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Robust missile autopilot design based on dynamic surface control
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作者 ZHOU Jianping LI Wei +1 位作者 XIA Qunli JIANG Huan 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2023年第1期160-171,共12页
Since the dynamical system and control system of the missile are typically nonlinear, an effective acceleration tracking autopilot is designed using the dynamic surface control(DSC)technique in order to make the missi... Since the dynamical system and control system of the missile are typically nonlinear, an effective acceleration tracking autopilot is designed using the dynamic surface control(DSC)technique in order to make the missile control system more robust despite the uncertainty of the dynamical parameters and the presence of disturbances. Firstly, the nonlinear mathematical model of the tail-controlled missile is decomposed into slow acceleration dynamics and fast pitch rate dynamics based on the naturally existing time scale separation. Secondly, the controller based on DSC is designed after obtaining the linear dynamics characteristics of the slow and fast subsystems. An extended state observer is used to detect the uncertainty of the system state variables and aerodynamic parameters to achieve the compensation of the control law. The closed-loop stability of the controller is derived and rigorously analyzed. Finally, the effectiveness and robustness of the design is verified by Monte Carlo simulation considering different initial conditions and parameter uptake. Simulation results illustrate that the missile autopilot based DSC controller achieves better performance and robustness than the other two well-known autopilots.The method proposed in this paper is applied to the design of a missile autopilot, and the results show that the acceleration tracking autopilot based on the DSC controller can ensure accurate tracking of the required commands and has better performance. 展开更多
关键词 acceleration autopilot nonlinear missile dynamics time-scale separation extended state observer dynamic surface control(DSC)
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Adaptive Fuzzy Dynamic Surface Control of Flexible-Joint Robot Systems With Input Saturation 被引量:23
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作者 Song Ling Huanqing Wang Peter X.Liu 《IEEE/CAA Journal of Automatica Sinica》 EI CSCD 2019年第1期97-107,共11页
In this paper, we propose an adaptive fuzzy dynamic surface control(DSC) scheme for single-link flexible-joint robotic systems with input saturation. A smooth function is utilized with the mean-value theorem to deal w... In this paper, we propose an adaptive fuzzy dynamic surface control(DSC) scheme for single-link flexible-joint robotic systems with input saturation. A smooth function is utilized with the mean-value theorem to deal with the difficulties associated with input saturation. An adaptive DSC design with an auxiliary first-order filter is used to solve the "explosion of complexity"problem. It is proved that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded, and the tracking error eventually converges to a small neighborhood around zero. The main advantage of the proposed method is that only one adaptation parameter needs to be updated,which reduces the computational burden significantly. Simulation results demonstrate the feasibility of the proposed scheme and the comparison results show that the improved DSC method can reduce the computational burden by almost two thirds in comparison with the standard DSC method. 展开更多
关键词 Adaptive fuzzy control dynamic surface control (DSC) flexible-joint (FJ) robots single-link tracking control
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Output-feedback Dynamic Surface Control for a Class of Nonlinear Non-minimum Phase Systems 被引量:5
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作者 Shanwei Su 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI 2016年第1期96-104,共9页
In this paper, an output-feedback tracking controller is proposed for a class of nonlinear non-minimum phase systems.To keep the unstable internal dynamics bounded, the method of output redefinition is applied to let ... In this paper, an output-feedback tracking controller is proposed for a class of nonlinear non-minimum phase systems.To keep the unstable internal dynamics bounded, the method of output redefinition is applied to let the stability of the internal dynamics depend on that of redefined output, thus we only need to consider the new external dynamics rather than internal dynamics in the process of designing control law. To overcome the explosion of complexity problem in traditional backstepping design, the dynamic surface control(DSC) method is firstly used to deal with the problem of tracking control for the nonlinear non-minimum phase systems. The proposed outputfeedback DSC controller not only forces the system output to asymptotically track the desired trajectory, but also drives the unstable internal dynamics to follow its corresponding bounded and causal ideal internal dynamics, which is solved via stable system center method. Simulation results illustrate the validity of the proposed output-feedback DSC controller. 展开更多
