Fiber winding tension is an important factor in the molding techniques of composite material which influences the quality of winding product directly, and the tension control is a key technique in fiber winding techni...Fiber winding tension is an important factor in the molding techniques of composite material which influences the quality of winding product directly, and the tension control is a key technique in fiber winding techniques. This paper introduces a closed-loop tension control system with the programmable logic controller (PLC) with function modules as its control kernel, the alternating current (AC) servo motor as execute element and the radius-following device to accomplish the real-time radius compensation. The mechanism of the tension control system is analyzed and the numerical model is set up. The compensation technique of the radius of the scroll is analyzed. Experimental results show that the system is well qualified with high control precision and high reaction speed.展开更多
The control of the stability of the filament tension is one of the crucial techniques ensuring the component quality of the composite materials. The open-loop tension control system, with industrial control computer a...The control of the stability of the filament tension is one of the crucial techniques ensuring the component quality of the composite materials. The open-loop tension control system, with industrial control computer as the core, magnetic particle clutch as the actuator, equipped with compensation technique is researched and manufactured. It can assure the tension control stability of the yarn in filament winding process and increase the control precision of the whole system.展开更多
In the fiber winding process,strong disturbance,uncertainty,strong coupling,and fiber friction complicate the winding constant tension control.In order to effectively reduce the influence of these problems on the tens...In the fiber winding process,strong disturbance,uncertainty,strong coupling,and fiber friction complicate the winding constant tension control.In order to effectively reduce the influence of these problems on the tension output,this paper proposed a tension fluctuation rejection strategy based on feedforward compensation.In addition to the bias harmonic curve of the unknown state,the tension fluctuation also contains the influence of bounded noise.A tension fluctuation observer(TFO)is designed to cancel the uncertain periodic signal,in which the frequency generator is used to estimate the critical parameter information.Then,the fluctuation signal is reconstructed by a third-order auxiliary filter.The estimated signal feedforward compensates for the actual tension fluctuation.Furthermore,a time-varying parameters fractional-order PID controller(TPFOPID)is realized to attenuate the bounded noise in the fluctuation.Finally,TPFOPID is enhanced by TFO and applied to control a tension control system considering multi-source disturbances.The stability of the method is analyzed by using the Lyapunov theorem.Finally,numerical simulations verify that the proposed scheme improves the tracking ability and robustness of the system in response to tension fluctuations.展开更多
A winding system is a time-varying system that considers complex nonlinear characteristics,and how to control the stability of the winding tension during the winding process is the primary problem that has hindered de...A winding system is a time-varying system that considers complex nonlinear characteristics,and how to control the stability of the winding tension during the winding process is the primary problem that has hindered development in this field in recent years.Many nonlinear factors affect the tension in the winding process,such as friction,structured uncertainties,unstructured uncertainties,and external interference.These terms severely restrict the tension tracking performance.Existing tension control strategies are mainly based on the composite control of the tension and speed loops,and previous studies involve complex decoupling operations.Owing to the large number of calculations required for this method,it is inconvenient for practical engineering applications.To simplify the tension generation mechanism and the influence of the nonlinear characteristics of the winding system,a simpler nonlinear dynamic model of the winding tension was established.An adaptive method was applied to update the feedback gain of the continuous robust integral of the sign of the error(RISE).Furthermore,an extended state observer was used to estimate modeling errors and external disturbances.The model disturbance term can be compensated for in the designed RISE controller.The asymptotic stability of the system was proven according to the Lyapunov stability theory.Finally,a comparative analysis of the proposed nonlinear controller and several other controllers was performed.The results indicated that the control of the winding tension was significantly enhanced.展开更多
Automatic splicing of interrupted yarns in ring spinning has always been a problem in the industry.Factors such as low yarn strengths and environmental influence on yarn tensions make it difficult to control the yarn ...Automatic splicing of interrupted yarns in ring spinning has always been a problem in the industry.Factors such as low yarn strengths and environmental influence on yarn tensions make it difficult to control the yarn tension during the robotic splicing process.The purpose of this research is to design active disturbance rejection control(ADRC)for a third-order nonlinear tension system subject to external disturbances.Firstly,a third-order extended state observer(ESO)is designed to achieve the suppression and the compensation of the internal modeling error and the external disturbances of the system.Secondly,the adaptive gain error feedback control and the filtering process are designed to reduce the influence of sensor noise on the disturbance observation.Finally,the tension control during the splicing process is simulated and experimented,and the experiments show that the method has good robustness in the tension tracking task under a dynamic environment,which verifies the effectiveness of the method.展开更多
