CN108297737B - Meandering stability control system and method for independently driven wheelset of rail vehicle - Google Patents

Abstract

The invention discloses a snaking stability control system and method for a rail vehicle independent driving wheel pair, wherein the system comprises: an independent driving wheel pair electromechanical coupling system; the acquisition module is used for acquiring the rotating speed of the motor output shaft and the current flowing through the motor armature; the state observer is used for obtaining the state quantity of the system according to the rotating speed of the output shaft of the motor and the current flowing through the armature of the motor; and the motor controller calculates the control voltage of the driving motor according to the state quantity of the system when the independent driving wheel pair generates snaking motion, and controls the electromechanical coupling system of the independent driving wheel pair through the control voltage, so that the snaking stability of the independent driving wheel pair is controlled. The system can control the transverse movement of the independent driving wheel to the electromechanical coupling system through the driving motor, thereby controlling the snaking stability of the independent driving wheel and effectively improving the stability of the system.

Description

Meandering stability control system and method for independently driven wheelset of rail vehicle

technical field

The invention relates to the technical field of vehicles, in particular to a meandering stability control system and method for independently driving wheel pairs of rail vehicles.

Background technique

With the continuous expansion of the city scale, urban rail vehicles with the characteristics of large capacity, fast speed and punctuality have become an indispensable and important part of the urban transportation system. The transportation system in the city is very complex, with congested roads and dense high-rise buildings. In order to allow the wider application of rail vehicles, it is necessary to have small-radius curves in the track alignment.

As shown in Figure 1, the traditional fixed wheelset uses the tread taper to compensate the linear speed difference between the left and right wheels due to the fixed connection of the left and right wheels. When turning with a small radius, the compensation range will be exceeded, so that the rim and the Wheel-rail contact, which not only increases the driving resistance, but also causes derailment accidents in severe cases, so the traditional consolidated wheelset has poor passing ability of small radius. As shown in Figure 2, the main feature of an independent wheelset is that the wheels on both sides can rotate independently, which enables the wheels on the left and right sides to have different rotational speeds, so that they can better pass small radius curves. However, the independent wheelset breaks the self-guided driving mechanism based on the longitudinal creep torque of the traditional consolidated wheelset, so that it has no self-guidance and lacks self-aligning ability.

In the related art, an independent driving wheel pair based on the independent driving of the left and right wheels is proposed, and constant speed control is carried out under straight driving conditions. The method for controlling the rotational speed of the wheels of a vehicle simultaneously solves the problem of passing performance of small radius curves and the problem of self-guidance of independent wheel sets.

The independent driving wheelset under constant speed control theoretically has a driving performance close to that of the traditional consolidated wheelset. Under the action of the longitudinal creep moment, similar to the lateral dynamic characteristics of the consolidated wheelset, there will be lateral displacement and yaw angle. The meandering motion of alternating reciprocating vibration not only affects the ride comfort of the vehicle, but also becomes unstable when the lateral motion exceeds a certain critical speed, resulting in wheel flange contact until derailment.

SUMMARY OF THE INVENTION

The present invention aims to solve one of the technical problems in the related art at least to a certain extent.

Therefore, an object of the present invention is to propose a meandering stability control system for an independently driven wheel pair of a rail vehicle, which can effectively improve the stability of the independently driven wheel pair.

Another object of the present invention is to provide a meandering stability control method for an independently driven wheel pair of a rail vehicle.

In order to achieve the above object, an embodiment of the present invention proposes a meandering stability control system for an independently driven wheel pair of a rail vehicle, including: an electromechanical coupling system for the independent drive wheel pair; a collection module for collecting the rotational speed and The current flowing through the motor armature; the state observer, which is used to obtain the state quantity of the system according to the speed of the motor output shaft and the current flowing through the motor armature; the motor controller, which generates meandering motion in the independent driving wheel pair At the time, the control voltage of the driving motor is calculated according to the state quantity of the system, and the electromechanical coupling system of the independent driving wheel pair is controlled by the control voltage of the motor, so as to perform meandering stability control on the independent driving wheel pair.