关键词 Non-minimum phase system OUTPUT-FEEDBACK trajectory tracking internal dynamics dynamic surface control(DSC)
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Output Feedback Dynamic Surface Controller Design for Airbreathing Hypersonic Flight Vehicle 被引量:4
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作者 Delong Hou Qing Wang Chaoyang Dong 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI 2015年第2期186-197,共12页
This paper addresses issues related to nonlinear robust output feedback controller design for a nonlinear model of airbreathing hypersonic vehicle. The control objective is to realize robust tracking of velocity and a... This paper addresses issues related to nonlinear robust output feedback controller design for a nonlinear model of airbreathing hypersonic vehicle. The control objective is to realize robust tracking of velocity and altitude in the presence of immeasurable states, uncertainties and varying flight conditions.A novel reduced order fuzzy observer is proposed to estimate the immeasurable states. Based on the information of observer and the measured states, a new robust output feedback controller combining dynamic surface theory and fuzzy logic system is proposed for airbreathing hypersonic vehicle. The closedloop system is proved to be semi-globally uniformly ultimately bounded(SUUB), and the tracking error can be made small enough by choosing proper gains of the controller, filter and observer. Simulation results from the full nonlinear vehicle model illustrate the effectiveness and good performance of the proposed control scheme. 展开更多
关键词 Hypersonic flight vehicle immeasurable states output feedback control model uncertainties fuzzy logic system dynamic surface control
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Dynamic Surface Control with Nonlinear Disturbance Observer for Uncertain Flight Dynamic System 被引量:3
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作者 李飞 胡剑波 +1 位作者 吴俊 王坚浩 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI CSCD 2015年第4期469-476,共8页
A new robust control method of a nonlinear flight dynamic system with aerodynamic coefficients and external disturbance has been proposed.The proposed control system is a combination of the dynamic surface control(DSC... A new robust control method of a nonlinear flight dynamic system with aerodynamic coefficients and external disturbance has been proposed.The proposed control system is a combination of the dynamic surface control(DSC)and the nonlinear disturbance observer(NDO).DSC technique provides the ability to overcome the″explosion of complexity″problem in backstepping control.NDO is adopted to observe the uncertainties in nonlinear flight dynamic system.It has been proved that the proposed design method can guarantee uniformly ultimately boundedness of all the signals in the closed-loop system by Lyapunov stability theorem.Finally,simulation results show that the proposed controller provides better performance than the traditional nonlinear controller. 展开更多
关键词 nonlinear disturbance observer(NDO) dynamic surface control(DSC) UNCERTAINTIES flight control
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Adaptive dynamic surface control for quadrotor-slung load transportation system with uncertainties
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作者 DING Feng HUANG Jian +3 位作者 SUN Chong AI Yong XU WenXia YANG ChenGuang 《Science China(Technological Sciences)》 SCIE EI CAS CSCD 2023年第10期2917-2929,共13页
Quadrotors play a significant role in our lives and are transforming our lives.Transporting cable-suspended loads is an unavoidable quadrotor application trend and a hot research topic in the control field.Nonetheless... Quadrotors play a significant role in our lives and are transforming our lives.Transporting cable-suspended loads is an unavoidable quadrotor application trend and a hot research topic in the control field.Nonetheless,the load swing and unpredictability pose significant challenges to the quadrotor's stability.In this paper,an anti-swing controller with an inner-outer control strategy for the quadrotor-slung load transportation system is presented.To facilitate the controller design,the outer position dynamics are restructured in the form of cascades.Then,a virtual controller is created to force the underactuated states to the dynamic surface to ensure the position subsystem's stability.To improve robustness,an adaptive law is used to eliminate the effects of uncertain cable length.Lastly,a dynamic surface controller for the inner attitude subsystem is presented to drive the actual force to the virtual force.It is demonstrated that the control strategy can stabilize the quadrotor despite mass and cable length uncertainties.Comparative results are provided to demonstrate the efficacy and durability of the proposed method. 展开更多
关键词 quadrotor-slung load transportation system dynamic surface control adaptive law cascade system model uncertainties
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Shallow Tunneling Method and Control Measure for Ground Surface Settlement
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作者 Jinxiao Jia Xiong Zhou 《Journal of World Architecture》 2023年第3期46-52,共7页
