不确定时滞系统的鲁棒绝对稳定性研究

基于Lyapunov稳定性理论，采用线性矩阵不等式处理方法，研究具有参数不确定性的时滞系统鲁棒绝对稳定性问题．导出了用线性矩阵不等式系统可行性描述的系统鲁棒绝对稳定的滞后依赖型条件，据此可计算出最大的允许时滞界．通过求解一组线性矩阵不等式，给出使得闭环系统鲁棒绝对稳定的无记忆状态反馈控制律设计方法。     

Optimal decentralized control of large scale systems

This paper presents a new optimized decentralized controller design method for solving the tracking and disturbance rejection problems for large-scale linear time-invariant systems, using only low-order decentralized controllers. To illustrate the type of results which can be obtained using the new optimized decentralized control design method, the control of a large flexible space structure is studied and compared with the standard centralized LQR-observer controller. The order of the resultant decentralized controller is much smaller than that of the standard centralized LQR-observer controller. The proposed controller also has certain fail-safe properties and, in addition, it can be five orders of magnitude more robust than the standard LQR-observer controller based on their real stability radii. The new decentralized controller design method is applied to a large flexible space structure system with 5 inputs and 5 outputs and of order 24.     

Robust performance analysis for uncertain negative‐imaginary systems

Negative‐imaginary systems are important in engineering practice as this class of systems appears quite often in practical problems, for example, lightly damped flexible structures with collocated position sensors and force actuators. In this paper, an analytical framework for robust performance of uncertain negative‐imaginary systems is proposed. The results are obtained by transforming negative‐imaginary systems into a bounded‐real framework via the positive‐real property. This paper deals with all the significant technical difficulties that appear due to the transformation and the punctured j ω‐axis frequency condition of negative‐imaginary systems. The problem is equivalently cast into a structured singular value condition that gives a quantitative performance test for this class of systems. This result also gives an analytical framework for robust stability when the perturbations are mixture of bounded‐real and negative‐imaginary uncertainties. A numerical example is presented to show the usefulness of the proposed methods. Copyright © 2011 John Wiley & Sons, Ltd.     

Robust control of a class of sampled-data systems with LTI uncertainties

The robust stability and robust performance in sampled-data control is studied for systems with LTI uncertainties. A class of problems is considered, which allows an exact characterization of robust stability of the sampled-data system in terms of the _H norm of a finite-dimensional discrete transfer function. In the problem class certain assumptions on the product of the uncertainty weight and the anti-aliasing prefilter are imposed. In return, the robustness conditions can be stated in a particularly compact form, in which the robust stability and performance problems for LTI perturbations reduce to standard finite-dimensional discrete robust stability and performance problems. The robust stability condition for LTI uncertainties is also compared to the robustness condition based on the small gain theorem. The analysis provides a method to estimate the conservatism of the small gain robustness condition directly in terms of the anti-aliasing prefilter and frequency weights. As a by-product of this analysis a non-trivial class of sampled-data systems is identified for which the small gain theorem gives a non-conservative condition for robust stability to norm-bounded LTI uncertainties.     

The decentralized control of large flexible space structures

The decentralized robust servomechanism problem with constant disturbances/set points is considered in this paper for large flexible space structures (LFSS). It is shown that for LFSS which have colocated, mutually dual sensors and actuators, the decentralized fixed modes [1] of the system are precisely equal to the centralized fixed modes [2] of the system. Simple necessary and sufficient conditions are then obtained for a solution to exist for the robust decentralized servomechanism problem [3] for the system. A controller is demonstrated which, for this class of LFSS systems, eliminates the "spillover problem." A two-hundreth-order numerical example of an LFSS control problem using the Purdue model [4] is included to illustrate the results.     