According to the meandering stability control system of the independently driven wheelset of the rail vehicle according to the embodiment of the present invention, the state quantity of the system can be obtained through the rotational speed of the motor output shaft and the current flowing through the motor armature, so as to calculate the control voltage of the driving motor, so that by driving the The control voltage of the motor controls the electromechanical coupling system of the independent driving wheel pair to control the meandering stability of the independent driving wheel pair, which effectively improves the stability of the system.

In addition, the meandering stability control system for the independently driven wheel pair of the rail vehicle according to the above-mentioned embodiment of the present invention may also have the following additional technical features:

Further, in an embodiment of the present invention, the motor controller is further configured to: when the independent driving wheel pair is in a state of alternating lateral displacement and swing angle vibration, according to the state quantity of the system, the horizontal The displacement target value is 0 or the control target is converged within a preset range, the control voltage of the driving motor is calculated by a control algorithm, and the control voltage of the driving motor is output through the power circuit device, so as to carry out the control of the driving wheel pair. Stability Control.

Further, in an embodiment of the present invention, the electromechanical coupling system for the independent driving wheel pair includes: the independent driving wheel pair; two driving motors and necessary transmission mechanisms.

Further, in an embodiment of the present invention, the acquisition module includes: a motor speed sensor and an armature current sensor.

Further, in an embodiment of the present invention, the state quantities of the system include lateral displacement, yaw angle, lateral velocity and yaw angular velocity of the wheelset.

Further, in an embodiment of the present invention, the state observer is further configured to estimate the state quantity of the system according to the state observer according to the rotational speed of the motor output shaft and the current flowing through the motor armature.

In order to achieve the above object, another embodiment of the present invention proposes a meandering stability control method for an independently driven wheel pair of a rail vehicle, which includes the following steps: collecting the rotational speed of the motor output shaft and the current flowing through the motor armature; The state quantity of the system is obtained from the rotational speed of the motor output shaft and the current flowing through the motor armature; the control voltage of the driving motor is calculated according to the state quantity of the system, and the independent driving wheel pair is controlled according to the control voltage of the driving motor. Electromechanical coupling system for meandering stability control of independently driven wheelsets.

According to the method for controlling meandering stability of an independently driven wheelset of a rail vehicle according to the embodiment of the present invention, the state quantity of the system can be obtained through the rotational speed of the motor output shaft and the current flowing through the motor armature, so as to calculate the control voltage of the driving motor, so that by driving the The control voltage of the motor controls the electromechanical coupling system of the independent driving wheel pair to control the meandering stability of the independent driving wheel pair, which effectively improves the stability of the system.

In addition, the meandering stability control method for the independently driven wheel pair of a rail vehicle according to the above-mentioned embodiment of the present invention may also have the following additional technical features:

Further, in an embodiment of the present invention, when the independent driving wheel pair is in a state of alternating lateral displacement and shaking angle, according to the state quantity of the system, the lateral displacement target value is 0 or converges to a predetermined value. Set the control target within the range, calculate the control voltage of the driving motor through a control algorithm, and output the control voltage of the driving motor through a power circuit device, so as to perform stability control on the driving wheel pair.

Further, in an embodiment of the present invention, the state quantities of the system include lateral displacement, yaw angle, lateral velocity and yaw angular velocity of the wheelset.

Further, in an embodiment of the present invention, the state quantity of the system is estimated according to the state observer according to the rotational speed of the motor output shaft and the current flowing through the motor armature.

Additional aspects and advantages of the present invention will be set forth, in part, from the following description, and in part will be apparent from the following description, or may be learned by practice of the invention.

Description of drawings

The above and/or additional aspects and advantages of the present invention will become apparent and readily understood from the following description of embodiments taken in conjunction with the accompanying drawings, wherein:

Fig. 1 is the schematic diagram of the traditional consolidation wheelset;

Figure 2 is a schematic diagram of an independent wheelset;

3 is a schematic diagram of an independent driving wheel pair in the related art;

Figure 4 is a schematic diagram of a lateral motion curve under the control of equal rotational speeds of wheels on both sides of an independent drive wheel pair;

Fig. 5 is the schematic diagram of the qualitative analysis of serpentine motion in the related art;

6 is a schematic structural diagram of a meandering stability control system for an independently driven wheel pair of a rail vehicle according to an embodiment of the present invention;

7 is a schematic structural diagram of an electromechanical control system for an independent drive wheel pair according to an embodiment of the present invention;

8 is a schematic diagram of a simulation result of an independent driving wheel pair under lateral displacement PID control with a state observer according to an embodiment of the present invention;

9 is a schematic diagram of a simulation result of an independent driving wheel pair under state feedback control with a state observer according to an embodiment of the present invention;

FIG. 10 is a flowchart of a method for controlling meandering stability of an independently driven wheel pair of a rail vehicle according to an embodiment of the present invention.

