由降阶模型设计全阶模型的H~∞鲁棒控制器

由降阶模型设计全阶模型的Ｈ~∞鲁棒控制器王炎生，陈宗基（北京航空航天大学自动控制系北京１０００８３）关键词：模型降阶，Ｈ~∞鲁棒控制器，控制输入约束１引言近年来，具有良好鲁棒性的Ｈ”方法已经越来越多地应用于飞机控制系统设计研究中．但由于像飞机这样的被控...     

弹性飞行器的H∞控制器设计与仿真

弹性飞行器动力学模型用很多自由度来描述弹性模态和刚性模态,由此引起的模型不确定性及建模误差,使用常规控制器很难保证系统的鲁棒稳定性.为此,采用H∞混合灵敏度控制方法设计了能控制弹性飞行器姿态运动又能快速抑制结构振动的鲁棒控制器,采用平衡截断法对此高阶控制器进行了降阶,得到6阶和4阶控制器,对于降阶控制器的控制效果进行了仿真研究.仿真结果表明,降阶后的控制器能很好地实现对原全阶控制器的近似,系统增强稳定性.鲁棒性能满足设计的要求,为飞行系统提供了设计依据.     

精馏塔H∞非脆弱鲁棒控制的研究

指出了对精馏塔采用高阶常规鲁棒设计的控制器进行降阶所得控制器具有脆弱性,不能保证设计要求的鲁棒性,精馏塔在设计范围内摄动时,系统出现渐扩发散现象.提出将精馏塔控制器摄动转化为被控对象摄动.给出了不需要控制器降阶的精馏塔H∞非脆弱鲁棒PI控制器设计方法.对MIMO精馏塔系统,给出了可简化求解过程的PI控制器形式.讨论了精馏塔非脆弱鲁棒控制不确定性权函数和性能权函数的选择,求解了H∞非脆弱鲁棒PI控制器.仿真结果表明,该精馏塔控制系统具有较好的适应性.     

精馏塔H_∞非脆弱鲁棒控制的研究

指出了对精馏塔采用高阶常规鲁棒设计的控制器进行降阶所得控制器具有脆弱性,不能保证设计要求的鲁棒性,精馏塔在设计范围内摄动时,系统出现渐扩发散现象。提出将精馏塔控制器摄动转化为被控对象摄动。给出了不需要控制器降阶的精馏塔H∞非脆弱鲁棒PI控制器设计方法。对MIMO精馏塔系统,给出了可简化求解过程的PI控制器形式。讨论了精馏塔非脆弱鲁棒控制不确定性权函数和性能权函数的选择,求解了H∞非脆弱鲁棒PI控制器。仿真结果表明,该精馏塔控制系统具有较好的适应性。     

基于模型降阶的最优分数阶PID控制器设计

由于一些受控对象较为复杂或者模型系统阶次较高,使得控制器的设计变得非常困难,这会造成控制系统的鲁棒性和动态特性下降;文章在H2范数模型降阶的基础上提出一种新的降阶模型结构,它可以使降阶后的模型扩展到分数阶并且更加精确地逼近各种高阶系统,并以降阶后模型的幅频、相频和对象增益变化的鲁棒特性为约束条件进行最优分数阶PID控制器的设计;仿真实验证明,与原有闭环控制系统相比,基于模型降阶的最优分数阶PID控制器控制下的闭环系统具有更好的动态性能,并且鲁棒性较强。     

基于鲁棒可靠性的不确定时滞系统最优H∞控制器设计

用区间变量描述控制系统参数的不确定性,提出了不确定时滞系统鲁棒H_∞控制的鲁棒可靠性方法,基于鲁棒可靠性的不确定时滞系统最优状态反馈H_∞控制器设计方法,将系统的最优控制器设计归结为基于线性矩阵不等式(LMI)的优化问题．所设计的控制器可以在满足对所有不确定性鲁棒可靠的前提条件下,具有最优的H_∞鲁棒性能,并能在控制系统的设计中综合考虑控制性能、控制代价和鲁棒可靠性．数值算例说明了所提方法的有效性和可行性．     

一类多不确定性系统鲁棒H∞控制器的LMI设计方法

对同时具有加型参数不确定性以及积分二次约束(IQC,integral quadratic constraint) 不确定性环节的一类线性系统,给出设计其鲁棒H∞状态反馈控制器和动态输出反馈降阶控制 器的设计方法.在具体推导过程中,首先基于动态耗散理论,考虑了无输入情况下系统只具不 确定性闭环环节时的鲁棒H∞稳定性问题.然后基于这一条件,针对典型的无源类和有限增益 类不确定性,推出了系统同时具有多不确定性时进行鲁棒H∞状态反馈控制器和动态输出反馈降 阶控制器设计的充分条件.所有可解条件都可化为标准的LMI(1inear matrix inequality)求解.     

