Mixed H/sub 2//H/sub /spl infin// design for a decentralized discrete variable structure control with application to mobile robots

In this paper, a decentralized discrete variable structure control via mixed H/sub 2//H/sub /spl infin// design was developed. In the beginning, the H/sub 2/-norm of output error and weighted control input was minimized to obtain a control such that smaller energy consumption with bounded tracking error was assured. In addition, a suitable selection of this weighted function (connected with frequency) could reduce the effect of disturbance on the control input. However, an output disturbance caused by the interactions among subsystems, modeling error, and external load deteriorated system performance or even brought about instability. In this situation, the H/sub /spl infin//-norm of weighted sensitivity between output disturbance and output error was minimized to attenuate the effect of output disturbance. Moreover, an appropriate selection of this weighted function (related to frequency) could reject the corresponding output disturbance. No solution of Diophantine equation was required; the computational advantage was especially dominated for low-order system. For further improving system performance, a switching control for every subsystem was designed. The proposed control (mixed H/sub 2//H/sub /spl infin// DDVSC) was a three-step design method. The stability of the overall system was verified by Lyapunov stability criterion. The simulations and experiments of mobile robot were carried out to evaluate the usefulness of the proposed method.     

Fuzzy Mixed H2/H∞ Optimization-Based Decentralized Model Reference Control and Application to Piezo-Driven XY Table Systems

In this paper, a decentralized model reference control via fuzzy mixed H²/H^infin optimization design was developed. Each subsystem contained L linear pulse transfer function systems (LPTFSs). The reference model for every LPTFS was first designed to shape the response of the ith closed-loop subsystem. Then the H² -norm of the output error (i.e., the difference between the output of the reference model and the system) and weighted control input of the jth LPTFS was minimized to obtain a control such that smaller energy consumption with bounded tracking error of the jth LPTFS was achieved. However, an output disturbance of the jth LPTFS caused by the interactions among the LPTFSs, the interconnections among the subsystems, modeling errors, and external loads deteriorated system performance or even resulted in instability. In this situation, the H ^infin-norm of weighted sensitivity between output disturbance and output error of the jth LPTFS was minimized to attenuate its effect. A nonlinear control based on output error for every LPTFS was also established to improve robust performance. The stability of the overall system was then verified by Lyapunov stability criterion. The application to piezo-driven XY table system (PD-XY-TS) was carried out to confirm the usefulness of the proposed control     

A fuzzy decentralized variable structure tracking control with optimal and improved robustness designs: theory and applications

To begin with, each subsystem of a nonlinear interconnected system was approximated by a weighted combination of L linear pulse transfer function systems (LPTFSs). For every nominal LPTFS of the mth subsystem, a dead-beat to its switching surface was first designed. The output disturbance of the mth LPTFS included the interconnections coming from the other subsystems, the approximation error of the mth subsystem, and the interactions resulting from the other LPTFSs. In general, this output disturbance was not small and contains various frequencies. Under this circumstances, the H/sup /spl infin//-norm of the weighted sensitivity function between the mth switching surface and its corresponding output disturbance was minimized. In addition, an appropriate selection of the weighted function for the sensitivity could reject the corresponding mode of the output disturbance. Although the effect of the output disturbance is attenuated and partially rejected, a better performance could be enhanced by a switching control based on the Lyapunov redesign. In addition, the stability of the overall system was verified by Lyapunov stability theory. The simulations for the LPTFSs with different delays or nonminimum phases or unstable features were arranged to evaluate the effectiveness of the proposed control. Finally, the application to the trajectory tracking of the robot arm including the fuzzy modeling was carried out to confirm the practicality of the proposed control.     

Optimal and reinforced robustness designs of fuzzy variable structure tracking control for a piezoelectric actuator system

In this paper, a piezoelectric actuator (PEA) system is approximated by N subsystems, which are described by pulse transfer functions. The approximation error between the PEA system and the fuzzy linear pulse transfer function system is represented by additive nonlinear time-varying uncertainties in every subsystem. First, a dead-beat to the switching surface for every ideal subsystem is designed. It is called the "variable structure tracking control". The output disturbance of the ith subsystem is caused by the approximation error of fuzzy-model and the interaction dynamics resulting from other subsystems. In general, it is not small. Then, the H/sup /spl infin//-norm of the sensitivity function between the switching surface and the output disturbance is minimized. It is the "optimal robustness". Although the effect of the output disturbance is attenuated, a better performance can be reinforced by a switching control which is based on the Lyapunov redesign. This is the final step for the robustness design of control, which is "reinforced robustness". The stability of the overall system is verified by Lyapunov stability theory. Experimental work of a PEA system was carried out to confirm the validity of the proposed control.     

