A novel hybrid robust three-axis attitude control approach, namely HRTAC, is considered along with the well-known developments in the area of space systems, since there is a consensus among the related experts that th...A novel hybrid robust three-axis attitude control approach, namely HRTAC, is considered along with the well-known developments in the area of space systems, since there is a consensus among the related experts that the new insights may be taken into account as decision points to outperform the available materials. It is to note that the traditional control approaches may generally be upgraded, as long as a number of modifications are made with respect to state-of-the-art, in order to propose high-precision outcomes. Regarding the investigated issues, the robust sliding mode finite-time control approach is first designed to handle three-axis angular rates in the inner control loop, which consists of the pulse width pulse frequency modulations in line with the control allocation scheme and the system dynamics. The main subject to employ these modulations that is realizing in association with the control allocation scheme is to be able to handle a class of overactuated systems, in particular. The proportional derivative based linear quadratic regulator approach is then designed to handle three-axis rotational angles in the outer control loop, which consists of the system kinematics that is correspondingly concentrated to deal with the quaternion based model. The utilization of the linear and its nonlinear terms, simultaneously, are taken into real consideration as the research motivation, while the performance results are of the significance as the improved version in comparison with the recent investigated outcomes. Subsequently, there is a stability analysis to verify and guarantee the closed loop system performance in coping with the whole of nominal referenced commands. At the end, the effectiveness of the approach considered here is highlighted in line with a number of potential recent benchmarks.展开更多
This paper investigates the design of an attitude autopilot for a dual-channel controlled spinning glideguided projectile(SGGP),addressing model uncertainties and external disturbances.Based on fixed-time stable theor...This paper investigates the design of an attitude autopilot for a dual-channel controlled spinning glideguided projectile(SGGP),addressing model uncertainties and external disturbances.Based on fixed-time stable theory,a disturbance observer with integral sliding mode and adaptive techniques is proposed to mitigate total disturbance effects,irrespective of initial conditions.By introducing an error integral signal,the dynamics of the SGGP are transformed into two separate second-order fully actuated systems.Subsequently,employing the high-order fully actuated approach and a parametric approach,the nonlinear dynamics of the SGGP are recast into a constant linear closed-loop system,ensuring that the projectile's attitude asymptotically tracks the given goal with the desired eigenstructure.Under the proposed composite control framework,the ultimately uniformly bounded stability of the closed-loop system is rigorously demonstrated via the Lyapunov method.Validation of the effectiveness of the proposed attitude autopilot design is provided through extensive numerical simulations.展开更多
This paper investigates the finite-time attitude tracking problem for rigid spacecraft. Two backstepping finite-time slid- ing mode control laws are proposed to solve this problem in the presence of inertia uncertaint...This paper investigates the finite-time attitude tracking problem for rigid spacecraft. Two backstepping finite-time slid- ing mode control laws are proposed to solve this problem in the presence of inertia uncertainties and external disturbances. The first control scheme is developed by combining sliding mode con- trol with a backstepping technique to achieve fast and accurate tracking responses. To obtain higher tracking precision and relax the requirement of the upper bounds on the uncertainties, a se- cond control law is also designed by combining the second or- der sliding mode control and an adaptive backstepping technique. This control law provides complete compensation of uncertainty and disturbances. Although it assumes that the uncertainty and disturbances are bounded, the proposed control law does not require information about the bounds on the uncertainties and disturbances. Finite-time convergence of attitude tracking errors and the stability of the closed-loop system are ensured by the Lya- punov approach. Numerical simulations on attitude tracking control of spacecraft are provided to demonstrate the performance of the proposed controllers.展开更多
A novel high-order sliding mode control strategy is proposed for the attitude control problem of reentry vehicles in the presence of parametric uncertainties and external disturbances, which results in the robust and ...A novel high-order sliding mode control strategy is proposed for the attitude control problem of reentry vehicles in the presence of parametric uncertainties and external disturbances, which results in the robust and accurate tracking of the aerodynamic angle commands with the finite time convergence. The proposed control strategy is developed on the basis of integral sliding mode philosophy, which combines conventional sliding mode control and a linear quadratic regulator over a finite time interval with a free-final-state and allows the finite-time establishment of a high-order sliding mode. Firstly, a second-order sliding mode attitude controller is designed in the proposed high-order siding mode control framework. Then, to address the control chattering problem, a virtual control is introduced in the control design and hence a third-order sliding mode attitude controller is developed, leading to the chattering reduction as well as the control accuracy improvement. Finally, simulation examples are given to illustrate the effectiveness of the theoretical results.展开更多
