KR102121393B1 - Position Control Method And Position Controller - Google Patents

Abstract

An embodiment of the present invention relates to a position control method and a position controller for a low-cost system. According to an embodiment of the present invention, the position control method may comprise the steps of: obtaining an output of a P-controller and an output of an I-controller; detecting a position error of the output of the P-controller based on an allowable range for an error of a preset reference position; setting a gain of the I-controller as a minimum value if the position error reaches the boundary of the allowable range; and outputting a position control transfer function using the output of the P-controller and an output by the set gain of the I-controller.

Description

Position control method and position controller

The embodiments below relate to a position control method and a position controller.

In recent years, many mechanical parts used in automobiles are being replaced by highly efficient electrical parts. Hybrid electric vehicles or electric vehicles, Motor Driven Power Steering (MDPS) and Integrated Starter and Generator (ISG) reduce driving efficiency and use of fossil fuels.

These changes can spread to transmission systems and engine valve systems. Among them, the exhaust gas recirculation (EGR) valve is a target mechanical component that can replace a small DC motor. However, because the typical mechanical system used for valves has very low permissible cost and very small space for implementation, the electrical system including the actuator must be effective in terms of size and cost.

On the other hand, the mechanical operating system designed at low cost has a very large difference between coulomb friction and static friction, so existing linear control systems such as P, PI or PID to improve the accuracy and speed of position control. It is difficult to solve.

The following paper was proposed as a method to control the position of friction.

D.T. Kim, and Z. J. Zhang: "Position Control of a Pneumatic Cylinder Considering Friction Compensation", Journal of Korean Soc. Fluid Power Constr. Equip., Vol. 10, No. 1, pp. 1-6, 2013

Embodiments are intended to provide a position control method for a low-cost system and a position controller for performing the same. In detail, to provide a position control method capable of adapting to a low-cost system by analyzing a mechanical model of the EGR valve and defining the cause of the positional vibration that occurs in order to provide stable position control, and to provide a position controller that performs the same.

The position control method performed by the position controller according to one side includes: obtaining an output of a P controller and an output of an I controller; Detecting a position error of the output of the P controller based on an allowable range for an error of a predetermined reference position; Setting the gain of the I controller to a predetermined value when the position error reaches the boundary of the allowable range; And outputting a position control transfer function using the output of the P controller and the output of the set gain of the I controller.

The predetermined value may be a value that reduces the gain of the I controller.

When the position error is within the allowable range, the step of maintaining a gain of the I controller may be further included.

The position transfer function can be modeled with a current command.

The friction torque applied to the position controller includes coulomb friction torque of gears and joints included in a control target system; Static friction torque of the gear and joint; And a strebec speed.

The position controller according to one side includes one or more processors; Memory; And one or more programs stored in the memory and configured to be executed by the one or more processors, the programs comprising: obtaining the output of the P controller and the output of the I controller; Detecting a position error of the output of the P controller based on an allowable range for an error of a predetermined reference position; Setting the gain of the I controller to a predetermined value when the position error reaches the boundary of the allowable range; And a position control transfer function using the output of the P controller and the output of the set gain of the I controller.

It is possible to provide a position control method for a low cost system and a position controller performing the same through an embodiment of the present invention. In detail, it is possible to provide a position control method capable of adapting to a low-cost system and a position controller performing the same, by first analyzing the mechanical model of the EGR valve and defining the cause of the position vibration generated for stable position control.

1 is a view for explaining the mechanical configuration of the EGR valve.
2 is an experimentally measured spring torque.
3 is an experimentally measured friction torque.
4 is the static friction torque measured at the zero valve position.
5 is a diagram for comparing a position control method according to an embodiment with a position control method of a general P-PI controller as an example of the operation of the control system.
6 is a flowchart of a method for controlling a position in one embodiment.
7 is a graph for explaining the operation of the PI controller in one embodiment.
8 is a graph for setting the gain of the I controller according to the position error in one embodiment.
9 is a block diagram illustrating a configuration of a position controller in one embodiment.
10 is a view showing the setting for the experiment of the embodiment.
11 is a graph of position dynamic response in one embodiment.
12 is a graph for comparing performance of an existing position control method and a position control method according to an embodiment in one embodiment.

