线性二次型调节器最优输出反馈律的研究

线性二次型调节器问题是一类重要的最优控制问题，在现代控制理论中占有重要地位。本文引入随机性能指标，讨论线性二次型调节器关于输出的最优反馈律，并对有限时间的状态调节器问题提供了一种计算其最优输出反馈增益矩阵的算法设计。本文给出的解决线性调节器系统的最优输出反馈方案，可降低调节器的复杂程度，便于工程实现，因而具有一定的学术意义和应用价值。     

自动空中加油杆LQR控制器设计

针对硬式空中加油过程中加油杆在外界干扰下可能存在不稳定的问题,本文提出了一种线性二次型最优控制方法。首先建立加油杆的数学模型,推算出其状态空间方程,然后设计相应的控制律并搭建simulink仿真模块。仿真结果表明,加入线性二次型最优控制的反馈单元后,飞机的俯仰角和滚转角很快收敛为0,系统响应稳定。     

基于倒立摆的两种控制策略的研究

倒立摆系统被广泛应用于检验各种控制理论和控制策略的有效性中.分析了两种简单而有效的控制策略:极点配置法和线性二次最优控制策略的LQR法,并通过Matlab仿真对单极倒立摆系统进行了控制效果的对比,从理论和仿真结果上讨论了这两种控制策略的优缺点.     

倒立摆状态反馈极点配置与LQR控制Matlab实现

为了实现对绝对不稳定的非线性多变量倒立摆系统的控制,采用了状态反馈极点配置和LQR控制2种方法。状态反馈极点配置是将多变量系统的闭环系统极点配置在期望的位置上,从而使系统满足瞬态和稳态性能指标。LQR算法是在一定的性能指标下,利用最少的控制能量,来达到最小的状态误差。通过Matlab软件仿真实验,发现2种控制方法对于倒立摆这种不稳定的系统有一定的控制作用,证明了两种控制方案的可行性和有效性。仿真表明二次型最优控制有较小的振荡和超调量,对系统有更好的控制效果。     

二级倒立摆的自适应神经网络控制

倒立摆系统是一种典型的非线性、多变量、不稳定系统,目前,对于这种复杂对象的控制问题在控制领域具有十分重要的研究价值。针对此种非线性系统的控制问题,提出一种智能控制方法来解决这个问题。通过应用神经网络控制和模糊控制相结合的方式,集合二者的优点,提出一种将BP算法与最小二乘算法相结合的算法,对Takagi-Sugeno模糊推理系统中的参数进行优化修正,设计一种自适应神经网络的模糊推理系统来控制倒立摆,实验结果证明该理论是准确可行的,与LQR实时控制相比响应速度快、精度高。     

两轮自平衡机器人系统设计、建模及LQ控制

设计一个以TMS320F2812DSP为控制核心、2个独立驱动的同轴直流电机为执行机构的两轮自平衡机器人,其姿态传感器包括倾角仪、速率陀螺和电机编码器。依据经典牛顿力学建立线性系统数学模型,采用LQR方法得到系统的反馈系数后,进行系统仿真实验和实际物理系统实验。实验结果表明,该系统的建模和控制器的设计是合理和有效的,且所设计的DSP控制程序可以方便的实现其他控制算法,并且可得到系统运行时各状态的值,为数据分析和传感器信号的处理提供方便。     

LQR在单级倒立摆系统中的应用

单级倒立摆控制是一个即复杂而又对准确性、快速性要求很高的非线性不稳定系统控制问题。单级倒立摆数学模型的建立对研究其稳定性具有指导作用。针对多变量、非线性、强耦合性的倒立摆系统,运用牛顿动力学方法建立其动力学方程,并进行线性化处理,得到状态空间模型。然后对该模型分别进行LQR控制,在MATLAB环境下进行仿真。实验结果表明,二次型最优控制具有良好的响应性能和算法简单等特点,在实际应用中具有重要意义。     

基于遗传算法的四旋翼飞行器最优控制

通过对四旋翼飞行器进行动力学分析得到力学平衡方程,基于此建立了四旋翼飞行器的数学模型并得出其状态空间表达式。通过线性二次型设计控制系统,将开环不稳定系统构造成闭环稳定系统,并给出了线性二次型最优控制率表达式。为解决试验法难以确定最优加权矩阵的问题,利用遗传算法对线性二次型最优控制加权矩阵进行优化设计,寻找最优加权矩阵。通过Matlab以及Simulink,对基于遗传算法的四旋翼飞行器最优控制系统进行了仿真,并与基于试验法的线性二次型控制做对比。从仿真结果看,基于遗传算法的线性二次型最优控制使得四旋翼飞行器具有良好的动态性能。     