Robust MIMO disturbance observer analysis and design with application to active car steering

A multi‐input–multi‐output extension of the well‐known two control degrees‐of‐freedom disturbance observer architecture that decouples the problem into single‐input–single‐output disturbance observer loops is presented in this paper. Robust design based on mapping D‐stability and the frequency domain specifications of weighted sensitivity minimization and phase margin bound to a chosen controller parameter space is presented as a part of the proposed design approach. The effect of the choice of disturbance observer Q filter on performance is explained with a numerical example. This is followed by the use of structured singular values in the robustness analysis of disturbance observer controlled systems subject to structured, real parametric and mixed uncertainty in the plant. A design and simulation study based on a four wheel active car steering control example is used to illustrate the methods presented in the paper. Copyright © 2009 John Wiley & Sons, Ltd.     

Global H infinty control and almost disturbance decoupling for a class of interconnected non-linear systems

This paper is concerned with a global H infinity control problem for a class of interconnected non-linear systems. We first consider a fairly general clas of large-scale non-linear systems with strong non-linear interconnections. It is shown that the decentralized H infinity control problem for the system can be converted into the centralized control problems associated with a set of auxiliary systems. The solutions to the latter problems in general rely on solutions of their associated Hamilton-Jacobi-Isaacs (HJI) inequalities. Realizing that finding a global solution of the HJI inequality is usually impossible, we then consider a global decentralized almost disturbance decoupling problem (DADDP) and a global decentralized inverse H infinity control problem (DIHCP) for a class of interconnected systems with lower triangular structure. The DADDP is concerned with the design of decentralized control laws that achieve an arbitrarily small disturbance input to the controlled output. The DIHCP involves seeking not only control laws but also state-dependent weights of the control inputs such that the associated global decentralized control problem is solvable. It is shown that the solutions to both the DADDP and DIHCP can be obtained via a recursive design technique. L2-gain from the     

Robust disturbance attenuation with stability for a class of uncertain singularly perturbed systems

In this paper, the problem of robust stability and robust disturbance attenuation is investigated for a class of singularly perturbed linear systems with norm-bounded parameter uncertainties in both state and output equations. Based on the slow and fast subsystems, a composite linear controller is designed such that both robust stability and a prescribed H infinity performance for the full-order system are achieved, irrespective of the uncertainties. Our results show that the above problem can be converted to an H infinity control problem for a related singularly perturbed linear system without parameter uncertainty. Thus, the existing results on H infinity control of singularly perturbed systems can be applied to obtain solutions to the problem of robust H infinity control for the uncertain systems, which is independent of the singular perturbation epsilon when epsilon is sufficiently small. An example is given to show the potential of the proposed technique.     

一类带不确定输入动态非线性系统的鲁棒H∞控制

研究一类带不确定输入动态非线性系统的H∞控制问题.在输入动态存在的条件下, 利用反传设计方法构造了鲁棒状态反馈控制器,使得闭环系统在零初始状态下从干扰到输出的 L2增益任意小,同时在干扰输入恒为零时闭环系统是全局渐近稳定的.     

LPV系统加权函数法的鲁棒跟踪设计

线性时变系统的重要一类是处理对象中状态空间矩阵的时变物理参数,如何设计控制器使系统满足设计指标是控制中的关键问题。研究了基于加权函数法的线性变参数(LPV)系统设计方法与过程,并指出了参数不确定系统的信号跟踪、系统的稳定性和干扰抑制问题,这三者与控制性能指标设计问题之间是可以相互转化的。通过选择加权函数,转变为线性分式的控制问题求解,从而达到提高系统的鲁棒性能,降低保守性的目的。最后,通过实际的感应电机转子磁链跟踪系统,采用基于LPV鲁棒加权函数法设计其控制器,仿真实现了它对输入磁链参考信号的有效跟踪,且它能有效抑制外界干扰,从而验证了此方法设计的控制器的有效性。     

Anti‐windup design of active disturbance rejection control for sampled systems with input delay

A novel anti‐windup design of active disturbance rejection control (ADRC) is proposed for industrial sampled systems with input delay and saturation. By using a generalized predictor to estimate the delay‐free system output, a modified extended state observer is designed to simultaneously estimate the system state and disturbance, which could become an anti‐windup compensator when the input saturation occurs. Accordingly, a feedback controller is analytically designed for disturbance rejection. By proposing the desired closed‐loop transfer function for the set‐point tracking, a prefilter is designed to tune the tracking performance while guaranteeing no steady‐state output tracking error. A sufficient condition for the closed‐loop system stability is established with proof for practical application subject to the input delay variation. Illustrative examples from the literature are used to demonstrate the effectiveness and merit of the proposed control design.     