In order to ensure that the tunnel deformation and surface settlement are controlled within the allowable range during the construction process,the design unit has compiled technical measures and monitoring schemes fo... In order to ensure that the tunnel deformation and surface settlement are controlled within the allowable range during the construction process,the design unit has compiled technical measures and monitoring schemes for ground settlement control of this project.Based on the example of a shallow tunneling project on Subway line 8,this paper analyzes and discusses the shallow tunneling method in detail and puts forward corresponding technical measures for ground settlement control. 展开更多
关键词 Shallow tunneling Ground surface settlement control Advance ductule
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Surface control of layered double hydroxides by in-situ initiating&terminating polymerization
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作者 Dan Tong Yuquan Zhu +3 位作者 Kaitao Li Kuilin Du Wendi Liu Yanjun Lin 《Nano Research》 SCIE EI CSCD 2022年第2期1538-1546,共9页
Appropriate surface modification or functionalization is prerequisite for the application of inorganic nanoparticles.And surface control between organic and inorganic interface plays an important role in constructing ... Appropriate surface modification or functionalization is prerequisite for the application of inorganic nanoparticles.And surface control between organic and inorganic interface plays an important role in constructing organic-inorganic composites.In-situ polymerization has been extensively studied to improve the compatibility and dispersibility of inorganic nanoparticles,but the polymerized nanoparticles tend to concatenate and form large composites,restricting further applications.Herein,uniform and dense polyacrylic acid(PAA)membranes have been grafted on layered double hydroxide(LDH)nanosheets via an in-situ initiating and terminating radical graft polymerization method.With initiating and terminating on the same particle,the size,morphology and density of grafted PAA onto the surface of LDHs can be controlled by adjusting the ratio of initiated sites to terminated sites,the amount of redox initiator or monomer.As a result,with only 17.33%organic grafting ratio,PAA@LDHs with largely improved compatibility can be monodispersed in polyethylene(PE)and polyvinyl chloride(PVC)matrices,which is determined by a fluorescence microscope technique. 展开更多
关键词 surface control in-situ polymerization organic-inorganic interface layered double hydroxides
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Adaptive leader follower control for multiple quadrotors via multiple surfaces control
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作者 ABBAS Rabah 伍清河 《Journal of Beijing Institute of Technology》 EI CAS 2016年第4期526-532,共7页
Based on the multiple surface and fixed undirected communication topology,the adaptive leader follower control for multiple quadrotors is discussed.Our approach is based on leader follower architecture.Multiple surfac... Based on the multiple surface and fixed undirected communication topology,the adaptive leader follower control for multiple quadrotors is discussed.Our approach is based on leader follower architecture.Multiple surface control(MSC)is used to design consensus controller to make multiple quadrotors construct a formation during flying with the presence of uncertainty item caused by the ground effect during landing or taking off.Simulation results are presented to validate the effectiveness of the proposed controller. 展开更多
关键词 QUADROTOR leader follower multiple surface control(MSC) unmanned aerial vehicle(UAV)
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Dynamic surface control and active disturbance rejection control-based integrated guidance and control design and simulation for hypersonic reentry missile
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作者 Cong Zhang Yun-Jie Wu 《International Journal of Modeling, Simulation, and Scientific Computing》 EI 2016年第3期216-242,共27页
This paper proposes a novel integrated guidance and control(IGC)method combining dynamic surface control(DSC)and active disturbance rejection control(ADRC)for the guidance and control system of hypersonic reentry miss... This paper proposes a novel integrated guidance and control(IGC)method combining dynamic surface control(DSC)and active disturbance rejection control(ADRC)for the guidance and control system of hypersonic reentry missile(HRM)with bounded uncertainties.First,the model of HRM is established.Second,the proposed IGC method based on DSC and ADRC is designed.The stability of closed-loop system is proved strictly.It is worth mentioning that the ADRC technique is used to estimate and compensate the disturbance in the proposed IGC system.This makes the closed-loop system a better performance and reduces the chattering caused by lumped disturbances.Finally,a series of simulations and comparisons with a 6-DOF non-linear missile that includes all aerodynamic effects are demonstrated to illustrate the effectiveness and advantage of the proposed IGC method. 展开更多
关键词 Hypersonic reentry missile integrated guidance and control dynamic surface control active disturbance rejection control SIMULATION
