时滞相关非脆弱鲁棒静态输出反馈控制策略及其在主动悬架中的应用
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摘要
静态输出反馈(SOF)控制器因其结构简单而需要的在线计算工作量很少，从而可以降低控制器实现成本，但其求解较难。因此SOF控制器设计问题是控制理论和应用中最重要的研究焦点之一。众所周知，在包括车辆主动悬架在内的多种工程系统的设计过程中，被控对象的不确定性和系统的时滞是通常遇到的问题。容许控制器本身不确定性的非脆弱控制问题研究具有十分重要的理论和实践意义。在车辆主动悬架系统的设计中最重要的是控制策略，主动悬架的总体性能取决于控制策略。因此，为了改善车辆乘坐舒适性、行驶平顺性和操纵稳定性等性能，应该设计出性能良好的控制器。
本文结合教育部新世纪优秀人才资助计划项目“惯性调控主动/半主动悬架技术研究”，针对具有输入时滞的不确定系统，直接而有效地设计时滞相关非脆弱鲁棒多目标SOF控制器，并通过应用于车辆主动悬架系统，验证本文所提出的设计方法在实际应用中的可行性和有效性。本文的研究工作内容包括以下几个方面：
1)为了设计SOF控制器，提出了有效地求解双线性矩阵不等式（BMI）问题的新型PSO-DE/LMI优化算法，然后以车辆主动悬架H∞SOF控制和H2SOF控制为研究对象，验证了此算法的可行性和有效性。
2)在多目标控制框架下，通过对混合H2/H∞控制问题、主动悬架H∞/L2-L∞SOF控制及H2/L2-L∞SOF控制的研究，进一步验证了基于PSO-DE/LMI优化算法的多目标SOF控制器设计方法的有效性。
3)基于Lyapunov-Krasovskii方法以BMI形式分别提出了新的时滞相关鲁棒H∞SOF控制器和L2-L∞SOF控制器的存在条件，利用这些条件和PSO-DE/LMI算法设计了时滞相关鲁棒H∞/L2-L∞SOF控制器，通过将此方法应用于车辆主动悬架系统仿真分析，验证了控制器的控制效果。
4)考虑到控制器本身的摄动，分别获得了BMI形式的时滞相关非脆弱鲁棒H∞SOF控制器和L2-L∞SOF控制器的存在条件，然后采用PSO-DE/LMI算法对主动悬架系统设计了控制器，并验证了得到的控制器的可行性和有效性。
本文还通过在频域和时域中与以往的设计方法进行详细的对比分析，对所提出的控制器设计方法的有效性及实用性进行了验证。此外，针对车辆主动悬架系统，通过机械系统动力学仿真分析软件ADMAS与MATLAB/Simulink的联合仿真，进一步验证了所提出的控制器设计方法的有效性。
Static output feedback (SOF) controller requires a small amount of onlinecomputational effort due to the simplicity of the structure. Consequently, it can reducethe cost of the controller implementation, but it is difficult to be solved. Therefore, thedesign of SOF controller is one of the most important problems in the control theoryand application. Moreover, as is well-known, model uncertainties and time-delay arecharacteristics that are commonly encountered in various engineering system, such asvehicle active suspension system. On the other hand, a study of a non-fragile controlthat can tolerate some level of controller parameter variations is theoretically andpractically significant. A key point of the vehicle active suspension system design toimprove the ride comfort is control strategy, and its effectiveness in relation to theperformance of active suspension system. Thus, the controller design of the activesuspension system with good performance to improve vehicle ride comfort andhandling stability has a very important significance.
The main research topic of this paper is to directly and effectively design adelay-dependent non-fragile robust multi-objective SOF controller for an uncertainsystem with input time-delay, and verify the feasibility and effectiveness of theproposed design approach by application to design an active suspension system.Detailed research contents are as follows:
1) In order to design a SOF controller, this paper presents a new PSO-DE/LMIoptimization algorithm that can solve a bilinear matrix inequality (BMI) problemeffectively, and then verifies the feasibility and effectiveness of this algorithm byapplication to design H∞SOF controller and H2SOF controller of the active suspension system.
2) In the framework of a multi-objective control, a design approach of themulti-objective SOF controller based on the PSO-DE/LMI algorithm is validatedfurther by H∞/L2-L∞SOF control and H2/L2-L∞SOF control for the active suspensionsystem.
3) By employing a Lyapunov-Krasovskii method, new existence conditions ofdelay-dependent robust H∞SOF controller and L2-L∞SOF controller are derivedrespectively in terms of the feasibility of BMIs，and then a delay-dependent H∞/L2-L∞SOF controller is designed by using these existence conditions and the PSO-DE/LMIoptimization algorithm. Moreover, the proposed controller design approach is verifiedby application to active suspension system.
4) By considering a controller itself perturbation, this paper presents newexistence conditions of delay-dependent non-fragile robust H∞SOF controller andL2-L∞SOF controller are derived respectively in terms of the feasibility of BMIs，andthen a delay-dependent non-fragile robust H∞/L2-L∞SOF controller is designed byusing these existence conditions and the PSO-DE/LMI optimization algorithm. Inaddition, the feasibility and effectiveness of the obtained controller is validated byapplication to design an active suspension system.
