SHI D F , HOU Y L , GU X H , et al. Improved finite control set optimal control for PMSM in rocket launcher servo system [J ] . Shock and Vibration , 2020 , 2020 ( 8 ): 1 - 11 .

HOU R M , WANG L , GAO Q , et al. Indirect adaptive fuzzy wavelet neural network with self-recurrent consequent part for AC servo system [J ] . ISA Transactions , 2017 , 70 : 298 - 307 . DOI: 10.1016/j.isatra.2017.04.010 http://doi.org/10.1016/j.isatra.2017.04.010 https://linkinghub.elsevier.com/retrieve/pii/S0019057817303816 https://linkinghub.elsevier.com/retrieve/pii/S0019057817303816

王荣林 , 陆宝春 , 侯润民 , 等 . 交流伺服系统分数阶PID改进型自抗扰控制 [J ] . 中国机械工程 , 2019 , 30 ( 16 ): 1989 - 1995 . 针对采用永磁同步电机驱动的火箭炮交流伺服系统存在摩擦、惯性力矩、变负载及不同工况下内外扰动等复杂非线性问题,考虑到自抗扰控制(ADRC)抗内外干扰能力强和分数阶PID控制动态性能好，设计了一种分数阶PID改进型自抗扰控制器(FOPID-IADRC)。为了取得良好的动态性能和减少参数计算量，采用分数阶PID控制器取代非线性状态误差反馈器；引入粒子群优化算法，对FOPID控制器的5个控制参数进行实时在线自整定。仿真和半实物台架实验结果表明：该控制策略能够有效抑制位置扰动，具有良好的动态性能和较强的抗干扰能力。

WANG R L , LU B C , HOU R M , et al. FOPID improved ADRC in AC servo systems [J ] . China Mechanical Engineering , 2019 , 30 ( 16 ): 1989 - 1995 . (in Chinese) Aiming at the complicated nonlinear problems such as frictions,moments of inertia,variable loads and internal and external disturbances under different working conditions in AC servo systems of rocket launchers driven by PMSM, considering the strong internal and external interference resistances of ADRC and the excellent dynamic performance characteristics of FOPID control,an improved auto disturbance rejection controller optimized by FOPID controller(FOPID-IADRC) was designed herein.In order to achieve good dynamic performances and reduce the parameters' calculations,the non-linear state error feedback was substituted by FOPID controller.PSO algorithm was adopted to realize real-time self-tune of 5 parameters of FOPID controller.The simulation and semi-physical bench test results show that the control strategy may effectively resist position disturbances,and has good dynamic performances and strong anti-interference ability.

高强 , 侯润民 , 杨国来 , 等 . 基于分数阶神经滑模的某顶置火炮调炮控制 [J ] . 兵工学报 , 2013 , 34 ( 10 ): 1311 - 1317 . DOI: 10. 3969/ j. issn. 1000-1093. 2013. 10. 018 http://doi.org/10. 3969/ j. issn. 1000-1093. 2013. 10. 018 针对某顶置火炮高低向调炮控制系统存在的强非线性特征,提出了一种分数阶神经网 络滑模控制(FNSMC)策略。引入分数阶微积分(FOC),设计了分数阶PID 型滑模面,获得了用于 火炮控制的具有分数阶动力学特征的等效控制量。采用饱和函数作为切换函数,基于RBF 神经网 络对其切换增℃进行在线动态调节,以获得动态最优性能。通过数值仿真分析比较了引入FOC 后 滑模控制系统的动静态特性,结果表明:分数阶滑模控制(FSMC)系统能够更为快速平滑的趋近稳 态,这将有效抑制抖振现象,减小控制系统响应时间。半实物仿真试验结果表明:所提出的FNSMC 策略明显优于传统整数阶神经网络滑模控制( CNSMC),具有更强的鲁棒性及更高的控制精度,可 以很好实现预期的快速、平稳和高精度调炮。

