【作者】 王永帅； 陈增强； 孙明玮； 孙青林；

【Author】 WANG Yong-shuai;CHEN Zeng-qiang;SUN Ming-wei;SUN Qing-lin;College of Computer and Control Engineering, Nankai University;

【机构】 南开大学人工智能学院；

【摘要】 自抗扰控制技术是一种新型的、不依赖被控对象模型的、易于操作的控制方法,可以较好地处理非线性、强耦合、多变量问题,已成功应用于各种复杂系统。因此,研究自抗扰控制技术的稳定性和鲁棒性具有重要意义。针对非线性系统、大时滞系统和非最小相位大时滞系统,设计了线性自抗扰控制器,分析了闭环控制系统的稳定性和鲁棒性问题,主要做了以下三个工作:(1)基于一、二阶非线性被控对象,将闭环系统的输出误差和估计误差结合分析,利用李雅普诺夫函数得到了自抗扰控制系统全局渐近稳定的条件。当总扰动已知且导数满足利普希茨条件时,定量求得了控制参数可行域。当总扰动未知时,还需满足其二阶导数为零的条件。特别地,针对一阶系统,利用Markus-Yamabe定理得到了降阶自抗扰控制系统全局渐近稳定性,数学证明和仿真结果说明了结论的正确性。(2)针对一阶惯性大时滞被控对象,将Smith预估器与自抗扰技术结合,设计了ADRC-Smith控制器。对于全阶控制器,利用劳斯判据分析了控制系统的稳定条件,当被控对象存在不确定性时,获得了Smith预估器的设计原则和控制参数的调节规律。对于降阶控制器,应用劳斯判据得到了参数摄动范围,并求得了摄动范围内的相角裕度。仿真结果证明ADRC-Smith控制器的鲁棒性优于单独自抗扰控制器。(3)基于含不稳定极点和大时滞的非最小相位被控对象,单独自抗扰控制器不能获得理想的控制效果,而加入Smith预估器使得被控对象对扰动极其敏感。因此,通过引入两个比例反馈实现非最小相位不确定被控对象的稳定控制,利用奈氏曲线和伯德图分析了其频域特性,蒙特卡罗试验证明了该方法的强鲁棒性。更多还原

【Abstract】 Active disturbance rejection control(ADRC) is a novel control method which is easy to implement and not model based. It can well deal with nonlinearity, strong couplings and multivariable systems, and has been successfully applied to a variety of complex systems. Therefore, it is of great significance to analyze the stability and robustness of ADRC technique. Based on nonlinear systems, large time-delay systems and non-minimum phase systems with large time-delay, a linear form of ADRC(LADRC) is designed, and the stability and robustness of closed-loop control systems are analyzed. The following three tasks are considered.(1) For first-order and second-order nonlinear systems, an analysis is conducted by combining output error and estimation error, and the globally and asymptotically stable conditions for LADRC systems are obtained. To be specific, when plant dynamics are known and satisfy a Lipschitz condition, the feasible region of control parameters is quantitatively acquired. If dynamics are uncertain, another condition that the second derivative is zero should also be satisfied. Specially, for first-order systems, Markus-Yamabe theorem is applied to analyze the global and asymptotical stability of reduced-order LADRC system. Both mathematical proofs and simulation results show the correctness of the conclusions.(2) Based on the first-order inertia systems with large time-delay, an ADRC-Smith controller is designed by combining ADRC with Smith predictor. For full-order controller, the stable conditions are obtained using Routh criterion, and design principles of Smith predictor and parameter regulation are concluded when uncertainties exist. For reduced-order controller, Routh criterion is employed to get the feasible region of perturbations, in which the phase margin is calculated. Furthermore, simulation results proved that ADRC-Smith controller has better robustness than ADRC technique.(3) For non-minimum phase plant with unstable poles and large time-delay, ADRC controller cannot receive ideal performance, and will become extremely sensitive to uncertainties when utilizing Smith predictor. Thus two proportional feedback links are introduced to achieve stable for uncertain non-minimum phase plant. Besides, Nyquist and Bode diagram are adopted to carry out frequency analysis, and Monte Carlo simulation results show the strong robustness.更多还原