Abstract: The current method to solve the problem of active suspension control for a vehicle is often dealt with a quarter-car or half-car model. But it is not enough to use this kind of model for practical applicatio...Abstract: The current method to solve the problem of active suspension control for a vehicle is often dealt with a quarter-car or half-car model. But it is not enough to use this kind of model for practical applications. In this paper, based on considering the influence of factors such as, seat and passengers, a MDOF(multi-degree-of-freedom) model describing the vehicle motion is set up. The MODF model, which is 8DOF of four independent suspensions and four wheel tracks, is more applicable by comparison of its analysis result with some conventional vehicle models. Therefore, it is more suitable to use the 8DOF full-car model than a conventional 4DOF half-car model in the active control design for car vibration. Based on the derived 8DOF model, a controller is designed by using LQ (linear quadratic ) control theory, and the appropriate control scheme is selected by testing various performance indexes. Computer simulation is carried out for a passenger car running on a road with step disturbance and random road disturbance expressed by Power Spectral Density (PSD). Vibrations corresponding to ride comfort are derived under the foregoing road disturbances. The response results for uncontrolled and controlled system are compared. The response of vehicle vibration is greatly suppressed and quickly damped, which testifies the effect of the active suspension. The results achieved for various controllers are compared to investigate the influence of different control schemes on the control effect.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
Double cost function linear quadratic regulator (DLQR) is developed from LQR theory to solve an optimal control problem with a general nonlinear cost function. In addition to the traditional LQ cost function, anothe...Double cost function linear quadratic regulator (DLQR) is developed from LQR theory to solve an optimal control problem with a general nonlinear cost function. In addition to the traditional LQ cost function, another free form cost function was introduced to express the physical need plainly and optimize weights of LQ cost function using the search algorithms. As an instance, DLQR was applied in determining the control input in the front steering angle compensation control (FSAC) model for heavy duty vehicles. The brief simulations show that DLQR is powerful enough to specify the engineering requirements correctly and balance many factors effectively. The concept and applicable field of LQR are expanded by DLQR to optimize the system with a free form cost function.展开更多
The current literature lacks uniform calculation methods for following trajectory control for autonomous vehicles,including the calculation of errors,determination of tracking points,and design of feedforward controll...The current literature lacks uniform calculation methods for following trajectory control for autonomous vehicles,including the calculation of errors,determination of tracking points,and design of feedforward controllers.Hence,a complete calculation method is proposed to address this gap.First,a control equation in the form of an error is obtained according to the dynamic equation of the vehicle coordinate system and the trajectory following model.Secondly,the deviation of the vehicle state is obtained according to the current vehicle s state and the following control model.Finally,a linear quadratic regulator(LQR)controller with feedforward control is designed according to the characteristics of the dynamic equation.With the proposed LQR,the simulation of computational time,anti-interference,and reliability analysis of the trajectory following control is performed by programming using MATLAB.The simulation outcomes are then compared with the experimental results from the literature.The comparison indicates that the proposed complete calculation method is effective,reliable,and capable of achieving real-time and anti-interference following control performance.The simulation results with or without feedforward control show that the steady-state error is eliminated and that good control performance is obtained by introducing feedforward control.展开更多
Improving rollover and stability of the vehicles is the indispensable part of automotive research to prevent vehicle rollover and crashes.The main objective of this work is to develop active control mechanism based on...Improving rollover and stability of the vehicles is the indispensable part of automotive research to prevent vehicle rollover and crashes.The main objective of this work is to develop active control mechanism based on fuzzy logic controller(FLC) and linear quadratic regulator(LQR) for improving vehicle path following,roll and handling performances simultaneously.3-DOF vehicle model including yaw rate,lateral velocity(lateral dynamic) and roll angle(roll dynamic) were developed.The controller produces optimal moment to increase stability and roll margin of vehicle by receiving the steering angle as an input and vehicle variables as a feedback signal.The effectiveness of proposed controller and vehicle model were evaluated during fishhook and single lane-change maneuvers.Simulation results demonstrate that in both cases(FLC and LQR controllers) by reducing roll angle,lateral acceleration and side slip angles remain under 0.6g and 4° during maneuver,which ensures vehicle stability and handling properties.Finally,the sensitivity and robustness analysis of developed controller for varying longitudinal speeds were investigated.展开更多
