This paper investigates the attitude tracking control problem for the cruise mode of a dual-system convertible unmanned aerial vehicle(UAV)in the presence of parameter uncertainties,unmodeled uncertainties and wind di...This paper investigates the attitude tracking control problem for the cruise mode of a dual-system convertible unmanned aerial vehicle(UAV)in the presence of parameter uncertainties,unmodeled uncertainties and wind disturbances.First,a fixed-time disturbance observer(FXDO)based on the bi-limit homogeneity theory is designed to estimate the lumped disturbance of the convertible UAV model.Then,a fixed-time integral sliding mode control(FXISMC)is combined with the FXDO to achieve strong robustness and chattering reduction.Bi-limit homogeneity theory and Lyapunov theory are applied to provide detailed proof of the fixed-time stability.Finally,numerical simulation experimental results verify the robustness of the proposed algorithm to model parameter uncertainties and wind disturbances.In addition,the proposed algorithm is deployed in a open-source UAV autopilot and its effectiveness is further demonstrated by hardware-in-the-loop experimental results.展开更多
Hydraulic actuators are highly nonlinear when they are subjected to different types of model uncertainties and dynamic disturbances.These unfavorable factors adversely affect the control performance of the hydraulic a...Hydraulic actuators are highly nonlinear when they are subjected to different types of model uncertainties and dynamic disturbances.These unfavorable factors adversely affect the control performance of the hydraulic actuator.Although various control methods have been employed to improve the tracking precision of the dynamic system,optimizing and adjusting control gain to mitigate the hydraulic actuator model uncertainties remains elusive.This study presents an adaptive back-stepping sliding mode controller(ABSMC)to enhance the trajectory tracking precision,where the virtual control law is constructed to replace the position error.The adaptive control theory is introduced in back-stepping controller design to compensate for the model uncertainties and time-varying disturbances.Based on Lyapunov theory,the finite-time convergence of the position tracking errors is proved.Furthermore,the effectiveness of the developed control scheme is conducted via extensive comparative experiments.展开更多
Parking difficulties have become a social issue that people have to solve.Automated parking system is practicable for quick par operations without a driver which can also greatly reduces the probability of parking acc...Parking difficulties have become a social issue that people have to solve.Automated parking system is practicable for quick par operations without a driver which can also greatly reduces the probability of parking accidents.The paper proposes a Lyapunov-based nonlinear model predictive controller embedding an instructable solution which is generated by the modified rear-wheel feedback method(RF-LNMPC)in order to improve the overall path tracking accuracy in parking conditions.Firstly,A discrete-time RF-LNMPC considering the position and attitude of the parking vehicle is proposed to increase the success rate of automated parking effectively.Secondly,the RF-LNMPC problem with a multi-objective cost function is solved by the Interior-Point Optimization,of which the iterative initial values are described as the instructable solutions calculated by combining modified rear-wheel feedback to improve the performance of local optimal solution.Thirdly,the details on the computation of the terminal constraint and terminal cost for the linear time-varying case is presented.The closed-loop stability is verified via Lyapunov techniques by considering the terminal constraint and terminal cost theoretically.Finally,the proposed RF-LNMPC is implemented on a selfdriving Lincoln MKZ platform and the experiment results have shown improved performance in parallel and vertical parking conditions.The Monte Carlo analysis also demonstrates good stability and repeatability of the proposed method which can be applied in practical use in the near future.展开更多
Multidimensional integration and multifunctional com-ponent assembly have been greatly explored in recent years to extend Moore’s Law of modern microelectronics.However,this inevitably exac-erbates the inhomogeneity ...Multidimensional integration and multifunctional com-ponent assembly have been greatly explored in recent years to extend Moore’s Law of modern microelectronics.However,this inevitably exac-erbates the inhomogeneity of temperature distribution in microsystems,making precise temperature control for electronic components extremely challenging.Herein,we report an on-chip micro temperature controller including a pair of thermoelectric legs with a total area of 50×50μm^(2),which are fabricated from dense and flat freestanding Bi2Te3-based ther-moelectric nano films deposited on a newly developed nano graphene oxide membrane substrate.Its tunable equivalent thermal resistance is controlled by electrical currents to achieve energy-efficient temperature control for low-power electronics.A large cooling temperature difference of 44.5 K at 380 K is achieved with a power consumption of only 445μW,resulting in an ultrahigh temperature control capability over 100 K mW^(-1).Moreover,an ultra-fast cooling rate exceeding 2000 K s^(-1) and excellent reliability of up to 1 million cycles are observed.Our proposed on-chip temperature controller is expected to enable further miniaturization and multifunctional integration on a single chip for microelectronics.展开更多