GAO Q , HOU R M , YANG G L , et al. Adjustment and control of a certain top-mounted gun based on a novel fractional order neural sliding mode strategy [J ] . Acta Armamentarii , 2013 , 34 ( 10 ): 1311 - 1317 . (in Chinese) DOI: 10. 3969/ j. issn. 1000-1093. 2013. 10. 018 http://doi.org/10. 3969/ j. issn. 1000-1093. 2013. 10. 018 A novel fractional order neural sliding mode control (FNSMC) strategy is proposed for the nonlinearities of a gun control system (GCS) which is used to control the elevation of a certain topmounted gun. A fractional order PID type sliding surface is especially designed by introducing the fractional order calculus, and an equivalent control discipline with fractional order dynamics is induced. The saturation function is employed as switch function. To achieve the best control performances, a dynamic adjustment approach of the switch gain is introduced based on RBF neural network. The dynamic and static characteristics of the fractional order sliding mode control (FSMC) system are analyzed by numerical simulation, demonstrating that FSMC can reach up to the steady state more smoothly, which significantly suppresses the chatter effects and enhances the response rate of the control system. Finally, a series of experiments on a semi-physics simulation platform are conducted to investigate the performances of control system. The results show that the proposed FNSMC is of more excellence than the conventional integer order neural SMC(CNSMC). The FNSMC-based control system is of better tracking accuracy as well as high robustness, and the fast, smooth and accurate adjustments of the gun can be achieved.

冯亮 , 马晓军 , 李华 . 基于扩张状态观测器滤波的坦克炮控系统模型参考自适应控制 [J ] . 兵工学报 , 2009 , 30 ( 10 ): 1375 - 1381 . 坦克炮控系统是一类不确定、非线性的复杂系统。针对其在低速运行时产生“爬行”、振荡等的问题，依据扩张状态观测器(ESO)滤波和Popov超稳定理论，提出了一种基于ESO滤波的模型参考自适应控制方法。研究了坦克炮控系统的数学模型，给出了基本假设，设计了ESO滤波器和模型参考自适应控制器，并证明了其稳定性，最后通过仿真验证了该方法的有效性。仿真结果表明，该方法有效地消除了系统的末建模动态及外界扰动的影响，增强了系统的快速性，解决了系统的低速“爬行”问题，改善了系统的稳态性能，为炮控系统实际设计提供了一个可行的解决方案。

FENG L , MA X J , LI H . Method of model reference adaptive control for tank gun control system based on ESO filter [J ] . Acta Armamentarii , 2009 , 30 ( 10 ): 1375 - 1381 . (in Chinese) The tank gun control system is one uncertain and nonlinear system. A new method of model reference adaptive control for the system which contains crawl and vibration phenomena at a very low speed based on extended state observer(KSO) filter was presented by theory of the filter and hy-perstability.Matherratic model of the system was studied with the defined basic hypotheses. ESO nl- ter ana model reference adaptive controller were designed, the stability was proved; simulating was performed by a real example. The simulated results snow that the method eliminates influence of un-modeled dynamics and environmental disturbance on the system, enhances celerity of the system, solves crawl phenomenon at extremely low speed, improves steady-state performance, and provides a realistic new technique for the design of the system.

李伟 , 姜俊峰 , 任海波 , 等 . 行进间火炮指向稳定跟踪系统建模与控制 [J ] . 兵工学报 , 2018 , 39 ( 8 ): 1479 - 1490 . DOI: 10.3969/j.issn.1000-1093.2018.08.004 http://doi.org/10.3969/j.issn.1000-1093.2018.08.004 为使行进间火炮指向具备高射角条件下的稳定跟踪能力，提出了一种采用捷联惯性导航系统（SINS）测量火炮身管轴线指向，同时测量火炮身管运动角速率，完成火炮在大地坐标系下的稳定跟踪控制方法。稳定系统采用传统的三环控制，将系统的位置环和速度稳定环的主令和反馈都统一至大地坐标系下，SINS作为系统的位置环反馈，其航向和姿态测量值基于大地坐标系下完成解算。将安装在火炮上的SINS陀螺组测量值转换至大地坐标系下的火炮方位回转角速率和高低俯仰角速率，并乘以各自传动机构的传动比后，作为速率稳定环的反馈，实现速率稳定控制。考虑炮塔、火炮回转中心与重心不重合、载体处于六自由度运动状态等因素，采用Lagrange方法建立火炮、炮塔与载体之间动力学耦合模型，结合SINS测量模型、双电机拖动和电机伺服系统控制模型，对该控制方案进行了仿真验证。验证结果表明，火炮指向稳定跟踪系统实现方位和高低两个通道独立控制，使火炮指向在高角下保持高精度的稳定控制，在一定射角范围内具有良好跟踪性能，能够克服较宽频带载体姿态干扰，明显优于传统高炮位置解算式稳定。

LI W , JIANG J F , REN H B , et al. FOPID improved ADRC in AC servo systems [J ] . Acta Armamentarii , 2018 , 39 ( 8 ): 1479 - 1490 . (in Chinese)

KARAYUMAK T . Modelling and stabilization control of a main battle tank [D ] . Ankara, Turkey : Middle East Technical University , 2011 .