Matlab在现代控制理论教学中的应用

根据现代控制理论的特点,利用Matlab设计了现代控制理论课程的实验,并利用Matlab对现代控制理论进行分析。采用极点配置方法设计状态反馈控制器和线性二次最优控制设计状态反馈控制器,对倒立摆系统的数学模型进行仿真研究,并得到系统的闭环极点配置在P1,P2位置时系统状态响应曲线。设计了求解现代控制理论的能控性、能观性及极点配置等基本问题的人机界面。     

压电智能挠性板的主动振动控制研究

对挠性悬臂矩形板的主动振动控制进行了研究。给出了悬臂板的压电敏感器和致动器的布置准则，并推导了悬臂板的（包括弯曲和扭转振动模态）基于分布式压电致动器的压电致动方程，可以根据该方程设计悬臂板压电主动振动抑制的控制器。该文在控制方法上采用应变律反馈控制和线性二次型（LQR）控制，计算机数字仿真结果表明：设计的控制律对于悬臂板的弯曲和扭转振动是有效的。     

Piezoelectric vibration control for all-clamped panel using DOB-based optimal control

Considering the spillover and harmonic effect in real active vibration control, a novel composite controller based on disturbance observer (DOB) for the all-clamped panel is presented. The single-mode of the piezoelectric panel can be regarded as a second-order system. The unmodeled error of the current controlled mode, harmonic effects, uncontrolled mode effects, etc., are regarded as the lumped disturbances which can be estimated by the DOB, and the estimated value is used for the feed-forward compensation design. Then, an optimal linear quadratic regulator (LQR) strategy is employed for the feedback design. In order to solve the difficulty of determining the weight matrices of LQR, a chaos optimization method based on logistic map is proposed. So the weight matrices can be tuned automatically. Combining with a new transient performance function, the optimal weight matrices can be obtained. The composite controller can effectively suppress the lumped disturbances of the all-clamped panel. Experiment comparisons with conventional LQR are given to verify the effectiveness of the proposed method.     

Design of Suboptimal Constrained Nonlinear Quadratic Regulator via Invariant Sets Switching

A design method for a suboptimal constrained nonlinear quadratic regulator (CNLQR) via invariant sets switching is presented. The CNLQR has the merits of both the control invariant set and the gain scheduling, and solves the constrained nonlinear quadratic regulation problem effectively. It first calculates the equilibrium surface of the nonlinear system, and then obtains the off-line local LQR control laws and the corresponding control invariant sets for several equilibrium points. These control invariant sets cover the equilibrium surface such that the closed-loop stability of the nonlinear system can be guaranteed by switching the local LQR laws on-line. The algorithm is computationally efficient, because the state feedback control law and control invariant sets are all solved off-line so that the computational burden of on-line optimization is greatly reduced. A simulation example illustrating the method is presented.     

Linear Quadratic Control of a Loaded Agonist?Antagonist Muscle Pair

A discrete-time control law which gives the optimal applied force for a given position trajectory of a linear second-order external load is computed using linear quadratic regulator (LQR) theory. This control law is used with an existing first-order fixed interpulse interval (IPI) muscle force controller to regulate position in a simulated electrically stimulated loaded agonist-antagonist muscle system. Both force and position feedback are required to implement the control strategy. A nonlinear second-order model of a predominantly slow twitch muscle is used in the simulation. The results suggest that good position control of a loaded antagonist-agonist muscle system is possible if a linear model of the external load is appropriate.     

Robust Stabilization of Delayed Singular Systems with Linear Fractional Parametric Uncertainties

This paper deals with the problem of robust stabilization for delayed singular systems with parametric uncertainties. The parametric uncertainties are assumed to be of a linear fractional form involving all system matrices. Necessary and sufficient conditions for quadratic stability and quadratic stabilization are obtained. Moreover, the results generalize and improve previous works on delayed singular systems with norm-bounded parametric uncertainties. A strict linear matrix inequality (LMI) design approach is developed such that, when the LMI is satisfied, a desired robust state feedback control law can be constructed. A numerical example is provided to demonstrate the application of the proposed method.     

