The direct torque control of the dual star induction motor(DTC-DSIM) using conventional PI controllers is characterized by unsatisfactory performance, such as high ripples of torque and flux, and sensitivity to parame...The direct torque control of the dual star induction motor(DTC-DSIM) using conventional PI controllers is characterized by unsatisfactory performance, such as high ripples of torque and flux, and sensitivity to parametric variations. Among the most evoked control strategies adopted in this field to overcome these drawbacks presented in classical drive, it is worth mentioning the use of the second order sliding mode control(SOSMC) based on the super twisting algorithm(STA) combined with the fuzzy logic control(FSOSMC). In order to realize the optimal control performance, the FSOSMC parameters are adjusted using an optimization algorithm based on the genetic algorithm(GA). The performances of the envisaged control scheme, called G-FSOSMC, are investigated against G-SOSMC, G-PI and BBO-FSOSMC algorithms. The proposed controller scheme is efficient in reducing the torque and flux ripples, and successfully suppresses chattering. The effects of parametric uncertainties do not affect system performance.展开更多
The problem of the chattering phenomenon is still the main drawback of the classical sliding mode control. To resolve this problem, a discrete second order sliding mode control via input-output model is proposed in th...The problem of the chattering phenomenon is still the main drawback of the classical sliding mode control. To resolve this problem, a discrete second order sliding mode control via input-output model is proposed in this paper. The proposed control law is synthesized for decouplable multivariable systems. A robustness analysis of the proposed discrete second order sliding mode control is carried out. Simulation results are presented to illustrate the effectiveness of the proposed strategy.展开更多
In this paper, using finite-time control method, we consider the disturbance analysis of a second-order system with unknown but bounded disturbance. We show that the states of the second-order system will be stabilize...In this paper, using finite-time control method, we consider the disturbance analysis of a second-order system with unknown but bounded disturbance. We show that the states of the second-order system will be stabilized to a region containing the origin. The radius of this region is determined by the control parameters and can be rendered as small as desired. The rigorous stability analysis is also given. Compared with the conventional PD control law, the finite-time control law yields a better disturbance rejection performance. Numerical simulation results show the effectiveness of the method.展开更多
This paper investigates the cluster consensus problem for second-order multi-agent systems by applying the pinning control method to a small collection of the agents. Consensus is attained independently for different ...This paper investigates the cluster consensus problem for second-order multi-agent systems by applying the pinning control method to a small collection of the agents. Consensus is attained independently for different agent clusters according to the community structure generated by the group partition of the underlying graph and sufficient conditions for both cluster and general consensus are obtained by using results from algebraic graph theory and the LaSalle Invariance Principle. Finally, some simple simulations are presented to illustrate the technique.展开更多
In this paper, the problem of stabilizing an unstable second order delay system using classical proportional-integralderivative(PID) controller is considered. An extension of the Hermite-Biehler theorem, which is appl...In this paper, the problem of stabilizing an unstable second order delay system using classical proportional-integralderivative(PID) controller is considered. An extension of the Hermite-Biehler theorem, which is applicable to quasi-polynomials, is used to seek the set of complete stabilizing proportional-integral/proportional-integral-derivative(PI/PID) parameters. The range of admissible proportional gains is determined in closed form. For each proportional gain, the stabilizing set in the space of the integral and derivative gains is shown to be a triangle.展开更多
In this paper, formation tracking control problems for second-order multi-agent systems（MASs） with time-varying delays are studied, specifically those where the position and velocity of followers are designed to for...In this paper, formation tracking control problems for second-order multi-agent systems（MASs） with time-varying delays are studied, specifically those where the position and velocity of followers are designed to form a time-varying formation while tracking those of the leader. A neighboring relative state information based formation tracking protocol with an unknown gain matrix and time-varying delays is presented. The formation tracking problems are then transformed into asymptotically stable problems. Based on the Lyapunov-Krasovskii functional approach, conditions sufficient for second-order MASs with time-varying delays to realize formation tracking are examined. An approach to obtain the unknown gain matrix is given and, since neighboring relative velocity information is difficult to measure in practical applications, a formation tracking protocol with time-varying delays using only neighboring relative position information is introduced. The proposed results can be used on target enclosing problems for MASs with second-order dynamics and time-varying delays. An application for target enclosing by multiple unmanned aerial vehicles（UAVs） is given to demonstrate the feasibility of theoretical results.展开更多
