基于两时间尺度模型的直升机非线性控制器设计

提出一种基于两时间尺度模型的直升机非线性控制方法. 该方法利用直升机不同状态达到稳定的时间不同的特点, 将直升机模型分为快速和慢速两种模型. 反步控制方法和逆动力学控制方法分别被用于进行快慢两种模型控制器的设计, 并在控制过程中采用了不同的控制周期. 仿真结果表明, 利用上述方法设计的控制器, 对于阶跃变化和正弦变化的速度轨迹具有良好的跟踪效果.

     

Adaptive Fault Tolerant Control of Multi-time-scale Singularly Perturbed Systems

This paper studies the fault tolerant control, adaptive approach, for linear time-invariant two-time-scale and three-time-scale singularly perturbed systems in presence of actuator faults and external disturbances. First, the full order system will be controlled using ε-dependent control law. The corresponding Lyapunov equation is ill-conditioned due to the presence of slow and fast phenomena. Secondly, a time-scale decomposition of the Lyapunov equation is carried out using singular perturbation method to avoid the numerical stiffness. A composite control law based on local controllers of the slow and fast subsystems is also used to make the control law ε-independent. The designed fault tolerant control guarantees the robust stability of the global closed-loop singularly perturbed system despite loss of effectiveness of actuators. The stability is proved based on the Lyapunov stability theory in the case where the singular perturbation parameter is sufficiently small. A numerical example is provided to illustrate the proposed method.     

Symbolic realization of asymptotic time-scale and eigenstructure assignment design method in multivariable control

This paper reports on a symbolic realization of the asymptotic time-scale and eigenstructure assignment (ATEA) state feedback design technique for multivariable control. The resulting state feedback laws are parameterized in a scalar ε. Under these state feedback laws, the closed-loop system possesses a pre-specified time-scale and its eigenstructure approaches a pre-specified one, as the value of the parameter ε approaches zero. By appropriately specifying the time-scale and the eigenstructure, the feedback laws can be obtained to solve various control problems, such as the H ₂ and H _∞ suboptimal control, and almost disturbance decoupling problems. We present, in this paper, the software implementation of the ATEA design algorithm using the MATLAB symbolic programming technique. Our m-functions are capable of returning a result, which is explicitly expressed in terms of a symbolic variable epsilon, which represents ε. The controller design for a piezoelectric bimorph actuator is used to illustrate how the symbolic realization works.     

Singular perturbation analysis of a flexible beam used in underwater exploration

This article focuses on the analysis of a flexible beam based on two approaches of singular perturbations and feedback linearisation. First, a model is obtained for a flexible beam consisting of flexible joints and actuators for underwater positioning and/or tracking control leading to a singularly perturbed structure based on the slow phenomena due to the rigid portion and fast phenomena due to the flexible part of the system. Next, two ways are given for introducing the small parameter responsible for time-scale behaviour, one using a separate small parameter for each beam joint and beam link and the second using a single small parameter with appropriate scaling. Using the singular perturbation approach, the original systems are decoupled into slow and fast subsystems. The main objective is to use a feedback linearisation approach and design a proportional-integral-derivative computed-torque, composite (slow and fast) controller for improving the tracking performance. An illustrative example is provided.     

Order-reducing approximation of two-time-scale discrete linear time-varying systems

In this paper we study a two-time-scale discrete-time linear time-varying system. We heuristically find a reduced-order approximation to its asymptotic behaviour as the time-scale separation tends to infinity. This approximation results in a white noise representation of the fast state vector, and a corresponding approximation error in the slow state vector. After introducing the approximate system we define concepts of continuity and rate of variation which are needed in the discrete-time analysis. We then prove that as the time-scale separation increases, the state of the reduced-order system asymptotically coincides with the slow state of the original system in the mean-square sense on compact time intervals. We also find the order of the slow state approximation error covariance.     

Visual architecture and cognitive architecture

Traditional architectures have fundamental epistemological problems. Perception is inherently resource limited so controlling perception involves all the same AI-complete problems of reasoning about time and resources as the full-scale planning problem. Allowing a planner to transparently assume that the information it needs will automatically be present and up-to-date in the model thus presupposes a solution to a problem at least as difficult as planning itself. Although one can imagine many possible solutions to this problem, such as allowing the planner to recurse on its own epistemological problems, there have been no convincing attempts at this. In this paper, I compare behaviour-based and traditional systems in terms of their representational power and the strengths of their implicit epistemological theories. I argue that both have serious limitations and that those limitations are not addressed simply by joining the two into a hybrid. I discuss my work with using vision to support real-time activity and give an example of an interesting intermediate point between reactive and classical architectures that preserves the simplicity and parallelism of behaviour-based systems while supporting ‘symbolic’ representations. Traditionally, AI theories have assumed, either implicitly or explicitly, an architecture in which modules of the mind (perception, reasoning, motor control, etc.) are linked by way of some centralized database like structure, often referred to as a world model. Recently, a number of alternative architectures have been proposed which, to greater or lesser degrees, claim to do away with world models or with representations entirely. Many of the criticisms of traditional architectures revolve around speed and timescale. Planning, so the story goes, is slow but flexible, while feedback loops are fast but stupid. A common approach, both in this special issue and in the literature in general, is to adopt a hybrid which fuses a slow planner running on a long time-scale and a set of fast feedback loops running on a short time-scale. The problem with this argument is that planning is not slow, it is combinatorially explosive. Running an O(2 ⁿ ) algorithm on a time-scale ten times slower is the same as running it on a computer ten times faster : it simply lets one increase n by three. If time-scale were the true problem, faster CPUs would make tiered architectures obsolete in a few years. I believe the true issues are not speed, in the sense of time-scale, but combinatorics and epistemology. The former has been extensively discussed, so I will focus on epistemology. Clearly, if an agent architecture is to be successful it must take into account the capacities and limitations of perception. In this paper I discuss the influence of perceptual architecture on agent architecture, argue that the recent wave of tiered architectures do not adequately address these problems, and discuss my work on using vision to support real-time activity.     

