Mixed sensitivity H_∞ control for LTI systems with varying time delays

Designing a robust controller for a system with timevarying delays poses a major challenge. In this paper, we propose a method based on mixed sensitivity H∞ for the control of linear time invariant（LTI） systems with varying time delays. The time delay is assumed bounded and the upper bound is known. In the technique we propose, the delay affecting the plant to be controlled is treated as an unmodeled uncertainty（in form of multiplicative uncertainty）. That uncertainty is approximated and then an H∞based controller, for the plant represented by the multiplicative uncertainty and the nominal model, is calculated. The obtained H∞controller is used to control the LTI systems with varying time delays. Simulation examples are given to illustrate the effectiveness of the proposed method.

H_∞-Mixed Sensitivity Design of Roll Channel of Bank-to-Turn Autopilot for Small Diameter Bomb

According to requirements of the bank-to-turn (BTT) control for a small diameter bomb (SDB), the robust design problem for the roll autopilot was studied by H∞-mixed sensitivity control method. A roll channel dynamics model was established. Considering the couple between the yaw and roll channel as uncertain disturbance, the roll autopilot was designed using dual-loop scheme which takes a linear quadratic regulator (LQR) as inner-loop, to ensure the control effect of the certain part in model, and an H∞-mixed sensitivity control as outer-loop, to restrain coupling disturbance and strengthen the system's robust performance. The dynamic tracking performance and the robustness for the parameter disturbance of the roll controller were analyzed. The simulated results show that the roll control system functions better and robustly.

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.

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.

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).

Mixed L_1/H-infinity control for uncertain linear singular systems

The mixed L1/H-infinity control problem for a class of uncertain linear singular systems is considered using a matrix inequality approach. The purpose is to design a state feedback control law such that the resultant closed-loop system is regular, impulse-free, stable and satisfies some given mixed L1/H-infinity performance. A sufficient condition for the existence of such control law is given in terms of a set of matrix inequalities by the introduction of inescapable set and ＊-norm. When these matrix inequalities are feasible, an explicit expression of the desired state feedback control law is given. A numerical example is used to demonstrate the applicability of the proposed approach.

H_∞ SYNCHRONIZATION CONTROL OF LINEAR SYSTEMS AND ITS APPLICATION TO WAFER-RETICAL STAGE

For the outputs of two nth-order linear control systems to work insynchronization and meanwhile to track their commands, a H_(infinity) synchronization control schemeis presented. In terms of two uncoupled single variable linear systems, a multivariable coupledsystem is established by choosing one output and the difference of the two outputs as a new outputvector, so that both command tracking and synchronization properties can be demonstrated by aH_(infinity) performance index. To improve the synchronization and trailing performance and toguarantee the system robust stability, the mixed sensitivity H_(infinity), design methodology isadopted. The presented synchronization scheme is then extended to the case where one of the twosystems include two input variables, and then applied to the position synchronization control of awafer-retical stage. The wafer-reticle stage consists of a wafer stage, a reticle coarse stage, anda reticle fine stage. The reticle coarse stage picks up the reticle fine stage. The three stagesought to tack their commands, but synchronization between the wafer stage and the reticle fine stagemust be stressed in the tracking process. In the application, by appropriately determining theweighting matrices for the sensitivity function and the complementary sensitivity function, asatisfactory KL synchronization controller is obtained to realize highly accurate positionsynchronization, and to guarantee tracking performance. The above results are verified by simulationexperiments.

H_∞ Control of Bio-dissimilation Process of Glycerol to 1,3-Propanediol

A robust controller is designed by using the bilinear transformation and H∞ mixed sensitivity method for bio-dissimilation process of glycerol to 1,3-propanediol. Under the controller the system works near an optimal steady-state for the volumetric productivity of 1,3-propanediol attaining its maximization. The design procedure is carried out by tuning the transformation parameter and DC gain of the performance weighted function, which is an iterative and optimal search process. Simulation results are presented which show that the designed robust controller not only ensures the robust stability of the system in face of the parametric variations in the model, but also makes the system have a favourable robust tracking performance. The validity of the proposed H∞ controller has been tested.

Soft initial-rotation and H_∞ robust constant rotational speed control for rotational MEMS gyro

A novel soft initiai-rotation control system and an H∞ robust constant rotational speed controller （RCRSC） for a rotational MEMS （micro-electro-mechanical system） gyro are presented. The soft initial-rotation control system can prevent the possible tumbling down of the suspended rotor and ensure a smooth and fast initial-rotation process. After the initial-rotation process, in order to maintain the rotational speed accurately constant, the RCRSC is acquired through the mixed sensitivity design approach. Simulation results show that the actuation voltage disturbances from the internal carrier waves in the gyro is reduced by more than 15.3 dB, and the speed fluctuations due to typical external vibrations ranging from 10 Hz to 200 Hz can also be restricted to 10^-3 rad/s order.

H_∞ control design for unstable plants

For the control of unstable plants,it is required that the Nyquist locus of the system should encircle anticlockwise the point-1+j0,and the performance weighting function must be selected based on the specific requirement of the mid-frequency gain. Besides,the performance limitation imposed by the Bode's integral also must be considered. Therefore the H∞ design for unstable plants is different from that in the regular case. It is pointed out that the sensitivity function for unstable plants must remain constant over the mid-frequency range to ensure a robust design. The selection of weighting functions to meet these requirements in the H∞ design is discussed in detail in the paper. A mixed sensitivity H∞ design example is also given to demonstrate the special considerations of the design.

