisensor system with only uncertain noise variances. According to the minimax robust estimation principle, based on the worst‐case subsystems with conservative upper bounds of uncertain noise variances, the robust local steady‐state Kalman estimators (predictor, filter, and smoother) are presented in a unified framework. Applying the optimal fusion algorithm weighted by matrices, the robust distributed weighted state fusion steady‐state Kalman estimators are derived for the considered system. In addition, by using the proposed model transformation approach, the centralized fusion system is obtained, furthermore the robust centralized fusion steady‐state Kalman estimators are proposed. The robustness of the proposed estimators is proved by using a combination method consisting of augmented noise approach, decomposition approach of nonnegative definite matrix, matrix representation approach of quadratic form, and Lyapunov equation approach, such that for all admissible uncertainties, the actual steady‐state estimation error variances of the estimators are guaranteed to have the corresponding minimal upper bounds. The accuracy relations among the robust local and fused steady‐state Kalman estimators are proved. An example with application to autoregressive signal processing is proposed, which shows that the robust local and fusion signal estimation problems can be solved by the state estimation problems. Simulation example verifies the effectiveness and correctness of the proposed results.     

Using set invariance to design robust interval observers for discrete‐time linear systems

Based on interval and invariant set computation, an interval version of the Luenberger state observer for uncertain discrete‐time linear systems is proposed in this work. This new interval observer provides a punctual estimation of the state vector and guaranteed bounds on the estimation error. An off‐line and an on‐line approach to characterize, in a guaranteed way, the estimation error are introduced. Compared with the existing approaches, the proposed interval observer design method is not restrictive in terms of required assumptions, complexity, and on‐line computation time. Furthermore, the convergence issue of the estimation error is well established and to reduce the conservatism of the estimated state enclosure induced by the bounded additive state disturbance and noise measurement, an H_∞ method to compute the optimal observer gain is proposed. The performance of the proposed state estimation approach are highlighted on different illustrative examples.     

Feedback predictive control for constrained fuzzy systems with Markovian jumps

In this paper, a feedback model predictive control method is presented to tackle control problems with constrained multivariables for uncertain discrete‐time nonlinear Markovian jump systems. An uncertain Markovian jump fuzzy system (MJFS) is obtained by employing the Takagi‐Sugeno (T‐S) fuzzy model to represent a discrete‐time nonlinear system with norm bounded uncertainties and Markovain jump parameters. To achieve more generality, the transition probabilities of the Markov chain are assumed to be partly unknown and partly accessible. The predictive formulation adopts an on‐line optimization paradigm that utilizes the closed‐loop state feedback controller and is solved using the standard semi‐definite programming (SDP). To reduce the on‐line computational burden, a mode independent control move is calculated at every sampling time based on a stochastic fuzzy Lyapunov function (FLF) and a parallel distributed compensation (PDC) scheme. The robust mean square stability, performance minimization and constraint satisfaction properties are guaranteed under the control move for all admissible uncertainties. A numerical example is given to show the efficiency of the developed approach. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

带有不确定性的多电机卷绕系统的分散最优保性能控制

针对具有参数不确定、强耦合的多电机卷绕系统,提出一种分散最优保性能控制方法.首先,将多电机卷绕系统看成由若干动态区间子系统组成的综合系统,引入区间矩阵以处理子系统模型中的设定值改变和不确定参数;在此基础上设计基于状态反馈的分散最优保性能控制器,得到控制器存在的线性矩阵不等式(LMI)充分条件;最后以三电机卷绕系统为研究对象,对所设计的控制器进行仿真和平台实验,实验结果表明,所提出的分散最优保性能控制能有效降低控制代价,增强系统的抗干扰能力,保证张力和速度的控制精度.