To get better tracking performance of attitude command over the reentry phase of vehicles, the use of state-dependent Riccati equation (SDRE) method for attitude controller design of reentry vehicles was investigated....To get better tracking performance of attitude command over the reentry phase of vehicles, the use of state-dependent Riccati equation (SDRE) method for attitude controller design of reentry vehicles was investigated. Guidance commands are generated based on optimal guidance law. SDRE control method employs factorization of the nonlinear dynamics into a state vector and state dependent matrix valued function. State-dependent coefficients are derived based on reentry motion equations in pitch and yaw channels. Unlike constant weighting matrix Q, elements of Q are set as the functions of state error so as to get satisfactory feedback and eliminate state error rapidly, then formulation of SDRE is realized. Riccati equation is solved real-timely with Schur algorithm. State feedback control law u(x) is derived with linear quadratic regulator (LQR) method. Simulation results show that SDRE controller steadily tracks attitude command, and impact point error of reentry vehicle is acceptable. Compared with PID controller, tracking performance of attitude command using SDRE controller is better with smaller control surface deflection. The attitude tracking error with SDRE controller is within 5°, and the control deflection is within 30°.展开更多
This paper presents a scheme of fault diagnosis for flexible satellites during orbit maneuver. The main contribution of the paper is related to the design of the nonlinear input observer which can avoid false alarm ar...This paper presents a scheme of fault diagnosis for flexible satellites during orbit maneuver. The main contribution of the paper is related to the design of the nonlinear input observer which can avoid false alarm arising from the disturbance from orbit control force. The effects of orbit control force on the fault diagnosis system for satellite attitude control systems, including the disturbing torque caused by the misalignments and the model uncertainty caused by the fuel consumed, are discussed, where standard Lu- enberger observer cannot work well. Then the nonlinear unknown input observer is proposed to decouple faults from disturbance, Besides, a linear matrix inequality approach is adopted to reduce the effect of nonlinear part and model uncertainties on the observer. The numerical and semi-physical simulation demonstrates the effectiveness of the proposed observer for the fault diagnosis system of the satellite during orbit maneuver.展开更多
The output feedback control for spacecraft attitude tracking system is investigated in this study. It is assumed that angular velocity measurements are not available for feedback control.A technique named adding power...The output feedback control for spacecraft attitude tracking system is investigated in this study. It is assumed that angular velocity measurements are not available for feedback control.A technique named adding power integrator(API) is adopted to estimate the pseudo-angular-velocity. Then we design a finite-time attitude control law, which only utilizes the relative attitude information. The stability analyses of the feedback system are proved as well, which shows the attitude tracking errors will converge into a region of zero even the external disturbances exist. The simulation results illustrate the high precision and robust attitude control performance of the proposed control strategy.展开更多
To solve the problem of attitude synchronization control for spacecraft formation flying(SFF)suffering from external disturbances under a directed communication topology,a sliding mode disturbance observer(SMDO)based ...To solve the problem of attitude synchronization control for spacecraft formation flying(SFF)suffering from external disturbances under a directed communication topology,a sliding mode disturbance observer(SMDO)based on the finite-time control strategy is developed to observe the time-varying external disturbance via estimating the upper bound of its first derivative.Meanwhile,the rotation matrix is employed to describe the attitude of SFF for the purpose of the avoidance of singularity and unwinding phenomenon.As for the attitude synchronization and the tracking control architecture,a sliding mode surface(SMS)is given such that the control objective can be achieved.The effectiveness and the validity of the proposed method are elaborated via theoretical analysis and numerical simulations.展开更多
