线性连续时滞系统最优预见重复控制

针对一类线性连续时滞系统,提出一种最优预见重复控制设计方法.首先,通过一种等价变换,将被控时滞系统转化为无时滞系统.然后,利用L阶差分算子提升技巧,获得包含状态变量导数和跟踪误差的增广连续系统.在此基础上,通过定义一种新的性能指标,将预见重复控制设计问题转化为连续非自治系统的线性二次调节问题.进一步,基于最优控制理论,得到包含状态反馈、误差积分、重复控制、时滞补偿和预见补偿的最优预见重复控制器.该控制器包含了已有文献的多种控制器形式.最后,通过一个数值仿真实例,说明所提方法的有效性.     

Optimal anti-windup synthesis for repetitive controllers

Repetitive controllers use internal models that provide very high gain at a selected fundamental frequency and its harmonics, additionally, some of the internal models may result unstable, as in the high order repetitive control approach. These characteristics make the repetitive control system susceptible to exhibit wind-up when actuator saturation occurs. This paper proposes an anti-windup scheme for repetitive control based on the model recovery anti-windup strategy. The proposed scheme provides low order, low computational burden and also isolation of the controller from the saturation effects. The anti-windup compensator is constructed from the plant model and provides an additional linear feedback path aimed at enhancing system performance. This feedback path is designed to obtain a deadbeat behaviour, which makes the system recovery faster. Finally, internal stability and deadbeat features are designed in a compact procedure based on linear matrix inequalities and an optimal linear quadratic design. Experimental validation of the proposed anti-windup compensator is provided using a mechatronic plant.     

Weighted max-norm estimate of two-stage splitting method for solving a class of nonlinear complementarity problems

In this paper, an asymptotically stable optimal control is proposed for the trajectory tracking of a cylindrical robotic arm. The proposed controller uses the linear quadratic regulator method and its Riccati equation is considered as an adaptive function. The tracking error of the proposed controller is guaranteed to be asymptotically stable. A simulation shows the effectiveness of the proposed algorithm.     

一种飞控系统不确定性建模方法及其鲁棒控制

针对大包线飞行控制系统, 本文通过摄动参数标称化及多个工作点的数据拟合, 并将拟合误差视为范数有界不确定性, 给出了一种不确定模型描述方法, 以降低系统描述的保守性. 基于二次稳定性准则, 运用线性矩阵不等式的处理方法, 得到了大包线飞控系统动态输出反馈控制器的存在条件和设计方法. 进一步, 通过合适的匹配摄动参数和求解凸优化问题, 以参数向量2--范数的形式给出了闭环系统保持鲁棒稳定所允许的参数最大摄动范围估计方法, 建立了系统摄动参数与二次稳定性之间的联系. 最后通过对飞行控制系统的算例仿真, 验证了文中方法的有效性和可行性.     

不确定时滞系统的全局鲁棒最优滑模控制

针对一类不确定性时滞系统, 研究线性二次型最优调节器的鲁棒性设计问题. 首先基于级数近似方法, 将原标称时滞系统的最优调节器问题转化为迭代求解一族不含时滞的两点边值问题, 从而获得标称时滞系统最优控制的近似解. 然后将滑模控制理论应用于最优调节器的设计, 使得系统对于不确定性具有全局的鲁棒性, 并且其理想滑动模态与标称系统的最优闭环控制系统相一致, 从而实现了全局鲁棒最优滑模控制. 仿真示例将所提出的方法与相应的二次型最优控制进行比较, 验证了该方法的有效性和优越性.     