This paper,evaluate the effectiveness of a proposed speed loop pseudo derivative feedforward(PDFF)controller-based direct torque controller(DTC)for a PMSM drive against the performance of existing PI speed controller-...This paper,evaluate the effectiveness of a proposed speed loop pseudo derivative feedforward(PDFF)controller-based direct torque controller(DTC)for a PMSM drive against the performance of existing PI speed controller-based DTC and hysteresis current controller(HCC).The proposed PDFF-based speed regulator effectively reduces oscillation and overshoot associated with rotor angular speed,electromagnetic torque,and stator current.Two case studies,one using forward-to-reverse motoring operation and the other involving reverse-to-forward braking operation,has been validated to show the effectiveness of the proposed control strategy.The proposed controller's superior performance is demonstrated through experimental verification utilizing an FPGA controller for a 1.5 kW PMSM drive laboratory prototype.展开更多
This paper proposes an adaptive nonlinear proportional-derivative(ANPD)controller for a two-wheeled self-balancing robot(TWSB)modeled by the Lagrange equation with external forces.The proposed control scheme is design...This paper proposes an adaptive nonlinear proportional-derivative(ANPD)controller for a two-wheeled self-balancing robot(TWSB)modeled by the Lagrange equation with external forces.The proposed control scheme is designed based on the combination of a nonlinear proportional-derivative(NPD)controller and a genetic algorithm,in which the proportional-derivative(PD)parameters are updated online based on the tracking error and the preset error threshold.In addition,the genetic algorithm is employed to adaptively select initial controller parameters,contributing to system stability and improved control accuracy.The proposed controller is basic in design yet simple to implement.The ANPD controller has the advantage of being computationally lightweight and providing high robustness against external forces.The stability of the closed-loop system is rigorously analyzed and verified using Lyapunov theory,providing theoretical assurance of its robustness.Simulations and experimental results show that the TWSB robot with the proposed ANPD controller achieves quick balance and tracks target values with very small errors,demonstrating the effectiveness and performance of the proposed controller.The proposed ANPD controller demonstrates significant improvements in balancing and tracking performance for two-wheeled self-balancing robots,which has great applicability in the field of robot control systems.This represents a promising solution for applications requiring precise and stable motion control under varying external conditions.展开更多
Detumbling operation toward a rotating target with nutation is meaningful for debris removal but challenging. In this study, a deformable end-effector is first designed based on the requirements for contacting the nut...Detumbling operation toward a rotating target with nutation is meaningful for debris removal but challenging. In this study, a deformable end-effector is first designed based on the requirements for contacting the nutating target. A dual-arm robotic system installed with the deformable end-effectors is modeled and the movement of the end-tips is analyzed. The complex operation of the contact toward a nutating target places strict requirements on control accuracy and controller robustness. Thus, an improvement of the tracking error transformation is proposed and an adaptive sliding mode controller with prescribed performance is designed to guarantee the fast and precise motion of the effector during the contact detumbling.Finally, by employing the proposed effector and the controller,numerical simulations are carried out to verify the effectiveness and efficiency of the contact detumbling toward a nutating target.展开更多
Linear temporal logic(LTL)is an intuitive and expressive language to specify complex control tasks,and how to design an efficient control strategy for LTL specification is still a challenge.In this paper,we implement ...Linear temporal logic(LTL)is an intuitive and expressive language to specify complex control tasks,and how to design an efficient control strategy for LTL specification is still a challenge.In this paper,we implement the dynamic quantization technique to propose a novel hierarchical control strategy for nonlinear control systems under LTL specifications.Based on the regions of interest involved in the LTL formula,an accepting path is derived first to provide a high-level solution for the controller synthesis problem.Second,we develop a dynamic quantization based approach to verify the realization of the accepting path.The realization verification results in the necessity of the controller design and a sequence of quantization regions for the controller design.Third,the techniques of dynamic quantization and abstraction-based control are combined together to establish the local-to-global control strategy.Both abstraction construction and controller design are local and dynamic,thereby resulting in the potential reduction of the computational complexity.Since each quantization region can be considered locally and individually,the proposed hierarchical mechanism is more efficient and can solve much larger problems than many existing methods.Finally,the proposed control strategy is illustrated via two examples from the path planning and tracking problems of mobile robots.展开更多
