Dynamic modeling and adaptive robust boundary control of a flexible robotic arm with 2‐dimensional rigid body rotation

This paper investigates the control of a single‐link flexible robot manipulator with a tip payload appointed to rotate about 2 perpendicular axes in space. The control objective is to regulate the rigid body rotation of the manipulator with guaranteeing the stability of its vibration in the presence of exogenous disturbances. To achieve this, a Lyapunov‐based control design procedure is used and accomplished in some steps. First, the partial differential equation (PDE) dynamic model governing the rigid‐flexible hybrid motion of the arm is derived by applying Hamilton's principle. Next, based on the developed PDE model, an adaptive robust boundary control is established using the Lyapunov redesign approach. To this end, an adaptation mechanism is proposed so that the robust boundary control gains are dynamically updated online and there is no need for prior knowledge of disturbance upper bounds. The actuators and sensors are fully implemented at the arm boundary without using distributed actuators or sensors. Furthermore, in order to avoid control errors resulting from the spillover, control design is directly based on infinite‐dimensional PDE model without resorting to model truncation. Simulation results illustrate the efficacy of the considered method.     

Adaptive robust boundary control of coupled bending‐torsional vibration of beams with only one axis of symmetry

In control design for vibration of beams in literature, the beam section is considered to have two axes of symmetry so that the bending and torsional vibrations are uncoupled; thus, the bending vibration is controlled independently without twisting the beam. However, if the cross section of a beam has only one axis of symmetry, the bending and torsional vibrations become coupled and the beam will undergo twisting in addition to bending. This paper addresses Lyapunov‐based boundary control of coupled bending‐torsional vibration of beams with only one axis of symmetry. The control strategy is based on applying a transverse force and a torque at the free end of the beam. The control design is directly based on the system partial differential equations (PDEs) so that spillover instabilities that are a result of model truncation are avoided. Three cases are investigated. Firstly, it is shown that when exogenous disturbances do not affect the beam, a linear boundary control law can exponentially stabilize the coupled bending‐torsional vibration. Secondly, a nonlinear robust boundary control is established that exponentially stabilizes the beam in the presence of boundary and spatially distributed disturbances. Thirdly, to rule out the need for prior knowledge of disturbances upper‐bound, the proposed robust control is redesigned to achieve an adaptive robust control that stabilizes the beam in the presence of disturbances with unknown upper‐bound. The efficacy of the proposed controls is illustrated by simulation results. Copyright © 2016 John Wiley & Sons, Ltd.     

Robust boundary stabilization of a vibrating rectangular plate using disturbance adaptation

This paper considers robust boundary control with disturbance adaptation to stabilize the vibration of a rectangular plate under disturbances with unknown upper‐bounds. Disturbances are considered to be distributed both over the plate interior domain and along the boundary (in‐domain and boundary distributed disturbances). Applying Hamilton's principle, the dynamics of the plate is represented in the form of a fourth‐order partial differential equation subject to static and dynamic boundary conditions. The proposed model considers the membrane effect of axial force and the effect of actuator mass dynamics on the plate vibration. A robust boundary control is established that stabilizes the plate in presence of both in‐domain and boundary disturbances. A rigorous Lyapunov stability analysis shows that the vibration of the plate is uniformly ultimately bounded and converges to the vicinity of zero by proper selection of control gains. For the vanishing in‐domain disturbances, it is seen that exponential stability is achieved by the proposed control. Next, a disturbance adaptation law is introduced to stabilize the plate vibration in response to disturbances with unknown bounds, and the stability of the robust boundary control with disturbance adaptation is studied using Lyapunov. Simulation results verify the efficiency of the suggested control. Copyright © 2016 John Wiley & Sons, Ltd.     

Robust adaptive control for non‐linear systems in generalized output‐feedback canonical form

Design of global robust adaptive output‐feedback dynamic compensators for stabilization and tracking of a class of systems that are globally diffeomorphic into systems in generalized output‐feedback canonical form is investigated. This form includes as special cases the standard output‐feedback canonical form and various other forms considered previously in the literature. Output‐dependent non‐linearities are allowed to enter both additively and multiplicatively. The system is allowed to contain unknown parameters multiplying output‐dependent non‐linearities and, also, unknown non‐linearities satisfying certain bounds. Under the assumption that a constant matrix can be found to achieve a certain property, it is shown that a reduced‐order observer and a backstepping controller can be designed to achieve practical stabilization of the tracking error. If this assumption is not satisfied, it is shown that the control objective can be achieved by introducing additional dynamics in the observer. Sufficient conditions under which asymptotic tracking and stabilization can be achieved are also given. This represents the first robust adaptive output‐feedback tracking results for this class of systems. Copyright © 2003 John Wiley & Sons, Ltd.     