The specific structural or functional descriptions disclosed in this specification have been exemplified for the purpose of describing embodiments according to technical concepts only, and the embodiments may be implemented in various other forms and are limited to the embodiments described herein. Does not work.

Terms such as first or second may be used to describe various components, but these terms should be understood only for the purpose of distinguishing one component from other components. For example, the first component may be referred to as the second component, and similarly, the second component may also be referred to as the first component.

When an element is said to be "connected" or "connected" to another component, it is understood that other components may be directly connected to or connected to the other component, but there may be other components in between. It should be. On the other hand, when a component is said to be "directly connected" or "directly connected" to another component, it should be understood that no other component exists in the middle. Expressions describing the relationship between the components, for example, "between" and "immediately between" or "adjacent to" and "directly adjacent to" should be interpreted similarly.

Singular expressions include plural expressions unless the context clearly indicates otherwise. In this specification, the terms "include" or "have" are intended to designate the presence of a feature, number, step, action, component, part, or combination thereof as described, one or more other features or numbers, It should be understood that the existence or addition possibilities of steps, actions, components, parts or combinations thereof are not excluded in advance.

Unless otherwise defined, all terms used herein, including technical or scientific terms, have the same meaning as commonly understood by a person skilled in the art. Terms such as those defined in a commonly used dictionary should be interpreted as having meanings consistent with meanings in the context of related technologies, and should not be interpreted as ideal or excessively formal meanings unless explicitly defined herein. Does not.

Hereinafter, embodiments will be described in detail with reference to the accompanying drawings. The same reference numerals in each drawing denote the same members.

In an embodiment, a position control method for applying to a low cost system may utilize a P control and PI control method. Under a high-friction mechanical system, since it is difficult to accurately and quickly control a linear controller, the control performance is generally improved through feedforward compensation. However, the feed-forward compensation method can improve the dynamic characteristics of the controller, but it is not a solution for unstable control performance due to the difference in static characteristics and friction torque.

Through an embodiment, to provide a position control method capable of adapting to a low-cost system and a position controller performing the same, by first analyzing the mechanical model of the EGR valve for stable position control and defining the cause of the position vibration that occurs.

1 is a view for explaining the mechanical configuration of the EGR valve.

Typical EGR valves are springs (101) for restoring the initial position of the valves, joints (102) and gears (103) for converting power from rotation, and direct currents, which are the source and actuator of the mechanical system, respectively. It is composed of a motor 104 and a throttle valve (105).

As with the general structure of the EGR valve, the motor operating the system of the embodiment is a DC motor, and the torque generated by the DC motor is modeled as in Equation 1.

Here, k _t is the torque constant, and i _a is the armature current of the DC motor.

In addition, Equation 1 can also be described as a general equation of Equation 2.

_r 는 회전 각, T _fric 은 마찰 토크, T _spring 은 스프링 토크, T _L 은 부하 토크(load torque)를 나타낸다.Where J is the inertia,

_r is the rotation angle, T _fric is the friction torque, T _spring is the spring torque, T _L is the load torque.

The rotation angle is transmitted to the linear position by mechanical joints and gears, and the linear position can be expressed as Equation 3.

_L 은 조인트 각도,

_L0 은 초기 설정된 조인트 각도 값을 의미하며, 조인트 각도는 수학식 4와 같이 나타낼 수 있다. 여기서, n은 기어의 비를 나타낸다.Where r is the joint distance,

_L is the joint angle ,

_L0 means an initial joint angle value, and the joint angle can be expressed as Equation (4). Here, n represents the gear ratio.

The spring force according to the linear position is expressed by Equation 5 below.

Here, k _spr is a constant representing the spring characteristic, and x ₀ means the initial linear position. The spring strength can be transmitted to the load-side torque as in Equation 6 below.

Equation 7 shows that the spring torque is affected only by the spring position, but the spring torque is influenced not only by the position, but also by the speed direction. To reflect this, the spring coulomb friction torque of equation (9) can be defined.

When the motor speed is reversed, the spring coulomb friction torque can be expressed as a negative number. As a result, the spring torque can be expressed as Equation (10).

Meanwhile, the EGR valve system is affected by joints and gears as well as springs. The use of low cost joints and gears creates nonlinear static friction, such as lead-screws. As shown in Equation 11, a LuGre friction model can be derived.