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.

基于H_∞鲁棒控制的挠性卫星姿态控制

针对存在未建模动态、模型参数不确定性和外力矩扰动的挠性卫星,通过选择合适的加权函数将挠性卫星姿态控制问题转化为H∞混合灵敏度问题。采用H∞优化方法设计了鲁棒控制器。最后对卫星姿态控制系统进行了仿真研究,结果表明采用鲁棒控制器的姿控系统较传统的PID控制的姿控系统具有更好的鲁棒稳定性和抗干扰性能。

热连轧卷取机踏步系统鲁棒H_∞控制研究

针对热连轧过程中的带头损失问题,开发带有位置调节和压力调节的步进式电液伺服系统,并应用一种简化的H∞控制混合灵敏度算法对系统进行闭环增益设定,其核心是确定闭环系统传递函数即T的最终希望的形状,直接设计出K,从而避免了权函数的选择。研究结果表明用此法设计的H∞控制器对于步进控制系统是有效的。

基于H_∞混合灵敏度方法的超声波电机调速控制

为提高行波型超声波电机转速跟踪的准确性和平稳性,改善因调频调速非线性带来的调速性能变化,将H∞混合灵敏度方法应用于转速控制器的设计.采用参数辨识法建立电机的频率转速模型,线性化得到电机的标称模型,将静态模型的非线性转化为标称模型的增益摄动,将动态模型的参数变化转化为标称模型的高阶未建模误差,把电机的转速模型表示为标称模型与误差模型和.根据模型误差界和调速性能指标,求取混合灵敏度加权函数,将控制器设计转化为标准的H∞优化问题,通过Matlab工具求解鲁棒控制器.仿真验证了转速闭环的稳定鲁棒性,使用数字信号处理芯片TMS320F28335在实际控制回路中实现该控制器,并测试电机调速性能.实验结果表明,鲁棒控制器应用于超声波电机调速系统可以取得良好的控制效果.

磁悬浮球的H_∞控制研究

设计了一种磁悬浮球实验系统,建立了磁悬浮球的控制模型。基于H∞混合灵敏度控制理论,研究了加权阵的选取规律和方法,设计了磁悬浮球的H∞鲁棒控制器。开发了功率驱动系统和光电位置检测系统,并用DSP系统实现了H∞控制算法。仿真分析和实验结果表明:该磁悬浮系统具有较高的控制精度和鲁棒性,解决了磁悬浮系统中的建模精度低,外界干扰难以避免等棘手问题。

H_∞控制器应用于船舶自动舵

应用Ｈ∞控制的Ｓ／Ｔ混合灵敏度方法于船舶自动舵设计。按机理估算模型乘性摄动上限，据此确定优化指标中的权函数Ｗ２。利用设计的控制器对闭环系统在多种环境条件下进行了仿真研究，结果是满意的。

H_∞混合灵敏度控制在液压伺服系统中的应用

运用 H∞ 混合灵敏度控制理论 ,针对液压伺服系统的特点 ,通过仿真 ,总结了一般加权阵的选取规律和方法 ,提出采用线性矩阵不等式设计典型电液位置伺服系统 H∞ 控制器的计算方法 ,并设计了控制器 ,使系统在保证鲁棒稳定性的同时可以确保系统的瞬态性能指标。通过设计举例说明了控制器的设计方法 ,并通过与原系统参数摄动时系统特性的比较 ,验证了 H∞控制器不仅可以提高系统的频宽 ,改善系统的响应速度 ,而且可以改善参数变化对系统性能的影响 ,从而说明了 H∞ 控制器的有效性。

机翼颤振的混合灵敏度H_∞鲁棒控制器设计

主动颤振抑制技术是未来弹性飞行器设计中的一项关键技术,越来越受到广泛的关注。但传统的LQG方法鲁棒性很差,限制了其实际应用。本文采用混合灵敏度H∞控制方法,并结合回路成型技术设计了机翼颤振抑制的鲁棒控制器。此方法直接针对回路的灵敏度函数和补灵敏度函数性质,根据颤振抑制系统期望的回路频域特性要求,通过选择合适的加权函数形状获得了满意的闭环系统性能,从而实现对颤振的鲁棒抑制。其特点是能够方便直观的获得系统所期望的频域性能,并具有良好的鲁棒性和抑噪能力,非常有利于工程实用。最后利用典型的二维机翼俯仰沉浮气动弹性系统模型,分别采用混合灵敏度H∞控制器和LQG控制器对机翼颤振进行抑制。仿真结果表明,本文所设计的控制器将颤振速度提高了12.2%,能够更加有效地抑制机翼颤振。

天线指向机构位置伺服的H_∞-PID控制研究

针对大型卫星天线指向机构高精度高可靠性的要求,研制了一种永磁同步电机驱动的新型天线指向机构。在建立双质量体驱动模型的基础上,以ITAE(时间乘以误差绝对值积分)为优化指标,在H∞混合灵敏度约束下PID参数的稳定域内,采用遗传算法对PID控制器的参数进行了优化。最后采用优化的PID控制器对指向机构进行了控制仿真和实验验证,结果表明系统具有响应快速而平稳、抗负载扰动和模型误差能力强的特点。

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。