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Disturbance Observer-Based Safe Tracking Control for Unmanned Helicopters With Partial State Constraints and Disturbances
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作者 Haoxiang Ma Mou Chen Qingxian Wu 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2023年第11期2056-2069,共14页
In this paper, a disturbance observer-based safe tracking control scheme is proposed for a medium-scale unmanned helicopter with rotor flapping dynamics in the presence of partial state constraints and unknown externa... In this paper, a disturbance observer-based safe tracking control scheme is proposed for a medium-scale unmanned helicopter with rotor flapping dynamics in the presence of partial state constraints and unknown external disturbances. A safety protection algorithm is proposed to keep the constrained states within the given safe-set. A second-order disturbance observer technique is utilized to estimate the external disturbances. It is shown that the desired tracking performance of the controlled unmanned helicopter can be achieved with the application of the backstepping approach, dynamic surface control technique, and Lyapunov method. Finally, the availability of the proposed control scheme has been shown by simulation results. 展开更多
关键词 Disturbance observer dynamic surface control safe tracking control safety protection algorithm unmanned autonomous helicopter
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Internal Temperature of Skin when Surface Temperature Is Controlled with an Electromagnetic Beam
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作者 Hongyun Wang Wesley A. Burgei Hong Zhou 《Journal of Applied Mathematics and Physics》 2021年第3期427-440,共14页
We study the thermal effect on skin exposed to an electromagnetic beam of time-dependent power. We consider two types of beam power time schedules. In the controlled temperature exposure, the skin surface temperature ... We study the thermal effect on skin exposed to an electromagnetic beam of time-dependent power. We consider two types of beam power time schedules. In the controlled temperature exposure, the skin surface temperature is increased quickly to a prescribed level using a high beam power;then the surface temperature is maintained at the prescribed level by adjusting the beam power adaptively. In the constant power exposure, the applied beam power is relatively low and stays unchanged over the time. We start both types of exposures at the same time and compare their internal temperatures of skin when they have the same surface temperature. In a non-dimensionalized formulation, we show that at the moment when both exposure types reach the same prescribed surface temperature level, the controlled temperature exposure has a higher internal temperature at all depths. This conclusion is mathematically rigorous and is independent of skin material properties. 展开更多
关键词 Electromagnetic Beam of Time-Varying Power control of surface Temperature Thermal Effect of Beam Non-Dimensional Analysis
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Controlling Protein adsorption and cell adhesion with micro-patterned surfaces
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《Chinese Journal of Biomedical Engineering(English Edition)》 2001年第4期181-183,共3页
关键词 CELL controlling Protein adsorption and cell adhesion with micro-patterned surfaces PDMS
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Adaptive Robust Control for a Class of Uncertain MIMO Non-affine Nonlinear Systems 被引量:9
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作者 Longsheng Chen Qi Wang 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI 2016年第1期105-112,共8页
In this paper, the adaptive robust tracking control scheme is proposed for a class of multi-input and multioutput(MIMO) non-affine systems with uncertain structure and parameters, unknown control direction and unknown... In this paper, the adaptive robust tracking control scheme is proposed for a class of multi-input and multioutput(MIMO) non-affine systems with uncertain structure and parameters, unknown control direction and unknown external disturbance based on backstepping technique. The MIMO nonaffine system is first transformed into a time-varying system with strict feedback structure using the mean value theorem,and then the bounded time-varying parameters are estimated by adaptive algorithms with projection. To handle the possible"controller singularity" problem caused by unknown control direction, a Nussbaum function is employed, and the dynamic surface control(DSC) method is applied to solve the problem of"explosion of complexity" in backstepping control. It is proved that the proposed control scheme can guarantee that all signals of the closed-loop system are bounded through Lyapunov stability theorem and decoupled backstepping method. Simulation results are presented to illustrate the effectiveness of the proposed control scheme. 展开更多
关键词 MIMO non-affine nonlinear system dynamic surface control(DSC) Nussbaum function adaptive robust control
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Adaptive Pseudo Inverse Control for a Class of Nonlinear Asymmetric and Saturated Nonlinear Hysteretic Systems 被引量:4
