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Stabilization and Tracking Control of X‐Z Inverted Pendulum Using Flatness Based Active Disturbance Rejection Control 下载免费PDF全文
A flatness based robust active disturbance rejection control technique scheme with tracking differentiator is proposed for the problem of stabilization and tracking control of the X‐Z inverted pendulum known as a special underactuated, non‐feedback linearizable mechanical system. The differential parameterization on the basis of linearizing the system around an arbitrary equilibrium decouples the underactuated system into two lower order systems, resulting in two lower‐order extended state observers. Using a tracking differentiator to arrange the transient process utilizes the problem of stabilization and tracking control and gives a relatively small initial estimation error, which enlarges the range of the controller parameters. The convincing analysis of the proposed modified linear extended state observer is presented to show its high effectiveness on estimating the states and the extended states known as the total disturbances consisting of the unknown external disturbances and the nonlinearities neglected by the linearization. Simulation results on the stabilization and tracking control of the X‐Z inverted pendulum, including a comparative simulation with an all‐state‐feedback sliding mode controller are presented to show the advantages of the combination of flatness and active disturbance rejection control techniques. 相似文献
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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. 相似文献
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为提高倒立摆控制系统的抗扰动能力,降低其对未建模动态等的敏感度,研究了不确定平面二级倒立摆的鲁棒自适应控制器的设计方法。把倒立摆动力学模型分解为确定和不确定两部分,用一个非线性参数化模糊逻辑系统逼近平面二级倒立摆的不确定动态,采用李雅普诺夫稳定性理论推导出使平面二级倒立摆的状态误差渐近收敛的鲁棒控制器及自适应律。理论分析和仿真结果表明所提出的控制算法是有效的。 相似文献
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《Automatica》1996,32(6):933-937
The problem of balancing an inverted pendulum has been a benchmark example in demonstrating and motivating various control design techniques. In this paper, we provide a linear state feedback design technique for balancing an inverted pendulum. The pivot of this pendulum is mounted on a carriage that has limited horizontal travel. For any given (arbitrarily small) allowable travel of the carriage, our design yields a linear state feedback controller that balances the pendulum with an infinite amount of gain margin in the sense that, if the feedback gain is perturbed by any multiplying factor greater than one, the controller will still balance the pendulum without requiring greater traveling distance than the maximum allowable. 相似文献
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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。 相似文献
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针对直线一级倒立摆的稳定控制问题,设计了分数阶比例积分(FOPI和FO[PI])控制器。首先,根据Newton力学方法建立了倒立摆系统的数学模型。然后,采用基于向量的增益鲁棒性分数阶控制器参数求解简化算法,设计了分数阶比例积分控制器。最后,在MATLAB环境下进行了分数阶比例积分控制器参数整定方法的有效性验证,并且对倒立摆系统分别采用分数阶比例积分控制器和整数阶PID(IOPID)控制器进行了稳定控制仿真实验,并将得到的摆杆角度响应曲线进行了对比分析。结果表明:分数阶比例积分控制器对系统的稳定控制效果优于IOPID控制器,且在分数阶比例积分控制器中,FO[PI]控制器对系统稳定控制最好,响应时间较快、振荡幅值较小且具有鲁棒性。 相似文献
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Feedback control of nonlinear systems by extended linearization 总被引:1,自引:0,他引:1
For single-input, multiple-output, nonlinear systems, we consider a design method based on the family of linearizations of the system, parameterized by constant operating points. Nonlinear state feedback control laws and observer/state feedback control laws are designed such that the eigenvalues of the family of linearized closed-loop systems are placed at specified values that are locally invariant with respect to the closed-loop operating point. The method is illustrated by application to the problem of automatically balancing an inverted pendulum. 相似文献
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Event‐triggered predictive control for networked control systems with network‐induced delays and packet dropouts 下载免费PDF全文
This paper presents an event‐triggered predictive control approach to stabilize a networked control system subject to network‐induced delays and packet dropouts, for which the states are not measurable. An observer‐based event generator is first designed according to the deviation between the state estimation at the current time and the one at the last trigger time. A predictive control scheme with a selector is then proposed to compensate the effect of network‐induced delays and packet dropouts. Sufficient conditions for stabilization of the networked control system are derived by solving linear matrix inequalities and the corresponding gains of the controller and the observer are obtained. It is shown that the event‐triggered implementation is able to realize reduction in communication and save bandwidth resources of feedback channel networks. A simulation example of an inverted pendulum model illustrates the efficacy of the proposed scheme. 相似文献
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LQR控制器在含有系统噪声与量测噪声的旋转倒立摆系统应用中,难以获得精确的状态向量实现对系统的最优控制.为了提高LQR的控制精度,引入了无迹卡尔曼滤波(UKF)状态观测器,以获得系统的最优状态估计量,实现基于动态规划的自抗扰二次型最优反馈控策略.与卡尔曼滤波(KF)相比,UKF用于非线性系统的状态估计的主要优势是不需要线性化去计算状态转移矩阵,避免了系统线性化带来的模型误差.在含有系统噪声与量测噪声的旋转倒立摆仿真模型下,对基于KF和UKF的LQR控制器进行了仿真对比分析.仿真结果表明,UKF对系统响应时间、控制精度、鲁棒性的优化效果更好. 相似文献
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Functional observers are the primary solution to sundry estimation problems, wherein full- or reduced-order observer cannot be directly applied. This paper presents a functional observer-based sliding mode control method for the linear discrete-time delayed stochastic system. Stability analysis of sliding function is presented for the delayed stochastic system with a linear matrix inequality approach. The functional observer method for the linear discrete-time-delayed stochastic system is proposed based on the Kronecker product approach. Sliding mode controller is estimated using the functional observer method. Finally, to demonstrate the efficacy of the proposed design, comparison of its performance with some of the well-known existing state feedback controller is presented. 相似文献
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A high-precision fuzzy controller, based on a state observer, is developed for a class of nonlinear single-input-single-output (SISO) systems with system uncertainties and external disturbances. The state observer is introduced to resolve the problem of the unavailability of state variables. Assisted by the observer, a variable universe fuzzy system is designed to approximate the ideal control law. Being auxiliary components, a robust control term and a state feedback control term are designed to suppress the influence of the lumped uncertainties and remove the observation error, respectively. Different from the existing results, no additional dynamic order is required for the control design. All the adaptive laws and the control law are built based on the Lyapunov synthesis approach, and the signals involved in the closed-loop system are guaranteed to be uniformly ultimately bounded. Simulation results performed on Duffing forced oscillation demonstrate the advantages of the proposed control scheme. 相似文献