直线柔性连接两级倒立摆控制器设计

倒立摆系统是一个复杂的、非线性的、不稳定的高阶系统。倒立摆的控制一直是控制理论及应用的典型课题。分析了如何利用拉格朗日方程对直线柔性连接两级倒立摆系统建模，采用LQR法设计最优控制器，进行了具体架构以及阐述了此系统设计的控制器在实际物理系统中的实现问题。所设计的控制器对此倒立摆系统成功实施了控制，既证明了系统建模的正确性，也是倒立摆控制中的一项重大突破。相关研究成果将在航天科技及机器人学等领域发挥重要作用．     

平面一级倒立摆的稳定控制

平面倒立摆系统是进行控制理论研究的理想实验平台.在对平面一级倒立摆进行运动学和动力学分析的基础上,采用拉格朗日方程建立了它的动力学模型.分别设计了LQR控制器和模糊控制器,应用所设计的控制器对倒立摆系统进行了实时控制实验.验证了两种控制方法的优缺点.     

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.     

基于Lyapunov能量函数的倒立摆稳定控制

倒立摆是一种复杂的非线性控制系统.通过对其进行控制能够检验控制器的鲁棒性.基于一个能量形式的Lyapunov函数设计了倒立摆稳定控制器使得摆趋于上平衡位置,并且使得小车位移和角度都收敛于零.该控制策略基于系统的总能量,利用其耗散特性设计了Lyapunov函数,并证明了控制系统的稳定性.理论分析及仿真试验表明该控制器对于倒立摆控制具有很强的鲁棒性.     

车轨长度受限的并行双摆能量控制

采用牛顿-欧拉方法建立并行二级倒立双摆系统的数学模型.针对车轨长度受限的并行二级倒立摆系统,本文提出了一种基于能量控制思想和直接李雅普诺夫函数方法的摆起控制策略.所设计的控制器保证了小车的速度收敛到零和摆杆在达到垂直向上的位置时摆杆的能量为零.同时,它能实现对并行双摆的稳摆控制.控制器简单易行,参数调节方便.在并行二级倒立摆摆起控制器设计的基础上,简述了三级车摆的摆起控制器设计过程.最后,通过计算机仿真验证了控制方法在工作效率和抗干扰方面能保持良好的控制性能.     

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.     

小车二级摆摆起控制器设计

研究了小车二级并行摆系统及小车二级串行摆系统的摆起控制器设计问题,并给出了这两种系统的实验结果.首先,针对上述两种系统,设计了两步控制器,即1)摆起双摆达到倒立稳摆位置的控制器,2)进行稳摆控制的控制器.其次,由于小车二级摆位移受轨道长度限制,又考虑了小车位移的控制问题.上述两种实际系统的摆起及稳摆成功,验证了所提出设计方法的有效性.     

基于分区切换方法设计倒立摆系统的控制器

针对非线性倒立摆系统,利用小台车平移速度与摆偏角角速度之比,设计了分区的Lyapunov函数和基于自适应律的分段切换控制律。由于该方法考虑了导轨摩擦和节点摩擦对系统的影响,设计的控制律具有较强的鲁棒性,较好地解决了摆的偏角和小车位移非线性强耦合带来的困难,并且得到的是全局渐近稳定的结果。该方法计算简单,且自适应律的应用减少了保守性。最后通过倒立摆实例,利用所设计的控制器进行Matlab仿真,仿真结果验证了所设计控制器的可行性和有效性。     

基于T—S模糊模型的LQR控制器设计

基于T-S模糊模型的平行分配补偿控制器设计方法,结合线性二次型最优控制方法,设计了一个倒立摆系统状态反馈控制器.控制方法有效地将线性系统理论与模糊控制理论结合起来,可处理某些复杂的非线性自不稳定系统控制问题.针对倒立摆是一个非线性、不稳定、强耦合系统,利用MATLAB对其进行仿真实验,结果表明上述方法能够控制倒立摆稳定.TS-LQR控制器结合了模糊控制和LQR方法的优点,具有结构简单、易于实现以及稳定范围大、鲁棒性好的优点,可获得较好的动态性能和稳态性能.     