An adaptive regulation method for a class of uncertain time‐delay systems

In this paper, a new adaptive robust stabilization scheme is proposed for uncertain neutral time‐delay systems. No upper bounds on the uncertainties are assumed to be available. An update law is first used to find estimates of these upper bounds. A state‐feedback controller is then designed, which is shown to stabilize the underlying system under some mild conditions. The asymptotic stability of the state trajectories is proved using the Lyapunov–Krasovskii approach. An example is provided, which demonstrates the efficacy of the proposed adaptive control scheme. Copyright © 2012 John Wiley & Sons, Ltd.     

不确定微分代数系统的多指标非线性鲁棒自适应控制方法

针对含不确定因素的多输入多输出微分代数系统,提出一种多指标非线性鲁棒自适应控制方法(multi-index nonlinear robust adaptive control,MINRAC),并将其应用于汽门开度与发电机励磁的协调控制上。数字仿真表明：在系统参数不确定和存在外部扰动的情况下,该方法能够使得系统的多个指标都运行在期望的工作点上而不发生静态偏移。对于不同类型的扰动,如有功功率阶跃,三相短路,该控制方法都能很好地镇定系统,并且能够消除机端电压偏差。与多指标非线性控制(multi-index nonlinear control,MINC)和多指标非线性鲁棒控制(multi-index nonlinear robust control,MINRC)相比,该文提出的方法能更好地兼顾系统的动静态性能。     

Adaptive switching control of uncertain fractional systems: Application to Chua's circuit

Since the introduction of fractional‐order differential equations, there has been much research interest in synthesis and control of oscillatory, periodic, and chaotic fractional‐order dynamical systems. Therefore, in this article, the problem of stabilization and control of nonlinear three‐dimensional perturbed fractional nonlinear systems is considered. The major novelty of this article is handling partially unknown dynamics of nonlinear fractional‐order systems, as well as coping with input saturation along the existence of model variations and high‐frequency sensor noises via just one control input. The method supposes no known knowledge on the upper bounds of the uncertainties and perturbations. It is assumed that the working region of the input saturation function is also unknown. After the introduction of a simple finite‐time stable nonlinear sliding manifold, an adaptive control technique is used to reach the system variables to the sliding surface. Rigorous stability discussions are adopted to prove the convergence of the developed sliding mode controller. The findings of this research are illustrated using providing computer simulations for the control problem of the chaotic unified system and the fractional Chua's circuit model.     

Adaptive enhanced sliding mode control for permanent magnet synchronous motor drives

An adaptive enhanced sliding mode control (AESMC) scheme for the position tracking control of permanent magnet synchronous motor drives is proposed in this paper. The AESMC system is composed of three controllers: the adaptive model compensation controller, which is used to compensate for the parameter perturbations to achieve perfect tracking; the hitting controller, which is considered to attenuate the effect of external load disturbance and the compensation error; and the robust feedback controller, which is used to enhance the stability of the closed‐loop system and to improve the transient performance while the AESMC is in the learning process. Moreover, the bound of the lumped disturbance is assumed to be unknown, and an adaptive mechanism is investigated to estimate this bound. Simulation results show that the proposed AESMC scheme has a favorable tracking performance in spite of various model uncertainties. Copyright © 2015 John Wiley & Sons, Ltd.     

Pinning control and adaptive control for synchronization of linearly coupled reaction‐diffusion neural networks with mixed delays

This paper focuses on the pinning control and adaptive control for synchronization of an array of linearly coupled reaction‐diffusion neural networks with mixed delays (that is, discrete and infinite distributed delays) and Dirichlet boundary condition. Firstly, the asymptotical synchronization of coupled semilinear diffusion partial differential equations with mixed time delays is achieved by employing pinning control scheme. The pinning controller is obtained by using Lyapunov‐Krasovskii functional stability theory. The stability condition is represented by linear matrix inequality. The controller gain matrix is easy to be solved. Secondly, the adaptive synchronization condition of an array of linearly coupled reaction‐diffusion neural networks with mixed delays is obtained by using adaptive control scheme. Finally, two numerical examples of coupled semilinear diffusion partial differential equations with mixed time delays are given to illustrate the correctness of the obtained results.     

