Hanoi’s rapid urbanization has led to a surge in private vehicle ownership, particularly motorcycles, amidst inadequate public transportation infrastructure. Despite government efforts, many still prefer motorized tr...Hanoi’s rapid urbanization has led to a surge in private vehicle ownership, particularly motorcycles, amidst inadequate public transportation infrastructure. Despite government efforts, many still prefer motorized transport, citing mobility and safety concerns, exacerbated by insufficient pedestrian infrastructure. This study examines the motivations behind this reliance on motorized vehicles, particularly motorcycles, in Hanoi. Findings reveal safety and convenience as primary factors driving motorized transport use, especially for accessing bus stations. Economic incentives could promote non-motorized travel and public transport adoption. Policy implications highlight the importance of addressing economic factors and improving access infrastructure to manage motorized vehicle reliance and foster sustainable urban mobility in Hanoi.展开更多
In the context of induction motor control, there are various control strategies used to separately control torque and flux. One common approach is known as Field-Oriented Control (FOC). This technique involves transfo...In the context of induction motor control, there are various control strategies used to separately control torque and flux. One common approach is known as Field-Oriented Control (FOC). This technique involves transforming the three-phase currents and voltages into a rotating reference frame, commonly referred to as the “dq” frame. In this frame, the torque/speed and flux components are decoupled, allowing for independent control, by doing so, the motor’s speed can be regulated accurately and maintain a constant flux which is crucial to ensure optimal motor performance and efficiency. The research focused on studying and simulating a field-oriented control system using fuzzy control techniques for an induction motor. The aim was to address the issue of parameter variations, particularly the change in rotor resistance during motor operation, which causes the control system to deviate from the desired direction. This deviation implies to an increase in the magnetic flux value, specifically the flux component on the q-axis. By employing fuzzy logic techniques to regulate flux vector’s components in the dq frame, this problem was successfully resolved, ensuring that the magnetic flux value remains within the nominal limits. To enhance the control system’s performance, response speed, and efficiency of the motor, sliding mode controllers were implemented to regulate the current in the inner loop. The simulation results demonstrated the proficiency of the proposed methodology.展开更多
This paper introduces four PWM modes used in the sensorless brushless DC motor control system, analyzes their different influences on the commutation torque ripple in detail, and selects the best PWM mode in four give...This paper introduces four PWM modes used in the sensorless brushless DC motor control system, analyzes their different influences on the commutation torque ripple in detail, and selects the best PWM mode in four given types to reduce commutation torque ripple of Brushless OC(BLDC) motors. Simulation and experimental results show that the selection is correct and practical.展开更多
Based on analyzing the structure and working principle on electric vehicles (EVs) with dual motors coupled by planetarY gears, the control strategy of mode switching was proposed. The power interruption problem on E...Based on analyzing the structure and working principle on electric vehicles (EVs) with dual motors coupled by planetarY gears, the control strategy of mode switching was proposed. The power interruption problem on EVs with automatic mechanical transmission (AMT) shifting was resolved. Based on the speed-torque characteristics of the planetary gears and the principle of the auxiliary motor' s zero speed braking, control features of mode switching were introduced. The mode shifting between the main motor mode and dual motors coupled driving were studied. Matlab/Simulink was adopted as a platform to develop the simulation model of EVs with dual motors drive system and 3 gears AMT. Simulation results demonstrated that the power interruption of dual motors drive system was solved during mode switching. The power requirements of EVs were satisfied, too.展开更多
A full-order sliding mode control based on a fuzzy extended state observer is proposed to control the uncertain chaos in the permanent magnet synchronous motor. Through a simple coordinate transformation, the chaotic ...A full-order sliding mode control based on a fuzzy extended state observer is proposed to control the uncertain chaos in the permanent magnet synchronous motor. Through a simple coordinate transformation, the chaotic PMSM model is transformed into the Brunovsky canonical form, which is more suitable for the controller design. Based on the fuzzy control theory, a fuzzy extended state observer is developed to estimate the unknown states and uncertainties, and the restriction that all the system states should be completely measurable is avoided. Thereafter, a full-order sliding mode controller is designed to ensure the convergence of all system states without any chattering problem. Comparative simulations show the effectiveness and superior performance of the proposed control method.展开更多