Based on the pressure regulation circuit adopting electro-hydraulic proportional relief valve to control tension, a new type of electro-hydraulic compound control circuit with throttle control unit is presented, which...Based on the pressure regulation circuit adopting electro-hydraulic proportional relief valve to control tension, a new type of electro-hydraulic compound control circuit with throttle control unit is presented, which can obtain optimal dynamic damping ratio through real-time altering pressure-flow gain of the throttle control unit, improve the dynamic characteristic of tension follow-up control for the tension system with high inertia loads. Moreover, the characteristic when the cable linear velocity variation causes change of tension is investigated, and a compound control strategy is proposed. The theoretical analysis and experimental results show that the electro-hydraulic compound control circuit is effective and the characteristic of the compound control strategy is satisfactory.展开更多
High control performances cannot be obtained by most of the existing looper-tension control approaches through only considering controller designs based on continuous time models, which cannot meet the requirements of...High control performances cannot be obtained by most of the existing looper-tension control approaches through only considering controller designs based on continuous time models, which cannot meet the requirements of modern computer control systems with high control accuracy. In order to solve the above problems, a state feedback H∞ control method based on a discrete-time model for looper-tension control systems in hot rolling mills is presen- ted. The considered system is approximated by a discrete-time loope∞tension control system model. Based on a Lya- punov functional method, a state feedback H∞ control law is developed which makes the closed-loop system asymp totically stable with guaranteed H∞ performance. The controller gains are obtained by solving a set of linear matrix inequalities (LMIs). In contrast to the existing results, the proposed approach can obtain good H∞ performance and effectively reduce external disturbances. The strip tension is also less affected by the change of looper angel, so good control performances can be obtained. Moreover, this control scheme is easy to implement, and can be applied to other linear systems. A simulation example with practical parameters is provided to illustrate the effectiveness of the developed method.展开更多
Based on the analysis of the mechanism of wire tension control by using torque motors in the multi-wire saw machining process, some mathematical models of a tension control system are studied, and an adaptive algo- ri...Based on the analysis of the mechanism of wire tension control by using torque motors in the multi-wire saw machining process, some mathematical models of a tension control system are studied, and an adaptive algo- rithm is designed for controlling the wire tension. In this algorithm of tension control, the rotation speeds and waving angle of motors are measured and fed back to the controller, and the NLMS( normalized least mean squares) algorithm is used to calculate the adaptive correction value and control the wire tension accurately. The computer simulation results in Matlab software validate the high accuracy for controlling the system of the wire tension with the NLMS algorithm in the multi-wire saw machining process.展开更多
Filament winding has emerged as the main process for carbon fiber reinforced plastic(CFRP) fabrication, and tension control plays a key role in enhancing the quality of the winding products. With the continuous improv...Filament winding has emerged as the main process for carbon fiber reinforced plastic(CFRP) fabrication, and tension control plays a key role in enhancing the quality of the winding products. With the continuous improvement of prod?uct quality and e ciency, the precision of the tension control system is constantly improving. In this paper, a novel tension control method is proposed, which can regulate the fiber tension and transport speed of the winding process by governing the outputs of three di erent driven rollers(the torque of the unwind roll, the torque of the magnetic powder brake roller, and the speed of the master speed roller) in three levels. The mechanical structures and dynamic models of the driven rollers and idle rollers are established by considering the time?varying features of the roller radius and inertia. Moreover, the influence of parameters and speed variation on fiber tension is investigated using the increment model. Subsequently, the control method is proposed by applying fiber tension in three levels accord?ing to the features of the three driven rollers. An adaptive fuzzy controller is designed for tuning the PID parameters online to control the speed of the master speed roller. Simulation is conducted for verifying the performance and sta?bility of the proposed tension control method by comparing with those of the conventional PID control method. The result reveals that the proposed method outperforms the conventional method. Finally, an experimental platform is constructed, and the proposed system is applied to a winding machine. The performance and stability of the tension control system are demonstrated via a series of experiments using carbon fiber under di erent reference speeds and tensions. This paper proposes a novel tension control method to regulate the fiber tension and transport speed.展开更多
