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。     

基于DSP实现的一阶倒立摆控制

倒立摆是控制领域中典型的被控对象。本文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PID控制算法使摆杆稳定。整个控制过程由基于DSP(DigitalSignalProcessor)为核心的控制器来实现。经过实物检验,成功地实现了一级倒立摆的稳摆和起摆控制。     

基于非线性控制方法的倒立摆系统控制

应用非线性系统跟踪控制方法对倒立摆系统的控制进行研究.基于非线性系统控制方法对倒立摆系统摆的镇定问题、台车位置调节问题和鲁棒控制问题设计出了具体的控制器.最后给出了在所设计的各种控制器作用下系统的仿真结果,结果表明所设计的控制器对倒立摆系统的稳定控制具有良好的效果.     

二级直线倒立摆系统的实物控制

针对二级直线倒立摆系统,采用拉格朗日方程法建立其理论模型,分别使用线性二次最优控制（Linear Quadratic Regulator,LQR）及基于趋近律的滑模控制（Sliding Mode Control,SMC）算法来实现干扰存在情况下倒立摆的平衡控制。对于LQR算法,研究了矩阵[Q]和矩阵[R]与反馈控制矩阵[K]的定性关系,并经过反复多次实验,不断试凑,得到一组良好的控制参数,实现了倒立摆的稳定控制。SMC算法采用基于指数趋近律的控制方法进行了滑模变结构控制器的设计,并利用边界层法来进一步削弱抖振。最后通过仿真及实验,实现了倒立摆的实物平衡控制。     

基于能量控制与近似输出调节的二级倒立摆起摆和跟踪控制

二级倒立摆是一个典型的欠驱动非线性系统,其控制问题具有一定的挑战性.为了解决时变参考信号下二级倒立摆的起摆和跟踪控制问题,本文提出了一种基于能量控制与近似输出调节方法的起摆和三阶控制器设计方案.首先,采用能量控制方法将第1级摆杆从下垂位置摆起到倒立位置附近;其次,采用滑模控制方法将第1级摆杆稳定在倒立位置,同时,采用等效小车与能量控制相结合的方法将第2级摆杆摆起到倒立位置附近;最后,采用基于近似输出调节理论的多项式近似方法设计三阶控制器实现二级倒立摆的位置跟踪控制.仿真和实验结果均验证了该控制方案的有效性.     

直线一级倒立摆的视觉伺服控制

把视觉引入倒立摆的控制中,建立了视觉伺服的倒立摆系统.利用针孔摄像机的成像几何模型建立与图像坐标有关的状态空间方程,采用基于图像的视觉伺服控制方法,对摆杆在像平面上的位置进行实时控制.在Matlab环境下用LQR(Linear Quadratic Regulator)和极点配置法进行仿真,对比仿真结果.验证了系统方程推导的正确性,以及控制算法的有效性.     

基于MPC的二阶倒立摆稳定控制

倒立摆系统是一个典型的欠驱动、强耦合、非线性的机械系统,该文提出了利用模型预测控制（MPC）方法来实现二阶倒立摆系统的稳定控制。首先基于拉格朗日方程对二阶倒立摆系统进行线性化数学建模,其次在多参数二次规划方法的基础上建立了模型预测控制系统,利用Python编程对系统控制做了数值仿真计算,同时讨论了系统在复杂外界条件时的控制效果。研究结果表明,利用模型预测控制对二阶倒立摆系统的稳定控制效果良好。这对控制算法的验证以及其他非线性系统的稳定控制具有重要意义。     

基于简化模型的倒立摆控制实验研究

本文根据二级倒立摆系统的特点，对其离散数学模型进行了简化，基于这个简化模型，应用二次型性能和指标最优控制的方法，设计控制规律，避免了状态观测器的设计过程，实验结果证明了这种方法的可行性。     

单级倒立摆的PID控制研究

对单级倒立摆系统的平衡控制问题进行了研究，分别采用PD，PI和PID三种方案实现了单级倒立摆系统的平衡控制。首先，建立系统的数学模型，然后通过仿真实验设计并整定各方案的控制器参数，将所设计的控制器分别在实际的物理设备上进行实时控制实验，都成功地实现了倒立摆的平衡控制。实际控制结果验证了各方案的正确性和有效性。     

倒立摆与控制理论研究

介绍了倒立摆系统的几种主要控制方法,如线性控制、模糊控制、拟人智能控制和鲁俸控制,分析了各种方法的特点以及它们之间的联系,对各种方法的优缺点进行了评价.通过上述内容的介绍与探讨,充分展示了倒立摆作为一个典型控制对象,在控制理论研究中的重要地位.最后,揭示了研究倒立摆控制问题的现实意义,并对这一领域的前景提出展望.     

Exponential nonlinear observer based on the differential state-dependent Riccati equation

This paper presents a novel nonlinear continuous-time observer based on the differential state-dependent Riccati equation(SDRE) filter with guaranteed exponential stability.Although impressive results have rapidly emerged from the use of SDRE designs for observers and filters,the underlying theory is yet scant and there remain many unanswered questions such as stability and convergence.In this paper,Lyapunov stability analysis is utilized in order to obtain the required conditions for exponential stability of the estimation error dynamics.We prove that under specific conditions,the proposed observer is at least locally exponentially stable.Moreover,a new definition of a detectable state-dependent factorization is introduced,and a close relation between the uniform detectability of the nonlinear system and the boundedness property of the state-dependent differential Riccati equation is established.Furthermore,through a simulation study of a second order nonlinear model,which satisfies the stability conditions,the promising performance of the proposed observer is demonstrated.Finally,in order to examine the effectiveness of the proposed method,it is applied to the highly nonlinear flux and angular velocity estimation problem for induction machines.The simulation results verify how effectively this modification can increase the region of attraction and the observer error decay rate.     