An autonomous microgrid that runs on renewable energy sources is presented in this article.It has a supercon-ducting magnetic energy storage(SMES)device,wind energy-producing devices,and an energy storage battery.Howe...An autonomous microgrid that runs on renewable energy sources is presented in this article.It has a supercon-ducting magnetic energy storage(SMES)device,wind energy-producing devices,and an energy storage battery.However,because such microgrids are nonlinear and the energy they create varies with time,controlling and managing the energy inside them is a difficult issue.Fractional-order proportional integral(FOPI)controller is recommended for the current research to enhance a standalone microgrid’s energy management and performance.The suggested dedicated control for the SMES comprises two loops:the outer loop,which uses the FOPI to regulate the DC-link voltage,and the inner loop,responsible for regulating the SMES current,is constructed using the intelligent FOPI(iFOPI).The FOPI+iFOPI parameters are best developed using the dandelion optimizer(DO)approach to achieve the optimum performance.The suggested FOPI+iFOPI controller’s performance is contrasted with a conventional PI controller for variations in wind speed and microgrid load.The optimal FOPI+iFOPI controller manages the voltage and frequency of the load.The behavior of the microgrid as a reaction to step changes in load and wind speed was measured using the proposed controller.MATLAB simulations were used to evaluate the recommended system’s performance.The results of the simulations showed that throughout all interruptions,the recommended microgrid provided the load with AC power with a constant amplitude and frequency.In addition,the required load demand was accurately reduced.Furthermore,the microgrid functioned incredibly well despite SMES and varying wind speeds.Results obtained under identical conditions were compared with and without the best FOPI+iFOPI controller.When utilizing the optimal FOPI+iFOPI controller with SMES,it was found that the microgrid performed better than the microgrid without SMES.展开更多
In many Eastern and Western countries,falling birth rates have led to the gradual aging of society.Older adults are often left alone at home or live in a long-term care center,which results in them being susceptible t...In many Eastern and Western countries,falling birth rates have led to the gradual aging of society.Older adults are often left alone at home or live in a long-term care center,which results in them being susceptible to unsafe events(such as falls)that can have disastrous consequences.However,automatically detecting falls fromvideo data is challenging,and automatic fall detection methods usually require large volumes of training data,which can be difficult to acquire.To address this problem,video kinematic data can be used as training data,thereby avoiding the requirement of creating a large fall data set.This study integrated an improved particle swarm optimization method into a double interactively recurrent fuzzy cerebellar model articulation controller model to develop a costeffective and accurate fall detection system.First,it obtained an optical flow(OF)trajectory diagram from image sequences by using the OF method,and it solved problems related to focal length and object offset by employing the discrete Fourier transform(DFT)algorithm.Second,this study developed the D-IRFCMAC model,which combines spatial and temporal(recurrent)information.Third,it designed an IPSO(Improved Particle Swarm Optimization)algorithm that effectively strengthens the exploratory capabilities of the proposed D-IRFCMAC(Double-Interactively Recurrent Fuzzy Cerebellar Model Articulation Controller)model in the global search space.The proposed approach outperforms existing state-of-the-art methods in terms of action recognition accuracy on the UR-Fall,UP-Fall,and PRECIS HAR data sets.The UCF11 dataset had an average accuracy of 93.13%,whereas the UCF101 dataset had an average accuracy of 92.19%.The UR-Fall dataset had an accuracy of 100%,the UP-Fall dataset had an accuracy of 99.25%,and the PRECIS HAR dataset had an accuracy of 99.07%.展开更多
基金supported by National Natural Science Foundation of China (Grant Nos.52072309 and 62303379)Beijing Institute of Spacecraft System Engineering Research Project (Grant NO.JSZL2020203B004)+1 种基金Natural Science Foundation of Shaanxi Province,Chinese (Grant NOs.2023-JC-QN-0003 and 2023-JC-QN-0665)Industry-University-Research Innovation Fund of Ministry of Education for Chinese Universities (Grant NO.2022IT189)。
文摘This paper investigates the attitude tracking control problem for the cruise mode of a dual-system convertible unmanned aerial vehicle(UAV)in the presence of parameter uncertainties,unmodeled uncertainties and wind disturbances.First,a fixed-time disturbance observer(FXDO)based on the bi-limit homogeneity theory is designed to estimate the lumped disturbance of the convertible UAV model.Then,a fixed-time integral sliding mode control(FXISMC)is combined with the FXDO to achieve strong robustness and chattering reduction.Bi-limit homogeneity theory and Lyapunov theory are applied to provide detailed proof of the fixed-time stability.Finally,numerical simulation experimental results verify the robustness of the proposed algorithm to model parameter uncertainties and wind disturbances.In addition,the proposed algorithm is deployed in a open-source UAV autopilot and its effectiveness is further demonstrated by hardware-in-the-loop experimental results.
