A robust adaptive controller for Hammerstein nonlinear systems

Hammerstein nonlinear systems have appeared useful in modeling nonlinear processes encountered in engineering practice. Control algorithms may lead to unsatisfactory performance if the parametric model does not agree with the plant. To this end, this paper proposes a new robust adaptive control approach for discrete-time Hammerstein nonlinear systems which are more close to some industrial plants. The adaptive control law and recursive parameter estimation are updated by introducing the estimate of the model error as a feedback. Theoretical results show that parameter estimation convergence and closed-loop system stability can be guaranteed under mild conditions. Simulation examples including a continuous stirred tank reactor (CSTR) system are given to show the effectiveness of the obtained results.     

带有干扰的时变系统的变结构鲁棒控制

对含有未知时变参数和外界干扰的单输入单输出线性时变系统,给出了一种变结构鲁棒输出跟踪控制器.系统参数不限定为慢时变或者结构已知的,只要求光滑有界且所需高阶导数有界.通过引入辅助信号和带有记忆功能的正规化信号,以及适当选择控制器参数,该变结构控制器能保证闭环系统所有信号的有界性,跟踪误差能被调整到任意小的范围内.     

A robust direct adaptive controller

This paper proposes a new direct adaptive control algorithm which is robust with respect to additive and multiplicative plant unmodeled dynamics. The algorithm is designed based on the reduced-order plant, which is assumed to be minimum phase and of known order and relative degree, but is analyzed with respect to the overall plant which, due to the unmodeled dynamics, may be nonminimum phase and of unknown order and relative degree. It is shown that if the unmodeled dynamics are sufficiently small in the low-frequency range, then the algorithm guarantees boundedness of all signals in the adaptive loop and "small" residual tracking errors for any bounded initial conditions. In the absence of unmodeled dynamics, the residual tracking error is shown to be zero.     

A robust stochastic adaptive controller

The adaptive tracking problem is considered for discrete-time stochastic systems consisting of a modeled part being a stable ARMAX process and unmodeled dynamics dominated by a small constant ϵ multiplied by a quantity independent of ϵ but tending to infinity as the past input, output, and noise grow. The adaptive control law proposed is switched at stopping times and is disturbed by a sequence of random vectors bounded by an arbitrary small but fixed constant σ. It is shown that the closed-loop system is globally stable, the estimation errors for parameters contained in the modeled part of the order ϵ, and the tracking error differs from the minimum tracking error for systems without unmodeled dynamics by value of O(ϵ² )+O(σ²)     

时变不确定系统鲁棒控制器设计的新方法

基于包含两个二次项的分段Lyapunov函数,研究了线性时变不确定系统的鲁棒控制器设计问题.所考虑的系统由两个矩阵的凸组合构成,通过引入一个附加矩阵,推导出鲁棒控制器存在的充分条件.该控制器的状态反馈增益的求解问题可以转化为一组带有两个比例参数的线性矩阵不等式的凸优化问题.最后的数值示例说明了该设计方法的可行性.     

LMI-based analysis of robust adaptive control for linear systems with time-varying uncertainty

Passification-based adaptive control, also known as simple adaptive control, is studied with respect to its robustness to time-varying uncertainties. Results are formulated in terms of LMIs and are therefore testable in polynomial time using semi-definite programming solvers. The main result shows that the adaptive strategy allows, without measurement nor estimation of the uncertain parameters to guarantee asymptotic stability for a wide rage of these parameters. To achieve this result, the stability property is relaxed: convergence is proved to a small neighborhood of the origin, and attractive domain. It is also demonstrated that this attractor can be made as small as required the only limitation being implementation constraints.     

Stable robust adaptive controller

This paper presents a globally stable adaptive controller for linear discrete systems in the presence of unmodelled dynamics and bounded disturbances. The proposed formulation uses an augmented plant representation that incorporates P, Q and R weighting polynomials for the system output, input and setpoint respectively into the predictive control law. The algorithm also includes a normalized estimation scheme, based on a least-squares estimator, and a parameter adaptation stopping criterion to guarantee stability.     

A decentralized model reference adaptive variable structure controller for large-scale time-varying delay systems

In this note, the problem of decentralized model reference adaptive variable structure control for a class of perturbed large-scale systems with varying time-delay interconnections is investigated. Based on the Lyapunov stability theorem, an adaptive variable structure control strategy for solving the robust tracking problem without the knowledge of upper bound of perturbations is developed. The use of adaptive technique is to adapt the unknown upper bound of perturbations so that the objective of globally asymptotical stability is achieved. Once the system enters the sliding manifold, the dynamics of controlled systems are insensitive to matching perturbations. Finally, an example is given to demonstrate the feasibility of the proposed control scheme.     