A robust attitude controller for hydrofoil catamaran throughout its operating envelope is proposed, based on Tagaki-Sugeno (T-S) fuzzy model. Firstly, T-S fuzzy model and robust attitude control strategy for hydrofoil...A robust attitude controller for hydrofoil catamaran throughout its operating envelope is proposed, based on Tagaki-Sugeno (T-S) fuzzy model. Firstly, T-S fuzzy model and robust attitude control strategy for hydrofoil catamaran is presented by use of linear matrix inequality (LMI) techniques. Secondly, a nonlinear mathematical model of hydrofoil catamaran is established, acting as the platform for further researches. The specialty in interpolation of T-S fuzzy model guarantees that feedback gain can be obtained smoothly, while boat's speed is shifting over the operating envelope. The external disturbances are also attenuated to achieve H ∞ control performance, meanwhile. Finally, based on such a boat, HC200B-A1, simulation researches demonstrate the design procedures and the effectiveness of fuzzy robust attitude controller.展开更多
An attitude control algorithm for reusable launch vehicle(RLV) in reentry phase is proposed based on sliding mode variable structure control technique.The aerodynamic characteristics of RLV vary rapidly,and the seriou...An attitude control algorithm for reusable launch vehicle(RLV) in reentry phase is proposed based on sliding mode variable structure control technique.The aerodynamic characteristics of RLV vary rapidly,and the serious uncertainties and nonlinearities exist in the reentry flight phase.As an example,American X-34 technology demonstrator is investigated.The chattering brought by the variable structure control technique is eliminated efficiently by choosing a suitable reaching law and a sign function.A control mode of reaction control system is presented based on the RCS scheme of X-34 vehicle.As two different attitude control effectors,aerosurfaces and RCS,are employed in the reentry flight phase,a composite control strategy based on the dynamic pressure variety is presented.Also,an actuator model and a RCS thruster model are built.Analysis and nonlinear simulation results show that the sliding mode variable structure controller achieves better performance,the overshoot and steady-state error are only 0.7% and 0.04° respectively.展开更多
A finite time controller with PD-like structure for satellite attitude control is proposed in this paper.The controller is constructed with simple structure based on standard PD controller.The fractional order term is...A finite time controller with PD-like structure for satellite attitude control is proposed in this paper.The controller is constructed with simple structure based on standard PD controller.The fractional order term is designed hence system could both have strong robustness and finite time convergence rate,and the advantage of finite time control and PD control is combined in this paper.System convergence rate is discussed by Lyapunov method,and the constraint on control parameters is given by implementing the coupled term of angular velocity and attitude quaternion.Moreover,the accuracy at steady stage depending on control parameters is given hence system could converge to this field within finite time.System stability and performance is demonstrated by numerical simulation results.展开更多
The consensus problem of the distributed attitude synchronization in the spacecraft formation flying is considered.Firstly,the attitude dynamics of a rigid body spacecraft is described by modified Rodriguez parameters...The consensus problem of the distributed attitude synchronization in the spacecraft formation flying is considered.Firstly,the attitude dynamics of a rigid body spacecraft is described by modified Rodriguez parameters（MRPs）.Then global stable distributed cooperative attitude control laws are proposed for different cases.In the first case,the control law guarantees the state consensus during the attitude synchronization.In the second case,the control law ensures both the attitudes synchronizing to a desired constant attitude and the angular velocities converging at zero.In the third case,an attitude consensus control law with bounded control input is proposed.Finally,the effectiveness and validity of the control laws are demonstrated by simulations of six rigid bodies formation flying.展开更多
A spacecraft re-entry attitude control method using sliding mode control (SMC) theory is developed. The controller utilizes double-loop SMC scheme and provides the robust, de-coupled tracking of both the angular veloc...A spacecraft re-entry attitude control method using sliding mode control (SMC) theory is developed. The controller utilizes double-loop SMC scheme and provides the robust, de-coupled tracking of both the angular velocity and the shuttle orientation angles. In accordance with the hybrid-controlling characteristics of the aerodynamic surfaces and reaction control system of the spacecraft, the control torque commands are allocated into the actuators such as the aerodynamic surfaces and reaction control system by using the optimal control selection allocation algorithm. The simulation of the spacecraft re-entry attitude controlling demonstrates the robust, de-coupled tracking performance of the proposed method and its validity.展开更多