An attitude controller using the second order sliding mode control methodology with a backstepping approach（SOSMCB）is designed and implemented for a spinning missile with two internal moving mass blocks.The system c...An attitude controller using the second order sliding mode control methodology with a backstepping approach（SOSMCB）is designed and implemented for a spinning missile with two internal moving mass blocks.The system consists of a rigid body and two radial internal moving mass blocks and its mathematical model is established based on Newtonian mechanics.The control scheme integrates a second order sliding mode control algorithm into the last step of the backstepping approach,and its stability is proved by means of a Lyapunov function.The performance of the controller is demonstrated by numerical simulations,the results show that the attitude controller is stable and effective.展开更多
The modelling of risky asset by stochastic processes with continuous paths, based on Brow- nian motions, suffers from several defects. First, the path continuity assumption does not seem reason- able in view of the po...The modelling of risky asset by stochastic processes with continuous paths, based on Brow- nian motions, suffers from several defects. First, the path continuity assumption does not seem reason- able in view of the possibility of sudden price variations （jumps） resulting of market crashes. A solution is to use stochastic processes with jumps, that will account for sudden variations of the asset prices. On the other hand, such jump models are generally based on the Poisson random measure. Many popular economic and financial models described by stochastic differential equations with Poisson jumps. This paper deals with the approximate controllability of a class of second-order neutral stochastic differential equations with infinite delay and Poisson jumps. By using the cosine family of operators, stochastic analysis techniques, a new set of sufficient conditions are derived for the approximate controllability of the above control system. An example is provided to illustrate the obtained theory.展开更多
A difficult but important problem in optimal control theory is the design of an optimal feedback control, i.e., the design of an optimal control as function of the phase (state) coordinates [1,2]. This problem can be ...A difficult but important problem in optimal control theory is the design of an optimal feedback control, i.e., the design of an optimal control as function of the phase (state) coordinates [1,2]. This problem can be solved not often. We study here the autonomous nonlinear system of second order in general form. The constraints imposed on the control input can depend on the phase (state) coordinates of the system. The goal of the control is to maximize or minimize one phase coordinate of the considered system while other takes a prescribed in advance value. In the literature, optimal control problems for the systems of second order are most frequently associated with driving both phase coordinates to a prescribed in advance state. In this statement of the problem, the optimal control feedback can be designed only for special kind of systems. In our statement of the problem, an optimal control can be designed as function of the state coordinates for more general kind of the systems. The problem of maximization or minimization of the swing amplitude is considered explicitly as an example. Simulation results are presented.展开更多
This paper studies consensus control problems for a class of second-order multi-agent systems without relative velocity measurement. Some dynamic neighbour-based rules are adopted for the agents in the presence of ext...This paper studies consensus control problems for a class of second-order multi-agent systems without relative velocity measurement. Some dynamic neighbour-based rules are adopted for the agents in the presence of external disturbances. A sufficient condition is derived to make all agents achieve consensus while satisfying desired H∞ performance. Finally, numerical simulations are provided to show the effectiveness of our theoretical results.展开更多
In this paper, we study the containment control problem for nonlinear second-order systems with unknown parameters and multiple stationary/dynamic leaders. The topologies that characterize the interaction among the le...In this paper, we study the containment control problem for nonlinear second-order systems with unknown parameters and multiple stationary/dynamic leaders. The topologies that characterize the interaction among the leaders and the followers are directed graphs. Necessary and sufficient criteria which guarantee the control objectives are established for both stationary leaders(regulation case) and dynamic leaders(dynamic tracking case) based protocols. The final states of all the followers are exclusively determined by the initial values of the leaders and the topology structures. In the regulation case, all the followers converge into the convex hull spanned by the leaders,while in the dynamic tracking case, not only the positions of the followers converge into the convex hull but also the velocities of the followers converge into the velocity convex hull of the leaders.Finally, all the theoretical results are illustrated by numerical simulations.展开更多