交流电机无速度传感器矢量控制系统变结构MRAS转速辨识

针对变结构控制在参数变化等不确定因素满足"匹配条件"即变化有界时,具有抗外部干扰和内部参数摄动的鲁棒性,但实际中要确定不确定性参数变化的上下界有一定难度的特点。文中基于变结构控制和自适应控制理论,提出一种新颖的变结构模型参考自适应(VS-MRAS)观测器,用于交流电机无速度传感器矢量控制系统的转速辨识。该法将变结构和MRAS进行有机的整合,利用MRAS对系统参数变化的适应能力实时估算不确定因素变化的边界,以改善磁链观测的准确性,进而提高转速辨识的精度。利用仿真方法,对比分析了带速度检测装置的矢量控制系统、基于MRAS转速辨识的无速度传感器矢量控制系统和基于VS-MRAS转速辨识的无速度传感器矢量控制系统的3种情况下转速和磁链响应的动静态性能。证实该方法提高了转子磁链观测的准确度,改善了转速估计的动静态性能。     

基于零动态和变结构控制的发电机汽门和励磁非线性综合控制

针对电力系统暂态过程的非线性特性,利用励磁控制和汽门控制的特点,以功角和电压稳定为目标提出一种发电机汽门和励磁综合控制思想。励磁控制以稳定电压为目标,结合基于零动态和变结构控制的概念和原理进行设计,有效地维持了电压水平。汽门控制以功角稳定为目标,通过计算零动态系统的暂态能量函数,利用Lyapunov稳定理论,得到稳定流形作为切换面,然后设计相应的变结构非线性汽门控制律,将零动态系统限制在所设计的稳定流形上。变结构控制的特性使控制律具有一定的鲁棒性。汽门控制设计中未使用任何线性化方法,因而控制律对系统的非线性特性完全适应。试验结果表明所设计的控制器不仅对小干扰和大干扰暂态过程具有很好的稳定作用,而且在动态过程中能很好地稳定电压,动态过程具有更好的供电品质。     

An adaptive iterative learning algorithm for boundary control of a flexible manipulator

In this study, we consider the boundary control problem of a flexible manipulator in the presence of system parametric uncertainty and external disturbances. The dynamic behavior of the flexible manipulator is represented by partial differential equations (PDEs). Based on the Lyapunov method, we propose an adaptive iterative learning control scheme for trajectory tracking and vibration suppressing of a flexible manipulator. The proposed control scheme is designed using both a proportional‐derivative feedback structure and an iterative term. The learning convergence of iterative learning control is achieved through rigorous analysis without any simplification or discretization of the PDE dynamics. Finally, the results are illustrated using numerical simulations for control performance verification. Copyright © 2016 John Wiley & Sons, Ltd.     

Adaptive robust control of nonlinear systems with dynamic uncertainties

In this paper, the discontinuous projection‐based adaptive robust control (ARC) approach is extended to a class of nonlinear systems subjected to parametric uncertainties as well as all three types of nonlinear uncertainties—uncertainties could be state‐dependent, time‐dependent, and/or dynamic. Departing from the existing robust adaptive control approach, the proposed approach differentiates between dynamic uncertainties with and without known structural information. Specifically, adaptive robust observers are constructed to eliminate the effect of dynamic uncertainties with known structural information for an improved steady‐state output tracking performance—asymptotic output tracking is achieved when the system is subjected to parametric uncertainties and dynamic uncertainties with known structural information only. In addition, dynamic normalization signals are introduced to construct ARC laws to deal with other uncertainties including dynamic uncertainties without known structural information not only for global stability but also for a guaranteed robust performance in general. Copyright © 2008 John Wiley & Sons, Ltd.     

Model‐free fault‐tolerant control approach for uncertain state‐constrained linear systems with actuator faults

This paper investigates the robust adaptive fault‐tolerant control problem for state‐constrained continuous‐time linear systems with parameter uncertainties, external disturbances, and actuator faults including stuck, outage, and loss of effectiveness. It is assumed that the knowledge of the system matrices, as well as the upper bounds of the disturbances and faults, is unknown. By incorporating a barrier‐function like term into the Lyapunov function design, a novel model‐free fault‐tolerant control scheme is proposed in a parameter‐dependent form, and the state constraint requirements are guaranteed. The time‐varying parameters are adjusted online based on an adaptive method to prevent the states from violating the constraints and compensate automatically the uncertainties, disturbances, and actuator faults. The time‐invariant parameters solved by using data‐based policy iteration algorithm are introduced for helping to stabilize the system. Furthermore, it is shown that the states converge asymptotically to zero without transgression of the constraints and all signals in the resulting closed‐loop system are uniformly bounded. Finally, two simulation examples are provided to show the effectiveness of the proposed approach. Copyright © 2016 John Wiley & Sons, Ltd.     

Adaptive boundary control for flexible three‐dimensional Euler‐Bernoulli beam with input signal quantization

This paper proposes an adaptive boundary control scheme for the flexible three‐dimensional Euler‐Bernoulli beam with input signal quantization. Considering the coupling effect between the axial deformation and the transverse displacement, the dynamics of the flexible system are represented by partial differential equations and ordinary differential equations. Input signals in modern control systems are often quantized before being transmitted through communication channels in technology engineering. Logarithmic quantitative controllers are designed to suppress the vibration of the beam. It is proved that the proposed control scheme can be guaranteed in handling the vibration of the beam and input signal quantization simultaneously. Finally, numerical simulations illustrate the effectiveness of the results.     