Analysis and Verification of Repetitive Motion Planning and Feedback Control for Omnidirectional Mobile Manipulator Robotic Systems

Mobile manipulator robotic systems (MMRSs) composed of a manipulator and a mobile platform are investigated in this paper. In order for the mobile manipulator robotic system (MMRS) to return to its initial state when the manipulator’s end-effector is requested to execute cyclical tasks, a quadratic program (QP) based repetitive motion planning and feedback control (RMPFC) scheme is proposed and analyzed. Such an RMPFC scheme can not only mix motion planning and reactive control, but also consider the physical limits of the robotic system. Mathematically, the efficacy of the RMPFC scheme is verified via gradient dynamics analysis. To further demonstrate the effectiveness of the RMPFC scheme, a kinematically redundant MMRS composed of a three degrees-of-freedom (DOF) planar manipulator and an omnidirectional mobile platform is designed, modeled and analyzed. Then, repetitive motion planning and feedback control for the designed omnidirectional MMRS is studied. Besides, a numerical algorithm is developed and presented to solve the QP and resolve the redundancy of the robotic system. Moreover, computer simulations are comparatively performed on such an omnidirectional MMRS, and simulation results substantiate the effectiveness, accuracy and superiority of the proposed RMPFC scheme.     

Bi-Objective Optimal Control Modification Adaptive Control for Systems with Input Uncertainty

This paper presents a new model-reference adaptive control method based on a bi-objective optimal control formulation for systems with input uncertainty. A parallel predictor model is constructed to relate the predictor error to the estimation error of the control effectiveness matrix. In this work, we develop an optimal control modification adaptive control approach that seeks to minimize a bi-objective linear quadratic cost function of both the tracking error norm and the predictor error norm simultaneously. The resulting adaptive laws for the parametric uncertainty and control effectiveness uncertainty are dependent on both the tracking error and the predictor error, while the adaptive laws for the feedback gain and command feedforward gain are only dependent on the tracking error. The optimal control modification term provides robustness to the adaptive laws naturally from the optimal control framework. Simulations demonstrate the effectiveness of the proposed adaptive control approach.      

Position synchronised control of multiple robotic manipulators based on integral sliding mode

In this study, a new position synchronised control algorithm is developed for multiple robotic manipulator systems. In the merit of system synchronisation and integral sliding mode control, the proposed approach can stabilise position tracking of each robotic manipulator while coordinating its motion with the other manipulators. With the integral sliding mode, the proposed approach has insensitiveness against the lumped system uncertainty within the entire process of operation. Further, a perturbation estimator is proposed to reduce chattering effect. The corresponding stability analysis is presented to lay a foundation for theoretical understanding to the underlying issues as well as safely operating real systems. An illustrative example is bench tested to validate the effectiveness of the proposed approach.     

Predictive-repetitive control with constraints: From design to implementation

This paper addresses the design and implementation of predictive-repetitive control systems, including the case when constraints are imposed. The approach is based on a frequency response decomposition technique that detects the dominant frequency components of the reference signals and embeds them in the predictive-repetitive controller. Analysis and design make use of the frequency response of the closed-loop system and the choice of the structure of the repetitive controller is considered as a balance between the reduction of tracking errors and minimization of the effects on performance of unwanted elements, such as model uncertainty. The implementation of operational constraints on the amplitudes of the control signals, their increments and on the outputs is considered using an on-line solution constructed using quadratic programming and the identification of active constraints. Experimental results from application to a 2 degree-of-freedom robotic system are used to illustrate the design and implementation procedures developed.     

MODELING AND CONTROL OF THE ACTIVE SUSPENSION SYSTEM USING PROPORTIONAL INTEGRAL SLIDING MODE APPROACH

The purposes of this paper are to present a new method in modeling an active suspension system for half‐car model in state space form and to develop a robust strategy in controlling the active suspension system. Proportional integral sliding mode control strategy is proposed for the system. A simulation study is performed to prove the effectiveness and robustness of the control approach and performance of the controller is compared to the linear quadratic regulator and the existing passive suspension system.     