基于T-S型的平面倒立摆双闭环模糊控制研究

针对多变量、非线性、强耦合的平面一级倒立摆系统,设计了双闭环模糊控制器.在系统数学模型的基础上,将平面一级倒立摆系统近似分解成2个非耦合的独立运动,然后利用极点配置的反馈控制方法,设计了2个模糊控制器,分别控制两个独立运动.解决了模糊控制规则数随输入变量数指数增加问题,降低了倒立摆控制系统设计的难度和复杂度.     

Big Bang-Big Crunch optimized hierarchical sliding-mode control of X-Z inverted pendulum

The control of the X-Z inverted pendulum is a challenging work since the X-Z inverted pendulum is an underactuated, open-loop unstable and multi-input-multi-output (MIMO) nonlinear system. In this paper, we will present a novel state transformation method for the X-Z inverted pendulum and Big Bang–Big Crunch (BBBC) optimized hierarchical sliding-mode control (HSMC) structure. We will firstly show that through the proposed transformation, the model of the X-Z inverted pendulum can be transformed to a typical underactuated form. Thus, based on the obtained system model, the hierarchical sliding-mode control (HSMC) can be directly applied in the trajectory tracking control of the X-Z inverted pendulum. Then, to ensure a convergent performance of the auxiliary sliding surfaces, the BBBC method is applied to obtain the optimal coupling factors for the HSMC. The control performance of the proposed BBBC based HSMC structure is compared with that of the present SMC and the HSMC with particle swarm optimization (PSO). Simulation results show the effectiveness of the proposed controllers for the X-Z inverted pendulum.     

二级倒立摆在常规滑模变结构控制实验中的应用

二级倒立摆是一个高度非线性系统,具有强耦合和快速性的特点,必须采用有效的非线性系统的控制方法才可使其稳定在平衡位置.随着智能控制的发展,大多数研究人员和学者将变结构在倒立摆控制系统中的应用,作了大量的理论研究以及仿真实验,为实际应用作了铺垫.但是仿真实验在实际应用过程存在着较强的限制性,其表现为控制器结构越复杂,仿真结...     

A self-tuning PID control for a class of nonlinear systems based on the Lyapunov approach

In this paper, we will propose a self-tuning method for a class of nonlinear PID control systems based on Lyapunov approach. The three PID control gains are adjustable parameters and will be updated online with a stable adaptation mechanism such that the PID control law tracks certain feedback linearization control, which is previously designed. The stability of closed-loop nonlinear PID control system is analyzed and guaranteed by introducing a supervisory control and a modified adaptation law with projection. Finally, a tracking control of an inverted pendulum system is illustrated to demonstrate the control performance by using the proposed method.     

基于滑模变结构的倒立摆系统稳定控制

利用滑模变结构控制对一级倒立摆系统进行了有效控制.首先对一级倒立摆系统的模型进行线性化处理,再利用滑模变结构控制方法对此模型中摆的镇定、台车位置的调节和系统参数不确定性设计了具体的控制规律,并使用饱和函数的方法抑制系统的抖振.最后在Matlab/Simulink上进行了仿真实验,实验结果说明滑模变结构控制方法是有效的.     

Optimal PID Control of Spatial Inverted Pendulum With Big Bang – Big Crunch Optimization

As the extension of the linear inverted pendulum (LIP) and planar inverted pendulum (PIP), this paper proposes a novel spatial inverted pendulum (SIP). The SIP is the most general inverted pendulum (IP) than any existing IP. The model of the SIP is presented for the first time. The SIP inherits all the characteristics of the LIP and the PIP, which is a nonlinear, unstable and underactuated system. The SIP has five degrees of motion freedom and three control forces. Thus, it is a multiple-input and multiple-output (MIMO) system with nonlinear dynamics. To realize the spatial trajectory tracking of the SIP, the control structure with five PID controllers will be designed. The parameter tuning of the multiple PIDs is a challenging work for the proposed SIP model. To alleviate the difficulties of the parameter tuning for the multiple PID controllers, optimal PIDs can be achieved with the help of Big Bang-Big Crunch (BBBC) optimization. The BBBC algorithm can successfully optimize the parameters of the multiple PID controllers with high convergence speed. The optimization performance index of the BBBC algorithm is compared with that of the particle swarm optimization (PSO). Simulation results certify the rightness and effectiveness of the proposed control and optimization methods.      

