A comparative study of model predictive control(MPC)schemes and robust Hstate feedback control(RSC)method for trajectory tracking is proposed in this paper.The main objective of this paper is to compare MPC and RSC co...A comparative study of model predictive control(MPC)schemes and robust Hstate feedback control(RSC)method for trajectory tracking is proposed in this paper.The main objective of this paper is to compare MPC and RSC controllers’performance in tracking predefined trajectory under different scenarios.MPC controller is designed based on the simple longitudinal-yaw-lateral motions of a single-track vehicle with a linear tire,which is an approximation of the more realistic model of a vehicle with double-track motion with a non-linear tire mode.RSC is designed on the basis of the same method as adopted for the MPC controller to achieve a fair comparison.Then,three test cases are built in CarSim-Simulink joint platform.Specifically,the verification test is used to test the tracking accuracy of MPC and RSC controller under well road conditions.Besides,the double lane change test with low road adhesion is designed to find the maximum velocity that both controllers can carry out while guaranteeing stability.Furthermore,an extreme curve test is built where the road adhesion changes suddenly,in order to test the performance of both controllers under extreme conditions.Finally,the advantages and disadvantages of MPC and RSC under different scenarios are also discussed.展开更多
This paper presents a new method to eliminate the chattering of state feedback sliding mode control (SMC) law for the mobile control of an autonomous underwater vehicle (AUV) which is nonlinear and suffers from un...This paper presents a new method to eliminate the chattering of state feedback sliding mode control (SMC) law for the mobile control of an autonomous underwater vehicle (AUV) which is nonlinear and suffers from unknown disturbances system. SMC is a well-known nonlinear system control algorithm for its anti-disturbances capability, while the chattering on switch surface is one stiff question. To dissipate the well-known chattering of SMC, the switching manifold is proposed by presetting a Hurwitz matrix which is deducted from the state feedback matrix. Meanwhile, the best switching surface is achieved by use of eigenvalues of the Hurwitz matrix. The state feedback control parameters are not only applied to control the states of AUV but also connected with coefficients of switching surface. The convergence of the proposed control law is verified by Lyapunov function and the robust character is validated by the Matlab platform of one AUV model.展开更多
A new technique for considering the stabilizing time-variant state feedback gains is proposed from the viewpoint of information geometry. First, parametrization of the set of all stabilizing time-variant state feedbac...A new technique for considering the stabilizing time-variant state feedback gains is proposed from the viewpoint of information geometry. First, parametrization of the set of all stabilizing time-variant state feedback gains is given. Moreover, a diffeomorphic structure between the set of stabilizing time-variant state feedback gains and the Cartesian product of positive definite matrix and skew symmetric matrix satisfying certain algebraic conditions is constructed. Furthermore, an immersion and some results about the eigenvalue locations of stable state feedback systems are derived.展开更多
Using the Lyapunov function method,this paper investigates the design of state feedback stabilization controllers for fractional order nonlinear systems in triangular form,and presents a number of new results.First,so...Using the Lyapunov function method,this paper investigates the design of state feedback stabilization controllers for fractional order nonlinear systems in triangular form,and presents a number of new results.First,some new properties of Caputo fractional derivative are presented,and a sufficient condition of asymptotical stability for fractional order nonlinear systems is obtained based on the new properties.Then,by introducing appropriate transformations of coordinates,the problem of controller design is converted into the problem of finding some parameters,which can be certainly obtained by solving the Lyapunov equation and relevant matrix inequalities.Finally,based on the Lyapunov function method,state feedback stabilization controllers making the closed-loop system asymptotically stable are explicitly constructed.A simulation example is given to demonstrate the effectiveness of the proposed design procedure.展开更多
For the appearance of the additive perturbation of controller gain when the controller parameter has minute adjustment at the initial running stage of system,to avoid the adverse effects,this paper investigates the mi...For the appearance of the additive perturbation of controller gain when the controller parameter has minute adjustment at the initial running stage of system,to avoid the adverse effects,this paper investigates the mixed H_2/H_∞ state feedback attitude control problem of microsatellite based on extended LMI method.Firstly,the microsatellite attitude control system is established and transformed into corresponding state space form.Then,without the equivalence restriction of the two Lyapunov variables of H_2 and H∞performance,this paper introduces additional variables to design the mixed H_2/H_∞ control method based on LMI which can also reduce the conservatives.Finally,numerical simulations are analyzed to show that the proposed method can make the satellite stable within 20 s whether there is additive perturbation of the controller gain or not.The comparative analysis of the simulation results between extended LMI method and traditional LMI method also demonstrates the effectiveness and feasibility of the proposed method in this paper.展开更多
