连续时间多胞线性变参数系统变增益H∞/H2输出反馈控制

针对一类同时具有参数不确定性和外界干扰的非线性系统,提出了一种连续时间多胞线性变参数(LPV)系统变增益H_∞/H_2输出反馈控制方法.首先,对连续时间多胞LPV系统的变增益混合目标(H_∞/H_2指标和区域极点约束)输出反馈控制器综合方法进行了数学描述;其次,引入新的结构化松弛矩阵变量和参数依赖Lyapunov函数,将满足期望性能的混合目标鲁棒动态输出反馈控制问题转化为线性矩阵不等式框架内的有限维凸优化问题,进一步降低了所设计LPV控制器的保守性.最后,以四分之一车辆模型主动悬架系统为研究对象进行仿真,仿真结果验证了本文控制器的有效性.     

Mixed‐Objective Robust Dynamic Output Feedback Controller Synthesis for Continuous‐Time Polytopic Lpv Systems

A robust dynamic output feedback controller synthesis algorithm considering H_∞/H₂ performance and regional pole placement is addressed for a nonlinear system with parameter uncertainties and external disturbance. First, the formulation of a gain‐scheduled mixed‐objective robust dynamic output feedback controller for continuous‐time polytopic linear parameter varying (LPV) systems is presented. To reduce conservativeness, some auxiliary slack variables and parameter‐dependent Lyapunov functions are employed in addition to well‐established performance conditions. Then, sufficient conditions for the desired gain‐scheduled mixed‐objective robust dynamic output feedback controllers are cast into an efficiently tractable finite‐dimensional convex optimization problem in terms of linear matrix inequalities (LMIs). Finally, numerical simulation shows the validity of the proposed controller, which has good stability, strong robustness, satisfied disturbance attenuation ability, and smooth dynamic properties.     

Optimal static output feedback simultaneous regional pole placement.

The problem of optimal simultaneous regional pole placement for a collection of linear time-invariant systems via a single static output feedback controller is considered. The cost function to be minimized is a weighted sum of quadratic performance indices of the systems. The constrained region for each system can be the intersection of several open half-planes and/or open disks. This problem cannot be solved by the linear matrix inequality (LMI) approach since it is a nonconvex optimization problem. Based on the barrier method, we instead solve an auxiliary minimization problem to obtain an approximate solution to the original constrained optimization problem. Moreover, solution algorithms are provided for finding the optimal solution. Furthermore, a necessary and sufficient condition for the existence of admissible solutions to the simultaneous regional pole placement problem is derived. Finally, two examples are given for illustration.     

Semiglobal stabilization of saturated linear systems via multiple parametric Lyapunov equations

This paper investigates the problem of semiglobal stabilization with guaranteed flexible pole placement for saturated linear systems. To retain the advantages of the parametric Lyapunov equation, matrix‐partitioning idea is used to derive a new pole shift lemma. Starting from system matrix transformations, a recursive algorithm is proposed to shift every eigenvalue of a linear system separately without mode decomposition in each step. A new method introducing various parameters to every Lyapunov equation in each step is presented. As an application, the semiglobal stabilization with guaranteed flexible pole placement for saturated linear systems can be achieved by this method. Finally, its effectiveness and advantages are demonstrated via a simulation example. Copyright © 2013 John Wiley & Sons, Ltd.     

Analysis and Design of Robust Controllers Using the Interval Diophantine Equation

In this paper the design of pole placement feedback controllers for interval plants is addressed within an Interval Analysis framework. Three main topics connected by the concept of interval Diophantine equation are treated: a relatively straightforward investigation about robust coprimeness of interval polynomials, a reliable computing approach for the design of pole placement controllers in the presence of inaccuracies of interval type, and the design of robust controllers with regional pole placement specifications. After explicitly characterizing a convex subset of robust controllers, the problem of designing non-fragile controllers is formulated as a design centering problem, which is then solved by a global optimization algorithm. Numerical examples illustrate the main characteristics of the approach proposed.This paper has been partially supported by grants from Conselho Nacional de Desenvolvimento Científico e Tecnológico–Brazil.     

