Stability criteria for large-scale systems

Recent research into large-scale system stability has proceeded via two apparently unrelated approaches. For Lyapunov stability, it is assumed that the system can be broken down into a number of subsystems, and that for each subsystem one can find a Lyapunov function (or something akin to a Lyapunov function). The alternative approach is an input-output approach; stability criteria are derived by assuming that each subsystem has finite gain. The input-output method has also been applied to interconnections of passive and of conic subsystems. This paper attempts to unify many of the previous results, by studying linear interconnections of so-called "dissipative" subsystems. A single matrix condition is given which ensures both input-output stability and Lyapunov stability. The result is then specialized to cover interconnections of some special types of dissipative systems, namely finite gain systems, passive systems, and conic systems.     

Interconnected linear multivariable systems with delays: System properties and input-output stability

We consider an arbitrary interconnection of linear, time-invariant, distributed, multivariable subsystems; each subsystem is represented either by a strictly proper rational transfer function or by a finite sum of pure delay terms. Such models occur in transportation systems, in chemical processes, in production systems, in communication systems, and in models of boilers in nuclear power plants. Allowing inputs to be applied to any interconnection point, we show that, except for a special case, the input-output transfer function of such a system is in a class extensively stuided in the literature. Next we obtain necessary and sufficient conditions for input-output stability. An example illustrates the application of the test.     

参数不确定柔性机械手的终端滑模控制

针对参数不确定双臂柔性机械手系统, 提出一种基于遗传算法的终端滑模控制方法, 以实现其末端控制.基于输出重定义方法, 通过输入输出线性化, 将系统分解为输入输出子系统和内部子系统. 设计终端滑模控制策略,使输入输出子系统有限时间内收敛到零, 内部子系统变为零动态子系统; 采用遗传算法优化零动态子系统参数, 使其在平衡点附近渐近稳定. 根据Lyapunov稳定性理论算出末端输出位移的误差范围. 仿真结果证明该方法有效性.     

Input-output decoupling with stability for Hamiltonian systems

The input-output decoupling problem with stability for Hamiltonian systems is treated using decoupling feedbacks, all of which make the system maximally unobservable. Using the fact that the dynamics of the maximal unobservable subsystem are again Hamiltonian, an easily checked condition for input-output decoupling with (critical) stability is deduced.     

参数不确定柔性机械手的快速终端滑模控制

针对具有参数不确定性的柔性机械手,采用重新定义系统输出的方法,将系统分解为输入输出子系统和零动态子系统.对于输入输出子系统提出了一种递阶快速终端滑模控制策略,使得输入输出子系统在有限时间内收敛.将零动态子系统在平衡点近似线性化以选择控制器的设计参数,使零动态子系统在平衡点附近渐近稳定,从而保证了整个柔性机械手系统的渐近稳定,对系统中的不确定性具有较强的鲁棒性.仿真结果验证了所提方法的正确性.     

基于线性化法柔性机械臂控制器的设计

利用输入输出线性化的方法，柔性机械臂的模型可分解为两个子系统：输入输出子系统和零动态子系统。输入输出子系统采用模糊控制。通过分析零动态子系统特征值和重新定义的系统输出中的设计参数之间的关系，确定设计参数，并使得零动态子系统渐近稳定于平衡点．从而保证整个系统渐近稳定。     

基于神经滑模的柔性连杆机械手末端位置控制

：为了提高柔性机械手末端位置控制的鲁棒性和精度,提出了一种基于神经滑模的控制策略．首先采 用输入/输出线性化方法将动力学模型部分线性化,使之分成输入/输出子系统与内动态子系统．输入/输出子系统 采用神经滑模控制,内动态子系统采用状态反馈控制器镇定．随后,对控制系统内动态稳定性进行了分析,并在 两自由度柔性连杆机械手控制的仿真试验中得到了满意的结果．试验结果表明,在存在模型不确定性时,该控制 策略提高了控制系统的鲁棒性和控制精度．     

Recursive identification method for MISO Wiener-Hammerstein model

A simple technique for recursive identification of the Wiener-Hammerstein model with extension to the multi-input single-output (MISO) case is presented. We use a new transformation of the input-output difference equation where parameters to be estimated are those of each subsystem of the initial and unique realization. After that, a weighted extended least squares method is employed to estimate recursively and separately parameters of the linear subsystems and the static nonlinear element. The convergence analysis of the proposed procedure is also studied. Finally, a numerical example is provided to show the efficiency of the algorithm     

Approximation of cascade connected and feedback structured systems by Mullis-Roberts approximation

A method for constructing a reduced-order model retaining the internal structure of original high-order cascade connected and feedback structured systems is derived by the Mullis-Roberts algorithm. The reduced-order model obtained here is the optimal approximation in the sense that it minimizes the curvilinear integral of the squared norm of an approximation error at the unit circle of the 2-plane. The algorithm for obtaining the reduced-order models is described. One feature of the proposed algorithm is that it is possible to compute reduced-order models of each subsystem independently. The stability of the reduced-order model is not always guaranteed. However, the results of numerical computations show that the reduced-order systems remain stable for almost all randomly selected examples and approximate the input-output behaviour of original systems fairly well.     

