Tracking Performance of Electric Power Steering System Based on the Mixed H_2/H_∞ Strategy

The tracking performance of motor current is an important factor that affects the assistance torque of electric power steering （EPS） system. Bad tracking performance will cause assistant torque delay, and make road feeling bad, and is influenced by the input steering torque and system measuring noise. However the existing methods have some shortages on system＇s robust dynamic performance and robust stability. The mixed H2/H∞ strategy for recirculating ball-type EPS system in a pure electric bus is proposed, and vehicle dynamic model of the system is established. Due to the existence of system model uncertainty, disturbance signals, sensor noises and the demand of system dynamic performance, the indexes of robust performance and road feeling for drivers are defined as the appraisal control objectives. The H∞ method is introduced to design the H∞ controller, and the H2 method is applied to optimize the H∞ controller, thus the mixed H2/H∞ controller is designed. The response of EPS system to the motor current command with amplitude of 20 A, the road disturbance with amplitude of 500 N and the sensor random noise with the amplitude of 1 A is simulated. The simulation results show that the recirculating ball-type EPS system with the mixed H2/H∞ controller can attenuate the random noises and disturbances and track the boost curve well, so the mixed H2/H∞ controller can improve the system＇s robust performance and dynamic performance. For the purpose of verifying the performance of the designed control strategy, the motor current tracking performance ground tests are conducted with step response input of the steering wheel, double-lane steering test and lemniscate steering test, respectively. The tests show that the mixed H2/H∞ controller for the recirculating ball-type EPS system of pure electric bus is feasible. The designed controller can solve the robust performance and robust stability of the system, thus improve the tracking performance of the EPS system and provide satisfied road feeling for the drivers.

A new semi-active suspension control strategy through mixed H_2/H_∞ robust technique

A new semi-active suspension control strategy through mixed H2/H∞ robust technique was developed due to its flexibility and robustness to model uncertainties.A full car model with seven degrees of freedom was established to demonstrate the effectiveness of the new control approach.Magneto-rheological(MR) dampers were designed,manufactured and characterized as available semi-active actuators in the developed semi-active suspension system.The four independent mixed H2/H∞ controllers were devised in order to perform a distributed semi-active control system in the vehicle by which the response velocity and reliability can be improved significantly.The performance of the proposed new approach was investigated in time and frequency domains.A good balance between vehicle's comfort and road holding was achieved.An effective and practical control strategy for semi-active suspension system was thus obtained.This new approach exhibits some advantages in implementation,performance flexibility and robustness compared to existing methods.

Mixed H_2/H_∞ State Feedback Attitude Control of Microsatellite Based on Extended LMI Method

For the appearance of the additive perturbation of controller gain when the controller parameter has minute adjustment at the initial running stage of system,to avoid the adverse effects,this paper investigates the mixed H_2/H_∞ state feedback attitude control problem of microsatellite based on extended LMI method.Firstly,the microsatellite attitude control system is established and transformed into corresponding state space form.Then,without the equivalence restriction of the two Lyapunov variables of H_2 and H∞performance,this paper introduces additional variables to design the mixed H_2/H_∞ control method based on LMI which can also reduce the conservatives.Finally,numerical simulations are analyzed to show that the proposed method can make the satellite stable within 20 s whether there is additive perturbation of the controller gain or not.The comparative analysis of the simulation results between extended LMI method and traditional LMI method also demonstrates the effectiveness and feasibility of the proposed method in this paper.

汽车四轮转向系统的H_2/H_∞混合控制

为使汽车四轮转向系统具有良好的鲁棒性和干扰抑制性能 ,针对外界干扰 ,对汽车四轮转向系统模型进行了分析 ,并将其转化为H2 /H∞ 控制问题 ,运用Matlab的LMI控制工具箱设计了H2 /H∞ 混合最优控制器。仿真结果表明 ,设计的最优控制器具有良好控制效果。

A SISO mixed H2／l1 optimal control problem and its solution

Study of the SISO mixed H2/l1 problem for discrete time systems showed that there exists a unique optimal solution which can be approximated within any prescribed missing error bound in l2 norm with solvable suboptimal solutions and solvable superoptimal solutions.

Approximation methods of mixed l_1/H_2 optimization problems for MIMO discrete-time systems

The mixed l1/H2 optimization problem for MIMO (multiple input-multiple output) discrete-time systems is considered. This problem is formulated as minimizing the l1-norm of a closed-loop transfer matrix while maintaining the H2-norm of another closed-loop transfer matrix at prescribed level. The continuity property of the optimal value in respect to changes in the H2-norm constraint is studied. The existence of the optimal solutions of mixed l1/H2 problem is proved. Because the solution of the mixed l1/H2 problem is based on the scaled-Q method, it avoids the zero interpolation difficulties. The convergent upper and lower bounds can be obtained by solving a sequence of finite dimensional nonlinear programming for which many efficient numerical optimization algorithms exist.