Small video satellites have unique advantages of short development cycle,agile attitude maneuver,real-time video imaging.They have broad application prospects in space debris,faulty spacecraft,and other space target d...Small video satellites have unique advantages of short development cycle,agile attitude maneuver,real-time video imaging.They have broad application prospects in space debris,faulty spacecraft,and other space target detection and tracking.However,when a space target first enters the camera’s visual field,it has a relatively large angular velocity relative to the satellite,which makes it easy to deviate from the visual field and cause off-target problems.This paper proposes a novel visual tracking control method based on potential function preventing missed targets in space.Firstly,a circular area in the image plane is designed as a mandatory restricted projection area of the target and a visual tracking controller based on image error.Then,a potential function is designed to ensure continuous and stable tracking of the target after entering the visual field.Finally,the stability of the control is proved using Barbarat’s lemma.By setting the same conditions and comparing with the simulation results of the proportion-derivative(PD)control method,the results show that when there is a large relative attitude motion angular velocity between the target and the satellite,the track-ing method based on potential function can ensure that the tar-get does not deviate from the field-of-view during the tracking control process,and the projection of target is controlled to the desired position.The proposed control method is effective in eliminating tracking error and preventing off-target simultane-ously.展开更多
文摘A novel hybrid robust three-axis attitude control approach, namely HRTAC, is considered along with the well-known developments in the area of space systems, since there is a consensus among the related experts that the new insights may be taken into account as decision points to outperform the available materials. It is to note that the traditional control approaches may generally be upgraded, as long as a number of modifications are made with respect to state-of-the-art, in order to propose high-precision outcomes. Regarding the investigated issues, the robust sliding mode finite-time control approach is first designed to handle three-axis angular rates in the inner control loop, which consists of the pulse width pulse frequency modulations in line with the control allocation scheme and the system dynamics. The main subject to employ these modulations that is realizing in association with the control allocation scheme is to be able to handle a class of overactuated systems, in particular. The proportional derivative based linear quadratic regulator approach is then designed to handle three-axis rotational angles in the outer control loop, which consists of the system kinematics that is correspondingly concentrated to deal with the quaternion based model. The utilization of the linear and its nonlinear terms, simultaneously, are taken into real consideration as the research motivation, while the performance results are of the significance as the improved version in comparison with the recent investigated outcomes. Subsequently, there is a stability analysis to verify and guarantee the closed loop system performance in coping with the whole of nominal referenced commands. At the end, the effectiveness of the approach considered here is highlighted in line with a number of potential recent benchmarks.
基金supported by the National Natural Science Foundation of China(Grant Nos.52272358 and 62103052)。
文摘This paper investigates the design of an attitude autopilot for a dual-channel controlled spinning glideguided projectile(SGGP),addressing model uncertainties and external disturbances.Based on fixed-time stable theory,a disturbance observer with integral sliding mode and adaptive techniques is proposed to mitigate total disturbance effects,irrespective of initial conditions.By introducing an error integral signal,the dynamics of the SGGP are transformed into two separate second-order fully actuated systems.Subsequently,employing the high-order fully actuated approach and a parametric approach,the nonlinear dynamics of the SGGP are recast into a constant linear closed-loop system,ensuring that the projectile's attitude asymptotically tracks the given goal with the desired eigenstructure.Under the proposed composite control framework,the ultimately uniformly bounded stability of the closed-loop system is rigorously demonstrated via the Lyapunov method.Validation of the effectiveness of the proposed attitude autopilot design is provided through extensive numerical simulations.
文摘This paper investigates the finite-time attitude tracking problem for rigid spacecraft. Two backstepping finite-time slid- ing mode control laws are proposed to solve this problem in the presence of inertia uncertainties and external disturbances. The first control scheme is developed by combining sliding mode con- trol with a backstepping technique to achieve fast and accurate tracking responses. To obtain higher tracking precision and relax the requirement of the upper bounds on the uncertainties, a se- cond control law is also designed by combining the second or- der sliding mode control and an adaptive backstepping technique. This control law provides complete compensation of uncertainty and disturbances. Although it assumes that the uncertainty and disturbances are bounded, the proposed control law does not require information about the bounds on the uncertainties and disturbances. Finite-time convergence of attitude tracking errors and the stability of the closed-loop system are ensured by the Lya- punov approach. Numerical simulations on attitude tracking control of spacecraft are provided to demonstrate the performance of the proposed controllers.