Control of linear systems subject to time-domain constraints with polynomial pole placement and LMIs

This note focuses on the control of continuous-time linear systems subject to time-domain constraints (input amplitude limitation, output overshoot) on closed-loop signals. Using recent results on positive polynomials, it is shown that finding a Youla-Kuc/spl breve/era polynomial parameter of fixed degree (hence, a controller of fixed order) such that time-domain constraints are satisfied amounts to solving a convex linear matrix inequality (LMI) optimization problem as soon as distinct strictly negative closed-loop poles are assigned by pole placement. Proceeding this way, time-domain constraints are handled by an appropriate choice of the closed-loop zeros.     

Linear pole-placement anti-windup control for input saturation nonlinear system based on Takagi Sugeno fuzzy model

An anti-windup controller for multi-input nonlinear system is proposed in this paper. The proposed method does not need to calculate every time for every fuzzy rules comparing with traditional linear pole placement of T-S(Takagi-Sugeno) fuzzy. This means fewer LMIs(linear matrix inequality) will be needed and its solution will be guaranteed as much as possible. For different saturation limit, different D-stable disk center and radius of pole placement can be selected to eliminate input saturation effect directly. Nonlinear system will be transferred to T-S fuzzy model first. Then, by employing a series of transition matrix, nonlinear system will be transferred into a nearly linear format accompanied by a nonlinear part. Finally, by designing a proper controller, linear pole placement method can be used and the controller gains can be calculated out with LMIs.

     

An anti-windup technique for LMI regions

The anti-windup problem seeks to minimize closed loop performance deterioration due to input nonlinearities, such as saturation, for a given linear time-invariant plant and controller. This paper presents a linear matrix inequality (LMI) based method that attempts to minimize performance deterioration while explicitly restricting the anti-windup closed loop dynamics. The restriction placed on the dynamics is described via LMI regions, which is a form of regional pole placement. Finally, the techniques discussed in this paper are demonstrated on an electro-hydraulic testbed.     

A unified method for optimal arbitrary pole placement

We consider the classic problem of pole placement by state feedback. We offer an eigenstructure assignment algorithm to obtain a novel parametric form for the pole-placing feedback matrix that can deliver any set of desired closed-loop eigenvalues, with any desired multiplicities. This parametric formula is then exploited to introduce an unconstrained nonlinear optimisation algorithm to obtain a feedback matrix that delivers the desired pole placement with optimal robustness and minimum gain. Lastly we compare the performance of our method against several others from the recent literature.     

Gain Scheduled LPV H∞ Control Based on LMI Approach for a Robotic Manipulator

A new approach to the design of a gain scheduled linear parameter‐varying (LPV) H_∞ controller, which places the closed‐loop poles in the region that satisfies the specified dynamic response, for an n‐joint rigid robotic manipulator, is presented. The nonlinear time‐varying robotic manipulator is modeled to be a LPV system with a convex polytopic structure with the use of the LPV convex decomposition technique in a filter introduced. State feedback controllers, which satisfy the H_∞ performance and the closed‐loop pole‐placement requirements, for each vertex of the convex polyhedron parameter space, are designed with the use of the linear matrix inequality (LMI) approach. Based on these designed feedback controllers for each vertex, a LPV controller with a smaller on‐line computation load and a convex polytopic structure is synthesized. Simulation and experiment results verify that the robotic manipulator with the LPV controller always has a good dynamic performance along with the variations of the joint positions. © 2002 Wiley Periodicals, Inc.     

超混沌系统的一种模糊滑模控制

采用T-S模糊模型对超混沌系统建模,用区域极点配置技术和线性矩阵不等式技术构造满足动静态性能要求的滑模面．在此基础上设计满足指数趋近律的模糊滑模控制器．通过将该控制器应用到Rossler超混沌系统中,验证了所提出方案的有效性.     

考虑执行器故障圆盘极点可靠配置

针对线性定常系统,本文提出考虑执行器故障的圆盘极点可靠配置问题．在更一般、更实际的执行器故障模型的基础上,给出了将极点配置到指定圆盘内可靠控制存在的充分条件．通过求解LMI（线性矩阵不等式）完成状态反馈可靠控制器的设计．仿真不仅验证了本文提出设计方法的可行性,而且也说明了可靠配置的必要性。     

Robust control of polytopic systems by convex optimization

Robust control synthesis of linear time-invariant SISO polytopic systems is investigated using the polynomial approach. A convex set of all stabilizing controllers for a polytopic system is given over an infinite-dimensional space. A finite-dimensional approximation of this set is obtained using the orthonormal basis functions and represented by a set of LMIs thanks to the KYP lemma. Then, an LMI based convex optimization problem for robust pole placement with sensitivity function shaping in two- and infinity-norm is proposed. The simulation results show the effectiveness of the proposed method.     