关于自适应控制系统的鲁棒稳定性条件

本文用统一的方法对于由自适应控制系统的鲁棒稳定性分析提出的一类时变动态系统的有界解问题给出了一个充分条件。它为鲁棒自适应控制器的设计以及进行相应的理论分析带来了方便。     

带有非线性不确定参数的线性系统的鲁棒稳定性和鲁棒镇定问题

研究带有非线性不确定参数的线性系统的鲁棒稳定性和鲁棒镇定问题。讨论一种有很强实际应用背景并允许带有二次不确定参数的模型,研究该系统的鲁棒稳定性和鲁棒镇定问题。以ＬＭＩ的形式给出了判据,并举例证明了该方法的优越性。     

Adaptive neural network output feedback control for flexible multi-link robotic manipulators

In this paper, a novel approach for adaptive control of flexible multi-link robots in the joint space is presented. The approach is valid for a class of highly uncertain systems with arbitrary but bounded dimension. The problem of trajectory tracking is solved through developing a stable inversion for robot dynamics using only joint angles measurement; then a linear dynamic compensator is utilised to stabilise the tracking error for the nominal system. Furthermore, a high gain observer is designed to provide an estimate for error dynamics. A linear in parameter neural network based adaptive signal is used to approximate and eliminate the effect of uncertainties due to link flexibilities and vibration modes on tracking performance, where the adaptation rule for the neural network weights is derived based on Lyapunov function. The stability and the ultimate boundedness of the error signals and closed-loop system is demonstrated through the Lyapunov stability theory. Computer simulations of the proposed robust controller are carried to validate on a two-link flexible planar manipulator.     

Controller design for flexible structure vibration suppression with robustness to contacts

Model-based feedback control of vibration in flexible structures can be complicated by the possibility that interaction with an external body occurs. If not accounted for, instability or poor performance may result. In this paper, a method is proposed for achieving robust vibration control of flexible structures under contact. The method uses robust linear state feedback, coupled with a state estimation scheme utilizing contact force measurement. Uncertain contact characteristics are modelled by a sector-bounded non-linear function, such that state feedback gains can be synthesized using a matrix inequality formulation of the Popov stability criterion. A separation theorem is used to establish a robust H₂ cost bound for the closed loop system. Experimental results from a multi-mode flexible structure testbed confirm that vibration attenuation and stability can be maintained over a broad range of contact characteristics, in terms of compliance and clearance.     

On robust control of a class of nonlinear mechanical systems with parametric uncertainty

This article presents a method to design a robust controller for a class of nonlinear mechanical systems. The parameters of the system are assumed uncertain in the sense that they are known only within intervals of known lower and upper limits. The method involves using Kharitonov stability theory of interval polynomials to design a robust stabilising controller for the considered class of systems. To formulate the interval parameter problem in joint space, the dynamic equation, which is derived in Cartesian space for parallel kinematic machines, is transformed to joint space using the Jacobian matrix and its time derivative. The nonlinear joint space model is linearised yielding an interval linear model and a robust controller with interval parameter gains is then found. A simulation study on a dynamic model of Stewart platform based parallel kinematics machine demonstrates the design procedure and shows its effectiveness.     

Design of robust stable controls for nonlinear objects

We consider a problem of discrete control for a class of nonlinear time-varying objects. Only set estimations for object parameters are available. The aim is to design controls that ensure robust stability of closed-loop systems in a given domain of state space. Since the considered class of objects is large enough not to have a stabilizing control, the proposed design method has to verify at the last step if the obtained conditions of robust stability are satisfied for a nonlinear system “in a given domain.”     

不确定时滞系统无记忆鲁棒镇定控制

本文研究了一类状态和控制同时存在滞后的线性时变不确定时滞系统的鲁棒镇定控制问题，针对所有容许的时变未知且有界的不确定性，得到了确保闭环系统二次稳定的充分条件。文中进一步把不确定时滞系统的二次镇定控制器设计问题等价为线性时不变系统的状态反馈标准Ｈ∞控制问题，并由此得到鲁棒镇定控制器综合设计方法。     

Robust design of stochastic controllers for nonlinear systems

The previous results are generalized on the stabilizing property of a control scheme designed for a class of discrete-time nonlinear stochastic systems. First, the existing controller is made more robust with a prescribed degree of stability by proper modifications. Next, the inherent robustness is illustrated by a design utilizing erroneous noise characteristics. Reconsideration of the stability analysis used allows one to treat a larger class of nonlinear stochastic systems with more general structures     