基金supported by the fund of Henan Key Laboratory of Superhard Abrasives and Grinding Equipment,Henan University of Technology(Grant No.JDKFJJ2023005)the Key Science and Technology Program of Henan Province(Grant Nos.242102221001 and 232102220085)the Science and Technology Key Project Foundation of Henan Provincial Education Department(Grant No.23A460014).
文摘Hydraulic actuators are highly nonlinear when they are subjected to different types of model uncertainties and dynamic disturbances.These unfavorable factors adversely affect the control performance of the hydraulic actuator.Although various control methods have been employed to improve the tracking precision of the dynamic system,optimizing and adjusting control gain to mitigate the hydraulic actuator model uncertainties remains elusive.This study presents an adaptive back-stepping sliding mode controller(ABSMC)to enhance the trajectory tracking precision,where the virtual control law is constructed to replace the position error.The adaptive control theory is introduced in back-stepping controller design to compensate for the model uncertainties and time-varying disturbances.Based on Lyapunov theory,the finite-time convergence of the position tracking errors is proved.Furthermore,the effectiveness of the developed control scheme is conducted via extensive comparative experiments.
基金Supported by National Key R&D Program of China (Grant No.2021YFB2501800)National Natural Science Foundation of China (Grant No.52172384)+1 种基金Science and Technology Innovation Program of Hunan Province of China (Grant No.2021RC3048)State Key Laboratory of Advanced Design and Manufacturing Technology for Vehicle of China (Grant No.72275004)。
文摘Parking difficulties have become a social issue that people have to solve.Automated parking system is practicable for quick par operations without a driver which can also greatly reduces the probability of parking accidents.The paper proposes a Lyapunov-based nonlinear model predictive controller embedding an instructable solution which is generated by the modified rear-wheel feedback method(RF-LNMPC)in order to improve the overall path tracking accuracy in parking conditions.Firstly,A discrete-time RF-LNMPC considering the position and attitude of the parking vehicle is proposed to increase the success rate of automated parking effectively.Secondly,the RF-LNMPC problem with a multi-objective cost function is solved by the Interior-Point Optimization,of which the iterative initial values are described as the instructable solutions calculated by combining modified rear-wheel feedback to improve the performance of local optimal solution.Thirdly,the details on the computation of the terminal constraint and terminal cost for the linear time-varying case is presented.The closed-loop stability is verified via Lyapunov techniques by considering the terminal constraint and terminal cost theoretically.Finally,the proposed RF-LNMPC is implemented on a selfdriving Lincoln MKZ platform and the experiment results have shown improved performance in parallel and vertical parking conditions.The Monte Carlo analysis also demonstrates good stability and repeatability of the proposed method which can be applied in practical use in the near future.
基金The authors thank D.Berger,D.Hofmann and C.Kupka in IFW Dresden for helpful technical support.H.R.acknowledges funding from the DFG(Deutsche Forschungsgemeinschaft)within grant number RE3973/1-1.Q.J.,H.R.and K.N.conceived the work.With the support from N.Y.and X.J.,Q.J.and T.G.fabricated the thermoelectric films and conducted the structural and compositional characterizations.Q.J.prepared microchips and fabricated the on-chip micro temperature controllers.Q.J.and N.P.carried out the temperature-dependent material and device performance measurements.Q.J.and H.R.performed the simulation and analytical calculations.Q.J.,H.R.and K.N.wrote the manuscript with input from the other coauthors.All the authors discussed the results and commented on the manuscript.