A complex autonomous inventory coupled system is considered. It can take, for example, the form of a network of chemical or biochemical reactors, where the inventory interactions perform the recycling of by-products b...A complex autonomous inventory coupled system is considered. It can take, for example, the form of a network of chemical or biochemical reactors, where the inventory interactions perform the recycling of by-products between the subsystems. Because of the flexible subsystems interactions, each of them can be operated with their own periods utilizing advantageously their dynamic properties. A multifrequency second-order test generalizing the p-test for single systems is described. It can be used to decide which kind of the operation (the static one, the periodic one or the multiperiodic one) will intensify the productivity of a complex system. An illustrative example of the multiperiodic optimization of a complex chemical production system is presented.展开更多
This paper investigates the consensus tracking problems of second-order multi-agent systems with a virtual leader via event-triggered control. A novel distributed event-triggered transmission scheme is proposed, which...This paper investigates the consensus tracking problems of second-order multi-agent systems with a virtual leader via event-triggered control. A novel distributed event-triggered transmission scheme is proposed, which is intermittently examined at constant sampling instants. Only partial neighbor information and local measurements are required for event detection. Then the corresponding event-triggered consensus tracking protocol is presented to guarantee second-order multi-agent systems to achieve consensus tracking. Numerical simulations are given to illustrate the effectiveness of the proposed strategy.展开更多
Eigenstructure assignment using the proportional-plus-derivative feedback controller in a class of secondorder dynamic system is investigated. Simple, general, complete parametric expressions for both the closed-loop ...Eigenstructure assignment using the proportional-plus-derivative feedback controller in a class of secondorder dynamic system is investigated. Simple, general, complete parametric expressions for both the closed-loop eigenvector matrix and the feedback gains are established based on two simple Smith form reductions. The approach utilizes directly the original system data and involves manipulations only on n-dimensional matrices. Furthermore, it reveals all the degrees of freedom which can be further utilized to achieve additional system specifications. An example shows the effect of the proposed approach.展开更多
In this paper eigenstructure assignment via proportional-plus-derivative feedback is investigated for a class of second-order descriptor linear systems. Under certain conditions, simple, general and complete parametri...In this paper eigenstructure assignment via proportional-plus-derivative feedback is investigated for a class of second-order descriptor linear systems. Under certain conditions, simple, general and complete parametric solutions of both finite closed-loop eigenvector matrices and feedback gain matrices are derived. The parametric approach utilizes directly original system data, involves manipulations only on n-dimensional matrices, and reveals all the design degrees of freedom which can be further utilized to achieve certain additional system specifications. A numerical example shows the effect of the proposed approach.展开更多
Geomaterials are known to be non-associated materials. Granular soils therefore exhibit a variety of failure modes, with diffuse or localized kinematical patterns. In fact, the notion of failure itself can be confusin...Geomaterials are known to be non-associated materials. Granular soils therefore exhibit a variety of failure modes, with diffuse or localized kinematical patterns. In fact, the notion of failure itself can be confusing with regard to granular soils, because it is not associated with an obvious phenomenology. In this study, we built a proper framework, using the second-order work theory, to describe some failure modes in geomaterials based on energy conservation. The occurrence of failure is defined by an abrupt increase in kinetic energy. The increase in kinetic energy from an equilibrium state, under incremental loading, is shown to be equal to the difference between the external second-order work,involving the external loading parameters, and the internal second-order work, involving the constitutive properties of the material. When a stress limit state is reached, a certain stress component passes through a maximum value and then may decrease. Under such a condition, if a certain additional external loading is applied, the system fails, sharply increasing the strain rate. The internal stress is no longer able to balance the external stress, leading to a dynamic response of the specimen. As an illustration, the theoretical framework was applied to the well-known undrained triaxial test for loose soils. The influence of the loading control mode was clearly highlighted. It is shown that the plastic limit theory appears to be a particular case of this more general second-order work theory. When the plastic limit condition is met, the internal second-order work is nil. A class of incremental external loadings causes the kinetic energy to increase dramatically, leading to the sudden collapse of the specimen, as observed in laboratory.展开更多