The saturation problem is the one of the most common handicaps for applying to real applications, especially the actuator saturation. This paper focuses on the robustness of the sliding mode control （SMC） which inco...The saturation problem is the one of the most common handicaps for applying to real applications, especially the actuator saturation. This paper focuses on the robustness of the sliding mode control （SMC） which incorporates a saturation constraint technique compared to classical linear quadratic regulator （LQR） with saturation. In the first step, the authors present a design methodology of SMC of a class of linear saturated systems. The authors present the structure of the saturation, after that the synthesis of the sliding surface is formulate as a problem of root clustering, which leads to the development of a continuous and non-linear control law that ensures the reaching condition of the sliding mode. The second step is devoted to present briefly the LQR controller technique. Finally, to validate results, the authors demonstrate an example of a quarter of vehicle system.展开更多
This paper addresses to the problem of designing, modeling and practical realization of robust model predictive control for finite and infinite prediction horizon which ensures a parameter dependent quadratic stabilit...This paper addresses to the problem of designing, modeling and practical realization of robust model predictive control for finite and infinite prediction horizon which ensures a parameter dependent quadratic stability and guaranteed cost for linear polytopic uncertain systems. The model predictive controller design procedure based on BMI and LMI is reduced to off-line output feedback gain calculation. A numerical examples and an application to a real process is given to illustrate the effectiveness of the proposed method.展开更多
Energy management strategies based on optimal control theory can achieve minimum fuel consumption for hybrid electric vehicles, but the requirement for driving cycles known in prior leads to a real-time problem. A rea...Energy management strategies based on optimal control theory can achieve minimum fuel consumption for hybrid electric vehicles, but the requirement for driving cycles known in prior leads to a real-time problem. A real-time optimization power-split strategy is proposed based on linear quadratic optimal control. The battery state of charge sustainability and fuel economy are ensured by designing a quadratic performance index combined with two rules. The engine power and motor power of this strategy are calculated in real-time based on current system state and command, and not related to future driving conditions. The simulation results in ADVISOR demonstrate that, under the conditions of various driving cycles, road slopes and vehicle parameters, the proposed strategy significantly improves fuel economy, which is very close to that of the optimal control based on Pontryagin's minimum principle, and greatly reduces computation complexity.展开更多
This paper studies the problem of partially observed optimal control for forward-backward stochastic systems which are driven both by Brownian motions and an independent Poisson random measure. Combining forward-backw...This paper studies the problem of partially observed optimal control for forward-backward stochastic systems which are driven both by Brownian motions and an independent Poisson random measure. Combining forward-backward stochastic differential equation theory with certain classical convex variational techniques, the necessary maximum principle is proved for the partially observed optimal control, where the control domain is a nonempty convex set. Under certain convexity assumptions, the author also gives the sufficient conditions of an optimal control for the aforementioned optimal optimal problem. To illustrate the theoretical result, the author also works out an example of partial information linear-quadratic optimal control, and finds an explicit expression of the corresponding optimal control by applying the necessary and sufficient maximum principle.展开更多
In this paper,three optimal linear formation control algorithms are proposed for first-order linear multiagent systems from a linear quadratic regulator(LQR) perspective with cost functions consisting of both interact...In this paper,three optimal linear formation control algorithms are proposed for first-order linear multiagent systems from a linear quadratic regulator(LQR) perspective with cost functions consisting of both interaction energy cost and individual energy cost,because both the collective ob ject(such as formation or consensus) and the individual goal of each agent are very important for the overall system.First,we propose the optimal formation algorithm for first-order multi-agent systems without initial physical couplings.The optimal control parameter matrix of the algorithm is the solution to an algebraic Riccati equation(ARE).It is shown that the matrix is the sum of a Laplacian matrix and a positive definite diagonal matrix.Next,for physically interconnected multi-agent systems,the optimal formation algorithm is presented,and the corresponding parameter matrix is given from the solution to a group of quadratic equations with one unknown.Finally,if the communication topology between agents is fixed,the local feedback gain is obtained from the solution to a quadratic equation with one unknown.The equation is derived from the derivative of the cost function with respect to the local feedback gain.Numerical examples are provided to validate the effectiveness of the proposed approaches and to illustrate the geometrical performances of multi-agent systems.展开更多