Optimal disturbance rejection control for singularly perturbed composite systems with time‐delay

The optimal control problem for a class of singularly perturbed time‐delay composite systems affected by external disturbances is investigated. The system is decomposed into a fast linear subsystem and a slow time‐delay subsystem with disturbances. For the slow subsystem, the feedforward compensation technique is proposed to reject the disturbances, and the successive approximation approach (SAA) is applied to decompose it into decoupled subsystems and solve the two‐point boundary value (TPBV) problem. By combining with the optimal control law of the fast subsystem, the feedforward and feedback composite control (FFCC) law of the original composite system is obtained. The FFCC law consists of analytic state feedback and feedforward terms and a compensation term which is the limit of the adjoint vector sequence. The compensation term can be obtained from an iteration formula of adjoint vectors. Simulation results are employed to test the validity of the proposed design algorithm. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

高超音速BTT巡航飞行器变结构控制系统设计

针对高超音速BTT巡航飞行器气动参数变化大,动力学特性具有气动、惯性交叉耦合和运动学耦合的特点,采用了基于反馈线性化和变结构理论的控制器设计方法.首先利用时间尺度理论将控制系统分为快变量和慢变量两个子系统,然后应用动态逆反馈分别对子系统进行线性化解耦,最后根据线性变结构理论单独设计各通道控制器.仿真结果显示基于方法设计的姿态控制器可以确保对指令跟踪的精确性和鲁棒性,姿态指令跟踪无静差,响应超调量小于10%.     

L1‐Gain Analysis and Control for Switched Positive Systems with Dwell Time Constraint

This paper studies the problems of L₁‐gain analysis and control for switched positive systems with dwell time constraint. The state‐dependent switching satisfies a minimal dwell time constraint to avoid possible arbitrary fast switching. By constructing multiple linear co‐positive Lyapunov functions, sufficient conditions of stability and L₁‐gain property are derived under the proposed switching strategy. Then, an effective state feedback controller is designed to ensure the positivity and L₁‐gain property of the closed‐loop system. Finally, a simulation example is given to illustrate the effectiveness of the proposed method.     

Composite nonlinear control with state and measurement feedback for general multivariable systems with input saturation

In this paper, we present a design procedure of composite nonlinear feedback control for general multivariable systems with actuator saturation. We consider both the state feedback case and the measurement feedback case without imposing any restrictive assumption on the given systems. The composite nonlinear feedback control consists of a linear feedback law and a nonlinear feedback law without any switching element. The linear feedback part is designed to yield a closed-loop system with faster rise time, while at the same time not exceeding the actuator limits for the desired command input levels. The nonlinear feedback law is used to reduce overshoot and undershoot caused by the linear part. As such, a highly desired tracking performance with faster settling time and smaller overshoot can be obtained. The result is illustrated by a numerical example, which shows that the proposed design method yields a very satisfactory performance.     

Robust H∞ control for uncertain singular systems with state delay

This paper addresses the problem of robust H_∞ control for uncertain continuous singular systems with state delay. The singular system under consideration involves state time delay and time‐invariant norm‐bounded uncertainty. Based on the linear matrix inequality (LMI) approach, we design a memoryless state feedback controller law, which guarantees that, for all admissible uncertainties, the resulting closed‐loop system is not only regular, impulse free and stable, but also meets an H_∞‐norm bound constraint on disturbance attenuation. A numerical example is provided to demonstrate the applicability of the proposed method. Copyright © 2003 John Wiley & Sons, Ltd.     

Composite nonlinear feedback control for linear singular systems with input saturation

This paper investigates the composite nonlinear feedback (CNF) control technique for linear singular systems with input saturation. First, a linear feedback control law is designed for the step tracking control problem of linear singular systems subject to input saturation. Then, based on this linear feedback gain, a CNF control law is constructed to improve the transient performance of the closed-loop system. By introducing a generalized Lyapunov equation, this paper develops a design procedure for constructing the CNF control law for linear singular systems with input saturation. After decomposing the closed-loop system into fast subsystem and slow subsystem, it can be shown that the nonlinear part of the CNF control law only relies on slow subsystem. The improvement of transient performance by the proposed design method is demonstrated by an illustrative example.     