Detailed ways

The following describes in detail the embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals refer to the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary, and are intended to explain the present invention and should not be construed as limiting the present invention.

Before introducing the meandering stability control system and method for an independently driven wheelset of a rail vehicle according to an embodiment of the present invention, the meandering stability control of an independently driven wheelset of a rail vehicle in the related art is briefly introduced.

As shown in Figure 3, the related art is based on the independent wheel set, and the motor and the necessary transmission mechanism are arranged on both sides respectively, which becomes an electromechanical coupling system for independent driving of the wheel set, which can provide longitudinal drive or Braking torque, but when the independent driving wheel pair is driving in a straight line, the left and right wheels of the independent wheel pair are still required to rotate at the same speed. In the driving situation, the meandering stability problem of the traditional consolidated wheelset will still occur in the case of an independent wheelset.

As shown in Figure 4, in the simulation environment, if the speed difference between the two sides of the independent driving wheel pair can be controlled to be close to 0, then the independent driving wheel has the same meandering motion properties for the consolidated wheel pair; and from Figure 4, it can be seen that It can be seen that the meandering motion is a form of self-excited vibration in which the lateral displacement y of the wheelset and the shaking angle ψ alternately vibrate.

As shown in Figure 5, the meandering motion can be qualitatively given its generation mechanism. The consolidated wheel pair travels on a straight track. If the lateral direction is slightly offset to one side, the radius of gyration r of the wheel on this side is will increase, while the radius of gyration of the other wheel will decrease. Since the two wheels are mounted on one shaft, the torsional stiffness of this shaft is very large, it can be considered that the angular velocity ω of the two wheels is the same, and the linear velocity v=ωr, so the wheel on the side with the larger instantaneous radius of gyration The line speed is also high. Therefore, if the wheel remains pure rolling, the wheelset will return to the middle of the track again, with the yaw angle due to the taper of the tread. Due to the inertia of the motion of the wheelset, the wheelset will overshoot the center of the track and deflect to the other side. This process is repeated, resulting in a snake-like motion.

Based on the above problem, the present invention proposes a meandering stability control system and method for an independently driven wheel pair of a rail vehicle.

The following describes the meandering stability control system and method for the independently driven wheelset of a rail vehicle according to the embodiments of the present invention with reference to the accompanying drawings. First, the meandering stability of the independently driven wheelset for a rail vehicle according to the embodiment of the present invention will be described with reference to the accompanying drawings. Control System.

6 is a schematic structural diagram of a meandering stability control system for an independently driven wheel pair of a rail vehicle according to an embodiment of the present invention.

As shown in FIG. 6 , the meandering stability control system 10 of the independently driven wheelset of a rail vehicle includes: an electromechanical coupling system 100 of the independently driven wheelset, a collection module 200 , a state observer 300 and a motor controller 400 .

Among them, the collection module 200 is used to collect the rotational speed of the motor output shaft and the current flowing through the motor armature. The state observer 300 is used to estimate the state quantity of the system according to the rotational speed of the motor output shaft and the current flowing through the motor armature. The motor controller 400 calculates the control voltage of the driving motor according to the state quantity of the system when the independent driving wheel pair has a meandering motion, and controls the electromechanical coupling system of the independent driving wheel pair through the control voltage of the driving motor, so as to meander the independent driving wheel pair. Stability Control. The system 10 in the embodiment of the present invention can control the electromechanical coupling system of the independent driving wheel pair according to the control voltage of the driving motor, so as to perform meandering stability control on the independent driving wheel pair, thereby effectively improving the stability of the system.