An adaptive disturbance rejection control scheme for multivariable nonlinear systems

An adaptive disturbance rejection control scheme is developed for uncertain multi-input multi-output nonlinear systems in the presence of unmatched input disturbances. The nominal output rejection scheme is first developed, for which the relative degree characterisation of the control and disturbance system models from multivariable nonlinear systems is specified as a key design condition for this disturbance output rejection design. The adaptive disturbance rejection control design is then completed by deriving an error model in terms of parameter errors and tracking error, and constructing adaptive parameter-updated laws and adaptive parameter projection algorithms. All closed-loop signals are guaranteed to be bounded and the plant output tracks a given reference output asymptotically despite the uncertainties of system and disturbance parameters. The developed adaptive disturbance rejection scheme is applied to turbulence compensation for aircraft fight control. Simulation results from a benchmark aircraft model verify the desired system performance.     

Synthesis of Mixed Objective Output Feedback Robust Model Predictive Control

Aiming at the constrained polytopic uncertain system with energy‐bounded disturbance and unmeasurable states, a novel synthesis scheme to design the output feedback robust model predictive control(MPC)is put forward by using mixed H₂/H_∞ design approach. The proposed scheme involves an offline design of a robust state observer using linear matrix inequalities(LMIs)and an online output feedback robust MPC algorithm using the estimated states in which the desired mixed objective robust output feedback controllers are cast into efficiently tractable LMI‐based convex optimization problems. In addition, the closed‐loop stability and the recursive feasibility of the proposed robust MPC are guaranteed through an appropriate reformulation of the estimation error bound (EEB). A numerical example subject to input constraints illustrates the effectiveness of the proposed controller.     

Robust H infinity static output feedback control of fuzzy systems: an ILMI approach.

This paper examines the problem of robust H infinity static output feedback control of a Takagi-Sugeno fuzzy system. The proposed robust H infinity static output feedback controller guarantees the pounds 2 gain of the mapping from the exogenous disturbances to the regulated output to be less than or equal to a prescribed level. The existence of a robust H infinity static output feedback control is given in terms of the solvability of bilinear matrix inequalities. An iterative algorithm based on the linear matrix inequality is developed to compute robust H infinity static output feedback gains. To reduce the conservatism of the design, the structural information of membership function characteristics is incorporated. A numerical example is used to illustrate the validity of the design methodologies.     

三自由度直升机系统自适应模糊H∞混合灵敏度鲁棒控制

研究了三自由度直升机系统的飞行控制.针对该系统高阶次、非线性、强耦合、多输入多输出的特点,提出了一种基于自适应模糊理论的H∞混合灵敏度鲁棒控制方法.通过间接自适应模糊逻辑系统逼近非线性系统中的未知参数,增强了在线控制性能;结合H∞混合灵敏度鲁棒控制,抑制了外界的干扰和参数摄动;运用Laypunov理论证明了系统的全局稳定性.实际飞行结果表明:三自由度直升机系统具有良好的鲁棒性和稳定性,同时,证明了该控制方法的有效性和优越性.     

多约束主动悬架H2/H∞混合控制器设计

利用闭环极点配置中的D-稳定性原理,给出了有硬约束的H2/H∞混合控制器的LMI条件并应用于汽车主动悬架分析.用这种方法设计的控制器,通过H∞控制性能指标保证了系统输出信号与输入信号的总能量之比小于适当的γ值,并且利用H2控制,保证了输出信号的能量与输入信号的能量在时域上的峰值比低于一个适当的μ值,同时,将闭环系统的极点配置在复平面上的一个适当区域,可以保证系统具有一定的动态性能和稳定性,比较好的解决了系统性能和系统鲁棒性之间的折衷优化控制问题.     