基金supported by Major State Basic Research Development Program(2012CB720000)National Natural Science Foundation of China(11372034)Innovative Research Team of Beijing Institute of Technology
文摘A novel high-order sliding mode control strategy is proposed for the attitude control problem of reentry vehicles in the presence of parametric uncertainties and external disturbances, which results in the robust and accurate tracking of the aerodynamic angle commands with the finite time convergence. The proposed control strategy is developed on the basis of integral sliding mode philosophy, which combines conventional sliding mode control and a linear quadratic regulator over a finite time interval with a free-final-state and allows the finite-time establishment of a high-order sliding mode. Firstly, a second-order sliding mode attitude controller is designed in the proposed high-order siding mode control framework. Then, to address the control chattering problem, a virtual control is introduced in the control design and hence a third-order sliding mode attitude controller is developed, leading to the chattering reduction as well as the control accuracy improvement. Finally, simulation examples are given to illustrate the effectiveness of the theoretical results.
基金Project(51105287)supported by the National Natural Science Foundation of China
文摘To get better tracking performance of attitude command over the reentry phase of vehicles, the use of state-dependent Riccati equation (SDRE) method for attitude controller design of reentry vehicles was investigated. Guidance commands are generated based on optimal guidance law. SDRE control method employs factorization of the nonlinear dynamics into a state vector and state dependent matrix valued function. State-dependent coefficients are derived based on reentry motion equations in pitch and yaw channels. Unlike constant weighting matrix Q, elements of Q are set as the functions of state error so as to get satisfactory feedback and eliminate state error rapidly, then formulation of SDRE is realized. Riccati equation is solved real-timely with Schur algorithm. State feedback control law u(x) is derived with linear quadratic regulator (LQR) method. Simulation results show that SDRE controller steadily tracks attitude command, and impact point error of reentry vehicle is acceptable. Compared with PID controller, tracking performance of attitude command using SDRE controller is better with smaller control surface deflection. The attitude tracking error with SDRE controller is within 5°, and the control deflection is within 30°.
基金supported by the National Natural Science Foundation of China (61034005)the Natural Science Foundation of Jiangsu Province (BK2010072)
文摘This paper presents a scheme of fault diagnosis for flexible satellites during orbit maneuver. The main contribution of the paper is related to the design of the nonlinear input observer which can avoid false alarm arising from the disturbance from orbit control force. The effects of orbit control force on the fault diagnosis system for satellite attitude control systems, including the disturbing torque caused by the misalignments and the model uncertainty caused by the fuel consumed, are discussed, where standard Lu- enberger observer cannot work well. Then the nonlinear unknown input observer is proposed to decouple faults from disturbance, Besides, a linear matrix inequality approach is adopted to reduce the effect of nonlinear part and model uncertainties on the observer. The numerical and semi-physical simulation demonstrates the effectiveness of the proposed observer for the fault diagnosis system of the satellite during orbit maneuver.
基金supported by the National Natural Science Foundation of China(616731356140310361603114)
文摘The output feedback control for spacecraft attitude tracking system is investigated in this study. It is assumed that angular velocity measurements are not available for feedback control.A technique named adding power integrator(API) is adopted to estimate the pseudo-angular-velocity. Then we design a finite-time attitude control law, which only utilizes the relative attitude information. The stability analyses of the feedback system are proved as well, which shows the attitude tracking errors will converge into a region of zero even the external disturbances exist. The simulation results illustrate the high precision and robust attitude control performance of the proposed control strategy.
基金This work was supported by the National Natural Science Foundation of China(11772185)the Natural Science Foundation of Heilongjiang Province(F2017005)the Fundamental Research Funds for the Central Universities(HEUCFP201770).
文摘To solve the problem of attitude synchronization control for spacecraft formation flying(SFF)suffering from external disturbances under a directed communication topology,a sliding mode disturbance observer(SMDO)based on the finite-time control strategy is developed to observe the time-varying external disturbance via estimating the upper bound of its first derivative.Meanwhile,the rotation matrix is employed to describe the attitude of SFF for the purpose of the avoidance of singularity and unwinding phenomenon.As for the attitude synchronization and the tracking control architecture,a sliding mode surface(SMS)is given such that the control objective can be achieved.The effectiveness and the validity of the proposed method are elaborated via theoretical analysis and numerical simulations.
文摘A robust attitude controller for hydrofoil catamaran throughout its operating envelope is proposed, based on Tagaki-Sugeno (T-S) fuzzy model. Firstly, T-S fuzzy model and robust attitude control strategy for hydrofoil catamaran is presented by use of linear matrix inequality (LMI) techniques. Secondly, a nonlinear mathematical model of hydrofoil catamaran is established, acting as the platform for further researches. The specialty in interpolation of T-S fuzzy model guarantees that feedback gain can be obtained smoothly, while boat's speed is shifting over the operating envelope. The external disturbances are also attenuated to achieve H ∞ control performance, meanwhile. Finally, based on such a boat, HC200B-A1, simulation researches demonstrate the design procedures and the effectiveness of fuzzy robust attitude controller.