A new neural network-based approach for self-tuning control of nonlinear SISO discrete-time systems

This article presents a new neural network-based approach for self-tuning control of nonlinear single-input single-output (SISO) discrete-time dynamic systems. According to the approach, a neural network ARMAX (NN-ARMAX) model of the system is identified and continuously updated, using an online training algorithm. Control design is accomplished by solving an optimal discrete-time linear quadratic tracking problem using an observer-type linear state-space Kalman innovation model, which is built from the parameters of a local linear version of the NN-ARMAX model. The state-feedback control law is implemented using the Kalman state, which is calculated without estimating the noise covariance properties. The proposed control approach is shown to be very effective and outperforms the self-tuning control approach based on a linear ARMAX model on two simulation examples.     

Leader–follower tracking control with guaranteed consensus performance for interconnected systems with linear dynamic uncertain coupling

This paper considers the leader–follower tracking control problem for linear interconnected systems with undirected topology and linear dynamic coupling. Interactions between the systems are treated as linear dynamic uncertainty and are described in terms of integral quadratic constraints (IQCs). A consensus-type tracking control protocol is proposed for each system based on its state relative to its neighbours. In addition, a selected set of subsystems is used to control their relative states with respect to the leader. Two methods are proposed for the design of this control protocol. One method uses a coordinate transformation to recast the protocol design problem as a decentralised robust control problem for an auxiliary interconnected large-scale system. Another method is direct; it does not employ coordinate transformation, rather it also allows for more general linear uncertain interactions. Using these methods, sufficient conditions are obtained which guarantee that the system tracks the leader. These conditions guarantee a suboptimal bound on the system consensus and tracking performance. The proposed methods are compared using a simulation example, and their effectiveness is discussed. Also, algorithms are proposed for computing suboptimal controllers.     

Uncertainty modeling and robust minimax LQR control of multivariable nonlinear systems with application to hypersonic flight

For a class of multi‐input and multi‐output nonlinear uncertainty systems, a novel approach to design a nonlinear controller using minimax linear quadratic regulator (LQR) control is proposed. The proposed method combines a feedback linearization method with the robust minimax LQR approach in the presence of time‐varying uncertain parameters. The uncertainties, which are assumed to satisfy a certain integral quadratic constraint condition, do not necessarily satisfy a generalized matching condition. The procedure consists of feedback linearization of the nominal model and linearization of the remaining nonlinear uncertain terms with respect to each individual uncertainty at a local operating point. This two‐stage linearization process, followed by a robust minimax LQR control design, provides a robustly stable closed loop system. To demonstrate the effectiveness of the proposed approach, an application study is provided for a flight control problem of an air‐breathing hypersonic flight vehicle (AHFV), where the outputs to be controlled are the longitudinal velocity and altitude, and the control variables are the throttle setting and elevator deflection. The proposed method is used to derive a linearized uncertainty model for the longitudinal motion dynamics of the AHFV first, and then a robust minimax LQR controller is designed, which is based on this uncertainty model. The controller is synthesized considering seven uncertain aerodynamic and inertial parameters. The stability and performance of the synthesized controller is evaluated numerically via single scenario simulations for particular cruise conditions as well as a Monte‐Carlo type simulation based on numerous cases. It is observed that the control scheme proposed in this paper performs better, especially from the aspect of robustness to large ranges of uncertainties, than some controller design schemes previously published in the literature. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Measurement-based optimization of batch and repetitive processes using an integrated two-layer architecture

This paper is concerned with optimal control of batch and repetitive processes in the presence of uncertainty. An integrated two-layer optimization strategy is proposed, whereby within-run corrections are performed using a neighboring-extremal update strategy and run-to-run corrections are based on a constraint-adaptation scheme. The latter is appealing since a feasible operating strategy is guaranteed upon convergence, and its combination with neighboring-extremal updates improves the reactivity and convergence speed. Moreover, these two layers are consistent in that they share the same objective function. The proposed optimization scheme is declined into two versions, namely an indirect version based on the Pontryagin maximum principle and a direct version that applies a control parameterization and nonlinear programming techniques. Although less rigorous, the latter approach can deal with singular extremals and path constraints as well as handle active-set changes more conveniently. Two case studies are considered. The indirect approach is demonstrated for a level-control problem in an experimental two-tank system, whereas the direct approach is illustrated in numerical simulation on a fed-batch reactor for acetoacetylation of pyrrole. The results confirm that faster adaptation is possible with the proposed integrated two-layer scheme compared to either constraint adaptation or neighboring-extremal update alone.     