We propose a BPNN based adaptive sliding mode control scheme for speed tracking of a DC motor with unknown system nonlinearities. The input-output linearization technique is used to cancel the nonlinearities, and outp...We propose a BPNN based adaptive sliding mode control scheme for speed tracking of a DC motor with unknown system nonlinearities. The input-output linearization technique is used to cancel the nonlinearities, and output of the BPNN is incorporated into the controller in the proposed scheme. It is shown that the rotor speed of a DC motor can follow any arbitrarily selected trajectories under variable load torque. Then the application of the approach is tested via some simulations.展开更多
In this paper, we want to make a new type linear piezoelectric motor by mode shape coating or effective electrode surface coating. The mode shape is derived from the mechanical boundary conditions of the linear piezoe...In this paper, we want to make a new type linear piezoelectric motor by mode shape coating or effective electrode surface coating. The mode shape is derived from the mechanical boundary conditions of the linear piezoelectric motor. We only have access to the first three modes of formas, the effective electrode surface coating basis, as well as with the linear piezoelectric motor of normal shape do comparison. Next, we will inspect their gain or axial velocity through theoretical analysis, simulation and experiment. According to the results of the theoretical analysis, we have found that the gain or axial velocity of the linear piezoelectric motors of mode shape is much larger than the linear piezoelectric motors of normal shape. However, according to the results of simulation and experiments, we have found that the gain or axial velocity of the linear piezoelectric motors of mode shape is much greater than the linear piezoelectric motors of normal shape, which is about 1.2 to 1.4 times. The linear piezoelectric motor of mode shape 3 has the fastest axial velocity, which is about -48 mm/s and 48 mm/s under conditions of 180 Vp-p driving voltage, 21.2 kHz driving frequency (the third vibration modal), 25 gw loading and the position of loading or mass at x = 5 mm & 45 mm respectively. And its axial velocity is about 1.4 times the linear piezoelectric motor of normal shape under the same conditions. Overall, the mode shape coating helps to enhance the gain or axial velocity of the linear piezoelectric motor.展开更多
This article proposes an innovative strategy to the problem of non-linear estimation of states for electrical machine systems. This method allows the estimation of variables that are difficult to access or that are si...This article proposes an innovative strategy to the problem of non-linear estimation of states for electrical machine systems. This method allows the estimation of variables that are difficult to access or that are simply impossible to measure. Thus, as compared with a full-order sliding mode observer, in order to reduce the execution time of the estimation, a reduced-order discrete-time Extended sliding mode observer is proposed for on-line estimation of rotor flux, speed and rotor resistance in an induction motor using a robust feedback linearization control. Simulations results on Matlab-Simulink environment for a 1.8 kW induction motor are presented to prove the effectiveness and high robustness of the proposed nonlinear control and observer against modeling uncertainty and measurement noise.展开更多
The Electromagnetic Compatibility (EMC) of direct current (DC) motor windings is a system model which is used to reflect the functional characters of the system in the whole EMC specified frequency (150 KHz ~ 30 MHz)....The Electromagnetic Compatibility (EMC) of direct current (DC) motor windings is a system model which is used to reflect the functional characters of the system in the whole EMC specified frequency (150 KHz ~ 30 MHz). For most motor designing process, it is always used to evaluate the inductance of windings in lower or working frequency;however, when analyzing the conducted interference, it is necessary to take some pa-rameters in high frequency into account in building up the EMC model, such as the noticeable capacitance distributed among the windings or between windings and shells. Past research neglected the common-mode current generated by the high frequency interference within motor bearings coupled with shells, since the parasitic capacitance of rotor core comes from armature windings supplied sufficient paths. In EMC model-ing process for DC motor problem, first, test the impedance of windings by experiments;then, generate the equivalent circuit with overall parameters. At present, it is a difficulty that how to choose the parameters. Most researchers preferred to adopt analytical calculation results, however, it could not reflect the essence of the model since it requires many simplification. Based on this point, this paper adopted ant colony algorithm (ACA) with positive feedback to intelligently search and globally optimize the parameters of equivalent cir-cuit. Simulation result showed that the impedance of equivalent circuit calculated by this algorithm was the same as experimental result in the whole EMC frequency. In order to further confirm the validity of ACA, PSPICE circuit simulation was implemented to simulate the spectrum of common mode Electromagnetic Interference (EMI) of equivalent circuit. The simulation result accords well with the experiment result re-ceived by EMI receiver. So it sufficiently demonstrated correctness of ACA in the analysis of high frequency equivalent circuit.展开更多
