基于回路成形的鲁棒增益调度控制器设计

针对目前基于线性变参数系统的增益调度控制设计中存在的控制结构复杂性问题，提出一种基于回路成形的简单且易实现的增益调度控制结构.在此基础上，提出一个鲁棒增益调度控制设计方法.设计过程首先采用补偿器函数使得被控对象奇异值具有期望的形状，以保证被控对象的性能要求，然后利用小增益定理设计一个鲁棒控制器，得到具有良好性能的、结构简单的鲁棒增益调度控制器.最后针对一个化工过程，说明此方法的有效性.     

Robust Properties of Risk-Sensitive Control

The purpose of this paper is to characterize and prove robustness properties of risk-sensitive controllers precisely. In particular, we establish a stochastic version of the small gain theorem. This theorem is expressed in terms of an inequality which bounds the average output power in terms of the input power. Since this inequality is closely related to the risk-sensitive criterion, our stochastic small gain theorem can be expressed in terms of the risk-sensitive criterion. This provides a concrete motivation for the use of the risk-sensitive criterion stochastic robustness. Date received: September 10, 1998. Date revised: June 5, 2000.     

PID控制器增益的稳定范围研究

基于逆Nyquist曲线,提出了一种线性系统在PID控制下确定增益稳定范围的方法,为PID控制器增益的稳定提供了一条快速而有效的途径。由逆Nyquist曲线上的实部为极值的点,将PID增益分割成若干区间。再运用广义的Her—mite-Biehler定理得出一个推理和二个条件,通过纵向直线与逆Nyquist曲线的交点数,可获得系统在PID控制下增益稳定的区间。仿真实例验证了该方法的有效性。该方法应用简便,能有效解决PID控制下增益的稳定范围。     

An ISS small gain theorem for general networks

We provide a generalized version of the nonlinear small gain theorem for the case of more than two coupled input-to-state stable systems. For this result the interconnection gains are described in a nonlinear gain matrix, and the small gain condition requires bounds on the image of this gain matrix. The condition may be interpreted as a nonlinear generalization of the requirement that the spectral radius of the gain matrix is less than 1. We give some interpretations of the condition in special cases covering two subsystems, linear gains, linear systems and an associated lower-dimensional discrete time dynamical system.     

Revisiting the IISS Small‐Gain Theorem through Transient Plus ISS Small‐Gain Regulation

Recently, the small‐gain theorem for input‐to‐state stable (ISS) systems has been extended to the class of integral input‐to‐state stable (iISS) systems. Feedback connections of two iISS systems are robustly stable with respect to disturbance if an extended small‐gain condition is satisfied. It has been proved that at least one of the two iISS subsystems needs to be ISS for guaranteeing globally asymptotic stability and iISS of the overall system. Making use of this necessary condition for the stability, this paper gives a new interpretation to the iISS small gain theorem as transient plus ISS small‐gain regulation. The observation provides useful information for designing and analyzing nonlinear control systems based on the iISS small‐gain theorem.     

Robust phase margin, robust gain margin and Nyquist envelope of an interval plant family

In this paper, robust gain margin, robust phase margin and Nyquist envelope of interval systems are studied. It is first presented that the robust gain and phase margins of a control system with an interval plant family are achieved at one of the Kharitonov plant by using the interlacing theorem and virtual compensator concept. Then, using the generalized Hermite-Biehler theorem, it is shown that the outer boundary of the Nyquist envelope of a stable interval plant is covered by the Nyquist plots of the 16 Kharitonov plants family. Examples are given to illustrate the method presented.     

A small gain theorem for systems with non-causal subsystems

Small gain theorems are used to verify the stability of a feedback interconnection of causal stable systems. In this work, we extend the small gain condition to test the stability of a feedback interconnection of two stable systems at least one of which is non-causal. This result may find application in the robust controller design for time-delay systems.     

Some applications of small gain theorem to interconnected systems

Based on small gain theorem, decentralized control of interconnected systems is studied. Linear matrix inequality conditions are given for stabilizability of interconnected systems. Interconnections can be used to improve system robustness in the sense of small gain theorem. An example is given to illustrate the results. Finally, interconnected systems composed of symmetric subsystems are studied.     

Explicit construction of quadratic Lyapunov functions for the small gain,positivity, circle,and popov theorems and their application to robust stability. Part I: Continuous-time theory

The purpose of this paper is to construct Lyapunov functions to prove the key fundamental results of linear system theory, namely, the small gain (bounded real), positivity (positive real), circle, and Popov theorems. For each result a suitable Riccati-like matrix equation is used to explicitly construct a Lyapunov function that guarantees asymptotic stability of the feedback interconnection of a linear time-invariant system and a memoryless nonlinearity. Lyapunov functions for the small gain and positivity results are also constructed for the interconnection of two transfer functions. A multivariable version of the circle criterion, which yields the bounded real and positive real results as limiting cases, is also derived. For a multivariable extension of the Popov criterion, a Lure-Postnikov Lyapunov function involving both a quadratic term and an integral of the nonlinearity, is constructed. Each result is specialized to the case of linear uncertainty for the problem of robust stability. In the case of the Popov criterion, the Lyapunov function is a parameter-dependent quadratic Lyapunov function.     

Control schemes for stable teleoperation with communication delay based on IOS small gain theorem

The problem of stabilization of a force-reflecting telerobotic system in presence of time delay in the communication channel is addressed. We introduce an approach that is based on application of the input-to-output stability (IOS) small gain theorem for functional differential equations (FDEs). A version of the stabilization algorithm as well as its two adaptive extensions are proposed. For all these control schemes, the input-to-state stability (ISS) of the overall telerobotic system is guaranteed in the global, global practical, or semiglobal practical sense for any constant communication delay under the assumption that the environmental dynamics satisfy a weak form of finite-gain stability property. As an intermediate step, we formulate and prove a general IOS (ISS) small gain result for FDEs.     