平行二级倒立摆的稳定控制

将单一输入规则群动态加权模糊推理模型应用于平行二级倒立摆系统，设计出具有6个输入交量的模糊稳定控制器。该模糊控制器规则总数少，直观性强。计算机仿真表明，该模糊控制器能在短时间内同时实现两摆角度及小车位置的控制。     

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。     

倒立摆的可变增益迭代学习控制算法

对倒立摆系统的平衡控制问题进行研究。在建立系统数学模型的基础上,提出指数变增益迭代学习控制律,并设计了控制器。通过系统仿真实验,结果表明：与常规迭代学习控制律相比较,本文采用的方法收敛速度大大加快,系统动态性能得到很大改善。     

Sliding mode control design based on the state-dependent Riccati equation: theoretical and experimental implementation

In this paper, a suboptimal sliding mode control method is derived from combination of the sliding mode control (SMC) and the state-dependent Riccati equation (SDRE) technique, applied for a class of nonlinear closed-loop systems. One of the distinguished features of this control method is its robustness towards uncertainty. Due to lack of optimality in SMC method, in this paper, a robust and suboptimal method is presented by considering the SDRE in design of the sliding surface in two types of: algebraic and integral sliding surfaces. In addition, due to the use of the state-dependent differential Riccati equation in the integral form of sliding surface, proposed method is able to provide a robust attitude with desired finite-time control option. The sensitivity of various percentage of uncertainty in the physical structure of the system is studied and control strategies for general manipulators are provided. The proposed control structure was implemented on Scout robot theoretically and practically by the LabVIEW software; and the results were compared by considering the uncertainty in its structure. In comparison with conventional SMC, the proposed method reduced the required time to reach the sliding surface almost 50%.     

Minimum-time control for an inverted pendulum under force constraints

In order to numerically solve the minimum-time control problem of a linear system, the system is usually discretized with a fixed sampling period. Then the minimum count of control steps is searched to meet the constraints of the final state and the input variables. Since the count is a variable, there is no direct way for handling such problems except by exhaustive iteration. In contrast to the traditional methods, a new numerical technique was developed recently to avoid the exhaustive iteration. In this method, the control step is fixed and the sampling period is treated as a variable. Since this method requires only two iterations, it will reduce the computation time significantly. This paper applies this new numerical technique to generate the minimum-time trajectory between two end-points for an inverted pendulum under force constraints. Two main issues are addressed. The first one is the problem formulation in discrete-time domain and the second one is the generation of feasible solutions for the global search. Simulation examples are included for illustration.     

Wheeled inverted pendulum type assistant robot: design concept and mobile control

This paper describes the design concept of the human assistant robot I-PENTAR (Inverted PENdulum Type Assistant Robot) aiming at the coexistence of safety and work capability and its mobile control strategy. I-PENTAR is a humanoid type robot which consists of a body with a waist joint, arms designed for safety, and a wheeled inverted pendulum mobile platform. Although the arms are designed low-power and lightweight for safety, it is able to perform tasks that require high power by utilizing its self-weight, which is the feature of a wheeled inverted pendulum mobile platform. I-PENTAR is modeled as a three dimensional robot; with controls of inclination angle, horizontal position, and steering angle to achieve high mobile capability. The motion equation is derived considering the non-holonomic constraint of the two-wheeled mobile robot, and a state feedback control method is applied for basic mobile controls wherein the control gain is calculated by the LQR method. Through several experiments of balancing, linear running, and steering, it was confirmed that the robot could realize stable mobile motion in a real environment by the proposed controller.     

非线性倒立摆系统平衡点反馈控制参数的优化计算

本文基于圆轨倒立摆非线性系统模型,建立了平衡点状态反馈控制参数的高精度优化算法,编制计算程序确定出反馈控制参数,并对圆轨倒立摆平衡点的实例控制.与将系统线性化后的反馈参数的计算分析相比,本文研究方法具有较大平衡范围.仿真与实例平衡控制都表明了本文研究方法的可行性.     

一级倒立摆状态反馈控制系统设计

倒立摆控制系统是一个复杂的、不稳定的、非线性系统,对倒立摆系统的研究能有效的反映控制中的许多典型问题。对一级直线型倒立摆,首先运用牛顿运动定律建立倒立摆系统的运动方程,进而求出系统的状态空间表达式,建立数学模型。其次运用状态反馈极点配置法,以小车的位移、速度,摆杆与竖直向上的偏角、摆角变化速度作为四个状态变量,由给定的控制要求求出状态反馈增益矩阵,将极点配置在控制要求的位置。另外考虑到系统的某些状态如小车速度和摆杆角速度不容易直接测量等,本文分别基于小车和摆杆子系统设计了两个全维观测器,分别对状态量进行了重构并给出了仿真结果分析。     

三级倒立摆的自适应神经模糊控制

在三级倒立摆(TIP)系统中, 应用神经网络与模糊控制相结合的自适应神经模糊推理系统(adaptive neuralfuzzy inference system), 根据样本数据调整隶属函数和控制规则参数, 使得训练后ANFIS控制器很好地模拟期望的输入输出数据. 仿真结果表明所设计的ANFIS控制器对三级倒立摆系统的稳定控制是可行的. 与LQR控制相比, 基于ANFIS控制的倒立摆系统具有良好的动态性能和抗干扰性能.