文摘Multidimensional integration and multifunctional com-ponent assembly have been greatly explored in recent years to extend Moore’s Law of modern microelectronics.However,this inevitably exac-erbates the inhomogeneity of temperature distribution in microsystems,making precise temperature control for electronic components extremely challenging.Herein,we report an on-chip micro temperature controller including a pair of thermoelectric legs with a total area of 50×50μm^(2),which are fabricated from dense and flat freestanding Bi2Te3-based ther-moelectric nano films deposited on a newly developed nano graphene oxide membrane substrate.Its tunable equivalent thermal resistance is controlled by electrical currents to achieve energy-efficient temperature control for low-power electronics.A large cooling temperature difference of 44.5 K at 380 K is achieved with a power consumption of only 445μW,resulting in an ultrahigh temperature control capability over 100 K mW^(-1).Moreover,an ultra-fast cooling rate exceeding 2000 K s^(-1) and excellent reliability of up to 1 million cycles are observed.Our proposed on-chip temperature controller is expected to enable further miniaturization and multifunctional integration on a single chip for microelectronics.
基金supported by Prince Sultan University,Riyadh,Saudi Arabia,under research grant SEED-2022-CE-95。
文摘This paper,evaluate the effectiveness of a proposed speed loop pseudo derivative feedforward(PDFF)controller-based direct torque controller(DTC)for a PMSM drive against the performance of existing PI speed controller-based DTC and hysteresis current controller(HCC).The proposed PDFF-based speed regulator effectively reduces oscillation and overshoot associated with rotor angular speed,electromagnetic torque,and stator current.Two case studies,one using forward-to-reverse motoring operation and the other involving reverse-to-forward braking operation,has been validated to show the effectiveness of the proposed control strategy.The proposed controller's superior performance is demonstrated through experimental verification utilizing an FPGA controller for a 1.5 kW PMSM drive laboratory prototype.
文摘This paper proposes an adaptive nonlinear proportional-derivative(ANPD)controller for a two-wheeled self-balancing robot(TWSB)modeled by the Lagrange equation with external forces.The proposed control scheme is designed based on the combination of a nonlinear proportional-derivative(NPD)controller and a genetic algorithm,in which the proportional-derivative(PD)parameters are updated online based on the tracking error and the preset error threshold.In addition,the genetic algorithm is employed to adaptively select initial controller parameters,contributing to system stability and improved control accuracy.The proposed controller is basic in design yet simple to implement.The ANPD controller has the advantage of being computationally lightweight and providing high robustness against external forces.The stability of the closed-loop system is rigorously analyzed and verified using Lyapunov theory,providing theoretical assurance of its robustness.Simulations and experimental results show that the TWSB robot with the proposed ANPD controller achieves quick balance and tracks target values with very small errors,demonstrating the effectiveness and performance of the proposed controller.The proposed ANPD controller demonstrates significant improvements in balancing and tracking performance for two-wheeled self-balancing robots,which has great applicability in the field of robot control systems.This represents a promising solution for applications requiring precise and stable motion control under varying external conditions.
基金supported by the National Natural Science Foundation of China(11972077,11672035)。
文摘Detumbling operation toward a rotating target with nutation is meaningful for debris removal but challenging. In this study, a deformable end-effector is first designed based on the requirements for contacting the nutating target. A dual-arm robotic system installed with the deformable end-effectors is modeled and the movement of the end-tips is analyzed. The complex operation of the contact toward a nutating target places strict requirements on control accuracy and controller robustness. Thus, an improvement of the tracking error transformation is proposed and an adaptive sliding mode controller with prescribed performance is designed to guarantee the fast and precise motion of the effector during the contact detumbling.Finally, by employing the proposed effector and the controller,numerical simulations are carried out to verify the effectiveness and efficiency of the contact detumbling toward a nutating target.
基金supported by the Fundamental Research Funds for the Central Universities(DUT22RT(3)090)the National Natural Science Foundation of China(61890920,61890921,62122016,08120003)Liaoning Science and Technology Program(2023JH2/101700361).