This paper proposes a finite-time robust flight controller, targeting for a reentry vehicle with blended aerodynamic surfaces and a reaction control system（RCS）. Firstly, a novel finite-time attitude controller is p...This paper proposes a finite-time robust flight controller, targeting for a reentry vehicle with blended aerodynamic surfaces and a reaction control system（RCS）. Firstly, a novel finite-time attitude controller is pointed out with the introduction of a nonsingular finite-time sliding mode manifold. The attitude tracking errors are mathematically proved to converge to zero within finite time which can be estimated. In order to improve the performance, a second-order finite-time sliding mode controller is further developed to effectively alleviate chattering without any deterioration of robustness and accuracy. Moreover, an optimization control allocation algorithm, using linear programming and a pulse-width pulse-frequency（PWPF） modulator, is designed to allocate torque commands for all the aerodynamic surface deflections and on–off switching-states of RCS thrusters.Simulations are provided for the reentry vehicle considering uncertain parameters and external disturbances for practical purposes, and the results demonstrate the effectiveness and robustness of the attitude control system.展开更多
基金supported by National Natural Science Foundation of China(61104085,51505213)Natural Science Foundation of Jiangsu Province(BK20151463,BK20130744)+2 种基金Innovation Foundation of NJIT(CKJA201409,CKJB201209)sponsored by Jiangsu Qing Lan ProjectJiangsu Government Scholarship for Overseas Studies(JS-2012-051)
基金Project supported by the LEB Research LaboratoryDepartment of Electrical Engineering,University of Batna 2, Algeria。
文摘The direct torque control of the dual star induction motor(DTC-DSIM) using conventional PI controllers is characterized by unsatisfactory performance, such as high ripples of torque and flux, and sensitivity to parametric variations. Among the most evoked control strategies adopted in this field to overcome these drawbacks presented in classical drive, it is worth mentioning the use of the second order sliding mode control(SOSMC) based on the super twisting algorithm(STA) combined with the fuzzy logic control(FSOSMC). In order to realize the optimal control performance, the FSOSMC parameters are adjusted using an optimization algorithm based on the genetic algorithm(GA). The performances of the envisaged control scheme, called G-FSOSMC, are investigated against G-SOSMC, G-PI and BBO-FSOSMC algorithms. The proposed controller scheme is efficient in reducing the torque and flux ripples, and successfully suppresses chattering. The effects of parametric uncertainties do not affect system performance.
基金supported by the Ministry of Higher Education and Scientific Research in Tunisia
文摘The problem of the chattering phenomenon is still the main drawback of the classical sliding mode control. To resolve this problem, a discrete second order sliding mode control via input-output model is proposed in this paper. The proposed control law is synthesized for decouplable multivariable systems. A robustness analysis of the proposed discrete second order sliding mode control is carried out. Simulation results are presented to illustrate the effectiveness of the proposed strategy.
基金supported by National Natural Science Foundation of China (No.60504007)the PhD Programs Foundation of Ministry of Educationof China (No.20070286040)the Scientific Research Foundation of Graduate School of Southeast University
文摘In this paper, using finite-time control method, we consider the disturbance analysis of a second-order system with unknown but bounded disturbance. We show that the states of the second-order system will be stabilized to a region containing the origin. The radius of this region is determined by the control parameters and can be rendered as small as desired. The rigorous stability analysis is also given. Compared with the conventional PD control law, the finite-time control law yields a better disturbance rejection performance. Numerical simulation results show the effectiveness of the method.
基金Project supported by the National Natural Science Foundation of China (Grant No. 70571059)
文摘This paper investigates the cluster consensus problem for second-order multi-agent systems by applying the pinning control method to a small collection of the agents. Consensus is attained independently for different agent clusters according to the community structure generated by the group partition of the underlying graph and sufficient conditions for both cluster and general consensus are obtained by using results from algebraic graph theory and the LaSalle Invariance Principle. Finally, some simple simulations are presented to illustrate the technique.
文摘In this paper, the problem of stabilizing an unstable second order delay system using classical proportional-integralderivative(PID) controller is considered. An extension of the Hermite-Biehler theorem, which is applicable to quasi-polynomials, is used to seek the set of complete stabilizing proportional-integral/proportional-integral-derivative(PI/PID) parameters. The range of admissible proportional gains is determined in closed form. For each proportional gain, the stabilizing set in the space of the integral and derivative gains is shown to be a triangle.