ZHUANG H X , SUN Q L , CHEN Z Q , et al. Back-stepping active disturbance rejection control for attitude control of aircraft systems based on extended state observer [J ] . International Journal of Control, Automation and Systems , 2021 , 19 ( 6 ): 2134 - 2149 . DOI: 10.1007/s12555-019-1029-x http://doi.org/10.1007/s12555-019-1029-x

LI S Q , ZHANG K Z , LI J , et al. On the rejection of internal and external disturbances in a wind energy conversion system with direct-driven PMSG [J ] . ISA Transactions , 2015 , 61 : 95 - 103 . DOI: 10.1016/j.isatra.2015.12.014 http://doi.org/10.1016/j.isatra.2015.12.014 https://linkinghub.elsevier.com/retrieve/pii/S0019057815003183 https://linkinghub.elsevier.com/retrieve/pii/S0019057815003183

ZHANG Y , CHEN Z Q , ZHANG X H , et al. A novel control scheme for quadrotor UAV based upon active disturbance rejection control [J ] . Aerospace Science and Technology , 2018 , 79 : 601 - 609 . DOI: 10.1016/j.ast.2018.06.017 http://doi.org/10.1016/j.ast.2018.06.017 https://linkinghub.elsevier.com/retrieve/pii/S1270963818305315 https://linkinghub.elsevier.com/retrieve/pii/S1270963818305315

ATASSI A , KHALIL H . Separation results for the stabilization of nonlinear systems using different high-gain observer designs [J ] . Systems and Control Letters , 2000 , 38 : 183 - 191 .

柯栋梁 , 汪凤翔 , 李家祥 . 基于自适应高增益观测器的永磁同步电机预测电流控制方法 [J ] . 中国电机工程学报 , 2021 , 41 ( 2 ): 728 - 737 .

KE D L , WANG F X , LI J X . Predictive current control of permanent magnet synchronous motor based on an adaptive high-gain observer [J ] . Proceedings of the CSEE , 2021 , 41 ( 2 ): 728 - 737 . (in Chinese)

潘月斗 , 陈虎 . 基于高增益观测技术的高精度感应电机磁链观测器研究 [J ] . 控制与决策 , 2014 , 29 ( 8 ): 1495 - 1500 .

PAN Y D , CHEN H . Research on high gain technique based on-line fluxes estimation for IMs [J ] . Control and Decision , 2014 , 29 ( 8 ): 1495 - 1500 . (in Chinese)

韩京清 , 袁露林 . 跟踪-微分器的离散形式 [J ] . 系统科学与数学 , 1999 , 19 ( 3 ): 268 - 273 .

HAN J Q , YUAN L L . The discrete form of tracking- differentiator [J ] . Journal of System Science and Mathematical Sciences , 1999 , 19 ( 3 ): 268 - 273 . (in Chinese)

郑怀航 , 王军政 , 刘冬琛 , 等 . 融合前馈与姿态预测的并联稳定平台自抗扰控制策略 [J ] . 机械工程学报 , 2021 , 57 ( 9 ): 19 - 27 . DOI: 10.3901/JME.2021.09.019 http://doi.org/10.3901/JME.2021.09.019 针对并联式结构平台姿态稳定时对高频扰动信号跟踪的响应滞后以及负载、摩擦力等非线性因素等影响稳定精度问题，提出了一种融合前馈与姿态预测的并联稳定平台自抗扰控制（Active disturbance rejection control，ADRC）控制策略。通过对电动伺服缸、平台运动学建模，得到了电动伺服缸状态方程和平台稳定时电动缸位移与电动机电流控制量转化关系。基于ADRC扩张状态观测器对伺服电动缸在时变摩擦力和负载力等干扰下进行观测并补偿，并采用非线性跟踪微分器改善控制过程中电动机的超速报警与快速性之间的矛盾。最后将姿态预测方程与前馈控制相结合，提高了系统的响应速度，减小了稳定平台跟踪误差。在具有俯仰、横滚和垂直平移三个自由度的并联式稳定平台上进行仿真与试验，相比传统PID或ADRC控制方法，提出的控制策略不仅使稳定平台有很强的抗负载扰动能力，而且具有更快的响应速度和更高的稳定精度。

