Flight control for air-breathing hypersonic vehicles using linear quadratic regulator design based on stochastic robustness analysis

The flight dynamics model of air-breathing hypersonic vehicles (AHVs) is highly nonlinear and multivariable coupling, and includes inertial uncertainties and external disturbances that require strong, robust, and high-accuracy controllers. In this paper, we propose a linear-quadratic regulator (LQR) design method based on stochastic robustness analysis for the longitudinal dynamics of AHVs. First, input/output feedback linearization is used to design LQRs. Second, subject to various system parameter uncertainties, system robustness is characterized by the probability of stability and desired performance. Then, the mapping relationship between system robustness and LQR parameters is established. Particularly, to maximize system robustness, a novel hybrid particle swarm optimization algorithm is proposed to search for the optimal LQR parameters. During the search iteration, a Chernoff bound algorithm is applied to determine the finite sample size of Monte Carlo evaluation with the given probability levels. Finally, simulation results show that the optimization algorithm can effectively find the optimal solution to the LQR parameters.     

倒立摆系统的最优控制应用研究

针对倒立摆系统的不稳定性,对最优控制理论在倒立摆控制系统中的应用进行了分析,设计LQR控制器,并在倒立摆实验装置上进行了实验。实验结果表明设计的控制器是有效的,对倒立摆系统的平衡稳定控制效果好,提高了系统的抗干扰能力。     

Distributed LQR Design for Identical Dynamically Decoupled Systems

We consider a set of identical decoupled dynamical systems and a control problem where the performance index couples the behavior of the systems. The coupling is described through a communication graph where each system is a node and the control action at each node is only function of its state and the states of its neighbors. A distributed control design method is presented which requires the solution of a single linear quadratic regulator (LQR) problem. The size of the LQR problem is equal to the maximum vertex degree of the communication graph plus one. The design procedure proposed in this paper illustrates how stability of the large-scale system is related to the robustness of local controllers and the spectrum of a matrix representing the desired sparsity pattern of the distributed controller design problem.     

Zero dynamics stabilisation and adaptive trajectory tracking for WIP vehicles through feedback linearisation and LQR technique

This paper presents a composite control strategy integrating adaptive sliding-mode control and the linear quadratic regulator (LQR) technology for a wheeled inverted pendulum (WIP) vehicle system. The system can be partitioned into an actuated rotational subsystem and an underactuated longitudinal subsystem based on the different control input in the mathematical model. In particular, the instability analysis of zero dynamic for the underactuated longitudinal subsystem is investigated in detail using the feedback linearisation technology. Then, an adaptive sliding-mode control is designed for the trajectory tracking, where an adaptive algorithm is developed to handle with the parameter uncertainties. In addition, the LQR technique is employed to guarantee zero dynamics stability so as to achieve simultaneously the vehicle body stabilisation at the upright position. Simulation results show the good performance and strong robustness of the proposed control schemes.     

A revisit to the gain and phase margins of linear quadraticregulators

In this paper, we revisit the well-known robustness properties of the linear quadratic regulator (LQR), namely, the guaranteed gain margin of -6 to +∞ dB and phase margin of -60° to +60° for single-input systems. We caution that these guaranteed margins need to be carefully interpreted. More specifically, we show via examples that an LQR may have a very small margin with respect to the variations of the gain and/or phase of the open-loop plant. Such a situation occurs in most practical systems, where the set of measurable state variables cannot be arbitrarily selected. Therefore the lack of robustness of the LQR can be very popular and deserves attention     

一类不确定性鲁棒LQR的奇异值特性分析

针对系统矩阵存在的范数有界不确定性,基于一种鲁棒线性二次调节器(LinearQuadratic Regulators,LQR)的设计,利用其鲁棒回差方程,详细推导了这种鲁棒LQR灵敏度函数的奇异值最大值与规范LQR灵敏度函数的奇异值最大值之间的关系,证明这种鲁棒LQR相对于规范LQR具有较小的灵敏度函数的最大奇异值,灵敏度函数的奇异值特性分析说明这种鲁棒LQR设计相对规范LQR有较好的控制性能。表明灵敏度函数的奇异值特性分析,是一种有效的控制系统性能分析方法。     

单级旋转倒立摆的控制系统设计

介绍单级旋转倒立摆的控制系统设计.系统采用LQR算法控制旋转臂和摆杆位置,验证了小角度内平衡点附近线性化的合理性,结构简单且控制快速,具有良好的稳定性和鲁棒性.     

基于PID和LQR的四旋翼无人机控制系统研究

为提高四旋翼无人机的飞行稳定性、无人飞行器控制系统的鲁棒性和控制精度,以建立的四旋翼无人机飞行控制系统模型为基础,采用现代控制理论与传统控制论相结合的方法,针对姿态角速率、姿态角分别设计内环LQR(线性二次型调节器)控制器,及外环PID控制的双回路闲环控制器.充分利用PID控制器易于掌握且对模型要求精度低、LQR控制器能改善内回路的动态特性和稳态性能的特点,完成四旋翼无人机的飞行控制.通过实验遴选该双闭环控制器相关参数并进行优化,实验结果表明所设计的双回路控制器控制性能指标良好.     

非线性倒立摆系统的起摆和稳摆控制

介绍了基于数字信号处理器(DSP)控制直线型倒立摆系统的总体结构和工作原理,通过智能控制算法实现倒立摆的起摆控制。当摆杆的角度进入稳定区域时,通过线性二次型调节器(LQR)控制算法使摆杆稳定,并建立了电机电压与输出力矩之间的简单对应关系。实验表明,系统的稳定性好,抗干扰力强,而且采用DSP控制,有利于系统的小型化。     

Robust digital control of a high-performance engine

The design of a robust digital multivariable feedback control system for the F-100 turbofan jet engine is considered. The control system design problem is posed, and conditions for satisfying performance specifications and stability robustness are stated. The discrete LQG/LTR methodology is used to design a compensator that meets the stated specifications. New results for multi-input LQR loop shaping are derived. To get a reasonably low-order compensator, frequency-weighted reduced-order models are exploited, with the reduction error treated as an uncertainty.