Further, in an embodiment of the present invention, the motor controller 400 is further configured to: when the independent driving wheel pair is in a state of alternating lateral displacement and shaking angle vibration, according to the state quantity of the system, the lateral displacement target value is 0 Or convergence within a preset range is the control target, the control voltage of the driving motor is calculated by the control algorithm, and the control voltage of the driving motor is output through the power circuit device to perform stability control on the independent driving wheel pair.

Optionally, in an embodiment of the present invention, the electromechanical coupling system 100 for an independent driving wheel pair includes: an independent driving wheel pair, two driving motors and necessary transmission mechanisms.

Optionally, in an embodiment of the present invention, the acquisition module 200 includes: a motor speed sensor and an armature current sensor.

Wherein, in an embodiment of the present invention, the state quantity of the system includes the lateral displacement and the yaw angle of the wheelset.

Further, in an embodiment of the present invention, the state observer 300 is further configured to estimate the state quantity of the system according to the rotational speed of the motor output shaft and the current flowing through the motor armature.

It can be understood that, as shown in FIG. 7 , the electromechanical coupling system 100 of the independent drive wheel set according to the embodiment of the present invention includes an independent wheel set, two drive motors, and a necessary transmission mechanism between the independent wheel sets and the two drive motors. The part is the controlled object; the sensor, namely the acquisition module 200, the acquisition module 200 includes a motor speed sensor and an armature current sensor, and the acquisition module 200 is used to collect the rotational speed of the motor output shaft and the current flowing through the motor armature; the state observer 300 The acquired rotational speed of the motor output shaft and the current flowing through the motor armature can be used to estimate other physical quantities in the system 10 that cannot be directly measured, such as the lateral displacement and yaw angle of the wheelset, so as to realize feedback control. The common sensors that directly measure displacement in the industry mainly include laser displacement sensors and linear potentiometers, but they cannot be practically applied in rail vehicles. Only the "soft sensing" technology of state observer can be used to solve this problem. When the independently driven wheel pair is in a meandering motion, the wheel pair is in a state of alternating lateral displacement and shaking angle. According to the system physical quantities estimated by the state observer, the target value of lateral displacement is 0, or the target value of lateral displacement is 0 if it converges within the preset range. The control target is to use a certain control algorithm to calculate the control voltage of the driving motor used for control, and output the control voltage through the power circuit device to realize the meandering stability control of the independent driving wheel pair. The motor controller 400 can take the target value of lateral displacement as 0, or other stability indicators of lateral movement as the control target according to the system physical quantities estimated by the state observer when the independent driving wheel pair has a meandering motion, and use a certain control method. The algorithm calculates the control voltage of the driving motor used for control, and outputs the control voltage through the power circuit device, so as to realize the meandering stability control of the independent driving wheel pair.

For example, in an embodiment of the present invention, the state observer 300 adopts the Lomborg observer, the motor adopts PID control, and the initial traverse amount of the wheelset is set to 0.001m, the simulated vehicle speed is v=20/, the PID The adjustment parameters are K _py =-40, K _iy =0, K _dy =18, and a disturbance noise whose maximum amplitude is 1% of the initial transverse shift is superimposed on the system state quantity.

为两侧电机转速差之半，i为两侧电机电枢电流差之半。可以看出该控制方法对轮对的蛇行运动有一定的抑制作用，初始的横向位移逐渐收敛到0附近，大致在3s之后主要是干扰噪声引起的横向扰动。As shown in Figure 8, y is the lateral displacement of the wheelset, Ψ is the yaw angle of the wheelset,

is half of the speed difference of the motors on both sides, and i is half of the armature current difference of the motors on both sides. It can be seen that the control method has a certain inhibitory effect on the meandering motion of the wheelset. The initial lateral displacement gradually converges to around 0, and after about 3s, it is mainly the lateral disturbance caused by the interference noise.

In another embodiment of the present invention, the state observer 300 adopts the Lomborg observer, the motor adopts state feedback control, the initial traverse of the wheelset is set to 0.001m, the simulated vehicle speed is v=50/, and the system state An interfering noise with a maximum amplitude of 1% of the initial traverse is superimposed. The equation of state feedback control is u=-Kx, where u is half of the voltage difference between the motor armatures on both sides, K is the state feedback control law, and x is the state vector of the system. Using the system matrix, the state feedback control law K can be obtained by configuring the system poles.