基金co-supported by the National Natural Science Foundation of China (Nos. 61333011, 91216304 and 61121003)
文摘In this paper, formation tracking control problems for second-order multi-agent systems（MASs） with time-varying delays are studied, specifically those where the position and velocity of followers are designed to form a time-varying formation while tracking those of the leader. A neighboring relative state information based formation tracking protocol with an unknown gain matrix and time-varying delays is presented. The formation tracking problems are then transformed into asymptotically stable problems. Based on the Lyapunov-Krasovskii functional approach, conditions sufficient for second-order MASs with time-varying delays to realize formation tracking are examined. An approach to obtain the unknown gain matrix is given and, since neighboring relative velocity information is difficult to measure in practical applications, a formation tracking protocol with time-varying delays using only neighboring relative position information is introduced. The proposed results can be used on target enclosing problems for MASs with second-order dynamics and time-varying delays. An application for target enclosing by multiple unmanned aerial vehicles（UAVs） is given to demonstrate the feasibility of theoretical results.
基金Supported by the National Natural Science Foundation of China(11202023)
文摘An attitude controller using the second order sliding mode control methodology with a backstepping approach（SOSMCB）is designed and implemented for a spinning missile with two internal moving mass blocks.The system consists of a rigid body and two radial internal moving mass blocks and its mathematical model is established based on Newtonian mechanics.The control scheme integrates a second order sliding mode control algorithm into the last step of the backstepping approach,and its stability is proved by means of a Lyapunov function.The performance of the controller is demonstrated by numerical simulations,the results show that the attitude controller is stable and effective.
基金supported by the National Board for Higher Mathematics,Mumbai,India under Grant No.2/48(5)/2013/NBHM(R.P.)/RD-II/688 dt 16.01.2014
文摘The modelling of risky asset by stochastic processes with continuous paths, based on Brow- nian motions, suffers from several defects. First, the path continuity assumption does not seem reason- able in view of the possibility of sudden price variations （jumps） resulting of market crashes. A solution is to use stochastic processes with jumps, that will account for sudden variations of the asset prices. On the other hand, such jump models are generally based on the Poisson random measure. Many popular economic and financial models described by stochastic differential equations with Poisson jumps. This paper deals with the approximate controllability of a class of second-order neutral stochastic differential equations with infinite delay and Poisson jumps. By using the cosine family of operators, stochastic analysis techniques, a new set of sufficient conditions are derived for the approximate controllability of the above control system. An example is provided to illustrate the obtained theory.
文摘A difficult but important problem in optimal control theory is the design of an optimal feedback control, i.e., the design of an optimal control as function of the phase (state) coordinates [1,2]. This problem can be solved not often. We study here the autonomous nonlinear system of second order in general form. The constraints imposed on the control input can depend on the phase (state) coordinates of the system. The goal of the control is to maximize or minimize one phase coordinate of the considered system while other takes a prescribed in advance value. In the literature, optimal control problems for the systems of second order are most frequently associated with driving both phase coordinates to a prescribed in advance state. In this statement of the problem, the optimal control feedback can be designed only for special kind of systems. In our statement of the problem, an optimal control can be designed as function of the state coordinates for more general kind of the systems. The problem of maximization or minimization of the swing amplitude is considered explicitly as an example. Simulation results are presented.
基金supported by the National High Technology Research and Development Program of China (Grant Nos. 2007AA041104,2007AA041105 and 2007AA04Z163)
文摘This paper studies consensus control problems for a class of second-order multi-agent systems without relative velocity measurement. Some dynamic neighbour-based rules are adopted for the agents in the presence of external disturbances. A sufficient condition is derived to make all agents achieve consensus while satisfying desired H∞ performance. Finally, numerical simulations are provided to show the effectiveness of our theoretical results.
基金supported by the National Natural Science Foundation of China(61203354)
文摘In this paper, we study the containment control problem for nonlinear second-order systems with unknown parameters and multiple stationary/dynamic leaders. The topologies that characterize the interaction among the leaders and the followers are directed graphs. Necessary and sufficient criteria which guarantee the control objectives are established for both stationary leaders(regulation case) and dynamic leaders(dynamic tracking case) based protocols. The final states of all the followers are exclusively determined by the initial values of the leaders and the topology structures. In the regulation case, all the followers converge into the convex hull spanned by the leaders,while in the dynamic tracking case, not only the positions of the followers converge into the convex hull but also the velocities of the followers converge into the velocity convex hull of the leaders.Finally, all the theoretical results are illustrated by numerical simulations.