A sensorless optimal control system for an automotive electric power assist steering system

This paper considers the analysis and design of a double-pinion-type electric power assist steering (EPAS) control system. A simplified model of the augmented steering assembly-electric motor system is developed using Lagrangian dynamics, and an optimal controller structure for the model is proposed. Three main advances to the state of the art are presented in this paper. First, a state-space design model is used rather than an input-output model. A state-space formulation for a system model that incorporates motor electrical dynamics is obtained with the assist motor angular position as the output. Second, linear quadratic regulator (LQR) and Kalman filter techniques are employed to arrive at an optimal controller for the EPAS system. The selection of weighting coefficients for the LQR cost function is discussed. Finally, the authors present a control strategy that eliminates the steering column torque sensor, a critical component in existing EPAS controller designs. The proposed control strategy presents an opportunity to improve EPAS system performance and also reduce system cost and complexity.     

基于dSPACE的三相PWM整流器最优控制

PWM整流器系统通常采用双闭环控制。其电流环为一多输入多输出强耦合的系统,普遍应用PI调节器结合前馈解耦的方法。本文针对电流环的特点,设计了LQR调节器,进一步提高了控制系统的性能。本文选取id,iq作为系统状态变量,建立PWM整流器电流环的系统状态方程,通过求解Riccati方程得到所求控制器。搭建了基于dSPACE...     

Totally invariant state feedback controller for position control ofsynchronous reluctance motor

A new totally invariant state feedback controller is designed by combining the classical state feedback controller and the variable-structure control (VSC). The combination of these two different control methods has the advantages of both their merits: (1) the easy design of the state feedback and (2) the strong robustness of the VSC. In other words, the system performance can be simply designed for the nominal system by using the classical state feedback, which includes such well-known techniques as the pole placement or the linear quadratic method. Then, VSC is used to ensure the control effect. To demonstrate the effectiveness of the totally invariant state feedback controller, it is applied to the position control of a synchronous reluctance motor. Simulation results are first given. In addition, a prototype hardware system is built and experimentally evaluated     

Digital Controller Design for Analog Systems Represented by Multiple Input–Output Time-Delay Transfer Function Matrices with Long Time Delays

This paper presents a digital controller design methodology for multivariable analog systems represented by minimally realizable multiple input–output time-delay transfer function matrices with long time delays. First, the analog transfer function matrix with multiple input–output time delays is minimally realized and represented by a delay-free state-space model and a multiple output-delay function. For a specific multiple time-delay transfer function matrix with complex poles, a minimal realization scheme is newly proposed. Then the minimized delay-free state-space model is utilized for linear quadratic regulator (LQR) design. Furthermore, the designed analog LQR is digitally redesigned via a predictive state-matching method for finding a low-gain digital controller from the pre-designed high-gain analog controller. For implementation of the digitally redesigned controller, a digital observer is constructed for the multiple time-delay system with long time delays. An illustrative example is given to demonstrate the effectiveness of the proposed method.     

Robust output regulation of a class of smart actuators described by a minimum phase LPV dynamics

This paper presents a new control strategy for a class of minimum phase linear parameter-varying (LPV) systems representative of smart material actuators. In position control applications of such devices, one is typically interested in achieving output regulation with an arbitrary exponential decay rate. In principle, this problem can be tackled by assigning an exponential decay rate to the full system state, by means of well-established linear matrix inequalities (LMI) methods. For the class of systems under investigation, however, this approach leads to excessively large controller gains in case the desired decay rate is faster than the open-loop zero dynamics. In addition, the existence of unmeasurable state variables related to the material microstructure makes it not possible to directly implement full state feedback laws which are commonly adopted in LPV theory. To overcome these issues, a new design strategy is proposed. The key idea relies on arbitrarily shaping the output exponential decay rate without requiring fast convergence of the full state vector. This goal is achieved by means of a partial state feedback control law which solely depends on the measurable system states. A LMI algorithm is also developed to systematically address the design of the partial state feedback controller. The method is validated by means of simulations on generic examples, as well as via experiments on a mechatronic positioning system based on a dielectric elastomer membrane. In case the desired output convergence speed is faster than the open-loop zero dynamics, it is shown that the new approach leads to better transient behaviors and significantly smaller controller gains than standard LPV design techniques.