Decentralised adaptive robust control of uncertain large-scale interconnected systems with multiple time-varying delays

The problem of decentralised adaptive robust stabilisation is considered for a class of uncertain large-scale time-delay interconnected dynamical systems. It is assumed that the upper bounds of the uncertainties, interconnection terms and external disturbances are unknown, and that the time-varying delays are any nonnegative continuous and bounded functions, and do not require that their derivatives have to be less than one. For such a class of uncertain large-scale time-delay interconnected systems, a new method is presented whereby a class of continuous memoryless decentralised local adaptive robust state feedback controllers is proposed. It is also shown that the solutions of uncertain large-scale time-delay interconnected systems can be guaranteed to be uniformly exponentially convergent towards a ball which can be as small as desired. In addition, since the proposed decentralised local adaptive robust state feedback controllers are completely independent of time delays, the results obtained in this article may also be applicable to a class of large-scale interconnected dynamical systems with uncertain time delays. Finally, a numerical example is given to demonstrate the validity of the results.     

A minimal k-step delay controller for robust tracking of non-minimum phase systems

This paper considers the problem of look-ahead robust tracking for a non-minimum phase system under a sensitivity constraint. Because of non-minimum phase zeros, the exact tracking of arbitrary reference input is impossible. However, with an introduction of some delay, tracking is possible within any given “tolerance” ?₁ > 0. It is shown in the paper that the minimum delay required to satisfy the tracking performance is decoupled from a sensitivity/disturbance rejection constraint. Moreover, it is shown that calculation of the minimum delay reduces to a binary search problem.     

A novel Takagi-Sugeno-based robust adaptive fuzzy sliding-mode controller

In this paper, a nonlinear dynamic system is first approximated by N fuzzy-based linear state-space subsystems. To track a trajectory dominant by a specific frequency, the reference models with desired amplitude and phase features are established by the same fuzzy sets of the system rule. Similarly, the same fuzzy sets of the system rule are employed to design robust fuzzy sliding-mode control (RFSMC) and adaptive fuzzy sliding-mode control (AFSMC). The difference between RFSMC and AFSMC is that AFSMC contains an updating law to learn system uncertainties and then an extra compensation is designed. It is different from the most previous papers to learn the whole nonlinear functions. As the norm of the sliding surface is inside of a defined set, the updating law starts; simultaneously, as it is outside of the other set, the updating law stops. For the purpose of smoothing the possibility of discontinuous control input, a transition between RFSMC and AFSMC is also assigned. Under the circumstances, the proposed control [robust adaptive fuzzy sliding-mode control (RAFSMC)] can automatically tune as a RFSMC or an AFSMC; then the advantages coming from the RFSMC and AFSMC are obtained. Finally, the stabilities of the overall system of RFSMC, AFSMC, and RAFSMC are verified by Lyapunov stability theory. The compared simulations among RFSMC, AFSMC, and RAFSMC are also carried out to confirm the usefulness of the proposed control scheme.     

一类复杂控制系统分散自适应鲁棒控制器设计

基于模糊逻辑系统具有充分利用语言信息和逼近连续函数性质的思想,分析研究了一类非线性不确定复杂系统的自适应控制问题.利用系统的数学模型和模糊逻辑系统对不确定性的输出信息,设计出了复杂系统的分散自适应鲁棒控制器和模糊逻辑系统参数估计的自适应律,在较弱的假设条件下,证明了这种控制器使被控系统的状态及参数估计误差一致终极有界.仿真实例表明,所提出的方法是有效的.     

A robust adaptive tracking controller using neural networks for a class of nonlinear systems

A neural networkbased robust adaptive tracking control scheme is proposed for a class of nonlinear systems. It is shown that, unlike most neural control schemes using the back-propagation training technique, one hidden layer neural controller is designed in the Lyapunov sense, and the parameters of the neural controller are then adaptively adjusted for the compensation of unknown dynamics and nonlinearities. Using this scheme, not only strong robustness with respect to unknown dynamics and nonlinearities can be obtained, but also asymptotic error convergence between the plant output and the reference model output can be guaranteed. A simulation example based on a one-link non-linear robotic manipulator is given in support of the proposed neural control scheme.     