车辆座椅悬架系统的建模与H∞鲁棒控制研究

建立了四自由度的“车—椅—人”悬架系统动力学和数学模型．运用H∞鲁棒控制理论为车辆座椅悬架系统设计了鲁棒控制器，并且借助Matlab软件对鲁棒控制器和最优控制器的控制性能进行了仿真分析．仿真结果表明：与最优控制器相比所设计的鲁棒控制器能更好地抑制座椅悬架系统的垂直振动加速度，在共振频率附近其减振幅度能达到50%～60%，大大提高了乘坐舒适性，并且该系统能够承受一定的模型参数不确定性，具有良好的鲁棒稳定性．     

一种改进的同伦算法与H∞鲁棒控制器设计

提出了一种具有阶次限制的鲁棒控制器设计方法, 该算法将控制系统的性能指标转化为灵敏度函数问题, 并利用Nevanlinna-Pick插值算法进行求解. 提出了一种改进的同伦算法, 将其用于求解由灵敏度函数产生的非线性方程. 基于改进同伦算法设计的鲁棒控制器 不仅避免了传统H∞控制中加权函数的选择问题, 而且克服了鲁棒控制器阶次较高的缺陷. 最后,文章以4阶系统为例, 设计了具有阶次限制的H∞鲁棒控制器, 通过与传统鲁棒控制器的比较可以看出, 基于本文方法设计的控制器不仅具有较低的阶次, 而且其控制性能也具有明显的优越性.     

全局最优鲁棒控制器设计

研究了一类时变不确定系统,证明了求解全局最优鲁棒性能问题的一线线性矩阵不等式（LMI）,给出了相应的全局最优鲁棒控制器的具体设计方法,并通过算例对控制器的设计作了进一步的说明。     

降阶的鲁棒分散自适应反推控制

针对一类含有未建模动态的关联系统,考虑了降阶的鲁棒分散自适应反推控制问题.首先通过一系列坐标变换,将原系统重新参数化,然后引入降阶观测器,得到一个误差系统.基于该系统,给出了一种降阶自适应反推控制器的设计方案.证明了自适应控制系统的所有信号全局一致有界,调节误差渐近收敛到零.控制器阶次的降低使得本文的设计方案更具应用价值.     

Reduced-Order GPIO Based Dynamic Event-Triggered Tracking Control of a Networked One-DOF Link Manipulator Without Velocity Measurement

In networked robot manipulators that deeply integrate control, communication and computation, the controller design needs to take into consideration the limited or costly system resources and the presence of disturbances/uncertainties. To cope with these requirements, this paper proposes a novel dynamic event-triggered robust tracking control method for a one-degree of freedom (DOF) link manipulator with external disturbance and system uncertainties via a reduced-order generalized proportional-integral observer (GPIO). By only using the sampled-data position signal, a new sampled-data robust output feedback tracking controller is proposed based on a reduced-order GPIO to attenuate the undesirable influence of the external disturbance and the system uncertainties. To save the communication resources, we propose a discrete-time dynamic event-triggering mechanism (DETM), where the estimates and the control signal are transmitted and computed only when the proposed discrete-time DETM is violated. It is shown that with the proposed control method, both tracking control properties and communication properties can be significantly improved. Finally, simulation results are shown to demonstrate the feasibility and efficacy of the proposed control approach.      

Robust stabilization of singularly perturbed nonlinear systems

Consider a singularly perturbed nonlinear system endowed with a control input and suppose a static nonlinear feedback law is designed. We show that the operations ‘compute the reduced order system’ (i.e., let the singular perturbation parameter μ = 0) and ‘close the feedback loop’ commute, i.e. the closed loop reduced-order system is unambiguously determined. We then show that, if the reduced order system associated with the original system is stabilizable or has uncertainties matched with the input (a condition frequently used in the design of robust controllers), then the closed loop reduced-order system enjoys the same property. As shown by an example, this result can be used to simplify the structure of a composite controller.     