A new small‐gain theorem with an application to the stabilization of the chemostat

New small‐gain results are obtained for nonlinear feedback systems under relaxed assumptions. Specifically, during a transient period, the solutions of the feedback system may not satisfy some key inequalities that previous small‐gain results usually utilize to prove stability properties. The results allow the application of the small‐gain perspective to various systems that satisfy less‐demanding stability notions than the input‐to‐output stability property. The robust global feedback stabilization problem of an uncertain time‐delayed chemostat model is solved by means of the new small‐gain results. Copyright © 2011 John Wiley & Sons, Ltd.     

Computation of stabilizing PID gain regions based on the inverse Nyquist plot

Based on the inverse Nyquist plot, a method is presented to determine the stabilizing PID gain regions for linear systems. It does not depend on the integral and the derivative parameters. The two stable conditions are derived from a generalization of the Hermite-Biehler theorem. Two kinds of key points can be obtained from the inverse Nyquist plot. The PID gain would be divided into several regions by abscissas of these key points. According to the number of intersection of the inverse Nyquist plot and the vertical line, the stabilizing PID gain regions can be determined. Examples are given to show the benefits of the proposed method.     

一种具有借鉴意义的传感器输入标定技术

传感器获取现场信号的准确与否,直接影响到整个工业自动化系统的测量与控制精度。为了获取真实的现场信息,要对计算机系统接入模拟传感器输出的模拟量电信号进行不失真的变换。文中提出了一种针对力和位移传感器的输入标定技术,并根据理想传感器灵敏度计算了硬件增益和通道增益,同时以软件方式进行了修正。通过工程实际验证,这种方法标定结果准确,便于操作,具有工程推广价值。     

Robust global stabilization of a class of uncertain feedforward nonlinear systems

The problem of global asymptotically stabilizing a certain class of uncertain feedforward nonlinear systems is considered. The control law is obtained by nesting saturation functions whose amplitude can be rendered arbitrarily small. With respect to previous works on the subject the design procedure is able to deal with uncertain (possibly time-varying) parameters ranging within the prescribed compact sets which can affect also the linear approximation of the system. The small gain theorem for nonlinear systems which are input to state stable “with restrictions” is shown to be a key tool for designing a state feedback saturated control law.     

基于GL847的扫描图像校正

扫描仪在扫描成像过程中,诸多因素会给扫描图像带来误差和扭曲,因而必须对其加以校正。在分析扫描仪误差产生原理的基础上,详细讨论了基于GL847的扫描图像增益与偏移校正机制,提出了一种有效的扫描图像校正参数获取方法。     

Lurie系统的鲁棒量化控制

研究了Lurie系统的鲁棒量化状态反馈控制问题, 其中的量化器为静态对数量化器. 首先, 根据Lurie系统自身特点以及对数量化器的特性, 将量化状态反馈控制作用下的Lurie系统建模成具有两个扇形约束的不确定系统. 然后分别考虑了没有量化和有量化作用两种情形, 利用小增益定理, 得到了闭环系统内稳定的充分必要条件, 并进一步给出了相应的状态反馈控制律. 最后, 数值例子表明了本文方法的有效性.     

采样系统鲁棒稳定性分析的新方法

The lifting technique is now the most popular tool for dealing with sampled-data control systems. However, for the robust stability problem the system norm is not preserved by the lifting as expected. And the result is generally conservative under the small gain condition. The reason for the norm difference by the lifting is that the state transition operator in the lifted system is zero in this case. A new approach to the robust stability analysis is proposed. It is to use an equivalent discrete-time uncertainty to replace the continuous-time uncertainty. Then the general discretized method can be used for the robust stability problem, and it is not conservative. Examples are given in the paper.     

A robust control approach to stabilization of networked control systems with time-varying delays

The stabilization problem is studied for networked control systems (NCSs) with time-varying delay that may be larger than one sampling period. By considering state feedback controllers, the closed-loop NCS is described as a switched delay system, which is then represented as an interconnected feedback system. A sufficient BIBO stability condition is derived for the closed-loop NCS by using the small gain theorem and the average dwell time technique. Design procedures for the BIBO stabilizing controllers are also presented. An example is given to demonstrate the effectiveness of the proposed method.     

Characterization of some gain conditions via the Hamilton-Jacobi inequality

This paper gives a characterization of three gain conditions, i.e., L_2∞ gain, L_2∞ gain subject to an L₂ gain constraint, and the Hankel gain, of nonlinear systems via the Hamilton-Jacobi inequalities. It is shown that the obtained results for the L_2∞ gain and the Hankel gain are analog to that derived for the L₂ gain so far.     

Order-dependent and delay-dependent conditions for stability and stabilization of fractional-order time-varying delay systems using small gain theorem

In this paper, the stability and stabilization problems for fractional-order time-varying delay systems are investigated. Firstly, by casting the stability problem as one of robust stability analysis problems and utilizing the small gain theorem, an order-dependent and delay-dependent stability condition for fractional-order time-varying delay systems is developed. Taking advantage of the information of order and delay, the stability condition is less conservative than the existing results. Then, state feedback controllers that stabilize fractional-order time-varying delay systems are developed. To tackle the computational difficulty of the controller design method, a local optimization algorithm is proposed. Finally, numerical examples are provided to illustrate that the proposed criteria are valid and less conservative than the existing ones.