控制输入受限的拦截卫星轨道鲁棒H2/H∞控制

针对拦截卫星在执行轨道拦截任务的过程中存在不确定参数和不同类型外界干扰的轨道控制问题,研究了基于鲁棒H2/H∞稳定的控制器设计方法.首先,考虑参数不确定性、外界干扰、系统的H2/H∞性能和有限时间性能、控制输入限幅和极点配置,建立了相对运动轨道模型和相应的约束条件,并由此提出了控制器设计目标.然后采用线性不等式技术提出并证明了控制器存在的充分条件,并将控制器的设计转化为一个凸优化问题进行求解.仿真结果表明,设计的控制器能够使系统稳定并满足各项约束,且对系统不确定性具有较好的鲁棒性以及对外界干扰有一定的抑制作用.     

State-feedback H2/H-infinity controller design with D-stability constraints for stochastic systems

This paper addresses the state-feedback H2/H-infinity controller design that satisfies D-stability constraints for stochastic systems. Firstly, the concept of regional stability for stochastic systems is defined in linear matrix inequality(LMI) regions; Secondly, the characterization about stochastic D-stability is presented. This paper introduces a new technique to solve the regional stability problem for stochastic systems, which is different from the pole placement technique ever used in deterministic systems. Based on this, in the state-feedback case, mixed H2/H-infinity synthesis with D-stability constraints is discussed via LMI optimization.     

机器人多胞变增益输出反馈H∞控制

针对n类关节的刚性机器人,提出一种设计包含极点配置的多胞变增益输出反馈H_∞控制器的新方法.利用平衡族附近的线性化,机器人系统可化为一关于平衡族的连续线性变参数系统,通过引入滤波器得到易于设计变增益控制器的增广对象,并将其凸分解为多胞表示,基于二次D 稳定和二次H_∞性能概念,利用多胞特性将整个控制器设计转化为对胞体顶点控制器的设计,然后利用LMI方法,对多胞的各顶点分别设计满足H_∞∞性能和动态特性的输出反馈控制器,最后综合顶点控制器得到具有同     

Design of robust <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript>-controller for energetic boiler plant

A problem of robust controller design for control of a boiler plant is solved using an H _∞ loop-shaping method with constraints imposed on regional pole placement of transfer functions of the closed-loop system, and linear matrix inequalities tools. Requirements to the closed-loop system are formulated both in the form of frequency constraints on singular values of transfer function of the open-loop system, and in the form of pole placement constraints for the transfer function of the closed-loop system as a given region on the complex plane. A reduction of the full-order H _∞-controller obtained in the design procedure is performed.     

State-feedback H2/H-infinity controller design with D-stability constraints for stochastic systems

This paper addresses the state-feedback H2/H-infinity controller design that satisfies D-stability constraints for stochastic systems. Firstly, the concept of regional stability for stochastic systems is defined in linear matrix inequality（LMI） regions; Secondly, the characterization about stochastic D-stability is presented. This paper introduces a new technique to solve the regional stability problem for stochastic systems, which is different from the pole placement technique ever used in deterministic systems. Based on this, in the state-feedback case, mixed H2/H-infinity synthesis with D-stability constraints is discussed via LMI optimization.     

State-feedback H2/H-infinity controller design with D-stability constraints for stochastic systems

This paper addresses the state-feedback H₂/H-infinity controller design that satisfies D-stability constraints for stochastic systems. Firstly, the concept of regional stability for stochastic systems is defined in linear matrix inequality(LMI) regions; Secondly, the characterization about stochastic D-stability is presented. This paper introduces a new technique to solve the regional stability problem for stochastic systems, which is different from the pole placement technique ever used in deterministic systems. Based on this, in the state-feedback case, mixed H₂/H-infinity synthesis with D-stability constraints is discussed via LMI optimization.     

期望指标下一类线性周期系统鲁棒状态估计

针对满足多重区域指标约束的鲁棒滤波问题 ,以离散线性周期系统为研究对象 ,利用周期系统参数在某区间变化的特性 ,将周期系统满足极点或极点 /协方差指标的估计问题转化为区间系统的鲁棒估计问题。采用线性矩阵不等式 (L MIs)法进行凸优化 ,求解对应区间系统的满意估计增益 ,并设计相应鲁棒状态估计器。数值算例验证了相关的结论。