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作者 Xiuyu Zhang Ruijing Jing +3 位作者 Zhiwei Li Zhi Li Xinkai Chen Chun-Yi Su 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2021年第4期916-928,共13页
This paper aims at eliminating the asymmetric and saturated hysteresis nonlinearities by designing hysteresis pseudo inverse compensator and robust adaptive dynamic surface control(DSC)scheme.The"pseudo inverse&q... This paper aims at eliminating the asymmetric and saturated hysteresis nonlinearities by designing hysteresis pseudo inverse compensator and robust adaptive dynamic surface control(DSC)scheme.The"pseudo inverse"means that an on-line calculation mechanism of approximate control signal is developed by applying a searching method to the designed temporary control signal where the true control signal is included.The main contributions are summarized as:1)to our best knowledge,it is the first time to compensate the asymmetric and saturated hysteresis by using hysteresis pseudo inverse compensator because the construction of the true saturated-type hysteresis inverse model is very difficult;2)by designing the saturated-type hysteresis pseudo inverse compensator,the construction of true explicit hysteresis inverse and the identifications of its corresponding unknown parameters are not required when dealing with the saturated-type hysteresis;3)by combining DSC technique with the tracking error transformed function,the"explosion of complexity"problem in backstepping method is overcome and the prespecified tracking performance is achieved.Analysis of stability and experimental results on the hardware-inloop platform illustrate the effectiveness of the proposed adaptive pseudo inverse control scheme. 展开更多
关键词 Adaptive dynamic surface control adaptive pseudo inverse control asymmetric and saturated hysteresis robust control
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Robust Tracking Control of Uncertain MIMO Nonlinear Systems with Application to UAVs 被引量:3
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作者 Yanlong Zhou Mou Chen Changsheng Jiang 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI 2015年第1期25-32,共8页
In this paper, we consider the robust adaptive tracking control of uncertain multi-input and multi-output(MIMO) nonlinear systems with input saturation and unknown external disturbance. The nonlinear disturbance obser... In this paper, we consider the robust adaptive tracking control of uncertain multi-input and multi-output(MIMO) nonlinear systems with input saturation and unknown external disturbance. The nonlinear disturbance observer(NDO)is employed to tackle the system uncertainty as well as the external disturbance. To handle the input saturation, an auxiliary system is constructed as a saturation compensator. By using the backstepping technique and the dynamic surface method,a robust adaptive tracking control scheme is developed. The closed-loop system is proved to be uniformly ultimately bounded thorough Lyapunov stability analysis. Simulation results with application to an unmanned aerial vehicle(UAV) demonstrate the effectiveness of the proposed robust control scheme. 展开更多
关键词 Nonlinear system unmanned aerial vehicle(UAV) input saturation disturbance observer backstepping control dynamic surface control(DSC)
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Fuzzy Adaptive Tracking Control of Uncertain Strict-Feedback Nonlinear Systems with Disturbances Based on Generalized Fuzzy Hyperbolic Model
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作者 Jingxuan Shi Zhongjun Yang 《Journal of Computer and Communications》 2020年第10期50-59,共10页
In this paper, a fuzzy adaptive tracking control for uncertain strict-feedback nonlinear systems with unknown bounded disturbances is proposed. The generalized fuzzy hyperbolic model (GFHM) with better approximation p... In this paper, a fuzzy adaptive tracking control for uncertain strict-feedback nonlinear systems with unknown bounded disturbances is proposed. The generalized fuzzy hyperbolic model (GFHM) with better approximation performance is used to approximate the unknown nonlinear function in the system. The dynamic surface control (DSC) is used to design the controller, which not only avoids the “explosion of complexity” problem in the process of repeated derivation, but also makes the control system simpler in structure and lower in computational cost because only one adaptive law is designed in the controller design process. Through the Lyapunov stability analysis, all signals in the closed loop system designed in this paper are semi-globally uniformly ultimately bounded (SGUUB). Finally, the effectiveness of the method is verified by a simulation example. 展开更多
关键词 Disturbances Uncertain Strict-Feedback Nonlinear Systems Adaptive control Generalized Fuzzy Hyperbolic Model Dynamic surface control
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Innovative backfilling longwall panel layout for better subsidence control effect-separating adjacent subcritical panels with pillars 被引量:21
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作者 Jialin Xu Dayang Xuan Changchun He 《International Journal of Coal Science & Technology》 EI CAS 2014年第3期297-305,共9页
