时滞系统的最优减振控制及在汽车悬挂系统中的应用研究
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摘要
本文首先综述了国内外关于时滞系统、非线性系统以及减振控制的研究方法、现状及成果；然后研究了线性时滞系统、非线性时滞系统的最优减振控制问题,给出了最优减振控制律及其存在唯一性条件和次优控制律,讨论了其物理可实现问题；并将所得到的结果利用汽车悬挂模型进行仿真实验。全文主要研究内容概括如下：
1、提出一种模型转换的方法,将时滞系统转换为形式上无时滞的系统,简化了求解最优控制的问题；然后通过求解矩阵方程,得到带有控制记忆项的最优控制律,补偿了时滞对系统产生的影响。
2、运用前馈控制的原理,对于已知动态特性、但未知初始条件的外部持续扰动,通过前馈-反馈控制器中所设计的前馈补偿项,消除或减弱扰动对系统的影响；通过设计状态降维观测器确保前馈控制的物理可实现性以及解决系统状态不完全可测的问题。
3、将模型转换与逐次逼近的方法拓展到设计非线性时滞系统最优减振控制律中,得到的最优控制律由精确反馈项、前馈控制项、时滞记忆项和伴随向量序列极限形式的补偿项组成,其中,反馈和前馈增益矩阵是通过求解Riccati和Sylvester矩阵方程得到,伴随向量补偿项是通过逐次逼近的迭代求解过程而获得。同时给出了次优控制律,它是通过截取伴随向量序列的有限次迭代值而得到。
4、将所设计的最优减振控制律用于汽车悬挂系统减振控制的仿真实验中。分别利用四分之一车、半车以及整车悬挂系统的动力学方程,建立了状态空问表示；建立了路面激励的外系统模型。通过对实际模型参数的数值仿真,验证所设计的减振控制律能够使各项性能指标达到最佳状态,确保了设计方法的有效性。
In this paper, firstly, the relative studies and results on the problem of optimal vibration control (OVC) for time-delay systems, nonlinear systems, and vibration control up to now are given in detail. Then the design of OVC law for time-delay systems and nonlinear time-delay systems are considered. The extence and uniqueness of the OVC law are studied and a suboptimal control law is given. The physical realization problem is discussed. The results are applied into simulations on suspension models to prove their effectiveness. The main contents are presented as follows.
1. The approach named model transformation for time-delay systems is introduced. The time-delay systems are transformed into equivalent nondelayed systems in form. The optimal control law is derived by solving Riccati and Sylvester equations. And the effects produced by the delays are compensated by the control memory term.
2. The theory of feedforward control is applied. For the disturbances with known dynamics and unknown initial conditions, the feedforward and feedback control law is designed, in which the feedforward control term compensates for the effects produce by disturbances. A reduced-order state observer is constructed to make the feedforward control physically realizable and solve the problem of unmeasured states.
3. For the nonlinear time-delay systems, the model transformation and successive approximation approach (SAA) are extended to design the OVC law. The OVC law obtained consists of accurate linear feedback, feedforward terms, memory terms for time-delays, and a nonlinear compensation term which is the limit of the adjoint vector sequence. The former can be obtained by solving a Riccati equation and a Sylvester equation, and the latter can be got by solving the linear nonhomogeneous sequences using SAA. Using a finite-step iteration of the adjoint vector among optimal solution sequence, a suboptimal control law can be obtained.
4. The designed control laws are applied to the numerical simulations on vibration control for suspension models. The state-space representations for a quarter-car model, a half-car model, and a full-car model are given based on their dynamical equations. The exosystems describing road vibrations are established. And the simulations results demonstrate the performances of car achive expected objectives and verify the effectiveness of desiged optimal control laws.
1、提出一种模型转换的方法,将时滞系统转换为形式上无时滞的系统,简化了求解最优控制的问题；然后通过求解矩阵方程,得到带有控制记忆项的最优控制律,补偿了时滞对系统产生的影响。
2、运用前馈控制的原理,对于已知动态特性、但未知初始条件的外部持续扰动,通过前馈-反馈控制器中所设计的前馈补偿项,消除或减弱扰动对系统的影响；通过设计状态降维观测器确保前馈控制的物理可实现性以及解决系统状态不完全可测的问题。
3、将模型转换与逐次逼近的方法拓展到设计非线性时滞系统最优减振控制律中,得到的最优控制律由精确反馈项、前馈控制项、时滞记忆项和伴随向量序列极限形式的补偿项组成,其中,反馈和前馈增益矩阵是通过求解Riccati和Sylvester矩阵方程得到,伴随向量补偿项是通过逐次逼近的迭代求解过程而获得。同时给出了次优控制律,它是通过截取伴随向量序列的有限次迭代值而得到。
4、将所设计的最优减振控制律用于汽车悬挂系统减振控制的仿真实验中。分别利用四分之一车、半车以及整车悬挂系统的动力学方程,建立了状态空问表示；建立了路面激励的外系统模型。通过对实际模型参数的数值仿真,验证所设计的减振控制律能够使各项性能指标达到最佳状态,确保了设计方法的有效性。
In this paper, firstly, the relative studies and results on the problem of optimal vibration control (OVC) for time-delay systems, nonlinear systems, and vibration control up to now are given in detail. Then the design of OVC law for time-delay systems and nonlinear time-delay systems are considered. The extence and uniqueness of the OVC law are studied and a suboptimal control law is given. The physical realization problem is discussed. The results are applied into simulations on suspension models to prove their effectiveness. The main contents are presented as follows.
1. The approach named model transformation for time-delay systems is introduced. The time-delay systems are transformed into equivalent nondelayed systems in form. The optimal control law is derived by solving Riccati and Sylvester equations. And the effects produced by the delays are compensated by the control memory term.
2. The theory of feedforward control is applied. For the disturbances with known dynamics and unknown initial conditions, the feedforward and feedback control law is designed, in which the feedforward control term compensates for the effects produce by disturbances. A reduced-order state observer is constructed to make the feedforward control physically realizable and solve the problem of unmeasured states.
3. For the nonlinear time-delay systems, the model transformation and successive approximation approach (SAA) are extended to design the OVC law. The OVC law obtained consists of accurate linear feedback, feedforward terms, memory terms for time-delays, and a nonlinear compensation term which is the limit of the adjoint vector sequence. The former can be obtained by solving a Riccati equation and a Sylvester equation, and the latter can be got by solving the linear nonhomogeneous sequences using SAA. Using a finite-step iteration of the adjoint vector among optimal solution sequence, a suboptimal control law can be obtained.
4. The designed control laws are applied to the numerical simulations on vibration control for suspension models. The state-space representations for a quarter-car model, a half-car model, and a full-car model are given based on their dynamical equations. The exosystems describing road vibrations are established. And the simulations results demonstrate the performances of car achive expected objectives and verify the effectiveness of desiged optimal control laws.
引文
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