This paper studies the existence and uniqueness of solutions of fully coupled forward-backward stochastic differential equations with Brownian motion and random jumps.The result is applied to solve a linear-quadratic ...This paper studies the existence and uniqueness of solutions of fully coupled forward-backward stochastic differential equations with Brownian motion and random jumps.The result is applied to solve a linear-quadratic optimal control and a nonzero-sum differential game of backward stochastic differential equations.The optimal control and Nash equilibrium point are explicitly derived. Also the solvability of a kind Riccati equations is discussed.All these results develop those of Lim, Zhou(2001) and Yu,Ji(2008).展开更多
文摘Abstract: The current method to solve the problem of active suspension control for a vehicle is often dealt with a quarter-car or half-car model. But it is not enough to use this kind of model for practical applications. In this paper, based on considering the influence of factors such as, seat and passengers, a MDOF(multi-degree-of-freedom) model describing the vehicle motion is set up. The MODF model, which is 8DOF of four independent suspensions and four wheel tracks, is more applicable by comparison of its analysis result with some conventional vehicle models. Therefore, it is more suitable to use the 8DOF full-car model than a conventional 4DOF half-car model in the active control design for car vibration. Based on the derived 8DOF model, a controller is designed by using LQ (linear quadratic ) control theory, and the appropriate control scheme is selected by testing various performance indexes. Computer simulation is carried out for a passenger car running on a road with step disturbance and random road disturbance expressed by Power Spectral Density (PSD). Vibrations corresponding to ride comfort are derived under the foregoing road disturbances. The response results for uncontrolled and controlled system are compared. The response of vehicle vibration is greatly suppressed and quickly damped, which testifies the effect of the active suspension. The results achieved for various controllers are compared to investigate the influence of different control schemes on the control effect.
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°.
文摘Double cost function linear quadratic regulator (DLQR) is developed from LQR theory to solve an optimal control problem with a general nonlinear cost function. In addition to the traditional LQ cost function, another free form cost function was introduced to express the physical need plainly and optimize weights of LQ cost function using the search algorithms. As an instance, DLQR was applied in determining the control input in the front steering angle compensation control (FSAC) model for heavy duty vehicles. The brief simulations show that DLQR is powerful enough to specify the engineering requirements correctly and balance many factors effectively. The concept and applicable field of LQR are expanded by DLQR to optimize the system with a free form cost function.
基金The National Key Research and Development Program of China(No.2019YFB2006404)Guangxi Science and Technology Major Project(No.GUIKE AA18242036,No.GUIKE AA18242037).
文摘The current literature lacks uniform calculation methods for following trajectory control for autonomous vehicles,including the calculation of errors,determination of tracking points,and design of feedforward controllers.Hence,a complete calculation method is proposed to address this gap.First,a control equation in the form of an error is obtained according to the dynamic equation of the vehicle coordinate system and the trajectory following model.Secondly,the deviation of the vehicle state is obtained according to the current vehicle s state and the following control model.Finally,a linear quadratic regulator(LQR)controller with feedforward control is designed according to the characteristics of the dynamic equation.With the proposed LQR,the simulation of computational time,anti-interference,and reliability analysis of the trajectory following control is performed by programming using MATLAB.The simulation outcomes are then compared with the experimental results from the literature.The comparison indicates that the proposed complete calculation method is effective,reliable,and capable of achieving real-time and anti-interference following control performance.The simulation results with or without feedforward control show that the steady-state error is eliminated and that good control performance is obtained by introducing feedforward control.
文摘Improving rollover and stability of the vehicles is the indispensable part of automotive research to prevent vehicle rollover and crashes.The main objective of this work is to develop active control mechanism based on fuzzy logic controller(FLC) and linear quadratic regulator(LQR) for improving vehicle path following,roll and handling performances simultaneously.3-DOF vehicle model including yaw rate,lateral velocity(lateral dynamic) and roll angle(roll dynamic) were developed.The controller produces optimal moment to increase stability and roll margin of vehicle by receiving the steering angle as an input and vehicle variables as a feedback signal.The effectiveness of proposed controller and vehicle model were evaluated during fishhook and single lane-change maneuvers.Simulation results demonstrate that in both cases(FLC and LQR controllers) by reducing roll angle,lateral acceleration and side slip angles remain under 0.6g and 4° during maneuver,which ensures vehicle stability and handling properties.Finally,the sensitivity and robustness analysis of developed controller for varying longitudinal speeds were investigated.