文摘Linear temporal logic(LTL)is an intuitive and expressive language to specify complex control tasks,and how to design an efficient control strategy for LTL specification is still a challenge.In this paper,we implement the dynamic quantization technique to propose a novel hierarchical control strategy for nonlinear control systems under LTL specifications.Based on the regions of interest involved in the LTL formula,an accepting path is derived first to provide a high-level solution for the controller synthesis problem.Second,we develop a dynamic quantization based approach to verify the realization of the accepting path.The realization verification results in the necessity of the controller design and a sequence of quantization regions for the controller design.Third,the techniques of dynamic quantization and abstraction-based control are combined together to establish the local-to-global control strategy.Both abstraction construction and controller design are local and dynamic,thereby resulting in the potential reduction of the computational complexity.Since each quantization region can be considered locally and individually,the proposed hierarchical mechanism is more efficient and can solve much larger problems than many existing methods.Finally,the proposed control strategy is illustrated via two examples from the path planning and tracking problems of mobile robots.
基金This research was funded by the Deputyship for Research and Innovation,Ministry of Education,Saudi Arabia,through the University of Tabuk,Grant Number S-1443-0123.
文摘An autonomous microgrid that runs on renewable energy sources is presented in this article.It has a supercon-ducting magnetic energy storage(SMES)device,wind energy-producing devices,and an energy storage battery.However,because such microgrids are nonlinear and the energy they create varies with time,controlling and managing the energy inside them is a difficult issue.Fractional-order proportional integral(FOPI)controller is recommended for the current research to enhance a standalone microgrid’s energy management and performance.The suggested dedicated control for the SMES comprises two loops:the outer loop,which uses the FOPI to regulate the DC-link voltage,and the inner loop,responsible for regulating the SMES current,is constructed using the intelligent FOPI(iFOPI).The FOPI+iFOPI parameters are best developed using the dandelion optimizer(DO)approach to achieve the optimum performance.The suggested FOPI+iFOPI controller’s performance is contrasted with a conventional PI controller for variations in wind speed and microgrid load.The optimal FOPI+iFOPI controller manages the voltage and frequency of the load.The behavior of the microgrid as a reaction to step changes in load and wind speed was measured using the proposed controller.MATLAB simulations were used to evaluate the recommended system’s performance.The results of the simulations showed that throughout all interruptions,the recommended microgrid provided the load with AC power with a constant amplitude and frequency.In addition,the required load demand was accurately reduced.Furthermore,the microgrid functioned incredibly well despite SMES and varying wind speeds.Results obtained under identical conditions were compared with and without the best FOPI+iFOPI controller.When utilizing the optimal FOPI+iFOPI controller with SMES,it was found that the microgrid performed better than the microgrid without SMES.
基金supported by the National Science and Technology Council under grants NSTC 112-2221-E-320-002the Buddhist Tzu Chi Medical Foundation in Taiwan under Grant TCMMP 112-02-02.
文摘In many Eastern and Western countries,falling birth rates have led to the gradual aging of society.Older adults are often left alone at home or live in a long-term care center,which results in them being susceptible to unsafe events(such as falls)that can have disastrous consequences.However,automatically detecting falls fromvideo data is challenging,and automatic fall detection methods usually require large volumes of training data,which can be difficult to acquire.To address this problem,video kinematic data can be used as training data,thereby avoiding the requirement of creating a large fall data set.This study integrated an improved particle swarm optimization method into a double interactively recurrent fuzzy cerebellar model articulation controller model to develop a costeffective and accurate fall detection system.First,it obtained an optical flow(OF)trajectory diagram from image sequences by using the OF method,and it solved problems related to focal length and object offset by employing the discrete Fourier transform(DFT)algorithm.Second,this study developed the D-IRFCMAC model,which combines spatial and temporal(recurrent)information.Third,it designed an IPSO(Improved Particle Swarm Optimization)algorithm that effectively strengthens the exploratory capabilities of the proposed D-IRFCMAC(Double-Interactively Recurrent Fuzzy Cerebellar Model Articulation Controller)model in the global search space.The proposed approach outperforms existing state-of-the-art methods in terms of action recognition accuracy on the UR-Fall,UP-Fall,and PRECIS HAR data sets.The UCF11 dataset had an average accuracy of 93.13%,whereas the UCF101 dataset had an average accuracy of 92.19%.The UR-Fall dataset had an accuracy of 100%,the UP-Fall dataset had an accuracy of 99.25%,and the PRECIS HAR dataset had an accuracy of 99.07%.