文摘An attitude control algorithm for reusable launch vehicle(RLV) in reentry phase is proposed based on sliding mode variable structure control technique.The aerodynamic characteristics of RLV vary rapidly,and the serious uncertainties and nonlinearities exist in the reentry flight phase.As an example,American X-34 technology demonstrator is investigated.The chattering brought by the variable structure control technique is eliminated efficiently by choosing a suitable reaching law and a sign function.A control mode of reaction control system is presented based on the RCS scheme of X-34 vehicle.As two different attitude control effectors,aerosurfaces and RCS,are employed in the reentry flight phase,a composite control strategy based on the dynamic pressure variety is presented.Also,an actuator model and a RCS thruster model are built.Analysis and nonlinear simulation results show that the sliding mode variable structure controller achieves better performance,the overshoot and steady-state error are only 0.7% and 0.04° respectively.
基金supported partially by National Natural Science Foundation of China(Project Nos.61903289 and 62073102)。
文摘A finite time controller with PD-like structure for satellite attitude control is proposed in this paper.The controller is constructed with simple structure based on standard PD controller.The fractional order term is designed hence system could both have strong robustness and finite time convergence rate,and the advantage of finite time control and PD control is combined in this paper.System convergence rate is discussed by Lyapunov method,and the constraint on control parameters is given by implementing the coupled term of angular velocity and attitude quaternion.Moreover,the accuracy at steady stage depending on control parameters is given hence system could converge to this field within finite time.System stability and performance is demonstrated by numerical simulation results.
基金supported by the National Science Foundation of China (6097406260972119)the Chinese Ministry of Science and Intergovernmental Cooperation Project(2009DFA12870)
文摘The consensus problem of the distributed attitude synchronization in the spacecraft formation flying is considered.Firstly,the attitude dynamics of a rigid body spacecraft is described by modified Rodriguez parameters（MRPs）.Then global stable distributed cooperative attitude control laws are proposed for different cases.In the first case,the control law guarantees the state consensus during the attitude synchronization.In the second case,the control law ensures both the attitudes synchronizing to a desired constant attitude and the angular velocities converging at zero.In the third case,an attitude consensus control law with bounded control input is proposed.Finally,the effectiveness and validity of the control laws are demonstrated by simulations of six rigid bodies formation flying.
文摘A spacecraft re-entry attitude control method using sliding mode control (SMC) theory is developed. The controller utilizes double-loop SMC scheme and provides the robust, de-coupled tracking of both the angular velocity and the shuttle orientation angles. In accordance with the hybrid-controlling characteristics of the aerodynamic surfaces and reaction control system of the spacecraft, the control torque commands are allocated into the actuators such as the aerodynamic surfaces and reaction control system by using the optimal control selection allocation algorithm. The simulation of the spacecraft re-entry attitude controlling demonstrates the robust, de-coupled tracking performance of the proposed method and its validity.
文摘Small video satellites have unique advantages of short development cycle,agile attitude maneuver,real-time video imaging.They have broad application prospects in space debris,faulty spacecraft,and other space target detection and tracking.However,when a space target first enters the camera’s visual field,it has a relatively large angular velocity relative to the satellite,which makes it easy to deviate from the visual field and cause off-target problems.This paper proposes a novel visual tracking control method based on potential function preventing missed targets in space.Firstly,a circular area in the image plane is designed as a mandatory restricted projection area of the target and a visual tracking controller based on image error.Then,a potential function is designed to ensure continuous and stable tracking of the target after entering the visual field.Finally,the stability of the control is proved using Barbarat’s lemma.By setting the same conditions and comparing with the simulation results of the proportion-derivative(PD)control method,the results show that when there is a large relative attitude motion angular velocity between the target and the satellite,the track-ing method based on potential function can ensure that the tar-get does not deviate from the field-of-view during the tracking control process,and the projection of target is controlled to the desired position.The proposed control method is effective in eliminating tracking error and preventing off-target simultane-ously.