文摘The saturation problem is the one of the most common handicaps for applying to real applications, especially the actuator saturation. This paper focuses on the robustness of the sliding mode control （SMC） which incorporates a saturation constraint technique compared to classical linear quadratic regulator （LQR） with saturation. In the first step, the authors present a design methodology of SMC of a class of linear saturated systems. The authors present the structure of the saturation, after that the synthesis of the sliding surface is formulate as a problem of root clustering, which leads to the development of a continuous and non-linear control law that ensures the reaching condition of the sliding mode. The second step is devoted to present briefly the LQR controller technique. Finally, to validate results, the authors demonstrate an example of a quarter of vehicle system.
文摘This paper addresses to the problem of designing, modeling and practical realization of robust model predictive control for finite and infinite prediction horizon which ensures a parameter dependent quadratic stability and guaranteed cost for linear polytopic uncertain systems. The model predictive controller design procedure based on BMI and LMI is reduced to off-line output feedback gain calculation. A numerical examples and an application to a real process is given to illustrate the effectiveness of the proposed method.
文摘Energy management strategies based on optimal control theory can achieve minimum fuel consumption for hybrid electric vehicles, but the requirement for driving cycles known in prior leads to a real-time problem. A real-time optimization power-split strategy is proposed based on linear quadratic optimal control. The battery state of charge sustainability and fuel economy are ensured by designing a quadratic performance index combined with two rules. The engine power and motor power of this strategy are calculated in real-time based on current system state and command, and not related to future driving conditions. The simulation results in ADVISOR demonstrate that, under the conditions of various driving cycles, road slopes and vehicle parameters, the proposed strategy significantly improves fuel economy, which is very close to that of the optimal control based on Pontryagin's minimum principle, and greatly reduces computation complexity.
基金This research is supported by the National Nature Science Foundation of China under Grant Nos 11001156, 11071144, the Nature Science Foundation of Shandong Province （ZR2009AQ017）, and Independent Innovation Foundation of Shandong University （IIFSDU）, China.
文摘This paper studies the problem of partially observed optimal control for forward-backward stochastic systems which are driven both by Brownian motions and an independent Poisson random measure. Combining forward-backward stochastic differential equation theory with certain classical convex variational techniques, the necessary maximum principle is proved for the partially observed optimal control, where the control domain is a nonempty convex set. Under certain convexity assumptions, the author also gives the sufficient conditions of an optimal control for the aforementioned optimal optimal problem. To illustrate the theoretical result, the author also works out an example of partial information linear-quadratic optimal control, and finds an explicit expression of the corresponding optimal control by applying the necessary and sufficient maximum principle.
基金supported by the National Natural Science Foundation of China(No.61375072)(50%)the Natural Science Foundation of Zhejiang Province,China(No.LQ16F030005)(50%)
文摘In this paper,three optimal linear formation control algorithms are proposed for first-order linear multiagent systems from a linear quadratic regulator(LQR) perspective with cost functions consisting of both interaction energy cost and individual energy cost,because both the collective ob ject(such as formation or consensus) and the individual goal of each agent are very important for the overall system.First,we propose the optimal formation algorithm for first-order multi-agent systems without initial physical couplings.The optimal control parameter matrix of the algorithm is the solution to an algebraic Riccati equation(ARE).It is shown that the matrix is the sum of a Laplacian matrix and a positive definite diagonal matrix.Next,for physically interconnected multi-agent systems,the optimal formation algorithm is presented,and the corresponding parameter matrix is given from the solution to a group of quadratic equations with one unknown.Finally,if the communication topology between agents is fixed,the local feedback gain is obtained from the solution to a quadratic equation with one unknown.The equation is derived from the derivative of the cost function with respect to the local feedback gain.Numerical examples are provided to validate the effectiveness of the proposed approaches and to illustrate the geometrical performances of multi-agent systems.
基金supported by National Natural Science Foundation of China(10671112)National Basic Research Program of China(973 Program)(2007CB814904)the Natural Science Foundation of Shandong Province(Z2006A01)
文摘This paper studies the existence and uniqueness of solutions of fully coupled forward-backward stochastic differential equations with Brownian motion and random jumps.The result is applied to solve a linear-quadratic optimal control and a nonzero-sum differential game of backward stochastic differential equations.The optimal control and Nash equilibrium point are explicitly derived. Also the solvability of a kind Riccati equations is discussed.All these results develop those of Lim, Zhou(2001) and Yu,Ji(2008).