In recent years,field trials of non-pillar longwall mining using complete backfill have been implemented successively in the Chinese coal mining industry.The objective of this paper is to get a scientific understandin... In recent years,field trials of non-pillar longwall mining using complete backfill have been implemented successively in the Chinese coal mining industry.The objective of this paper is to get a scientific understanding of surface subsidence control effect using such techniques.It begins with a brief overview on complete backfill methods primarily used in China,followed by an analysis of collected subsidence factors under mining with complete backfill.It is concluded that non-pillar longwall panel layout cannot protect surface structures against damages at a relatively large mining height,even though complete backfill is conducted.In such cases,separated longwall panel layout should be applied,i.e.,panel width should be subcritical and stable coal pillars should be left between the adjacent panels.The proposed method takes the principles of subcritical extraction and partial extraction;in conjunction with gob backfilling,surface subsidence can be effectively mitigated,thus protecting surface buildings against mining-induced damage.A general design principle and method of separated panel layout have also been proposed. 展开更多
关键词 Mining with backfill Longwall mining surface subsidence control Suberitical panel width Separatedpillar
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Degenerations of rational Bézier surface with weights in the form of exponential function 被引量:1
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作者 ZHANG Yue ZHU Chun-gang GUO Qing-jie 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2017年第2期164-182,共19页
Rational Bézier surface is a widely used surface fitting tool in CAD. When all the weights of a rational Bézier surface go to infinity in the form of power function, the limit of surface is the regular contr... Rational Bézier surface is a widely used surface fitting tool in CAD. When all the weights of a rational Bézier surface go to infinity in the form of power function, the limit of surface is the regular control surface induced by some lifting function, which is called toric degenerations of rational Bézier surfaces. In this paper, we study on the degenerations of the rational Bézier surface with weights in the exponential function and indicate the difference of our result and the work of Garc′?a-Puente et al. Through the transformation of weights in the form of exponential function and power function, the regular control surface of rational Bézier surface with weights in the exponential function is defined, which is just the limit of the surface.Compared with the power function, the exponential function approaches infinity faster, which leads to surface with the weights in the form of exponential function degenerates faster. 展开更多
关键词 rational Bézier surface WEIGHTS regular control surface toric degenerations exponential function
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A novel adaptive coordinated tracking control scheme for a morphing aircraft with telescopic wings
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作者 Enmei WANG Hao LU +2 位作者 Jianchun ZHANG Chenliang WANG Jianzhong QIAO 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 2024年第2期148-162,共15页
Inspired by flight biology,morphing flight technology has great potential to improve the adaptability and maneuverability of aircraft.This paper is devoted to the flight control problem of morphing aircraft,and aimed ... Inspired by flight biology,morphing flight technology has great potential to improve the adaptability and maneuverability of aircraft.This paper is devoted to the flight control problem of morphing aircraft,and aimed at safe and fuel-saving flight through morphing actively.Specifically,the longitudinal dynamics of a morphing aircraft with telescopic wings is modelled as a strict-feedback nonlinear system.Through fitting the expression of aerodynamic parameters by the mor-phing ratio,the model uncertainties induced by morphing errors are embedded in the dynamics.To meet the safety and fuel-saving requirements,an Adaptive Coordinated Tracking Control Scheme(ACTCS)is then proposed,which consists of a morphing control module and a tracking control module.For the morphing control module,an on-line morphing decision model is given in an optimization process with respect to the morphing ratio,and a second-order tracking filter is introduced to smooth the decision output and ensure the physical realizability.For the tracking control module,the novel adaptive controllers for the velocity and altitude subsystems are proposed based on the dynamic surface control method,in which adaptive mechanisms are designed to com-pensate for the model uncertainties.Finally,the proposed ACTCS is simulated in nine different cases of the test flight mission,to verify its effectiveness,robustness and fuel-saving effect. 展开更多
关键词 Morphing aircraft Adaptive tracking control Morphing decision Dynamic surface control Morphing error
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