The multiplicity of vector combinations for vectors of combined three-level inverters plays an important role, when deciding on the modulation scheme, to obtain minimum switching per inverter vector change, as describ...The multiplicity of vector combinations for vectors of combined three-level inverters plays an important role, when deciding on the modulation scheme, to obtain minimum switching per inverter vector change, as described in the next Section. This is not possible with reduced common-mode three-level inverter structure, obtained with a five-level cascaded H-bridge configuration, as the space vectors locations do not exhibit multiplicity. Moreover, the proposed configuration requires only two power supplies, whereas the scheme with the five-level H-bridge configuration requires six isolated power supplies.展开更多
The multiplicity of vector combinations for vectors of combined three-level inverters plays an important role, when deciding on the modulation scheme, to obtain minimum switching per inverter vector change, as describ...The multiplicity of vector combinations for vectors of combined three-level inverters plays an important role, when deciding on the modulation scheme, to obtain minimum switching per inverter vector change, as described in the next Section. This is not possible with reduced common-mode three-level inverter structure, obtained with a five-level cascaded H-bridge configuration, as the space vectors locations do not exhibit multiplicity. Moreover, the proposed configuration requires only two power supplies, whereas the scheme with the five-level H-bridge configuration requires six isolated power supplies.展开更多
In this paper, we try to use the coating of effective electrode surface and change the direction of polarization to design the mode shape piezoelectric motors of the first three modes. We also com-pare the gain of the...In this paper, we try to use the coating of effective electrode surface and change the direction of polarization to design the mode shape piezoelectric motors of the first three modes. We also com-pare the gain of the mode shape piezoelectric motors with respect to the normal shape piezoelectric motor, including rotational speed, loading ability, torque, phase angle conversion and efficiency. According to the results of theoretical and simulation analysis, we have found that the gain of the mode shape piezoelectric stators are larger than the normal shape piezoelectric stator on average. According to the results of experiments, we found that the gain of the rotational speed, loading ability, torque, driving phase angle conversion and efficiency of the mode shape (MS1 - 3) piezoelectric motors are higher than the normal shape piezoelectric motor (NS) under driving condition of the second vibration mode. Also, the gain of the rotational speed and loading ability of the mode shape 2 (MS2) piezoelectric motor are higher than other shapes piezoelectric motors (NS, MS1 and MS3) under driving condition of the second vibration mode. The used maximum rotational speed of the mode shape 2 (MS2) piezoelectric motor is up to 946 rpm under conditions of 180 Vp-p driving voltage, 10.7 kHz driving frequency, 0o driving phase angle and 13.0 gw net weight. The maximum loading ability and torque of the mode shape 2 (MS2) piezoelectric motor is respectively 451 gw and 0.91 mkgw-m under conditions of 180 Vp-p driving voltage, 10.7 kHz driving frequency, 0o driving phase angle and 173 rpm rotational speed. And the gain of efficiency (output power) and maximum loading ability (torque) of the mode shape 2 (MS2) piezoelectric motor are respectively 2.28 and 1.54 with respect to the normal shape piezoelectric motor under conditions of 180 Vp-p driving voltage, 10.7 kHz driving frequency and 0o driving phase angle. According to the results of the experiments, we have finally found that the piezoelectric motors (NS and MS1 - 3) can be driven only by the second vibration mode because the stator can produce elliptical motion and allows the rotor to generate orientation rotation. However, the first vibration mode can allow the rotor to be rotated very fast but it can’t make the rotation of the rotor orientation. Furthermore, we also found that the rotor can’t rotate by the third vibration mode because its vibration energy is absorbed by the structure itself, so causing the rotor stagnation.展开更多
This paper has developed a genetic algorithm (GA) optimization approach to search for the optimal locations to install bearings on the motorized spindle shaft to maximize its first-mode natural frequency (FMNF). First...This paper has developed a genetic algorithm (GA) optimization approach to search for the optimal locations to install bearings on the motorized spindle shaft to maximize its first-mode natural frequency (FMNF). First, a finite element method (FEM) dynamic model of the spindle-bearing system is formulated, and by solving the eigenvalue problem derived from the equations of motion, the natural frequencies of the spindle system can be acquired. Next, the mathematical model is built, which includes the objective function to maximize FMNF and the constraints to limit the locations of the bearings with respect to the geometrical boundaries of the segments they located and the spacings between adjacent bearings. Then, the Sequential Decoding Process (SDP) GA is designed to accommodate the dependent characteristics of the constraints in the mathematical model. To verify the proposed SDP-GA optimization approach, a four-bearing installation optimazation problem of an illustrative spindle system is investigated. The results show that the SDP-GA provides well convergence for the optimization searching process. By applying design of experiments and analysis of variance, the optimal values of GA parameters are determined under a certain number restriction in executing the eigenvalue calculation subroutine. A linear regression equation is derived also to estimate necessary calculation efforts with respect to the specific quality of the optimization solution. From the results of this illustrative example, we can conclude that the proposed SDP-GA optimization approach is effective and efficient.展开更多