The state feedback design for singularly perturbed systems described in Delta operator is considered. The composite state feedback controller for slow and fast subsystems is designed by using the direct method. The ob...The state feedback design for singularly perturbed systems described in Delta operator is considered. The composite state feedback controller for slow and fast subsystems is designed by using the direct method. The obtained results can bring previous conclusions of continuous and discrete time systems into the unified Delta framework. A simulation example is presented to demonstrate the validity and efficiency of the design.展开更多
The delay-dependent H-infinity analysis and H-infinity control problems for continuous time-delay systems are studied. By introducing an equality with some free weighting matrices, an improved criterion of delay-depen...The delay-dependent H-infinity analysis and H-infinity control problems for continuous time-delay systems are studied. By introducing an equality with some free weighting matrices, an improved criterion of delay-dependent stability with H-infinity performance for such systems is presented, and a criterion of existence and some design methods of delay-dependent H-infinity controller for such systems are proposed in term of a set of matrix inequalities, which is solved efficiently by an iterative algorithm. Further, the corresponding results for the delay-dependent robust H-infinity analysis and robust H-infinity control problems for continuous time-delay uncertain systems are given. Finally, two numerical examples are given to illustrate the efficiency of the proposed method by comparing with the other existing results.展开更多
The introduction of robust control theory into structure control, as well as design procedure of stabilizing controllers for structures with parameter uncertainty and model error is discussed. A stability bound is der...The introduction of robust control theory into structure control, as well as design procedure of stabilizing controllers for structures with parameter uncertainty and model error is discussed. A stability bound is derived from the polar decomposition of the nominal system matrix. In addition, our study shows that application of low pass filters avoids spillover by eliminating the unconsidered high frequency components. It is demonstrated, via an example, our approach leads to excellent control result and offers far better robustness than previous solutions.展开更多
The problems of robust exponential stability in mean square and delayed state feedback stabilization for uncertain stochastic systems with time-varying delay are studied. By using Jensen's integral inequality and com...The problems of robust exponential stability in mean square and delayed state feedback stabilization for uncertain stochastic systems with time-varying delay are studied. By using Jensen's integral inequality and combining with the free weighting matrix approach, new delay-dependent stability conditions and delayed state feedback stabilization criteria are obtained in terms of linear matrix inequalities. Meanwhile, the proposed delayed state feedback stabilization criteria are more convenient in application than the existing ones since fewer tuning parameters are involved. Numerical examples are given to illustrate the effectiveness of the proposed methods.展开更多
Aimed at the finite-time stabilization problem of a class of flexible manipulators,a finite-time state feedback stabilization controller was proposed in this paper.Firstly,the nonlinear model of flexible manipulators ...Aimed at the finite-time stabilization problem of a class of flexible manipulators,a finite-time state feedback stabilization controller was proposed in this paper.Firstly,the nonlinear model of flexible manipulators was transformed into linear system through the exact state feedback linearization,and then using the finite time stabilization control method of the linear system,a finite-time state feedback stabilization controller was designed for the flexible manipulators.Furthermore,it was proved that all the states of flexible manipulators could be stabilized to equilibrium in finite-time under the proposed controller.The simulation results show that the performance of the flexible manipulators under the proposed finite-time state feedback controller is better than the traditional state-feedback controller.The proposed finite-time stabilization controller can improve the performance of the flexible manipulators.展开更多
In this paper, for a class of high-order stochastic nonlinear systems with zero dynamics which are neither necessarily feedback linearizable nor affine in the control input, the problem of state feedback stabilization...In this paper, for a class of high-order stochastic nonlinear systems with zero dynamics which are neither necessarily feedback linearizable nor affine in the control input, the problem of state feedback stabilization is investigated for the first time. Under some weaker assumptions, a smooth state feedback controller is designed, which ensures that the closed-loop system has an almost surely unique solution on [0,∞), the equilibrium at the origin of the closed-loop system is globally asymptotically stable in probability, and all the states can be regulated to the origin almost surely. A simulation example demonstrates the control scheme.展开更多
