线性二次型最优控制闭环系统极点的必要条件

本文推导了线性二次型（LQ）最优控制闭环系统极点应满足的必要条件，以及与加权阵Q和R的等式关系     

A stochastic realization algorithm via block LQ decomposition in Hilbert space

A stochastic realization problem of a stationary stochastic process is re-visited, and a new stochastically balanced realization algorithm is derived in a Hilbert space generated by second-order stationary processes. The present algorithm computes a stochastically balanced realization by means of the singular value decomposition of a weighted block Hankel matrix derived by a “block LQ decomposition”. Extension to a stochastic subspace identification method explains how the proposed abstract algorithm is implemented in system identification.     

离散系统LQ调节器的鲁棒性分析

本文研究了离散ＬＱ调节器系统鲁棒稳定性问题，稳定的不确定参数是通过考虑参数摄动的方向而求得的，这种方法比现有文献提供的结果具有更好的稳定范围。     

Locally optimal controllers and globally inverse optimal controllers

In this paper we consider the problem of global asymptotic stabilization with prescribed local behavior. We show that this problem can be formulated in terms of control Lyapunov functions. Moreover, we show that if the local control law has been synthesized employing an LQ approach, then the associated Lyapunov function can be seen as the value function of an optimal problem with some specific local properties. We illustrate these results on two specific classes of systems: backstepping and feedforward systems. Finally, we show how this framework can be employed when considering the orbital transfer problem.     

挠性转子磁力轴承系统LQ最优控制研究

在高温气冷堆氦气透平发电系统（HTR—IOGT）的相似性模拟实验装置AMB—PⅡ上,开展针对磁力轴承支承下挠性转子系统的优化控制研究。采用离散质量的集总参数法建立了相应转子动力学模型,通过适当模态截断简化获得了转子系统的状态方程。研究了LQ最优控制方法,分析了权重参数的选择对控制器的影响。仿真实验表明,输出反馈LQ结合相位补偿的控制器,具有物理意义清晰、系统结构简单和参数易于调节等优点。在AMB—PⅡ实验台架上不仅实现了转子的稳定悬浮,而且能够有效地抑制转子的高阶挠性模态振动,使转子顺利通过了二阶挠性临界转速,最高达到450Hz。该方法的研究为今后高温气冷堆氦气透平工程的磁力轴承实际应用提供了良好的设计参考。     

A new approach to the cheap LQ regulator exploiting the geometric properties of the Hamiltonian system

The cheap LQ regulator is reinterpreted as an output nulling problem which is a basic problem of the geometric control theory. In fact, solving the LQ regulator problem is equivalent to keep the output of the related Hamiltonian system identically zero. The solution lies on a controlled invariant subspace whose dimension is characterized in terms of the minimal conditioned invariant of the original system, and the optimal feedback gain is computed as the friend matrix of the resolving subspace. This study yields a new computational framework for the cheap LQ regulator, relying only on the very basic and simple tools of the geometric approach, namely the algorithms for controlled and conditioned invariant subspaces and invariant zeros.     

Reliable Robust Preview Tracking Control Against Actuator Faults

In this paper we provide a solution to the reliable robust preview tracking problem against actuator faults for discrete LTI systems with polytopic uncertainties. This solution is in terms of the solvability of linear matrix inequalities (LMIs). The method is based on multi‐objective optimization and LQ tracking performance indices. To avoid the conservativeness problem associated with using a common LMI solution for the normal case and the fault cases, different LMI solutions are used in the proposed method. Two iterative algorithms are proposed and compared. Numerical examples are used to show the effectiveness of the algorithms.     

干摩擦LQ控制系统在简谐激励下响应的递推算法

本在用增量谐波平衡法求解系统响应和用子结构法求解Riccati方程的基础上，进一步研究了单自由度含有粘性阻尼双线性滞迟恢复力LQ控制系统在简谐激励下的响应计算问题，并给出相应算例，为干摩擦系统在工程中的应用提供了理论依据。     

LQ Speed Control of Pump Controlled Motor System

A linear quadric (LQ) optimal speed control algorithm is proposed for the speed control of a pump controlled motor hydraulic system. The control theme consists of optimal state feedback and disturbing compensation based on observation. The optimal state feedback bases on LQ cost function. The disturbing compensation is realized through reconstructing the state of load torque. A series of simulation are performed, and the results show that the control performance is satisfactory and can be maintained under changes of load torque.