一类非线性动态系统的混合H_2/H_∞模糊输出反馈跟踪控制

讨论一类非线性动态系统的混合H2/H∞模糊输出反馈跟踪控制问题。首先利用T-S模糊模型对系统进行建模,然后设计基于观测器的控制器,使跟踪误差尽可能的小,并且对于任何有界参考输入,满足给定的H∞跟踪性能,以及在满足给定的H∞跟踪性能下,达到H2次优控制性能,最后将观测器与控制器的设计问题转化为EVP(特征值问题)。

On the Dual of a Mixed H_2/l_1 Optimisation Problem

The general discrete-time Single-Input Single-Output （SISO） mixed H2/l1 control problem is considered in this paper. It is found that the existing results of duality theory cannot be directly applied to this infinite dimension optimisation problem. By means of two finite dimension approximate problems, to which duality theory can be applied, the dual of the mixed H2/l1 control problem is verified to be the limit of the duals of these two approximate problems.

H_2/H_∞混合优化问题综述

H2 /H∞ 混合优化设计方法由于其可以使系统同时获得较好的鲁棒稳定性和鲁棒性能 ,一经提出 ,立即受到研究者的广泛关注 .本文综述了 H2 /H∞ 混合优化方法的产生、发展及其特点 ,概要介绍了 H2 /H∞ 优化理论研究的最新进展及实践应用的主要结果 ,分析了 H2 /H∞ 混合优化理论在理论和实际应用中的发展方向 .

建筑结构振动主动控制的H_2/H_∞混合凸优化方案

在地震信号和建筑结构系统的范数分析基础上,使用了混合控制优化指标J作为优化目标,并给出其物理含义·针对H2控制方案和H∞控制方案的优缺点,通过LMI凸优化方法求解混合控制器,给出了在给定γ值的前提下极小化指标J的H2/H∞混合控制方案,并给出了仿真算例·

Growth of Mixed Rare Earth Tartrate Crystals (Y_(1-x)Sm_x)_2(C_4H_4O_6)_3·zH_2O from Silica Gels

Experiments performed on the grwth of mixed crystals of rare earth tartrates (Y1-xSmx)2 (C4H4O6)3.zH2O (0≤x≤1) from silica gels at 35~40℃ and 25~30℃ employing single-diffusion technique. are discussed. The crystals maintain spherulitic morphology, irrespective of the value of x, concentration of upper and lower reactants, gel pH, gel age and gel temperature. Formation Of Liesegang rings in this system is a temperature dependent phenomenon. It is shown that with the increase of the value of x the system passes from Liesegangring phenomenon to singlezone phenomenon. Operative mechanism of crystallization in the higher (35~40℃) and lower temperature ranges (25~30℃) is explained. Seeded growth experiments indicate the possibility of increasing the size of the spherulites in the gel medium

Designing mixed <i>H</i>₂/<i>H</i>_&infin;structure specified controllers using Particle Swarm Optimization (PSO) algorithm

This paper proposes an efficient method for designing accurate structure-specified mixed H2/H∞ optimal controllers for systems with uncertainties and disturbance using particle swarm (PSO) algorithm. It is designed to find a suitable controller that minimizes the performance index of error signal subject to an unequal constraint on the norm of the closed-loop system. Although the mixed H2/H∞ for the output feedback approach control is considered as a robust and optimal control technique, the design process normally comes up with a complex and non-convex optimization problem, which is difficult to solve by the conventional optimization methods. The PSO can efficiently solve design problems of multi-input-multi-output (MIMO) optimal control systems, which is very suitable for practical engineering designs. It is used to search for parameters of a structure-specified controller, which satisfies mixed performance index. The simulation and experimental results show high feasibility, robustness and practical value compared with the conventional proportional-integral-derivative (PID) and proportional-Integral (PI) controller, and the proposed algorithm is also more efficient compared with the genetic algorithm (GA).