Identification Recurrent Type 2 Fuzzy Wavelet Neural Network and L2‐Gain Adaptive Variable Sliding Mode Robust Control of Electro‐Hydraulic Servo System (EHSS)

An electro‐hydraulic servo system (EHSS) is a kind of system with the characteristics of time‐variant, serious nonlinearity, parameter and structural uncertainty, and uncertain load disturbance in most cases. These characteristics make it very difficult to realize highly accurate control by conventional methods. In order to solve the above problems, this paper introduces a recurrent type 2 fuzzy wavelet neural network to approximate the unknown nonlinear functions of the dynamic systems through tuning by the desired adaptive law. Based on the identification by recurrent type 2 fuzzy wavelet neural network, a L2 gain design method, combining gain adaptive variable sliding mode control with H infinity control, is proposed for load disturbance, thereby accommodating uncertainties that are the main factors affecting system stability and accuracy in EHSS. In this algorithm, a recurrent type 2 fuzzy wavelet neural network is employed to evaluate the unknown dynamic characteristics of the system and gain adaptive variable sliding mode control to compensate for evaluating errors, and H infinity control to suppress the effect on system by load disturbance. The experiment results show that the proposed system L2 gain design method can make the system exhibit strong robustness to parameter variation and load disturbance.     

H∞ tracking-based sliding mode control foruncertain nonlinear systems via an adaptive fuzzy-neural approach

A novel adaptive fuzzy-neural sliding-mode controller with H(infinity) tracking performance for uncertain nonlinear systems is proposed to attenuate the effects caused by unmodeled dynamics, disturbances and approximate errors. Because of the advantages of fuzzy-neural systems, which can uniformly approximate nonlinear continuous functions to arbitrary accuracy, adaptive fuzzy-neural control theory is then employed to derive the update laws for approximating the uncertain nonlinear functions of the dynamical system. Furthermore, the H(infinity) tracking design technique and the sliding-mode control method are incorporated into the adaptive fuzzy-neural control scheme so that the derived controller is robust with respect to unmodeled dynamics, disturbances and approximate errors. Compared with conventional methods, the proposed approach not only assures closed-loop stability, but also guarantees an H(infinity) tracking performance for the overall system based on a much relaxed assumption without prior knowledge on the upper bound of the lumped uncertainties. Simulation results have demonstrated that the effect of the lumped uncertainties on tracking error is efficiently attenuated, and chattering of the control input is significantly reduced by using the proposed approach.     

Robust mixed time-optimal control for third-order systems with model uncertainty

In this paper, a robust near time-optimal controller for some third-order uncertain systems with constrained input is presented. The response is usually composed of two parts. At first, the states move towards the goal state from arbitrary initial conditions by pure time-optimal control (bang-bang) and then there is sliding along a predetermined surface within an ellipsoid. The sliding surface is chosen in such a way that the integral of the absolute value of the system error is minimized. Using a combined control algorithm, robustness and stability of the system is guaranteed even with parameter uncertainty and disturbance. The error convergence rate is also improved compared with pure time-optimal control. Simulation results demonstrate the advanced performance of the proposed control algorithm.     

混合H2/H∞鲁棒控制器设计

在状态空间描述下,定义了混合H₂/H_∞控制的完整信息、完整控制、干扰顺馈、输出估计这4种典型情况.在二次稳定意义上,讨论了混合H₂/H_∞的性能指标,及这4种典型情况的混合H₂/H_∞线性反馈控制器设计,给出了充分必要条件.在典型情况分析的基础上,研究一般意义上的混合H₂/H_∞反馈控制器设计.H₂和H_∞的干扰输入阵及性能评价函数各不相同时的混合H₂/H_∞反馈控制器,与H₂和H_∞控制器设计相似,归结为解两个Riccati方程.但这两个Riccati方程含有参数,最优解要通过搜索这两个参数得到.结果包含了单纯的H₂和H_∞设计,可看作是H₂,H_∞和混合H₂/H_∞的统一设计方法.最后通过一个简单的例子,说明了控制器设计方法的可行性.     

Robust Double‐integral T‐S Fuzzy Output Regulation for Nonlinear Systems

This paper proposes a robust double‐integral T‐S fuzzy output regulator design for affine nonlinear systems in the presence of parametric uncertainty and external disturbance. First, we adopt double integrators (an error integrator and an input integrator) to obtain an augmented T‐S fuzzy model representation which has a common input matrix of fuzzy rules. This property yields less stability conditions. Next, by introducing a set of virtual desired variables (VDVs), a double‐integral VDV‐based fuzzy regulator is proposed to cope with unknown bias and to achieve asymptotical output regulation. Afterward, the controller is simplified to avoid VDV calculation and enhance robustness to uncertainty and external disturbance. In contrast to traditional regulation design, the double‐integral non‐VDV fuzzy regulator design reduces the number of fuzzy controller rules and stability LMIs. Moreover, the error coordinate transformation is removed and the uncertainty is allowed in this paper. Finally, a DC/DC buck converter system is taken as the example to demonstrate the expected performance.