ZHENG H H , WANG J Z , LIU D C , et al . Active disturbance rejection control strategy of parallel stable platform based on feedforward and attitude prediction [J ] . Journal of Mechanical Engineering , 2021 , 57 ( 9 ): 19 - 27 . (in Chinese) DOI: 10.3901/JME.2021.09.019 http://doi.org/10.3901/JME.2021.09.019 This research proposes an active disturbance rejection control (ADRC) method with a feed-forward compensator for a parallel stability platform based on its attitude prediction model. The time delay of the control system responding to high frequency inputs and the nonlinear disturbances arising from loading conditions and frictions are considered to improve the tracking performance. Through analyzing the dynamics of the electric cylinders and the kinematics of the parallel mechanism, the control model in state space together with the kinematic inverse model of the system are introduced. An extended state observer (ESO) is designed to observe the nonlinear disturbances of friction behaviors and loading conditions, and the non-linear tracking differentiator (TD) is used to realize a rapidly response of the electric cylinders without overspeed alarm. With the observation results and the TD, a closed-loop controller with a feed-forward compensator based on the attitude prediction model of the platform is presented to improve tracking accuracy and response speed. The control method is verified on a 3 degree-of-freedom (DOF) parallel stability platform, and comparative experimental results indicate that under different loading conditions, the proposed controller can achieve satisfactory tracking performance for the 3-DOF platform with an increased response speed and a reduced tracking error.

路遥 . 基于跟踪微分器的高超声速飞行器Backstepping 控制 [J ] . 航空学报 , 2021 , 42 (X): 324737 .

LU Y . Backstepping control for hypersonic flight vehicles based on tracking differentiator [J ] . Acta Aeronautica et Astronautica Sinica , 2021 , 42 (X): 324737 . (in Chinese)

ARIE L . Robust exact differentiation via sliding mode technique [J ] . Automatica , 1998 , 34 ( 3 ): 379 - 384 . DOI: 10.1016/S0005-1098(97)00209-4 http://doi.org/10.1016/S0005-1098(97)00209-4 https://linkinghub.elsevier.com/retrieve/pii/S0005109897002094 https://linkinghub.elsevier.com/retrieve/pii/S0005109897002094

YU J D , JIN S H . Sliding mode tracking differentiator with adaptive gains for filtering and derivative estimation of noisy signals [J ] . IEEE Access , 2021 , 9 : 86017 -86024. DOI: 10.1109/ACCESS.2021.3088544 http://doi.org/10.1109/ACCESS.2021.3088544 https://ieeexplore.ieee.org/document/9452130/ https://ieeexplore.ieee.org/document/9452130/

那靖 , 董宇 , 丁海港 , 等 . 含执行机构未知动态的液压伺服系统输出反馈控制 [J ] . 控制与决策 , 2020 , 35 ( 5 ): 1078 - 1084 .

NA J , DONG Y , DING H G , et al. Output feedback control for hydraulic servo systems with unknown actuator dynamics [J ] . Control and Decision , 2020 , 35 ( 5 ): 1078 - 1084 . (in Chinese)

王新华 , 陈增强 , 袁著祉 . 全程快速非线性跟踪-微分器 [J ] . 控制理论与应用 , 2003 , 20 ( 6 ): 875 - 878 .

WANG X H , CHEN Z Q , YUAN Z Z . Nonlinear tracking- differentiator with high speed in whole course [J ] . Control Theory &Applications , 2003 , 20 ( 6 ): 875 - 878 . (in Chinese)

邵星灵 , 王宏伦 , 张惠平 , 等 . 基于微分器的轨迹线性化控制方法及其应用 [J ] . 北京航空航天大学学报 , 2015 , 41 ( 7 ): 1259 - 1268 .

SHAO X L , WANG H L , ZHANG H P , et al. Control method and applications of robust trajectory linearization via nonlinear differentiators [J ] . Journal of Beijing University of Aeronautics and Astronautics , 2015 , 41 ( 7 ): 1259 - 1268 . (in Chinese)

DU X J , WANG J L , JEGATHEESAN V , et al. Dissolved oxygen control in activated sludge process using a neural network-based adaptive PID algorithm [J ] . Applied Sciences-Basel , 2018 , 8 ( 2 ): 1 - 21 .

KUNG Y S , THAN H , CHUANG T Y . FPGA-realization of a self-tuning PID controller for X-Y table with RBF neural network identification [J ] . Microsystem Technologies-Micro-And Nanosystems-Information Storage and Processing Systems , 2018 , 24 ( 1 ): 243 - 253 .

MA D R , SONG M X , YU P C , et al. Research of RBF-PID control in maglev system [J ] . Symmetry-Basel , 2020 , 12 ( 11 ): 1 - 15 .