As shown in FIG. 9 , in the high-speed situation of v=50/, the state feedback control with the state observer has a relatively good suppression effect on the meandering motion of the independent driving wheel pair. The initial lateral displacement gradually converges to 0. Except for the half i of the motor armature current difference on both sides, the noise superposition can be seen, and the other system state variables can hardly see the noise superposition.

According to the meandering stability control system of the independently driven wheelset of the rail vehicle proposed in the embodiment of the present invention, the state quantity of the system can be obtained through the rotational speed of the motor output shaft and the current flowing through the motor armature to calculate the control voltage of the driving motor, thereby The electromechanical coupling system of the independent driving wheel pair is controlled by the control voltage of the driving motor to control the meandering stability of the independent driving wheel pair, which effectively improves the stability of the system.

Next, a method for controlling meandering stability of an independently driven wheel pair of a rail vehicle according to an embodiment of the present invention will be described with reference to the accompanying drawings.

10 is a flowchart of a method for controlling meandering stability of an independently driven wheel pair of a rail vehicle according to an embodiment of the present invention.

As shown in Figure 10, the meandering stability control method of the independently driven wheel pair of the rail vehicle includes the following steps:

In step S1, the rotational speed of the motor output shaft and the current flowing through the motor armature are collected.

In step S2, the state quantity of the system is obtained according to the rotational speed of the motor output shaft and the current flowing through the motor armature.

In step S3, the control voltage of the driving motor is calculated according to the state quantity of the system, and the electromechanical coupling system of the independent driving wheel pair is controlled by the control voltage of the driving motor, so as to perform meandering stability control on the independent driving wheel pair.

Further, in an embodiment of the present invention, when the independent driving wheel pair is in a state of alternating lateral displacement and shaking angle, according to the state quantity of the system, the lateral displacement target value is 0 or converges within a preset range as The control target is to calculate the control voltage of the driving motor through the control algorithm, and output the control voltage of the driving motor through the power circuit device to control the stability of the independent driving wheel pair.

Further, in an embodiment of the present invention, the state quantity of the system includes the lateral displacement and the yaw angle of the wheelset.

Further, in an embodiment of the present invention, the state quantity of the system is estimated according to the state observer according to the rotational speed of the motor output shaft and the current flowing through the motor armature.

It should be noted that the foregoing explanations of the embodiment of the meandering stability control system for the independently driven wheelset of a rail vehicle are also applicable to the meandering stability control method of the independently driven wheelset of a rail vehicle in this embodiment, which will not be repeated here.

According to the meandering stability control method for the independently driven wheelset of the rail vehicle proposed in the embodiment of the present invention, the state quantity of the system can be obtained through the rotational speed of the motor output shaft and the current flowing through the motor armature to calculate the control voltage of the driving motor, thereby The electromechanical coupling system of the independent driving wheel pair is controlled by the control voltage of the driving motor to control the meandering stability of the independent driving wheel pair, which effectively improves the stability.

In the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "length", "width", "thickness", "upper", "lower", "front", " Rear, Left, Right, Vertical, Horizontal, Top, Bottom, Inner, Outer, Clockwise, Counterclockwise, Axial, The orientations or positional relationships indicated by "radial direction", "circumferential direction", etc. are based on the orientations or positional relationships shown in the accompanying drawings, which are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying the indicated devices or elements. It must have a specific orientation, be constructed and operate in a specific orientation, and therefore should not be construed as a limitation of the present invention.

In addition, the terms "first" and "second" are only used for descriptive purposes, and should not be construed as indicating or implying relative importance or implying the number of indicated technical features. Thus, a feature delimited with "first", "second" may expressly or implicitly include at least one of that feature. In the description of the present invention, "plurality" means at least two, such as two, three, etc., unless otherwise expressly and specifically defined.

In the present invention, unless otherwise expressly specified and limited, the terms "installed", "connected", "connected", "fixed" and other terms should be understood in a broad sense, for example, it may be a fixed connection or a detachable connection , or integrated; it can be a mechanical connection or an electrical connection; it can be directly connected or indirectly connected through an intermediate medium, it can be the internal connection of two elements or the interaction relationship between the two elements, unless otherwise specified limit. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific situations.