文摘A complex autonomous inventory coupled system is considered. It can take, for example, the form of a network of chemical or biochemical reactors, where the inventory interactions perform the recycling of by-products between the subsystems. Because of the flexible subsystems interactions, each of them can be operated with their own periods utilizing advantageously their dynamic properties. A multifrequency second-order test generalizing the p-test for single systems is described. It can be used to decide which kind of the operation (the static one, the periodic one or the multiperiodic one) will intensify the productivity of a complex system. An illustrative example of the multiperiodic optimization of a complex chemical production system is presented.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61203147,61374047,and 61403168)
文摘This paper investigates the consensus tracking problems of second-order multi-agent systems with a virtual leader via event-triggered control. A novel distributed event-triggered transmission scheme is proposed, which is intermittently examined at constant sampling instants. Only partial neighbor information and local measurements are required for event detection. Then the corresponding event-triggered consensus tracking protocol is presented to guarantee second-order multi-agent systems to achieve consensus tracking. Numerical simulations are given to illustrate the effectiveness of the proposed strategy.
文摘Eigenstructure assignment using the proportional-plus-derivative feedback controller in a class of secondorder dynamic system is investigated. Simple, general, complete parametric expressions for both the closed-loop eigenvector matrix and the feedback gains are established based on two simple Smith form reductions. The approach utilizes directly the original system data and involves manipulations only on n-dimensional matrices. Furthermore, it reveals all the degrees of freedom which can be further utilized to achieve additional system specifications. An example shows the effect of the proposed approach.
文摘In this paper eigenstructure assignment via proportional-plus-derivative feedback is investigated for a class of second-order descriptor linear systems. Under certain conditions, simple, general and complete parametric solutions of both finite closed-loop eigenvector matrices and feedback gain matrices are derived. The parametric approach utilizes directly original system data, involves manipulations only on n-dimensional matrices, and reveals all the design degrees of freedom which can be further utilized to achieve certain additional system specifications. A numerical example shows the effect of the proposed approach.
基金the French Research Network Me Ge (Multiscale and Multiphysics Couplings in Geo-environmental Mechanics GDR CNRS 3176/2340, 2008e2015) for having supported this work
文摘Geomaterials are known to be non-associated materials. Granular soils therefore exhibit a variety of failure modes, with diffuse or localized kinematical patterns. In fact, the notion of failure itself can be confusing with regard to granular soils, because it is not associated with an obvious phenomenology. In this study, we built a proper framework, using the second-order work theory, to describe some failure modes in geomaterials based on energy conservation. The occurrence of failure is defined by an abrupt increase in kinetic energy. The increase in kinetic energy from an equilibrium state, under incremental loading, is shown to be equal to the difference between the external second-order work,involving the external loading parameters, and the internal second-order work, involving the constitutive properties of the material. When a stress limit state is reached, a certain stress component passes through a maximum value and then may decrease. Under such a condition, if a certain additional external loading is applied, the system fails, sharply increasing the strain rate. The internal stress is no longer able to balance the external stress, leading to a dynamic response of the specimen. As an illustration, the theoretical framework was applied to the well-known undrained triaxial test for loose soils. The influence of the loading control mode was clearly highlighted. It is shown that the plastic limit theory appears to be a particular case of this more general second-order work theory. When the plastic limit condition is met, the internal second-order work is nil. A class of incremental external loadings causes the kinetic energy to increase dramatically, leading to the sudden collapse of the specimen, as observed in laboratory.
基金co-supported by the National Basic Research Program of China(No.2012CB720000)the National Natural Science Foundation of China(No.61104153)the Research Fund for the Doctoral Program of Higher Education of China(No.20091101110025)
文摘This paper proposes a finite-time robust flight controller, targeting for a reentry vehicle with blended aerodynamic surfaces and a reaction control system（RCS）. Firstly, a novel finite-time attitude controller is pointed out with the introduction of a nonsingular finite-time sliding mode manifold. The attitude tracking errors are mathematically proved to converge to zero within finite time which can be estimated. In order to improve the performance, a second-order finite-time sliding mode controller is further developed to effectively alleviate chattering without any deterioration of robustness and accuracy. Moreover, an optimization control allocation algorithm, using linear programming and a pulse-width pulse-frequency（PWPF） modulator, is designed to allocate torque commands for all the aerodynamic surface deflections and on–off switching-states of RCS thrusters.Simulations are provided for the reentry vehicle considering uncertain parameters and external disturbances for practical purposes, and the results demonstrate the effectiveness and robustness of the attitude control system.