文摘Hanoi’s rapid urbanization has led to a surge in private vehicle ownership, particularly motorcycles, amidst inadequate public transportation infrastructure. Despite government efforts, many still prefer motorized transport, citing mobility and safety concerns, exacerbated by insufficient pedestrian infrastructure. This study examines the motivations behind this reliance on motorized vehicles, particularly motorcycles, in Hanoi. Findings reveal safety and convenience as primary factors driving motorized transport use, especially for accessing bus stations. Economic incentives could promote non-motorized travel and public transport adoption. Policy implications highlight the importance of addressing economic factors and improving access infrastructure to manage motorized vehicle reliance and foster sustainable urban mobility in Hanoi.
文摘In the context of induction motor control, there are various control strategies used to separately control torque and flux. One common approach is known as Field-Oriented Control (FOC). This technique involves transforming the three-phase currents and voltages into a rotating reference frame, commonly referred to as the “dq” frame. In this frame, the torque/speed and flux components are decoupled, allowing for independent control, by doing so, the motor’s speed can be regulated accurately and maintain a constant flux which is crucial to ensure optimal motor performance and efficiency. The research focused on studying and simulating a field-oriented control system using fuzzy control techniques for an induction motor. The aim was to address the issue of parameter variations, particularly the change in rotor resistance during motor operation, which causes the control system to deviate from the desired direction. This deviation implies to an increase in the magnetic flux value, specifically the flux component on the q-axis. By employing fuzzy logic techniques to regulate flux vector’s components in the dq frame, this problem was successfully resolved, ensuring that the magnetic flux value remains within the nominal limits. To enhance the control system’s performance, response speed, and efficiency of the motor, sliding mode controllers were implemented to regulate the current in the inner loop. The simulation results demonstrated the proficiency of the proposed methodology.
文摘This paper introduces four PWM modes used in the sensorless brushless DC motor control system, analyzes their different influences on the commutation torque ripple in detail, and selects the best PWM mode in four given types to reduce commutation torque ripple of Brushless OC(BLDC) motors. Simulation and experimental results show that the selection is correct and practical.
基金Supported by Doctoral Fund of Ministry of Education of China(20101101110012)the National Natural Science Foundationof China(51175040)
文摘Based on analyzing the structure and working principle on electric vehicles (EVs) with dual motors coupled by planetarY gears, the control strategy of mode switching was proposed. The power interruption problem on EVs with automatic mechanical transmission (AMT) shifting was resolved. Based on the speed-torque characteristics of the planetary gears and the principle of the auxiliary motor' s zero speed braking, control features of mode switching were introduced. The mode shifting between the main motor mode and dual motors coupled driving were studied. Matlab/Simulink was adopted as a platform to develop the simulation model of EVs with dual motors drive system and 3 gears AMT. Simulation results demonstrated that the power interruption of dual motors drive system was solved during mode switching. The power requirements of EVs were satisfied, too.
基金supported by the National Natural Science Foundation of China(Grant Nos.61403343 and 61433003)the Scientific Research Foundation of Education Department of Zhejiang Province,China(Grant No.Y201329260)the Natural Science Foundation of Zhejiang University of Technology,China(Grant No.1301103053408)
文摘A full-order sliding mode control based on a fuzzy extended state observer is proposed to control the uncertain chaos in the permanent magnet synchronous motor. Through a simple coordinate transformation, the chaotic PMSM model is transformed into the Brunovsky canonical form, which is more suitable for the controller design. Based on the fuzzy control theory, a fuzzy extended state observer is developed to estimate the unknown states and uncertainties, and the restriction that all the system states should be completely measurable is avoided. Thereafter, a full-order sliding mode controller is designed to ensure the convergence of all system states without any chattering problem. Comparative simulations show the effectiveness and superior performance of the proposed control method.