不确定非线性系统的非光滑控制及应用

针对一类具有严格反馈结构形式的不确定非线性系统,研究非光滑鲁棒控制问题。在一定的假设条件下,基于backstepping设计方法,设计鲁棒非光滑控制律,证明闭环系统的鲁棒稳定性。将所得结果应用于飞行器的末制导问题,设计非光滑末制导律,并进行数值仿真研究。仿真结果说明了方法的有效性。     

Optimality of decentralized control for large-scale systems

A decentralized control scheme is given for the stabilization of large-scale linear systems composed of a number of controllable subsystems. A class of interconnection structures among subsystems is defined for which the overall system can always be stabilized by local state feedback which is optimal for a quadratic performance index. The resulting closed-loop system has robust stability properties against a wide range of variations in open-loop dynamics. Optimality of the decentralized control law is preserved for a modified performance index under perturbations in interconnections such that the strength of coupling does not increase. The class of decentrally stabilizable large-scale systems presented in this paper is the largest such class hitherto described by the structure of interconnections.     

Optimal root loci of flexible space structures

It is shown that simple generic properties can be proved for the optimal root loci of flexible space structures (FSS). It is proved that the angles and rates at which closed-loop poles depart from the open-loop poles can be found by inspection for any FSS with sufficiently widely space natural frequencies. Similar results also apply to the angles at which certain loci approach the transmission zeros of any FSS with compatible (physically colocated and coaxial) sensors and actuators, as a consequence of the special properties of the zeros of such systems. Finally, determining the number and orders of the Butterworth configurations of such as FSS is much more straightforward than for a general state-space system: it amounts only to checking whether structural displacements or their rates are the measured outputs. These results depend on the fundamental second-order nature of such systems, and five considerably more insight than is possible a priori for general linear multivariable systems     

Robust model predictive control of discrete nonlinear systems with time delays and disturbances via T–S fuzzy approach

In this paper, robust fuzzy model predictive control of a class of nonlinear discrete systems subjected to time delays and persistent disturbances is investigated. Based on the modeling method of delay difference inclusions, nonlinear discrete time-delay systems can be represented by T–S fuzzy systems comprised of piecewise linear delay difference equations. Moreover, Lyapunov–Razumikhin function (LRF), instead of Lyapunov–Krasovskii functional (LKF), is employed for time-delay systems due to its ability to reflect system original state space and its advantages in controller synthesis and computation. The robust positive invariance and input-to-state stability with respect to disturbance under such circumstances are investigated. A robust constraint set is adopted that the system state is converged to this set round the desired point. In addition, the controller synthesis conditions are derived by solving a set of matrix inequalities. Simulation results show that the proposed approach can be successfully applied to the well-known continuous stirred tank reactor (CSTR) systems subjected to time delay.     

Universal controllers for robust control problems

In this paper we discuss the construction of “universal” controllers for a class of robust stabilization problems. We give a general theorem on the construction of these controllers, which requires that a certain nonlinear inequality is solvablepointwisely or, equivalently, that arobust control Lyapunov function does exist. The constructive procedure producesalmost smooth controllers. The robust control Lyapunov functions extend to uncertain systems the concept of control Lyapunov functions. If such a robust control Lyapunov function also satisfies a small control property, the resulting stabilizing controller is also continuous in the origin of the state space. Applications of our results range from optimal to robust control.     

Inverse dynamics of articulated flexible structures: Simultaneous trajectory tracking and vibration reduction

This paper addresses the problem of inverse dynamics for articulated flexible structures with both lumped and distributed actuators. This problem arises, for example, in the combined vibration minimization and trajectory control of space robots and structures. For such flexible structures, closed loop passive joint based controllers have been shown to be effective in trajectory control by Paden et al. Crucial to the development of such closed loop controllers, which are robust to external perturbations, is the problem of dynamic inversion which yields the nominal state trajectories and the feedforward inputs. In this paper we propose a new inverse dynamics scheme for computing the nominal lumped and distributed feedforward inputs for tracking a prescribed trajectory.