周振雄 , 杨建东 , 曲永印 , 等 . 基于自抗扰控制器的磁浮平台水平推力控制 [J ] . 机械工程学报 , 2008 , 44 ( 9 ): 193 - 199 . 介绍一种新型的磁浮平台，针对该磁浮平台水平运动这一多变量、非线性、强耦合的系统，提出一种改进的自抗扰控制器，克服常规自抗扰控制器非线性状态误差反馈控制律中非线性函数的不平滑性，并探索出一套行之有效的控制器参数整定规则，同时利用扩张状态观测器观测出内部扰动和外部扰动，并对它们进行补偿。仿真对比分析和试验结果表明，这种改进的自抗扰控制器具有很好的动态、静态特性及鲁棒性。

ZHOU Z X , YANG J D , QU Y Y , et al. Horizontal thrust control of magnetic suspension platform based on active disturbance rejection controller [J ] . Journal of Mechanical Engineering , 2008 , 44 ( 9 ): 193 - 199 . (in Chinese) A novel planar magnetic suspension platform is introduced. In view of the horizontal movement of the magnetic suspension platform being a nonlinear, multivariable and strong coupling system, an improved active disturbance rejection controller (ADRC) is proposed. It can overcome the unsmoothness of non-linear function in nonlinear state error feedback (NLSEF) of conventional ADRC, and a set of effective rules of setting controller parameters is explored. Moreover, the internal disturbance and external disturbance are observed by using the extended state observer (ESO) and then compensated. The results of simulation and experiment indicate that the improved controller has excellent dynamic and static characteristics and robustness.

周振雄 , 曲永印 , 杨建东 , 等 . 一种改进型ADRC实现的机床进给用永磁直线同步电动机调速系统 [J ] . 中国机械工程 , 2008 , 19 ( 21 ): 2561 - 2565 .

ZHOU Z X , QU Y Y , YANG J D , et al. Speed regulation system of permanent magnet linear synchronous motor for machine tool feeding based on improved ADRC [J ] . China Mechanical Engineering , 2008 , 19 ( 21 ): 2561 - 2565 . (in Chinese)

周振雄 , 曲永印 , 杨建东 , 等 . 采用改进型自抗扰控制器的平面磁轴承悬浮控制 [J ] . 电工技术学报 , 2010 , 25 ( 6 ): 31 - 38 .

ZHOU Z X , QU Y Y , YANG J D , et al. Levitation control of a planar magnetic bearing based on improved ADRC [J ] . Transactions of China Electro-technical Society , 2010 , 25 ( 6 ): 31 - 38 . (in Chinese)

XU F X , ZHANG X J , SONG X H , et al. Composite control of RBF neural network and PD for nonlinear dynamic plants using U-model [J ] . Journal of Intelligent & Fuzzy Systems , 2018 , 35 ( 1 ): 565 - 575 .

LIU K , WU Y , ZHU T M , et al. Improved RBF network torque control in flexible manipulator actuated by PMAs [J ] . Robotica , 2019 , 37 ( 2 ): 264 - 280 . DOI: 10.1017/S0263574718001005 http://doi.org/10.1017/S0263574718001005 https://www.cambridge.org/core/product/identifier/S0263574718001005/type/journal_article https://www.cambridge.org/core/product/identifier/S0263574718001005/type/journal_article A Pneumatic Muscle Actuator (PMA) is a new pneumatic component sharing similar characteristics with biological muscles, and the flexible manipulator actuated by PMAs can better reflect the flexibility of the mechanism. First and foremost, based on the study of the characteristics of human shoulder joints, the configuration design of the flexible manipulator is analyzed, and its kinematics and dynamics models are established. Furthermore, with regard to the nonlinearity, time-invariance and uncertainty of the control system, three aspects of improvement are proposed, which are based on the Radial Basis Function (RBF) network torque control algorithm. The Genetic Algorithm is used to optimize the initial values of RBF network parameters; RBF network parameters are adjusted dynamically by using the additional momentum method; the Levenberg--Marquardt (LM) algorithm, instead of the gradient descent method, is adopted to adjust Proportion Integration Differentiation (PID) parameters online in real time. At last, to test the effects that the improved algorithm exerts on the flexible manipulator control system, some physical platform experiments are carried out. It turns out that the control accuracy and robustness of the improved algorithm are well improved, and the mechanism can be controlled better to track the circular arc trajectory. It lays fundamental importance to the practical application for the working environment.