文摘We propose a BPNN based adaptive sliding mode control scheme for speed tracking of a DC motor with unknown system nonlinearities. The input-output linearization technique is used to cancel the nonlinearities, and output of the BPNN is incorporated into the controller in the proposed scheme. It is shown that the rotor speed of a DC motor can follow any arbitrarily selected trajectories under variable load torque. Then the application of the approach is tested via some simulations.
文摘In this paper, we want to make a new type linear piezoelectric motor by mode shape coating or effective electrode surface coating. The mode shape is derived from the mechanical boundary conditions of the linear piezoelectric motor. We only have access to the first three modes of formas, the effective electrode surface coating basis, as well as with the linear piezoelectric motor of normal shape do comparison. Next, we will inspect their gain or axial velocity through theoretical analysis, simulation and experiment. According to the results of the theoretical analysis, we have found that the gain or axial velocity of the linear piezoelectric motors of mode shape is much larger than the linear piezoelectric motors of normal shape. However, according to the results of simulation and experiments, we have found that the gain or axial velocity of the linear piezoelectric motors of mode shape is much greater than the linear piezoelectric motors of normal shape, which is about 1.2 to 1.4 times. The linear piezoelectric motor of mode shape 3 has the fastest axial velocity, which is about -48 mm/s and 48 mm/s under conditions of 180 Vp-p driving voltage, 21.2 kHz driving frequency (the third vibration modal), 25 gw loading and the position of loading or mass at x = 5 mm & 45 mm respectively. And its axial velocity is about 1.4 times the linear piezoelectric motor of normal shape under the same conditions. Overall, the mode shape coating helps to enhance the gain or axial velocity of the linear piezoelectric motor.
文摘This article proposes an innovative strategy to the problem of non-linear estimation of states for electrical machine systems. This method allows the estimation of variables that are difficult to access or that are simply impossible to measure. Thus, as compared with a full-order sliding mode observer, in order to reduce the execution time of the estimation, a reduced-order discrete-time Extended sliding mode observer is proposed for on-line estimation of rotor flux, speed and rotor resistance in an induction motor using a robust feedback linearization control. Simulations results on Matlab-Simulink environment for a 1.8 kW induction motor are presented to prove the effectiveness and high robustness of the proposed nonlinear control and observer against modeling uncertainty and measurement noise.
文摘The Electromagnetic Compatibility (EMC) of direct current (DC) motor windings is a system model which is used to reflect the functional characters of the system in the whole EMC specified frequency (150 KHz ~ 30 MHz). For most motor designing process, it is always used to evaluate the inductance of windings in lower or working frequency;however, when analyzing the conducted interference, it is necessary to take some pa-rameters in high frequency into account in building up the EMC model, such as the noticeable capacitance distributed among the windings or between windings and shells. Past research neglected the common-mode current generated by the high frequency interference within motor bearings coupled with shells, since the parasitic capacitance of rotor core comes from armature windings supplied sufficient paths. In EMC model-ing process for DC motor problem, first, test the impedance of windings by experiments;then, generate the equivalent circuit with overall parameters. At present, it is a difficulty that how to choose the parameters. Most researchers preferred to adopt analytical calculation results, however, it could not reflect the essence of the model since it requires many simplification. Based on this point, this paper adopted ant colony algorithm (ACA) with positive feedback to intelligently search and globally optimize the parameters of equivalent cir-cuit. Simulation result showed that the impedance of equivalent circuit calculated by this algorithm was the same as experimental result in the whole EMC frequency. In order to further confirm the validity of ACA, PSPICE circuit simulation was implemented to simulate the spectrum of common mode Electromagnetic Interference (EMI) of equivalent circuit. The simulation result accords well with the experiment result re-ceived by EMI receiver. So it sufficiently demonstrated correctness of ACA in the analysis of high frequency equivalent circuit.