This paper focuses on the H∞ controller design for linear systems with time-varying delays and norm-bounded parameter perturbations in the system state and control/disturbance. On the existence of delayed/undelayed f...This paper focuses on the H∞ controller design for linear systems with time-varying delays and norm-bounded parameter perturbations in the system state and control/disturbance. On the existence of delayed/undelayed full state feedback controllers, we present a sufficient condition and give a design method in the form of Riccati equation. The controller can not only stabilize the time-delay system, but also make the H∞ norm of the closed-loop system be less than a given bound. This result practically generalizes the related results in current literature.展开更多
Based upon the theory of the nonlinear quadric two-person nonzero-sum differential game,the fact that the time-limited mixed H2/H∞ control problem can be turned into the problem of solving the state feedback Nash bal...Based upon the theory of the nonlinear quadric two-person nonzero-sum differential game,the fact that the time-limited mixed H2/H∞ control problem can be turned into the problem of solving the state feedback Nash balance point is mentioned. Upon this,a theorem about the solution of the state feedback control is given,the Lyapunov stabilization of the nonlinear system under this control is proved,too. At the same time,this solution is used to design the nonlinear H2/H∞ guidance law of the relative motion between the missile and the target in three-dimensional(3D) space. By solving two coupled Hamilton-Jacobi partial differential inequalities(HJPDI),a control with more robust stabilities and more robust performances is obtained. With different H∞ performance indexes,the correlative weighting factors of the control are analytically designed. At last,simulations under different robust performance indexes and under different initial conditions and under the cases of intercepting different maneuvering targets are carried out. All results indicate that the designed law is valid.展开更多
As saturation is involved in the stabilizing feedback control of a linear discrete-time system, the original global-asymptotic stabilization (GAS) may drop to region-asymptotic stabilization (RAS). How to test if the ...As saturation is involved in the stabilizing feedback control of a linear discrete-time system, the original global-asymptotic stabilization (GAS) may drop to region-asymptotic stabilization (RAS). How to test if the saturated feedback system is GAS or RAS? The paper presents a criterion to answer this question, and describes an algorithm to calculate an invariant attractive ellipsoid for the RAS case. At last, the effectiveness of the approach is shown with examples.展开更多
The problem of global stabilization by state feedback for a class of time-delay nonlinear system is considered. By constructing the appropriate Lyapunov-Krasovskii functionals (LKF) and using the backstepping design, ...The problem of global stabilization by state feedback for a class of time-delay nonlinear system is considered. By constructing the appropriate Lyapunov-Krasovskii functionals (LKF) and using the backstepping design, a linear state feedback controller making the closed-loop system globally asymptotically stable is constructed.展开更多
A robust adaptive control is proposed for a class of uncertain nonlinear non-affine SISO systems. In order to approximate the unknown nonlinear function, an affine type neural network(ATNN) and neural state feedback c...A robust adaptive control is proposed for a class of uncertain nonlinear non-affine SISO systems. In order to approximate the unknown nonlinear function, an affine type neural network(ATNN) and neural state feedback compensation are used, and then to compensate the approximation error and external disturbance, a robust control term is employed. By Lyapunov stability analysis for the closed-loop system, it is proven that tracking errors asymptotically converge to zero. Moreover, an observer is designed to estimate the system states because all the states may not be available for measurements. Furthermore, the adaptation laws of neural networks and the robust controller are given based on the Lyapunov stability theory. Finally, two simulation examples are presented to demonstrate the effectiveness of the proposed control method. Finally, two simulation examples show that the proposed method exhibits strong robustness, fast response and small tracking error, even for the non-affine nonlinear system with external disturbance, which confirms the effectiveness of the proposed approach.展开更多
The recently proposed data-driven pole placement method is able to make use of measurement data to simultaneously identify a state space model and derive pole placement state feedback gain. It can achieve this precise...The recently proposed data-driven pole placement method is able to make use of measurement data to simultaneously identify a state space model and derive pole placement state feedback gain. It can achieve this precisely for systems that are linear time-invariant and for which noiseless measurement datasets are available. However, for nonlinear systems, and/or when the only noisy measurement datasets available contain noise, this approach is unable to yield satisfactory results. In this study, we investigated the effect on data-driven pole placement performance of introducing a prefilter to reduce the noise present in datasets. Using numerical simulations of a self-balancing robot, we demonstrated the important role that prefiltering can play in reducing the interference caused by noise.展开更多
基金Supported by Natural Science Foundation of China(Grant Nos.52072051,51705044)Chongqing Municipal Natural Science Foundation of China(Grant No.cstc2020jcyj-msxmX0956)+1 种基金State Key Laboratory of Mechanical System and Vibration(Grant No.MSV202016)State Key Laboratory of Mechanical Transmissions(Grant No.SKLMT-KFKT-201806).