Discontinuous tape winding, which has obvious advantages in large extension ratio winding, is widely used in the molding of composites. Therefore, the research on technological parameters becomes the focus of many sch...Discontinuous tape winding, which has obvious advantages in large extension ratio winding, is widely used in the molding of composites. Therefore, the research on technological parameters becomes the focus of many scholars. However, how to accomplish the variable tension control is usually not fully considered. Accordingly, the constant extension ratio and the smoothness of winding process cannot be ensured. Aiming at the problem of tension control, this paper first gives a comparatively deep research on the control method and the interaction mechanism of tension, extension ratio, automatic lap and automatic rectification. Then, according to the winding process features, the mechanical device and the mathematical model of tension control system are established respectively. With regard to the characteristics of PID controller and fuzzy controller, the fuzzy self-tuning PID controller is designed. As a result, the variable tension control is realized during the winding and lapping process, and the constant extension ratio is guaranteed. Finally, a sample application is presented for demonstration. By presenting the variable tension control techniques for discontinuous tape winding, the constant extension ratio of tapes is achieved, the consecution and the automation degree of winding process is improved as well. Thus, the quality of wound products is guaranteed.展开更多
The mass production of primed electronics can be achieved by roll-to-roll(R2R) printing system, so highly accurate web tension is required that can minimize the register error and keep the thickness and roughness of...The mass production of primed electronics can be achieved by roll-to-roll(R2R) printing system, so highly accurate web tension is required that can minimize the register error and keep the thickness and roughness of printed devices in limits. The web tension of a R2R system is regulated by the use of integrated load cells and active dancer system for printed electronics applications using decentralized multi-input-single-output(MISO) regularized variable learning rate backpropagation artificial neural networks. The active dancer system is used before printing system to reduce disturbances in the web tension of process span. The classical PID control result in tension spikes with the change in roll diameter of winder and unwinder rolls. The presence of dancer in R2R system shows that improved web tension control in printing span and the web tension can be enhanced from 3.75 N to 4.75 N. The overshoot of system is less than ±2.5 N and steady state error is within ± 1 N where load cells have a signal noise of ±0.7 N. The integration of load cells and active dancer with self-adapting neural network control provide a solution to the web tension control of multispan roll-to-roll system.展开更多
Aimed at the complex demand of hot strip rolling mill in practicing, the configuration of the coiler and the technological process is analyzed. The arithmetic of coiling tension and the control process is introduced. ...Aimed at the complex demand of hot strip rolling mill in practicing, the configuration of the coiler and the technological process is analyzed. The arithmetic of coiling tension and the control process is introduced. The frame of the tension adjusting system is given. The coiler control system hardware is designed. The system is designed scientifically with steady control and meets demand of the market.展开更多
Winding/unwinding system control is a very important issue to web handling machines. In this paper, a novel adaptive H∞ control strategy is developed for winding process control. A gain scheduling scheme is proposed ...Winding/unwinding system control is a very important issue to web handling machines. In this paper, a novel adaptive H∞ control strategy is developed for winding process control. A gain scheduling scheme is proposed based on a neural fuzzy approximator to improve the transient response and enhance tension control;the controller’s convergence and adaptive capability can be further improved by an efficient hybrid training algorithm. The effectiveness of the proposed adaptive H∞ control is verified by experimental tests. Test results show that the developed gain approximator can adaptively accommodate parameter variations in the system and improve the control performance.展开更多
Influence of the combination of nutrient feed with dissolved oxygen control on taxol production in suspension cultures of Taxus chinensis (Pilg.) Rehd. was investigated in bioreactors. Addition of feeding medium with ...Influence of the combination of nutrient feed with dissolved oxygen control on taxol production in suspension cultures of Taxus chinensis (Pilg.) Rehd. was investigated in bioreactors. Addition of feeding medium with 20 g/L sucrose on day 16 enhanced both the biomass and taxol production in 5-L bioreactors. Further investigation of the fed-batch cultures in a 20-L bioreactor showed that cultivation under a low dissolved oxygen tension (DOT) of 20% for the entire culture resulted in the highest taxol content of 0.98 mg/g DW, while the taxol production was lower than that with 40% and 60% DOT. Moreover, taxol accumulation was remarkably improved by the cultivation of cells initially under DOT of 60% for 20 d followed by changing the DOT to 20% for another 12 d. By combining the use of these two strategies, a maximum taxol content of 18.7 mg/L was obtained in a 20-L bioreactor.展开更多
基金National Natural Science Foundation of China (50175020)
文摘Fiber winding tension is an important factor in the molding techniques of composite material which influences the quality of winding product directly, and the tension control is a key technique in fiber winding techniques. This paper introduces a closed-loop tension control system with the programmable logic controller (PLC) with function modules as its control kernel, the alternating current (AC) servo motor as execute element and the radius-following device to accomplish the real-time radius compensation. The mechanism of the tension control system is analyzed and the numerical model is set up. The compensation technique of the radius of the scroll is analyzed. Experimental results show that the system is well qualified with high control precision and high reaction speed.