Reliable H ∞ control of multiple time scales singularly perturbed systems with sensor failure

This paper studies the reliable H _∞ control for linear time-invariant multiparameter singularly perturbed systems against sensor failures. By time-scale decomposition, the full-order system is decomposed into slow and fast subsystems. After designing a reliable H _∞ controller for the global system, three reduced reliable H _∞ sub-controllers based on the slow and fast problems are obtained through the manipulation of the algebraic Riccati equations. The resulting control systems are reliable in that they provide guaranteed asymptotic stability and H _∞ performance when all control components are operational as well as when sensor failures occur.     

H∞ controller design for linear systems with time-invariant uncertainties

This paper considers the problem of designing robust H _∞ state feedback controller for linear continuous-time systems with time-invariant uncertainties. The main result given here concerns H _∞ controller design using the parameter dependent Lyapunov function approach and a new control law. A new condition ensuring the linear systems to be is asymptotically stable with a prescribed H _∞ performance is proposed in terms of a set of linear matrix inequalities (LMIs). Theoretic proof is given to show that the proposed condition is less conservative than existing results in the literature. An example is provided to demonstrate the efficiency of the proposed method.     

Robust sampled-data H∞ control of uncertain singularly perturbed systems using time-dependent Lyapunov functionals

In this paper, the problem of robust sampled-data H_∞ control of linear uncertain singularly perturbed systems is investigated. The parametric uncertainties are assumed to be time-varying and norm-bounded. Two types of controller design are considered: (1) with a fast sampling in the fast state and a slow one in the slow state, and (2) with a fast sampling in both states. For each type, a time-dependent Lyapunov functional associated with the sampling pattern is introduced to analyse the exponential stability and L₂-gain performance of the closed-loop system. Linear matrix inequalities based solutions of the robust sampled-data H_∞ control problem are derived. The new results are proved theoretically to be less conservative than the existing results. An illustrative example is given which substantiates the usefulness of the proposed method.     

Robust Reliable H∞ Control for Discrete‐Time Systems with Actuator Delays

This article focuses on the robust state feedback reliable H_∞ control problem for discrete‐time systems. Discrete‐time systems with time‐varying delayed control input are formulated. Based on the Lyapunov–Krasovskii method and linear matrix inequality (LMI) approach, delay‐dependent sufficient conditions are developed for synthesizing the state feedback controller for an uncertain discrete‐time system. The parameter uncertainty is assumed to be norm bounded. A design scheme for the state feedback reliable H_∞ controller is proposed in terms of LMIs, which can guarantee the global asymptotic stability and the minimum disturbance attenuation level. Finally, numerical examples are provided to illustrate the effectiveness and reduced conservatism of the proposed methods.     

RLV抗扰动非线性最优控制器设计

可重复使用运载器(RLV)再入面临严重的扰动影响,对此设计一种抗扰动非线性最优控制器(ADNOC)。首先,基于时标分离原理设计快、慢双回路控制结构;其次,将角速率动态变换处理成线性形式,通过依赖状态的黎卡提方程(SDRE)优化方法获得最优控制指令;然后,设计非线性扰动观测器用于估计外界干扰,并在非线性最优控制律中进行干扰补偿。仿真实验结果表明,所设计的控制器能良好地完成姿态跟踪控制,抑制扰动对姿态控制的影响,实现RLV的最优控制性能。     

State‐feedback disturbance attenuation for polytopic LPV systems with input saturation

This paper proposes a state‐feedback control law for linear parameter‐varying (LPV) systems with input saturation and disturbances. The proposed control law employs two control parts: a main control part for reducing the restricted ??₂ gain from the mismatched disturbance to the controlled output and an extra control part for eliminating the matched disturbance. Owing to this feature, the proposed control law provides a better disturbance attenuation performance than the conventional control law that deals with a unified disturbance regardless of the presence of matched and mismatched disturbances. Further, considering different forms of the feedback gain matrix K(θ(t)) and the Lyapunov function V(x(t)), three types of controllers are proposed. For each type, set invariance and the restricted ??₂ gain performance conditions are first formulated in terms of parameterized linear matrix inequalities (PLMIs) and then converted into linear matrix inequalities (LMIs) by using a parameter relaxation technique. Results from the simulation of numerical examples confirm the effectiveness of the proposed controllers. Copyright © 2009 John Wiley & Sons, Ltd.     

Feedback systems and multiple time-scales†

We study feedback design for systems with multiple time-scale structure uncovering an intrinsic time-scale structure for a state feedback system with full state output. From this we construct a multiple time-scale asymptotic observer and consider a system with state feedback via a two time-scale asymptotic observer. Finally we obtain more general results for a restricted class of systems.