INPUT‐STATE LINEARIZATION OF A ROTARY INVERTED PENDULUM

The aim of this paper is to design a nonlinear controller for the rotary inverted pendulum system using the input‐state linearization method. The system is linearized, and the conditions necessary for the system to be linearizable are discussed. The range of the equilibriums of the system is also investigated. Further, after the system is linearized, the linear servo controllers are designed based on the pole‐placement scheme to control the output tracking problem. The performance of the controller is studied with different system parameters. The computer simulations demonstrate that the controller can effectively track the reference inputs.     

Simulation studies of inverted pendulum based on PID controllers

The inverted pendulum problem is one of the most important problems in control theory and has been studied excessively in control literatures. When a control system have more than two PID controllers, the adjustment of PID parameters is not an easy problem. In this paper, PID controllers are applied to the stabilization and tracking control of three types of inverted pendulum. The way how to design the PID controllers is given step by step in this paper. Simulation results prove that the way to design of PID controllers is very simple and effective. The system design not only can realize stabilization and tracking control of three types of inverted pendulum, but also have robustness to outer large and fast disturbances.     

Neural network control for position tracking of a two-axis inverted pendulum system: experimental studies.

In this paper, experimental studies of a decentralized neural network control scheme of the reference compensation technique applied to control a 2-degrees-of-freedom (2-DOF) inverted pendulum on an x - y plane are presented. Each axis is controlled by two separate neural network controllers to have a decoupled control structure. Neural network controllers are applied not only to balance the angle of pendulum, but also to control the position tracking of the cart. The decoupled control structure can compensate for uncertainties and cancel coupling effects. Especially, a circular trajectory tracking task is tested for position tracking control of the cart while maintaining the angle of the pendulum. Experimental result shows that position control of the inverted pendulum and cart is successful.     

基于模糊加权的倒立摆混合控制

针对小车倒立摆系统,提出了一种线性状态反馈控制和滑模控制模糊加权的控制方法.滑模控制器的作用是将摆角控制在零的一个邻域内,在此邻域内首先采用近似的线性化模型来描述倒立摆系统,然后采用基于极点配置的方法设计系统的线性状态反馈控制器以使系统的状态稳定在给定值,两个控制器的输出通过加权求和作为倒立摆的控制作用.仿真结果证实了该方法的有效性.     

旋转二级倒立摆的控制系统设计与仿真

小车倒立摆系统是一个典型的多变量、非线性、强耦合和快速运动的自然不稳定系统,其控制问题被公认为控制理论的一个典型问题,是控制理论研究的典型实验平台.旋转二级倒立摆是一种新型的倒立摆装置,与同级的直线轨道倒立摆相比,结构简单紧凑,但模型更复杂和不稳定,对控制算法提出更高的要求,增加了控制难度.该文基于动力学理论分析旋转二级倒立摆系统的结构,建立了旋转二级倒立摆系统的数学模型状态空间方程,分析了系统的稳定性和可控性.采用二次型最优控制策略对旋转二级倒立摆系统进行控制系统设计,并借助Matlab平台进行了仿真实验.实验结果证明了其控制有效性,该控制结果与其它控制方法相比,有较优的稳态特性和快速性,系统处在较大的非平衡初始状态,旋转二级摆杆也能稳定地控制在倒立平衡位置附近.因此可以进一步扩展到多级旋转倒立摆的控制,对于实现其它不稳定系统的控制,也有着一定的借鉴价值.