Implementation of real-time distributed control for discrete event robotic systems using Petri nets

This article presents a systematic method of modeling and implementing real-time control for discrete-event robotic systems using Petri nets. Because, in complex robotic systems such as flexible manufacturing systems, the controllers are distributed according to their physical structure, it is desirable to realize real-time distributed control. In this article, the task specification of robotic processes is represented as a system control-level net. Then, based on the hierarchical approach, it is transformed into detailed subnets, which are decomposed and distributed into the local machine controllers. The implementation of real-time distributed control through communication between the system controller and the machine controllers on a microcomputer network is described for a sample robotic system. The proposed implementation method is sufficiently general, and can be used as an effective prototyping tool for consistent modeling, simulation, and real-time control of large and complex robotic systems.     

2-DOF并联机构动力学建模与迭代学习控制

针对一种直线电机驱动的2-DOF并联机构,结合直线电机的动力学特性,采用Lagrange方法对其进行动力学建模。考虑该机构重复性动作及其不确定性和非线性特点,提出一种自适应神经网络迭代学习控制方法。在该控制算法的作用下,系统输出能较好地跟踪给定输入。严格证明及仿真结果验证了该算法的有效性。     

基于输入输出线性化的连续系统非线性模型预测控制

非线性约束预测控制关键是求得可行性优化解. 输入输出反馈线性化是非线性控制一种常用的方法, 其系统的初始线性输入约束转化成非线性基于状态的约束, 因而无法采用常规的二次规划(QP)求解优化问题. 针对连续状态空间模型系统, 本文提出迭代二次规划方法来寻求非线性优化解. 为了保证算法的收敛性, 系统加入另外一种迭代算法来保证其在整个预测时域上能得到可行解. 仿真控制结果表明了该方法的有效性.     

Robust adaptive tracking control of robotic systems with uncertainties

To deal with the uncertainty factors of robotic systems, a robust adaptive tracking controller is proposed. The knowledge of the uncertainty factors is assumed to be unidentified; the proposed controller can guarantee robustness to parametric and dynamics uncertainties and can also reject any bounded, immeasurable disturbances entering the system. The stability of the proposed controller is proven by the Lyapunov method. The proposed controller can easily be implemented and the stability of the closed system can be ensured; the tracking error and adaptation parameter error are uniformly ultimately bounded （UUB）. Finally, some simulation examples are utilized to illustrate the control performance.     

基于模糊T-S模型的批过程建模与最优控制

基于模糊T-S模型,提出一种具有自学习能力的模糊方法用于批过程建模和最优控制.通过引入与均方误差相关的动态误差传递因子,使用改进的梯度下降法,本方法能够辨识模糊T-S预测模型.对于批过程的受限非线性最优控制,基于所辨识的预测模型,运用庞特里亚金最小值原理和平行分布补偿算法,本方法能够把一个复杂非线性系统最优控制设计问题转化为一些基于复杂T-S预测模型的局部线性系统的最优问题,从而给出一种有效和简单的模糊最优控制策略.所提方法用于一个半连续式反应器的建模和最优控制,仿真结果表明新方法是有效和准确的.     

柔性连接倒立摆系统的控制与实现

柔性连接的倒立摆系统是在直线倒立摆系统的基础上引入自由振荡环节,使闭环控制系统的响应频率受到弹簧振荡频率的限制,从而增加了对该系统控制器设计的难度。在建立被控系统动力学模型的基础上,通过数学分析,应用线性二次型最优控制策略进行状态反馈控制器的设计,成功地将柔性连接倒立摆系统稳定地平衡在倒立状态。仿真以及实际系统的实验均验证了所采用方法的有效性。最后对所实现的控制器的控制性能进行了分析。