垂直/短距起降飞机的轨迹跟踪控制器设计

针对垂直/短距起降飞行器在悬停状态下滚转力矩与横侧向推力存在强耦合、系统具有非最小相位特性的问题,本文设计了轨迹跟踪控制器.首先利用坐标变换和输入输出线性化将系统分解成最小相位子系统和非最小相位子系统.对非最小相位子系统,采用稳态系统中心的方法求解理想内部动态,并跟踪系统理想内模设计了LQR控制器,使得内部动态有界;对最小相位子系统设计了高增益控制器使得外部动态渐进稳定.仿真结果表明本文设计的控制器对给定轨迹和飞行器机动轨迹都有较好的跟踪效果,验证了控制器的有效性.     

Control of multi-axis robots with elastic joints via cascade compensation using the method of exact linearization

This paper presents a new method for the position control of industrial robots with elastic joints and where the dynamic of each actuator is described by a simplified model. The inverse dynamic of the system is computed and used to compensate the nonlinear terms and decouple the system through a coordinate transformation and nonlinear feedback (exact linearization). To simplify the algorithm for the inverse dynamic and hence reduce its computation, each actuator-link pair of the robot is considered as a 2-input 2-output nonlinear system, a link subsystem and an actuator subsystem. A cascade compensation using the exact linearization is then applied to each subsystem, thereby avoiding the computation of the first and second partial derivatives of the inverse of the inertia matrix and the vector of the coriolis and centrifugal forces. This gives a formalism that is relatively simple and efficient for symbolical computation, which is very important for the maintenance of accuracy. Similarly, a cascade linear controller is constructed for each subsystem of the resulting linear decoupled 2-input 2-output system. The basis vector functions for the coordinate transformation are so chosen that only one state of the link subsystem can theoretically not be measured directly or indirectly. To estimate this state, an observer with linear error dynamic is constructed. The applicability of this observer to this general case is also proved. Simulation results using the first three links of Puma 560 are finally presented.     

Finding maximum linear subsystems of nonlinear systems with outputs

The focus of this paper is to find the maximum input-output linearized subsystem. Necessary and sufficient conditions are presented under which there exist a static state feedback and a coordinate change to input-output linearize the system so that the linear subsystem has the largest dimension. A systematic method is also developed to compute the desired feedback and coordinate change     

多变量模型不确定系统的二阶滑模分解控制方法

提出一种多变量模型不确定系统的二阶终端滑模分解控制方法。通过状态变换和去耦合处理将系统转换为块能控标准型，它由输入输出子系统和穗定的零动态子系统组成。提出了特殊的二阶终端滑模超曲面和相应的控制策峪，使输入输出子系统状态渐近收敛到平衡点，零动态子系统随后也渐近收敛到平衡点。所提出方法对于控制维教较高的系统具有较大的意义，可简化设计，实现鲁棒分解控制。由于采用了二阶滑模的思想，可有效地消除系统的高频抖振。仿真实例表明了该方法的有效性。     

柔性机械手的鲁棒控制器设计

针对柔性机械手的动力学方程具有非最小相位的特点,运用重新定义的柔性机械手系统的输出,通过输入输出线性化,将系统分解为输入输出子系统和零动态子系统．考虑到柔性机械手系统存在的不确定性,设计终端滑模控制器,使输入输出子系统在有限时间内收敛到零．最优组合输出系数采用混沌遗传算法优化,以保证零动态子系统在平衡点附近渐近稳定,从而保证整个系统渐近稳定．仿真结果证明了设计方法的有效性．     

A subsystem design approach to continuous-time performance of decentralized multirate sampled-data systems

A decentralized controller design is presented for multirate sampled-data systems, where stability and input-output performance are considered in terms of continuous-time signals. The design procedure consists of analysis for the overall system and controller synthesis for individual subsystems. For the subsystem designs, a unique technique of removing lifting operation which is used in the analysis is proposed. Robust performance and robust stability in terms of continuous-time signals can be achieved by using the proposed design. A numerical example shows that the design method results in satisfactory controllers which guarantee closed-loop stability and performance in continuous time.