文摘A comparative study of model predictive control(MPC)schemes and robust Hstate feedback control(RSC)method for trajectory tracking is proposed in this paper.The main objective of this paper is to compare MPC and RSC controllers’performance in tracking predefined trajectory under different scenarios.MPC controller is designed based on the simple longitudinal-yaw-lateral motions of a single-track vehicle with a linear tire,which is an approximation of the more realistic model of a vehicle with double-track motion with a non-linear tire mode.RSC is designed on the basis of the same method as adopted for the MPC controller to achieve a fair comparison.Then,three test cases are built in CarSim-Simulink joint platform.Specifically,the verification test is used to test the tracking accuracy of MPC and RSC controller under well road conditions.Besides,the double lane change test with low road adhesion is designed to find the maximum velocity that both controllers can carry out while guaranteeing stability.Furthermore,an extreme curve test is built where the road adhesion changes suddenly,in order to test the performance of both controllers under extreme conditions.Finally,the advantages and disadvantages of MPC and RSC under different scenarios are also discussed.
基金supported by National Basic Research Program of China (973 Program) (No. 6138101004-3)Key Project of Innovation Knowledge of Chinese Academy of Sciences (No. YYYJ-0917)Innovation Knowledge of Chinese Academy of Sciences (No.O7A6210601)
文摘This paper presents a new method to eliminate the chattering of state feedback sliding mode control (SMC) law for the mobile control of an autonomous underwater vehicle (AUV) which is nonlinear and suffers from unknown disturbances system. SMC is a well-known nonlinear system control algorithm for its anti-disturbances capability, while the chattering on switch surface is one stiff question. To dissipate the well-known chattering of SMC, the switching manifold is proposed by presetting a Hurwitz matrix which is deducted from the state feedback matrix. Meanwhile, the best switching surface is achieved by use of eigenvalues of the Hurwitz matrix. The state feedback control parameters are not only applied to control the states of AUV but also connected with coefficients of switching surface. The convergence of the proposed control law is verified by Lyapunov function and the robust character is validated by the Matlab platform of one AUV model.
文摘A new technique for considering the stabilizing time-variant state feedback gains is proposed from the viewpoint of information geometry. First, parametrization of the set of all stabilizing time-variant state feedback gains is given. Moreover, a diffeomorphic structure between the set of stabilizing time-variant state feedback gains and the Cartesian product of positive definite matrix and skew symmetric matrix satisfying certain algebraic conditions is constructed. Furthermore, an immersion and some results about the eigenvalue locations of stable state feedback systems are derived.
基金supported by National Natural Science Foundation of China(61374065,61374002,61503225,61573215)the Research Fund for the Taishan Scholar Project of Shandong Province of Chinathe Natural Science Foundation of Shandong Province(ZR2015FQ003)
文摘Using the Lyapunov function method,this paper investigates the design of state feedback stabilization controllers for fractional order nonlinear systems in triangular form,and presents a number of new results.First,some new properties of Caputo fractional derivative are presented,and a sufficient condition of asymptotical stability for fractional order nonlinear systems is obtained based on the new properties.Then,by introducing appropriate transformations of coordinates,the problem of controller design is converted into the problem of finding some parameters,which can be certainly obtained by solving the Lyapunov equation and relevant matrix inequalities.Finally,based on the Lyapunov function method,state feedback stabilization controllers making the closed-loop system asymptotically stable are explicitly constructed.A simulation example is given to demonstrate the effectiveness of the proposed design procedure.