文摘The control of the stability of the filament tension is one of the crucial techniques ensuring the component quality of the composite materials. The open-loop tension control system, with industrial control computer as the core, magnetic particle clutch as the actuator, equipped with compensation technique is researched and manufactured. It can assure the tension control stability of the yarn in filament winding process and increase the control precision of the whole system.
基金funded by the National Natural Science Foundation of China(Grant Number 52075361)Shanxi Province Science and Technology Major Project(Grant Number 20201102003)+3 种基金Lvliang Science and Technology Guidance Special Key R&D Project(Grant Number 2022XDHZ08)National Natural Science Foundation of China(Grant Number 51905367)Shanxi Natural Science Foundation General Project(Grant Numbers 202103021224271,202203021211201)Shanxi Province Key Research and Development Plan(Grant Number 202102020101013).
文摘In the fiber winding process,strong disturbance,uncertainty,strong coupling,and fiber friction complicate the winding constant tension control.In order to effectively reduce the influence of these problems on the tension output,this paper proposed a tension fluctuation rejection strategy based on feedforward compensation.In addition to the bias harmonic curve of the unknown state,the tension fluctuation also contains the influence of bounded noise.A tension fluctuation observer(TFO)is designed to cancel the uncertain periodic signal,in which the frequency generator is used to estimate the critical parameter information.Then,the fluctuation signal is reconstructed by a third-order auxiliary filter.The estimated signal feedforward compensates for the actual tension fluctuation.Furthermore,a time-varying parameters fractional-order PID controller(TPFOPID)is realized to attenuate the bounded noise in the fluctuation.Finally,TPFOPID is enhanced by TFO and applied to control a tension control system considering multi-source disturbances.The stability of the method is analyzed by using the Lyapunov theorem.Finally,numerical simulations verify that the proposed scheme improves the tracking ability and robustness of the system in response to tension fluctuations.
基金Supported by National Key R&D Program of China (Grant No.2018YFB2000702)National Natural Science Foundation of China (Grant No.52075262)Fok Ying-Tong Education Foundation of China (Grant No.171044)。
文摘A winding system is a time-varying system that considers complex nonlinear characteristics,and how to control the stability of the winding tension during the winding process is the primary problem that has hindered development in this field in recent years.Many nonlinear factors affect the tension in the winding process,such as friction,structured uncertainties,unstructured uncertainties,and external interference.These terms severely restrict the tension tracking performance.Existing tension control strategies are mainly based on the composite control of the tension and speed loops,and previous studies involve complex decoupling operations.Owing to the large number of calculations required for this method,it is inconvenient for practical engineering applications.To simplify the tension generation mechanism and the influence of the nonlinear characteristics of the winding system,a simpler nonlinear dynamic model of the winding tension was established.An adaptive method was applied to update the feedback gain of the continuous robust integral of the sign of the error(RISE).Furthermore,an extended state observer was used to estimate modeling errors and external disturbances.The model disturbance term can be compensated for in the designed RISE controller.The asymptotic stability of the system was proven according to the Lyapunov stability theory.Finally,a comparative analysis of the proposed nonlinear controller and several other controllers was performed.The results indicated that the control of the winding tension was significantly enhanced.