This paper validated the practicability and validity of the proposed controlstrategies through the contrastive analysis in frequency domain and time domain withprevious design methods. In addition, aimed at the vehicle active suspension system,further validated the effectiveness of the proposed controller design approach byadopting the joint simulation of the dynamics simulation and analysis software ofmechanical system ADAMS and MATLAB/Simulink.
本文结合教育部新世纪优秀人才资助计划项目“惯性调控主动/半主动悬架技术研究”，针对具有输入时滞的不确定系统，直接而有效地设计时滞相关非脆弱鲁棒多目标SOF控制器，并通过应用于车辆主动悬架系统，验证本文所提出的设计方法在实际应用中的可行性和有效性。本文的研究工作内容包括以下几个方面：
1)为了设计SOF控制器，提出了有效地求解双线性矩阵不等式（BMI）问题的新型PSO-DE/LMI优化算法，然后以车辆主动悬架H∞SOF控制和H2SOF控制为研究对象，验证了此算法的可行性和有效性。
2)在多目标控制框架下，通过对混合H2/H∞控制问题、主动悬架H∞/L2-L∞SOF控制及H2/L2-L∞SOF控制的研究，进一步验证了基于PSO-DE/LMI优化算法的多目标SOF控制器设计方法的有效性。
3)基于Lyapunov-Krasovskii方法以BMI形式分别提出了新的时滞相关鲁棒H∞SOF控制器和L2-L∞SOF控制器的存在条件，利用这些条件和PSO-DE/LMI算法设计了时滞相关鲁棒H∞/L2-L∞SOF控制器，通过将此方法应用于车辆主动悬架系统仿真分析，验证了控制器的控制效果。
4)考虑到控制器本身的摄动，分别获得了BMI形式的时滞相关非脆弱鲁棒H∞SOF控制器和L2-L∞SOF控制器的存在条件，然后采用PSO-DE/LMI算法对主动悬架系统设计了控制器，并验证了得到的控制器的可行性和有效性。
本文还通过在频域和时域中与以往的设计方法进行详细的对比分析，对所提出的控制器设计方法的有效性及实用性进行了验证。此外，针对车辆主动悬架系统，通过机械系统动力学仿真分析软件ADMAS与MATLAB/Simulink的联合仿真，进一步验证了所提出的控制器设计方法的有效性。
Static output feedback (SOF) controller requires a small amount of onlinecomputational effort due to the simplicity of the structure. Consequently, it can reducethe cost of the controller implementation, but it is difficult to be solved. Therefore, thedesign of SOF controller is one of the most important problems in the control theoryand application. Moreover, as is well-known, model uncertainties and time-delay arecharacteristics that are commonly encountered in various engineering system, such asvehicle active suspension system. On the other hand, a study of a non-fragile controlthat can tolerate some level of controller parameter variations is theoretically andpractically significant. A key point of the vehicle active suspension system design toimprove the ride comfort is control strategy, and its effectiveness in relation to theperformance of active suspension system. Thus, the controller design of the activesuspension system with good performance to improve vehicle ride comfort andhandling stability has a very important significance.
The main research topic of this paper is to directly and effectively design adelay-dependent non-fragile robust multi-objective SOF controller for an uncertainsystem with input time-delay, and verify the feasibility and effectiveness of theproposed design approach by application to design an active suspension system.Detailed research contents are as follows:
1) In order to design a SOF controller, this paper presents a new PSO-DE/LMIoptimization algorithm that can solve a bilinear matrix inequality (BMI) problemeffectively, and then verifies the feasibility and effectiveness of this algorithm byapplication to design H∞SOF controller and H2SOF controller of the active suspension system.
2) In the framework of a multi-objective control, a design approach of themulti-objective SOF controller based on the PSO-DE/LMI algorithm is validatedfurther by H∞/L2-L∞SOF control and H2/L2-L∞SOF control for the active suspensionsystem.
3) By employing a Lyapunov-Krasovskii method, new existence conditions ofdelay-dependent robust H∞SOF controller and L2-L∞SOF controller are derivedrespectively in terms of the feasibility of BMIs，and then a delay-dependent H∞/L2-L∞SOF controller is designed by using these existence conditions and the PSO-DE/LMIoptimization algorithm. Moreover, the proposed controller design approach is verifiedby application to active suspension system.
4) By considering a controller itself perturbation, this paper presents newexistence conditions of delay-dependent non-fragile robust H∞SOF controller andL2-L∞SOF controller are derived respectively in terms of the feasibility of BMIs，andthen a delay-dependent non-fragile robust H∞/L2-L∞SOF controller is designed byusing these existence conditions and the PSO-DE/LMI optimization algorithm. Inaddition, the feasibility and effectiveness of the obtained controller is validated byapplication to design an active suspension system.
This paper validated the practicability and validity of the proposed controlstrategies through the contrastive analysis in frequency domain and time domain withprevious design methods. In addition, aimed at the vehicle active suspension system,further validated the effectiveness of the proposed controller design approach byadopting the joint simulation of the dynamics simulation and analysis software ofmechanical system ADAMS and MATLAB/Simulink.
引文
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