文摘The multiplicity of vector combinations for vectors of combined three-level inverters plays an important role, when deciding on the modulation scheme, to obtain minimum switching per inverter vector change, as described in the next Section. This is not possible with reduced common-mode three-level inverter structure, obtained with a five-level cascaded H-bridge configuration, as the space vectors locations do not exhibit multiplicity. Moreover, the proposed configuration requires only two power supplies, whereas the scheme with the five-level H-bridge configuration requires six isolated power supplies.
文摘The multiplicity of vector combinations for vectors of combined three-level inverters plays an important role, when deciding on the modulation scheme, to obtain minimum switching per inverter vector change, as described in the next Section. This is not possible with reduced common-mode three-level inverter structure, obtained with a five-level cascaded H-bridge configuration, as the space vectors locations do not exhibit multiplicity. Moreover, the proposed configuration requires only two power supplies, whereas the scheme with the five-level H-bridge configuration requires six isolated power supplies.
文摘In this paper, we try to use the coating of effective electrode surface and change the direction of polarization to design the mode shape piezoelectric motors of the first three modes. We also com-pare the gain of the mode shape piezoelectric motors with respect to the normal shape piezoelectric motor, including rotational speed, loading ability, torque, phase angle conversion and efficiency. According to the results of theoretical and simulation analysis, we have found that the gain of the mode shape piezoelectric stators are larger than the normal shape piezoelectric stator on average. According to the results of experiments, we found that the gain of the rotational speed, loading ability, torque, driving phase angle conversion and efficiency of the mode shape (MS1 - 3) piezoelectric motors are higher than the normal shape piezoelectric motor (NS) under driving condition of the second vibration mode. Also, the gain of the rotational speed and loading ability of the mode shape 2 (MS2) piezoelectric motor are higher than other shapes piezoelectric motors (NS, MS1 and MS3) under driving condition of the second vibration mode. The used maximum rotational speed of the mode shape 2 (MS2) piezoelectric motor is up to 946 rpm under conditions of 180 Vp-p driving voltage, 10.7 kHz driving frequency, 0o driving phase angle and 13.0 gw net weight. The maximum loading ability and torque of the mode shape 2 (MS2) piezoelectric motor is respectively 451 gw and 0.91 mkgw-m under conditions of 180 Vp-p driving voltage, 10.7 kHz driving frequency, 0o driving phase angle and 173 rpm rotational speed. And the gain of efficiency (output power) and maximum loading ability (torque) of the mode shape 2 (MS2) piezoelectric motor are respectively 2.28 and 1.54 with respect to the normal shape piezoelectric motor under conditions of 180 Vp-p driving voltage, 10.7 kHz driving frequency and 0o driving phase angle. According to the results of the experiments, we have finally found that the piezoelectric motors (NS and MS1 - 3) can be driven only by the second vibration mode because the stator can produce elliptical motion and allows the rotor to generate orientation rotation. However, the first vibration mode can allow the rotor to be rotated very fast but it can’t make the rotation of the rotor orientation. Furthermore, we also found that the rotor can’t rotate by the third vibration mode because its vibration energy is absorbed by the structure itself, so causing the rotor stagnation.
文摘This paper has developed a genetic algorithm (GA) optimization approach to search for the optimal locations to install bearings on the motorized spindle shaft to maximize its first-mode natural frequency (FMNF). First, a finite element method (FEM) dynamic model of the spindle-bearing system is formulated, and by solving the eigenvalue problem derived from the equations of motion, the natural frequencies of the spindle system can be acquired. Next, the mathematical model is built, which includes the objective function to maximize FMNF and the constraints to limit the locations of the bearings with respect to the geometrical boundaries of the segments they located and the spacings between adjacent bearings. Then, the Sequential Decoding Process (SDP) GA is designed to accommodate the dependent characteristics of the constraints in the mathematical model. To verify the proposed SDP-GA optimization approach, a four-bearing installation optimazation problem of an illustrative spindle system is investigated. The results show that the SDP-GA provides well convergence for the optimization searching process. By applying design of experiments and analysis of variance, the optimal values of GA parameters are determined under a certain number restriction in executing the eigenvalue calculation subroutine. A linear regression equation is derived also to estimate necessary calculation efforts with respect to the specific quality of the optimization solution. From the results of this illustrative example, we can conclude that the proposed SDP-GA optimization approach is effective and efficient.