文摘For the appearance of the additive perturbation of controller gain when the controller parameter has minute adjustment at the initial running stage of system,to avoid the adverse effects,this paper investigates the mixed H_2/H_∞ state feedback attitude control problem of microsatellite based on extended LMI method.Firstly,the microsatellite attitude control system is established and transformed into corresponding state space form.Then,without the equivalence restriction of the two Lyapunov variables of H_2 and H∞performance,this paper introduces additional variables to design the mixed H_2/H_∞ control method based on LMI which can also reduce the conservatives.Finally,numerical simulations are analyzed to show that the proposed method can make the satellite stable within 20 s whether there is additive perturbation of the controller gain or not.The comparative analysis of the simulation results between extended LMI method and traditional LMI method also demonstrates the effectiveness and feasibility of the proposed method in this paper.
基金This work was supported by the National Natural Science Foundation of China (No. 60474078,60304001).
文摘The state feedback design for singularly perturbed systems described in Delta operator is considered. The composite state feedback controller for slow and fast subsystems is designed by using the direct method. The obtained results can bring previous conclusions of continuous and discrete time systems into the unified Delta framework. A simulation example is presented to demonstrate the validity and efficiency of the design.
基金This work was supported by the National Natural Science Foundation of China (No. 60024301)Natural Science Fund of Shanxi Province of China(No. 20051032)
文摘The delay-dependent H-infinity analysis and H-infinity control problems for continuous time-delay systems are studied. By introducing an equality with some free weighting matrices, an improved criterion of delay-dependent stability with H-infinity performance for such systems is presented, and a criterion of existence and some design methods of delay-dependent H-infinity controller for such systems are proposed in term of a set of matrix inequalities, which is solved efficiently by an iterative algorithm. Further, the corresponding results for the delay-dependent robust H-infinity analysis and robust H-infinity control problems for continuous time-delay uncertain systems are given. Finally, two numerical examples are given to illustrate the efficiency of the proposed method by comparing with the other existing results.
文摘The introduction of robust control theory into structure control, as well as design procedure of stabilizing controllers for structures with parameter uncertainty and model error is discussed. A stability bound is derived from the polar decomposition of the nominal system matrix. In addition, our study shows that application of low pass filters avoids spillover by eliminating the unconsidered high frequency components. It is demonstrated, via an example, our approach leads to excellent control result and offers far better robustness than previous solutions.
基金supported by the National Natural Science Foundation of China(10971232)the Natural Science Foundation of Guangdong Province(101510090010000398351009001000002)
文摘The problems of robust exponential stability in mean square and delayed state feedback stabilization for uncertain stochastic systems with time-varying delay are studied. By using Jensen's integral inequality and combining with the free weighting matrix approach, new delay-dependent stability conditions and delayed state feedback stabilization criteria are obtained in terms of linear matrix inequalities. Meanwhile, the proposed delayed state feedback stabilization criteria are more convenient in application than the existing ones since fewer tuning parameters are involved. Numerical examples are given to illustrate the effectiveness of the proposed methods.
基金Sponsored by the Doctoral Fund of Ministry of Education of China(20070288022)the Natural Science Foundation of Jiangsu Province of China(BK2008404)the Young Teacher Academic Foundation of Nanjing University of Technology(39710013)
文摘Aimed at the finite-time stabilization problem of a class of flexible manipulators,a finite-time state feedback stabilization controller was proposed in this paper.Firstly,the nonlinear model of flexible manipulators was transformed into linear system through the exact state feedback linearization,and then using the finite time stabilization control method of the linear system,a finite-time state feedback stabilization controller was designed for the flexible manipulators.Furthermore,it was proved that all the states of flexible manipulators could be stabilized to equilibrium in finite-time under the proposed controller.The simulation results show that the performance of the flexible manipulators under the proposed finite-time state feedback controller is better than the traditional state-feedback controller.The proposed finite-time stabilization controller can improve the performance of the flexible manipulators.
基金Program for New Century Excellent Talents in University of China (NCET-05-0607)National Natural Science Fou-ndation of China (No.60774010)Project for Fundamental Research of Natural Sciences in Universities of Jingsu Province (No.07KJB510114)
文摘In this paper, for a class of high-order stochastic nonlinear systems with zero dynamics which are neither necessarily feedback linearizable nor affine in the control input, the problem of state feedback stabilization is investigated for the first time. Under some weaker assumptions, a smooth state feedback controller is designed, which ensures that the closed-loop system has an almost surely unique solution on [0,∞), the equilibrium at the origin of the closed-loop system is globally asymptotically stable in probability, and all the states can be regulated to the origin almost surely. A simulation example demonstrates the control scheme.