A new robust adaptive control algorithm for linear time-varying plants

Robustness is an important property of a control system. Robust adaptive control has been an active research area for more than a decade. Since it was shown that un-modelled dynamics or even a small bounded disturbance can cause most adaptive control algorithms to go unstable, various modifications of the adaptive control algorithms have been developed to counteract instability and improve robustness with respect to unmodelled dynamics and bounded disturbances. However, we know that most of the modified approaches to achieve robustness require knowledge of either the parameter of bounding function on the unmodelled dynamics, or the upper bound on the disturbances, or the bound on the norm of unknown matching controller/plant parameters, and such knowledge can hardly be obtained in practice. A new indirect adaptive control algorithm for linear time-varying plants is proposed to achieve robustness to a class of unmodelled dynamics, bounded disturbances and plant parameter time variations. A modified relative dead zone technique is used, so that knowledge of the parameters of the upper bounding function on the unmodelled dynamics and the disturbances is not required. The stability analysis and the robust performance of adoptively controlled time-varying systems are provided for the new scheme. A simulation example is given to show the effectiveness of the proposed algorithm.     

A robust adaptive performance enhancement controller using setmembership identification

A robust direct adaptive control scheme is proposed to enhance the performance of a fixed nominal controller. The key idea lies in the introduction of a set membership constraint in the estimation process. The set membership constraint results in an adaptive scheme that has a built-in discriminator to discard incoming data that carry little or no information content on the actual plant. The proposed scheme, which uses only informative data to refine the parameter estimates, is more robust than conventional methods that continuously update the parameter estimates     

A robust adaptive controller for constant turning force regulation

A robust adaptive controller for the constant turning force regulation problem under varying cutting conditions is presented. The control structure is an RST pole-placement controller based on a shaping method of the output sensitivity function proposed by Landau. The controller scheme is robust in the presence of cutting process nonlinearities and disturbances. The proposed adaptive scheme uses an estimation and controller algorithm including prior knowledge of the system. Simulations and experimental results obtained with an industrial lathe show the effectiveness of the proposed solution.     

Delay-dependent robust stabilization for systems with time-varying delays

This paper extends the results of the stability criterion, introduced in the literature, to the problem of stabilization for systems with time-varying delays. Unfortunately, the delay-dependent stabilization conditions using state/output-feedback controllers are not formulated as LMIs. To achieve a better degree of freedom in relaxing the resultant nonlinear terms, we do not assume any restriction on the form of variables, which is a generally adopted procedure in the structure-imposing relaxation methods. Instead, we develop a congruence transformation that has the effect of gathering the dispersed nonlinear terms and bundling them together into fewer and more intensive non-convex conditions. To relax these, an efficient iterative algorithm is proposed in the form of two-phase-based convex optimization problem. Numerical examples show that the results obtained by these criteria improve the allowable maximal delays over the existing results in the literature.     

On the extension of robust global adaptive control results to unstructured time-varying systems

This note extends the robust global direct adaptive control results of Kosut and Friedlander [1] and Kosut [2] to the case of linear finite-dimensional systems with unstructured time-varying uncertainties. Subject to conditions which include i) a certain operator (usually denotedH^{*}_{e0}) is strictly positive real and ii) the tuned error lies in L2, theorems are presented establishing the L2andL_{infty}stability of the adaptive control scheme.     

A sliding-mode based smooth adaptive robust controller for friction compensation

In this paper, a new approach employing both adaptive and robust methodologies is proposed for stick–slip friction compensation for tracking control of a one degree-of-freedom DC-motor system. It is well known that the major components of friction are Coulomb force, viscous force, exponential force (used to model the downward bend of friction at low velocity) and position-dependent force. Viscous force is linear and Coulomb force is linear in parameter; thus, these two forces can be compensated for by adaptive feedforward cancellation. Meanwhile, the latter two forces, which are neither linear nor linear in parameters, can only be partially compensated for by adaptive feedforward cancellation. Therefore, a robust compensator with an embedded adaptive law to ‘learn’ the upper bounding function on-line is proposed to compensate the uncancelled exponential and position-dependent friction. Lyapunov's direct method is utilized to prove the globally asymptotic stability of the servo-system under the proposed friction compensation method. Numerical simulations are presented as illustrations. © 1998 John Wiley & Sons, Ltd.