H_2/H_∞混合控制在双振动台解耦控制中的应用

研究了基于Η2 /Η∞ 混合控制的振动台解耦控制器的设计方法 ,用缩减了高阶模态的降阶模型所设计的控制器对原系统进行解耦控制 ,引入了模型不确定性 ,克服了传统的基于模型逆的解耦控制系统鲁棒性能较差的缺点。利用双自由度控制结构的特点 ,将问题分解为Η2 和 H∞两个最优控制器的设计过程 ,简化了问题求解的复杂性 ;通过整形技术提高了解耦控制的效果。与单步设计方法相比 ,这一双步设计方法更容易实现也更具有灵活性 ,能进一步提高系统的控制性能。仿真结果表明混合Η2 /Η∞解耦控制方法不仅具有良好的解耦性能 。

Enhancement of Ride Quality of Quarter Vehicle Model by Using Mixed H2/H with Pole-Placement

The aim of the present work is to illustrate the application of mixed H2/H∞ control theory with Pole-Placement in de- signing controller for semi-active suspension system. It is well known that the ride comfort is improved by reducing vehicle body acceleration generated by road disturbance. In order to study this phenomenon, Two Degrees of Freedom (DOF) in state space vehicle model was built in. However, the role of H is to minimize the disturbance effect on the output while H2 is used to improve the input of controller. Linear Matrix Inequality (LMI) technique is used to calculate the dynamic controller parameters. The simulation results show that the H2 and H techniques can effectively control the vibration of vehicle system where the reduction of suspension working space, dynamic tire load and body acceleration. Moreover, the simulation results show that the (RMS) of suspension working space was reduced by 44.5%, body acceleration and dynamic tire load are reduced by 18.5% and 20% respectively.

巡航导弹成像器稳定装置H_2/H_∞混合最优PID控制器设计

本文针对某巡航导弹成像器稳定装置同时在鲁棒稳定性和系统性能有着很高要求的特点 ,采用H2 /H∞ 混合优化的设计方法设计了H2 /H∞ 混合最优PID控制器。仿真和实验结果表明采用该设计方法设计的巡航导弹成像器稳定装置满足性能要求 ,而且比采用H∞

固定结构混合H_2/H_∞控制器参数的全局优化

首先运用增广 Hermite- Biehler定理 ,解析地给出使任意给定 (稳定或不稳定 )被控对象闭环稳定的控制器参数取值域 .然后 ,在该参数取值域内运用遗传优化算法得到了满足指定混合 H2 / H∞ 性能指标的 Pareto最优控制器参数值 .仿真例子验证了该方法的有效性 .

Syntheses, Characterization and Biological Activity of Coordination Compounds of 3-Hydroxy-2-methyl-4<i>H</i>-pyran-4-one and Its Mixed Ligand Complexes with 1,2-Diaminocyclohexane

Coordination compounds of 3-hydroxy-2-methyl-4H-pyran-4-one with iron(III), cobat(III) and chromium(III) were synthesized with M:L (1:2). Mixed ligand coordination compounds of 3-hydroxy-2-methyl-4H-pyran-4-one and 1,2-diaminocyclohexane using the same metal ions were also synthesized M:L1:L2 (1:1:1) where L1 is 3-hydroxy-2-methyl-4H-pyran-4-one and L2 is 1,2-diaminocyclohexane. The coordination compounds obtained were characterized using electronic and infrared spectral analyses, magnetic susceptibility and percentage metal analysis. They were also evaluated for their cytotoxic and antioxidant activities. The result obtained suggested that octahedral geometry was obtained for all the compounds, as a result of additional two molecules of the solvent coordinated to the metal ions. Both the primary and secondary ligands coordinated in a bidentate fashion. The synthesized compounds exhibited moderate cytotoxicity, although none was as active as the standard. The cobalt(III) mixed ligand complex elicited the highest activity. The synthesized compounds all exhibited good to moderate antioxidant activity.

土木工程结构抗震主动控制H_2/H_∞混合优化设计

将地震信号分解为有界集合描述的确定性部分和随机变量数字特征描述的不确定部分 ,在地震信号和结构系统的范数分析基础上 ,使用了混合控制优化指标J作为优化目标 ,并给出其物理含义。针对H2 控制方案和H∞ 控制方案的优缺点 ,给出了在给定γ值的前提下极小化指标J的H2 H∞ 混合控制方案 。

H_2/H_∞组合方法及其对导弹纵向运动的控制分析

在对Ｈ２／Ｈ∞组合控制问题描述和分析的基础上，总结了此类问题的一种求解算法，即转换为双线性矩阵不等式问题，通过迭代运算加以求解。以某型导弹纵向运动的控制为例，对Ｈ２／Ｈ∞组合算法进行了仿真计算，结果表明，该方法在一定程度上协调了系统的Ｈ２及Ｈ∞设计任务间的矛盾，使得所设计控制系统不但有着要求的噪声抑制能力，而且具有良好的鲁棒稳定性。

基于LMI的磁悬浮列车姿态H_∞/H_2混合控制

针对目前新型的单轨磁悬浮列车姿态控制问题 ,建立了磁悬浮列车姿态的状态空间模型 .在对该模型进行线性化后 ,设计了基于 LMI的 H∞ /H2 混合控制器 ,有效地控制了列车运行时发生的车厢上下振动及其倾斜 .通过系统仿真 ,得到此种控制器具有良好的控制性能 .