基金National Natural Science Foundation of China(No.52275478)Fundamental Research Funds for the Central Universities,China(No.2232024Y-01)DHU Distinguished Young Professor Program,China(No.LZB2023001)。
文摘Automatic splicing of interrupted yarns in ring spinning has always been a problem in the industry.Factors such as low yarn strengths and environmental influence on yarn tensions make it difficult to control the yarn tension during the robotic splicing process.The purpose of this research is to design active disturbance rejection control(ADRC)for a third-order nonlinear tension system subject to external disturbances.Firstly,a third-order extended state observer(ESO)is designed to achieve the suppression and the compensation of the internal modeling error and the external disturbances of the system.Secondly,the adaptive gain error feedback control and the filtering process are designed to reduce the influence of sensor noise on the disturbance observation.Finally,the tension control during the splicing process is simulated and experimented,and the experiments show that the method has good robustness in the tension tracking task under a dynamic environment,which verifies the effectiveness of the method.
基金This project is supported by National Natural Science Foundation of China (No.50475105).
文摘Based on the pressure regulation circuit adopting electro-hydraulic proportional relief valve to control tension, a new type of electro-hydraulic compound control circuit with throttle control unit is presented, which can obtain optimal dynamic damping ratio through real-time altering pressure-flow gain of the throttle control unit, improve the dynamic characteristic of tension follow-up control for the tension system with high inertia loads. Moreover, the characteristic when the cable linear velocity variation causes change of tension is investigated, and a compound control strategy is proposed. The theoretical analysis and experimental results show that the electro-hydraulic compound control circuit is effective and the characteristic of the compound control strategy is satisfactory.
基金Item Sponsored by National Natural Science Foundation of China(51374082)National High-Tech Research and Development Program(863Program)of China(2012AA050215)China Iron and Steel Research Foundation(12ZD0850A)
文摘High control performances cannot be obtained by most of the existing looper-tension control approaches through only considering controller designs based on continuous time models, which cannot meet the requirements of modern computer control systems with high control accuracy. In order to solve the above problems, a state feedback H∞ control method based on a discrete-time model for looper-tension control systems in hot rolling mills is presen- ted. The considered system is approximated by a discrete-time loope∞tension control system model. Based on a Lya- punov functional method, a state feedback H∞ control law is developed which makes the closed-loop system asymp totically stable with guaranteed H∞ performance. The controller gains are obtained by solving a set of linear matrix inequalities (LMIs). In contrast to the existing results, the proposed approach can obtain good H∞ performance and effectively reduce external disturbances. The strip tension is also less affected by the change of looper angel, so good control performances can be obtained. Moreover, this control scheme is easy to implement, and can be applied to other linear systems. A simulation example with practical parameters is provided to illustrate the effectiveness of the developed method.
基金supported by the National Natural Science Fundproject (50775207)Key Laboratory of E & M (Zhejiang University of Technology) Open Fund project (2009EP017)
文摘Based on the analysis of the mechanism of wire tension control by using torque motors in the multi-wire saw machining process, some mathematical models of a tension control system are studied, and an adaptive algo- rithm is designed for controlling the wire tension. In this algorithm of tension control, the rotation speeds and waving angle of motors are measured and fed back to the controller, and the NLMS( normalized least mean squares) algorithm is used to calculate the adaptive correction value and control the wire tension accurately. The computer simulation results in Matlab software validate the high accuracy for controlling the system of the wire tension with the NLMS algorithm in the multi-wire saw machining process.
基金Supported by National Natural Science Foundation of China(Grant No.51575018)
文摘Filament winding has emerged as the main process for carbon fiber reinforced plastic(CFRP) fabrication, and tension control plays a key role in enhancing the quality of the winding products. With the continuous improvement of prod?uct quality and e ciency, the precision of the tension control system is constantly improving. In this paper, a novel tension control method is proposed, which can regulate the fiber tension and transport speed of the winding process by governing the outputs of three di erent driven rollers(the torque of the unwind roll, the torque of the magnetic powder brake roller, and the speed of the master speed roller) in three levels. The mechanical structures and dynamic models of the driven rollers and idle rollers are established by considering the time?varying features of the roller radius and inertia. Moreover, the influence of parameters and speed variation on fiber tension is investigated using the increment model. Subsequently, the control method is proposed by applying fiber tension in three levels accord?ing to the features of the three driven rollers. An adaptive fuzzy controller is designed for tuning the PID parameters online to control the speed of the master speed roller. Simulation is conducted for verifying the performance and sta?bility of the proposed tension control method by comparing with those of the conventional PID control method. The result reveals that the proposed method outperforms the conventional method. Finally, an experimental platform is constructed, and the proposed system is applied to a winding machine. The performance and stability of the tension control system are demonstrated via a series of experiments using carbon fiber under di erent reference speeds and tensions. This paper proposes a novel tension control method to regulate the fiber tension and transport speed.
