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.

Hydrothermal Synthesis of H_3PW_(12)O_(40)/TiO_2 Nanometer Photocatalyst and Its Catalytic Performance for Methyl Orange

H3PW12O40/TiO2 nanometer photocatalyst was prepared by one step hydrothermal synthesis from H3PW12O40·nH20 and Ti（OBu）4, simultaneously realizing the load and modification of H3PW12O40. The catalyst was characterized by Fourier transform infrared spectroscopy（FTIR）, powder X-ray diffraction（XRD）, nitrogen adsorp- tion-desorption analysis and scanning electron microscopy（SEM）. The results show that the catalyst is Keggin struc- ture and crystallized in anatase structure, the diameter and specific area of the prepared catalyst are 3.8 nm and 177.9 m^2/g, respectively, and its dispersity is better. The photocatalytic properties were compared for TiO2H3PW12O40/TiO2 prepared by impregnation and H3PW12O40/TiO2 prepared by hydrothermal method with methyl orange as a probe. The effects of H3PW12O40 loadings, crystallization method, initial pH and concentration of dye solution on the degradation of methyl orange were investigated.

Effect of H_2S Flow Rate and Concentration on Performance of H_2S/Air Solid Oxide Fuel Cell

A solid state H2S/air electrochemical cell having the configuration of H2S, (MoS2+NiS+Ag)/YSZ/Pt, air has been examined with different H2S flow rates and concentrations at atmospheric pressure and 750-850 ℃. Performance of the fuel cell was dependent on anode compartment H2S flow rate and concentration. The cell open-circuit voltage increased with increasing H2S flow rate. It was found that increasing both H2S flow rate and H2S concentration improved current-voltage and power density performance. This is resulted from improved gas diffusion in anode and increased concentration of anodic electroactive species. Operation at elevated H2S concentration improved the cell performance at a given gas flow rate. However, as low as 5% H2S in gas mixture can also be utilized as fuel feed to cells. Highest current and power densities, 17500mA·cm-2 and 200mW·cm-2, are obtained with pure H2S flow rate of 50ml·min-1 and air flow rate of 100ml·min-1 at 850℃.

LMI Approach to Robust H_∞/H_2 Controller Design with Regional Poles Constraint of a Pump-Motor System

The time domain guideposts requirements of a pump-motor system is transfered into a series of constraints which express the robust performance upper bound and regional poles limits of the closed loop system. Then the servo system control problem is transferred into the problem of robust performance optimizing under regional poles constrains described by linear matrix inequality （LMI）. These LMIs are easy to solve through the Matlab LMI-toolbox. Simulations indicate that the controller has excellent dynamic, static and disturbance rejection performance, and the control system is robust and has perfect H2 performance to the bounded external torque disturbance.

Enhanced LMI Representations for H2 Performance of Polytopic Uncertain Systems: Continuous-time Case

Based on two recent results, several new criteria of H2 performance for continuous-time linear systems are established by introducing two slack matrices. When used in robust analysis of systems with polytopic uncertainties, they can reduce conservatism inherent in the earlier quadratic method and the established parameter-dependent Lyapunov function approach. Two numerical examples are included to illustrate the feasibility and advantage of the proposed representations.

Effects of ZnCl2/H2O/C2H5OH Treatment on the Filter Paper Performance

Bleached softwood kraft pulp (BSKP) fibers were pretreated in a 5 mol/L NaOH aqueous solution at 35℃ for 90 min. The ZnCl2/H2O/ C2H5OH was used to treat the pretreated BSKP fibers, filter papers were then prepared. In the course of processing, the effects of various molar ratios of ZnCl2/H2O/C2H5OH on the filter paper performance were evaluated. SEMEDX was conducted to analyze the physical configuration of the filter papers. Moreover, FT-IR and XPS were performed to further characterize the BSKP, the pretreated BSKP and the filter paper fibers. The results indicated that the fibers treated by ZnCl2/H2O/C2H5OH were swollen and exhibited slight fibrillation, leading to a looser fiber structure and therefore, enhanced filter paper performance. Air permeability increased from 161.7 L/(m2·s) to 1450.4 L/(m2·s) for the filter papers when the molar ratio of ZnCl2/H2O/C2H5OH was 1:14:1. The optimum molar ratio of ZnCl2/H2O/C2H5OH was found to be 1:14:1, and no significant effect of ZnCl2/H2O/C2H5OH on fibers’ functional groups was detected. These results showed that filtration performance of filter papers was improved when treated with the ZnCl2/H2O/C2H5OH solution.

H_2和H_∞主动悬架统一的理论框架与比较

以 2自由度 1/ 4车模型为例在鲁棒控制理论的统一框架下讨论H2 和H∞ 主动悬架的设计 ,并采用结构奇异值法和加权最坏RMS增益法对其鲁棒性能进行分析和比较。

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。

混合H_2/H_∞鲁棒控制在飞行控制中的应用

利用混合 H2 / H∞ 鲁棒控制技术 ,研究飞机纵向控制系统的综合问题。针对飞机控制系统含有大量的非线性和不确定因素 ,用混合 H2 / H∞ 鲁棒控制方法设计线性状态反馈控制器 ,使飞机控制系统在鲁棒稳定条件下 ,满足一定的性能指标。在国产某飞机纵向控制系统中的应用表明 ,所提出的方法是实用的和有效的。

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 .

不确定系统混合H_2/H_∞鲁棒控制的直接迭代LMI方法

设计多胞型不确定系统的控制器时,引入附加变量能够减小设计保守性,但这会使线性矩阵不等式(LMI)的维数大大增加,控制器难以求解.本文阐述了一种基于直接迭代线性矩阵不等式(DILMI)方法的混合H2/H∞鲁棒控制方法.首先借助于仿射二次稳定理论将整个多胞型不确定集合的稳定性问题转化为该集合各顶点的稳定性问题.利用参数依赖Lyapunov方法,给出了一个保证系统鲁棒稳定,并满足混合H2/H∞性能指标的充分条件.随后采用DILMI算法实现了Lyapunov变量和控制增益的解耦,无需引入附加变量就能够求解充分条件中的非凸优化问题.最后,关于F-16多胞型模型的飞行仿真验证了该方法的有效性.

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.

Robust H_∞ and H_2 Static Output Feedback Control of Discrete-time Piecewise Affine Singular Systems with Norm-bounded Uncertainties

This paper is concerned with the problem of designing robust H∞and H2static output feedback controllers for a class of discrete-time piecewise-affine singular systems with norm-bounded time-varying parameters uncertainties. Based on a piecewise singular Lyapunov function combined with S-procedure,Projection lemma and some matrix inequality convexifying techniques,sufficient conditions in terms of linear matrix inequalities are given for the existence of an output-feedback controller for the discrete-time piecewiseaffine singular systems with a prescribed H∞disturbance attenuation level,and the H2norm is smaller than a given positive number. It is shown that the controller gains can be obtained by solving a family of LMIs parameterized by one or two scalar variables. The numerical examples are given to illustrate the effectiveness of the proposed design methods.

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.

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).