Discrete-time sliding mode control of flexible rotor-magnetic bearing systems

This paper is concerned with the computer-based sliding mode control of flexible rotor—magnetic bearing systems (FR-MBS). The plant dynamics consisting of actuator dynamics and flexible rotor dynamics are described. The reduced-order model for controller design is given by eliminating higher-order modes of the mechanical and electrical magnetic interaction system. A discrete-time sliding mode controller with a new robust reduced-order variable structure system (VSS) observer is proposed and its robust performance is evaluated with several simulations based on a calculation model. This digital controller is implemented to replace a linear analogue PID compensator. Levitation tests using the proposed digital controller are performed and compared with those of the PID compensator. The unstable modes can be easily controlled with the good stability and the spillover phenomena due to ignored higher-order modes are not generated. It is indicated that the discrete-time sliding mode control has robustness to the model parameter variations and external disturbances. Using the discrete time sliding mode controller with the reduced-order VSS observer, the test rig of the magnetic bearing system can be successfully rotated in a speed range of 0–35 000 rpm, which includes the first critical shaft frequency of the flexible rotor.     

ISE tuning rule revisited

The integral square error (ISE) method is applied to approximate the internal model control (IMC) system by the PID control system. Simulations show that the proposed method to design PID controllers can relieve some disadvantages of the original ISE method and IMC-based PID controller design methods.     

不确定广义系统的降阶H-infinity控制器设计

研究基于函数观测器的不确定广义系统的降阶H-infinity控制器设计问题. 首先提出了基于严格线性矩阵不等式的不确定广义系统H-infinity控制的充分条件, 并用于状态反馈H-infinity控制设计. 然后对所得控制增益进行降阶观测, 基于广义Sylvester矩阵方程的显式通解, 考虑系统的H-infinity性能约束, 提出了降阶输出反馈控制器的参数化设计方法.     

Computer-aided methods for redesigning the stabilized pitch control system of a semi-active terminal homing missile

An unstable pitch control system of a terminal homing missile was formerly stabilized using a high order stabilization filter that was realized using active elements. A new dominant-data matching method is presented to redesign the high-order stabilization filter for obtaining reduced-order filters. As a result, the implementation cost is reduced and the reliability increased. An algebraic method is also applied to improve the performance of the redesigned pitch control system. In addition, the proposed dominant-data matching method can be applied to determine a reduced-order model of a high-order system. Unlike most existing model reduction methods, the reduced-order model has the exact assigned frequency-domain specifications of the original system. Computer-aided design methods can also be applied to design general control systems.     

Unified optimal projection equations for simultaneous reduced-order,robust modelling,estimation and control

An optimal design problem which unifies reduced-order modelling, estimation and control problems is stated. Necessary conditions for optimality are obtained in the form of a coupled system of modified Riccati and Lyapunov equations. The results permit treatment of several new problems, such as reduced-order dynamic compensation with partially known disturbances and unified reduced-order control and estimation. Upon appropriate specialization, results obtained previously for the individual problems of reduced-order modelling, estimation and control are recovered. An additional feature is the inclusion of parameter uncertainty bounds so that the necessary conditions for an auxiliary minimization problem serve as sufficient conditions for simultaneous robust, reduced-order modelling, estimation and control.     

L1 adaptive control for general partial differential equation (PDE) systems

This paper addresses the L₁ adaptive control problem for general Partial Differential Equation (PDE) systems. Since direct computation and analysis on PDE systems are difficult and time-consuming, it is preferred to transform the PDE systems into Ordinary Differential Equation (ODE) systems. In this paper, a polynomial interpolation approximation method is utilized to formulate the infinite dimensional PDE as a high-order ODE first. To further reduce its dimension, an eigenvalue-based technique is employed to derive a system of low-order ODEs, which is incorporated with unmodeled dynamics described as bounded-input, bounded-output (BIBO) stable. To establish the equivalence with original PDE, the reduced-order ODE system is augmented with nonlinear time-varying uncertainties. On the basis of the reduced-order ODE system, a dynamic state predictor consisting of a linear system plus adaptive estimated parameters is developed. An adaptive law will update uncertainty estimates such that the estimation error between predicted state and real state is driven to zero at each time-step. And a control law is designed for uncertainty handling and good tracking delivery. Simulation results demonstrate the effectiveness of the proposed modeling and control framework.     

不确定LTI-SISO系统的降阶时滞观测器控制

提出了降阶时滞观测器, 利用时滞来观测系统的不确定性和受到的外部干扰, 实现了不确定系统的鲁棒控制. 降阶时滞观测器控制系统中参考模型的阶数由系统的相对阶数决定, 而与系统阶数无关, 简化了控制器的设计, 有利于根据性能指标的要求获得合适的参考模型. 对于相对阶低于系统阶的一般对象, 通过引入低通滤波器也能实现降阶时滞滤波器控制. 大量的仿真结果表明, 降阶时滞观测器能够很好地抑制系统的不确定性和受到的外部干扰, 是一种性能优良的鲁棒控制方法.