基金This project was supported by the National Natural Science Foundation of China (No. 69974022).
文摘This paper focuses on the H∞ controller design for linear systems with time-varying delays and norm-bounded parameter perturbations in the system state and control/disturbance. On the existence of delayed/undelayed full state feedback controllers, we present a sufficient condition and give a design method in the form of Riccati equation. The controller can not only stabilize the time-delay system, but also make the H∞ norm of the closed-loop system be less than a given bound. This result practically generalizes the related results in current literature.
基金Sponsored by the National Natural Science Foundation of China (Grant No.90716028)
文摘Based upon the theory of the nonlinear quadric two-person nonzero-sum differential game,the fact that the time-limited mixed H2/H∞ control problem can be turned into the problem of solving the state feedback Nash balance point is mentioned. Upon this,a theorem about the solution of the state feedback control is given,the Lyapunov stabilization of the nonlinear system under this control is proved,too. At the same time,this solution is used to design the nonlinear H2/H∞ guidance law of the relative motion between the missile and the target in three-dimensional(3D) space. By solving two coupled Hamilton-Jacobi partial differential inequalities(HJPDI),a control with more robust stabilities and more robust performances is obtained. With different H∞ performance indexes,the correlative weighting factors of the control are analytically designed. At last,simulations under different robust performance indexes and under different initial conditions and under the cases of intercepting different maneuvering targets are carried out. All results indicate that the designed law is valid.
基金the State Key Development Program for Basic Research of China(2002CB312200)the National High Technology Research and Development Program of China(2007AA04Z193)
基金Supported by National Natural Science Foundation of P. R. China (60174040)
文摘As saturation is involved in the stabilizing feedback control of a linear discrete-time system, the original global-asymptotic stabilization (GAS) may drop to region-asymptotic stabilization (RAS). How to test if the saturated feedback system is GAS or RAS? The paper presents a criterion to answer this question, and describes an algorithm to calculate an invariant attractive ellipsoid for the RAS case. At last, the effectiveness of the approach is shown with examples.
基金Supported by the "973" Project of P. R. China (G1998020300)
文摘The problem of global stabilization by state feedback for a class of time-delay nonlinear system is considered. By constructing the appropriate Lyapunov-Krasovskii functionals (LKF) and using the backstepping design, a linear state feedback controller making the closed-loop system globally asymptotically stable is constructed.
基金Supported in part by the Chinese Outstanding Youth Science Foundation(69925308)supported by Program for Changjiang Scholars and Innovative Research Team in University
基金Supported by the Key Program of National Natural Science Foundation of China (60634020), Doctoral Program Foundation of Ministry of Education of China (20050533028, 20070533132), Natural Science Foundation of Hunan Province (06J35145), and Program for New Century Excellent Talents in University (NCET-07-0867)
基金Project(61433004)suppouted by the National Natural Science Foundation of China
文摘A robust adaptive control is proposed for a class of uncertain nonlinear non-affine SISO systems. In order to approximate the unknown nonlinear function, an affine type neural network(ATNN) and neural state feedback compensation are used, and then to compensate the approximation error and external disturbance, a robust control term is employed. By Lyapunov stability analysis for the closed-loop system, it is proven that tracking errors asymptotically converge to zero. Moreover, an observer is designed to estimate the system states because all the states may not be available for measurements. Furthermore, the adaptation laws of neural networks and the robust controller are given based on the Lyapunov stability theory. Finally, two simulation examples are presented to demonstrate the effectiveness of the proposed control method. Finally, two simulation examples show that the proposed method exhibits strong robustness, fast response and small tracking error, even for the non-affine nonlinear system with external disturbance, which confirms the effectiveness of the proposed approach.
文摘The recently proposed data-driven pole placement method is able to make use of measurement data to simultaneously identify a state space model and derive pole placement state feedback gain. It can achieve this precisely for systems that are linear time-invariant and for which noiseless measurement datasets are available. However, for nonlinear systems, and/or when the only noisy measurement datasets available contain noise, this approach is unable to yield satisfactory results. In this study, we investigated the effect on data-driven pole placement performance of introducing a prefilter to reduce the noise present in datasets. Using numerical simulations of a self-balancing robot, we demonstrated the important role that prefiltering can play in reducing the interference caused by noise.