In the present invention, unless otherwise expressly specified and limited, a first feature "on" or "under" a second feature may be in direct contact between the first and second features, or the first and second features indirectly through an intermediary touch. Also, the first feature being "above", "over" and "above" the second feature may mean that the first feature is directly above or obliquely above the second feature, or simply means that the first feature is level higher than the second feature. The first feature being "below", "below" and "below" the second feature may mean that the first feature is directly below or obliquely below the second feature, or simply means that the first feature has a lower level than the second feature.

In the description of this specification, description with reference to the terms "one embodiment," "some embodiments," "example," "specific example," or "some examples", etc., mean specific features described in connection with the embodiment or example , structure, material or feature is included in at least one embodiment or example of the present invention. In this specification, schematic representations of the above terms are not necessarily directed to the same embodiment or example. Furthermore, the particular features, structures, materials or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Furthermore, those skilled in the art may combine and combine the different embodiments or examples described in this specification, as well as the features of the different embodiments or examples, without conflicting each other.

Although the embodiments of the present invention have been shown and described above, it should be understood that the above-mentioned embodiments are exemplary and should not be construed as limiting the present invention. Embodiments are subject to variations, modifications, substitutions and variations.

Claims (6)

1. A hunting stability control system for a pair of independent drive wheels of a railway vehicle, comprising:

an independent driving wheel pair electromechanical coupling system;

the acquisition module is used for acquiring the rotating speed of the motor output shaft and the current flowing through the motor armature;

the state observer is used for obtaining the state quantity of the system according to the rotating speed of the motor output shaft and the current flowing through the motor armature; the state quantities of the system comprise the transverse displacement, the head shaking angle, the transverse speed and the head shaking angular speed of the wheel pair; and

the motor controller is used for calculating the control voltage of the driving motor according to the state quantity of the system when the independent driving wheel pair generates snaking motion, and controlling the electromechanical coupling system of the independent driving wheel pair through the control voltage of the driving motor so as to control the snaking stability of the independent driving wheel pair;

the motor controller is further configured to: when the independent driving wheel pair is in a state of alternately vibrating transverse displacement and a yaw angle, according to the state quantity of the system, the transverse displacement target value is 0 or the transverse displacement target value is converged in a preset range to serve as a control target, the control voltage of the driving motor is calculated through a control algorithm, and the control voltage of the driving motor is output through a power circuit device, so that the stability control is carried out on the independent driving wheel pair.

2. A hunting stability control system for independent drive wheel sets of rail vehicles according to claim 1, wherein said independent drive wheel set electromechanical coupling system comprises:

the independent driving wheel pair;

two driving motors and a transmission mechanism.

3. The hunting stability control system for a rail vehicle independent drive wheel pair of claim 1, wherein the acquisition module comprises:

a motor speed sensor and an armature current sensor.

4. A hunting stability control system for a pair of railway vehicle independent drive wheels according to claim 1, wherein the state observer is further configured to estimate the state quantity of the system according to the state observer based on the rotation speed of the motor output shaft and the current flowing through the motor armature.

5. A method for controlling the snaking stability of an independent driving wheel pair of a railway vehicle is characterized by comprising the following steps:

collecting the rotating speed of an output shaft of a motor and the current flowing through an armature of the motor;

obtaining the state quantity of the system according to the rotating speed of the motor output shaft and the current flowing through the motor armature; the state quantities of the system comprise the transverse displacement, the head shaking angle, the transverse speed and the head shaking angular speed of the wheel pair; and

calculating the control voltage of a driving motor according to the state quantity of the system, and controlling an independent driving wheel pair electromechanical coupling system according to the control voltage of the driving motor, so as to control the snaking stability of the independent driving wheel pair; when the independent driving wheel pair is in a state of alternately vibrating transverse displacement and a yaw angle, according to the state quantity of the system, the target value of the transverse displacement is 0 or the transverse displacement is converged in a preset range to serve as a control target, the control voltage of the driving motor is calculated through a control algorithm, and the control voltage of the driving motor is output through a power circuit device, so that the driving wheel pair is subjected to stability control.

6. A hunting stability control method of a pair of railway vehicle independent drive wheels according to claim 5, wherein the state quantity of the system is estimated from a state observer based on the rotation speed of the motor output shaft and the current flowing through a motor armature.

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