Robust adaptive constrained boundary control for a suspension cable system of a helicopter

In this article, the problems of modeling and controlling are investigated for a suspension cable system of a helicopter with input saturation, system parameter uncertainties, and external disturbances by using the boundary control method. In accordance with the Hamilton's principle, the model of the suspension cable system of a helicopter is established by using a set of partial differential and ordinary differential equations. Considering nonsymmetric saturation constraint, the auxiliary systems are designed to handle with the effect of input saturation. Considering Lyapunov's direct method and the designed auxiliary systems, two robust adaptive boundary controllers are provided by the actuators at the helicopter and the box. Under the proposed controllers, the error between the bottom payload and the target location and the vibration range are uniformly ultimately bounded. Moreover, they will converge to a small neighborhood of zero by selecting the suitable parameters. Meanwhile, to guarantee the validity of the proposed adaptive boundary control laws, some sufficient conditions are raised. Simulation results are provided to verify that the effectiveness of the designed controllers in this paper.     

Nonlinear partial differential equation modeling and adaptive fault-tolerant vibration control of flexible rotatable manipulator in three-dimensional space

In this article, we investigate the problem of nonlinear modeling and adaptive boundary vibration control with actuator failure for a flexible rotatable manipulator in three-dimensional space, which is made up of a rotatable base and a flexible manipulator. In order to accurately reflect the characteristics of the distributed parameters, the Hamilton principle is introduced to derive the dynamic model expressed by partial differential equations (PDEs). Based on the model, an innovative boundary control scheme is proposed to eliminate the deflection and vibration simultaneously, and to guarantee that the rotatable base and the flexible manipulator can track the desired angle respectively. The adaptive law is developed to estimate the loss of the actuator. The effectiveness of the designed controller is verified from both theoretical analysis and numerical simulation.     

Robust adaptive tracking control of uncertain discrete time systems

In this paper, the problem of robust adaptive tracking for uncertain discrete‐time systems is considered from the slowly varying systems point of view. The class of uncertain discrete‐time systems considered is subjected to both 𝓁_∞ to 𝓁_∞ bounded unstructured uncertainty and external additive bounded disturbances. A priori knowledge of the dynamic model of the reference signal to be tracked is not completely known. For such problem, an indirect adaptive tracking controller is obtained by frozen‐time controllers that at each time optimally robustly stabilize the estimated models of the plant and minimize the worst‐case steady‐state absolute value of the tracking error of the estimated model over the model uncertainty. Based on 𝓁_∞ to 𝓁_∞ stability and performance of slowly varying system found in the literature, the proposed adaptive tracking scheme is shown to have good robust stability. Moreover, a computable upper bound on the size of the unstructured uncertainty permitted by the adaptive system and a computable tight upper bound on asymptotic robust steady‐state tracking performance are provided. Copyright © 2005 John Wiley & Sons, Ltd.     

Sliding mode disturbance observer control based on adaptive synchronization in a class of fractional‐order chaotic systems

In this paper, a fractional‐order Dadras‐Momeni chaotic system in a class of three‐dimensional autonomous differential equations has been considered. Later, a design technique of adaptive sliding mode disturbance‐observer for synchronization of a fractional‐order Dadras‐Momeni chaotic system with time‐varying disturbances is presented. Applying the Lyapunov stability theory, the suggested control technique fulfils that the states of the fractional‐order master and slave chaotic systems are synchronized hastily. While the upper bounds of disturbances are unknown, an adaptive regulation scheme is advised to estimate them. The recommended disturbance‐observer realizes the convergence of the disturbance approximation error to the origin. Finally, simulation results are presented in one example to demonstrate the efficiency of the offered scheme on the fractional‐order Dadras‐Momeni chaotic system in the existence of external disturbances.     

Robust adaptive regulation of dynamically positioned ships with unknown dynamics and unknown disturbances

We develop a robust adaptive regulating control law for dynamically positioned ships subject to unknown dynamics and bounded unknown disturbances incorporating the radial basis function (RBF) neural network (NN), the dead zone adaptive technique, and a robust control term into the vectorial backstepping approach. The RBF NNs with the dead zone adaptive laws approximate the ship unknown dynamics. The adaptive law‐based robust control term compensates for unknown disturbances, NN approximation errors, and undesirable errors arising from the design procedures. The developed dynamic positioning (DP) control law regulates the ship position and heading to the desired values with arbitrarily small errors, while guaranteeing the uniform ultimate boundedness of all signals in the DP closed‐loop control system of ships. High‐fidelity simulations on two supply ships and comparisons demonstrate the effectiveness and the superiority of the developed DP control law.