基金supported by Shaanxi Provincial "13115" Important Scientific and Technological Innovation Fund of China (Grant No. 2009ZDKG-27)
文摘Discontinuous tape winding, which has obvious advantages in large extension ratio winding, is widely used in the molding of composites. Therefore, the research on technological parameters becomes the focus of many scholars. However, how to accomplish the variable tension control is usually not fully considered. Accordingly, the constant extension ratio and the smoothness of winding process cannot be ensured. Aiming at the problem of tension control, this paper first gives a comparatively deep research on the control method and the interaction mechanism of tension, extension ratio, automatic lap and automatic rectification. Then, according to the winding process features, the mechanical device and the mathematical model of tension control system are established respectively. With regard to the characteristics of PID controller and fuzzy controller, the fuzzy self-tuning PID controller is designed. As a result, the variable tension control is realized during the winding and lapping process, and the constant extension ratio is guaranteed. Finally, a sample application is presented for demonstration. By presenting the variable tension control techniques for discontinuous tape winding, the constant extension ratio of tapes is achieved, the consecution and the automation degree of winding process is improved as well. Thus, the quality of wound products is guaranteed.
基金supported by Basic Science Research Program through the National Research Foundation of Korea(NRF),Ministry of Education,Science and Technology,Korea(Grant No.2010-0026163)Strategy Technology Development Project,Ministry of Knowledge Economy,Korea(Grant No.10032149)
文摘The mass production of primed electronics can be achieved by roll-to-roll(R2R) printing system, so highly accurate web tension is required that can minimize the register error and keep the thickness and roughness of printed devices in limits. The web tension of a R2R system is regulated by the use of integrated load cells and active dancer system for printed electronics applications using decentralized multi-input-single-output(MISO) regularized variable learning rate backpropagation artificial neural networks. The active dancer system is used before printing system to reduce disturbances in the web tension of process span. The classical PID control result in tension spikes with the change in roll diameter of winder and unwinder rolls. The presence of dancer in R2R system shows that improved web tension control in printing span and the web tension can be enhanced from 3.75 N to 4.75 N. The overshoot of system is less than ±2.5 N and steady state error is within ± 1 N where load cells have a signal noise of ±0.7 N. The integration of load cells and active dancer with self-adapting neural network control provide a solution to the web tension control of multispan roll-to-roll system.
文摘Aimed at the complex demand of hot strip rolling mill in practicing, the configuration of the coiler and the technological process is analyzed. The arithmetic of coiling tension and the control process is introduced. The frame of the tension adjusting system is given. The coiler control system hardware is designed. The system is designed scientifically with steady control and meets demand of the market.
文摘Winding/unwinding system control is a very important issue to web handling machines. In this paper, a novel adaptive H∞ control strategy is developed for winding process control. A gain scheduling scheme is proposed based on a neural fuzzy approximator to improve the transient response and enhance tension control;the controller’s convergence and adaptive capability can be further improved by an efficient hybrid training algorithm. The effectiveness of the proposed adaptive H∞ control is verified by experimental tests. Test results show that the developed gain approximator can adaptively accommodate parameter variations in the system and improve the control performance.
文摘Influence of the combination of nutrient feed with dissolved oxygen control on taxol production in suspension cultures of Taxus chinensis (Pilg.) Rehd. was investigated in bioreactors. Addition of feeding medium with 20 g/L sucrose on day 16 enhanced both the biomass and taxol production in 5-L bioreactors. Further investigation of the fed-batch cultures in a 20-L bioreactor showed that cultivation under a low dissolved oxygen tension (DOT) of 20% for the entire culture resulted in the highest taxol content of 0.98 mg/g DW, while the taxol production was lower than that with 40% and 60% DOT. Moreover, taxol accumulation was remarkably improved by the cultivation of cells initially under DOT of 60% for 20 d followed by changing the DOT to 20% for another 12 d. By combining the use of these two strategies, a maximum taxol content of 18.7 mg/L was obtained in a 20-L bioreactor.