_s 는 스트리벡 속도(Stribeck velocity)를 의미한다.Where T _{ge _ col} is the Coulomb friction torque of the gear and joint, and T _{ge _ sta} is the static friction torque of the gear and joint ,

_s stands for Stribeck velocity.

In an embodiment, the modeled load torque can be experimentally measured to implement a controller that performs feedforward compensation. Feedforward compensation can reduce the burden on the feedback controller and improve control performance when it is necessary to control a nonlinear load with a linear controller.

2 shows the spring torque measured through the experiment.

3 shows the friction torque measured through the experiment.

The electric torque from the motor is proportional to the DC motor current in equation (1). That is, the current waveform can indirectly represent the generated torque.

The spring torque measurement result of FIG. 2 may be obtained through the following experiment.

1. Start speed control at initial EGR valve position

2. Apply speed reference from 10 rpm to 300 rpm

3. Measure the average current-the speed at which the lowest average current is observed is the strebec speed

4. Control the motor at the Strevec speed-the instantaneous current measured at steady state means the spring torque, assuming that the frictional torque at the Strevec speed can be neglected

5. Multiply the torque constant to convert the motor current into torque.

The static friction torque can be measured using the spring torque obtained as described above.

1. Start speed control at each EGR valve position

2. Set a small gain on the current controller to apply the ramp increase current reference

3. Measure the peak current point when a sudden current change occurs due to position change

4. Obtain static friction torque current by excluding spring torque from the measured value in 3

5. The static friction torque is multiplied by the torque constant to obtain the static friction torque.

In addition, the Coulomb friction torque can be obtained through the following procedure.

1. Start speed control at initial EGR valve position

2. Apply speed reference from 100 rpm to 300 rpm

3. Measure instantaneous current at steady state of each speed

4. Obtain the difference between the current measured at 300 rpm and the current measured at 100 rpm to remove the spring torque component

5. The result of 4 is multiplied by the torque constant and converted into torque. Coulomb friction torque obtained.

6. Divide the result of 5 by a predetermined speed (eg, 200 rpm) to obtain the Coulomb friction torque gain.

As shown in FIG. 2, spring torque is differently generated according to the valve position direction. If the valve position direction is to open the valve, the spring torque is increased due to the Coulomb friction of the spring torque shown in equation (8). If the valve position direction is to close the valve in reverse, the spring torque decreases.

3 shows that the friction torque at each position has almost the same static friction torque. Also, it shows that the static friction in the reverse direction has a different value from that in the forward direction.

Coulomb friction torque can be calculated on a simple basis. For example, the torque equation at 300 rpm can be expressed as Equation 12.

_r2 는 300rpm의 각속도이다.here,

_r2 is an angular speed of 300 rpm.

The term for inertia can be neglected if steady-state conditions are effective in identifying Coulomb friction torque. When using Equation 12, the difference in torque appearing in the process of 4 for obtaining the Coulomb friction torque can be calculated as in Equation 13.

_r1 은 100rpm의 각속도이다.here,

_r1 is an angular speed of 100 rpm.

As described above, if the positions match, the spring torque is not affected by the speed. Since the static friction torque is invalid during the constant speed operation, Equation 13 can be simply expressed as Equation 14.

If coulomb friction is proportional to velocity, it can be expressed as coulomb friction gain and velocity. Equation (14) can be expressed as Equation (15), assuming that the Coulomb friction gain is almost equal to all positions to simplify the Coulomb friction.

Here, B means Coulomb friction gain. In the embodiment, it is assumed that coulomb friction occurs above the Strebeck speed.

4 shows the measurement of static friction torque.

Green indicates current, purple indicates speed, and blue indicates position.

As shown, the current increases to overcome static friction, and the position of the valve does not move. When the current reaches the point indicated in Fig. 4, the generated torque exceeds the stop torque, and the valve starts to move, but the speed increases rapidly when the difference between the stop friction torque and the Coulomb friction torque is large. In the embodiment, the control speed is a Strebeck speed of 20 rpm, and the coulomb friction torque at that speed is 0.8 A. Since the static friction torque is 10.4 A, it means that the static friction torque exceeds 10 times the Coulomb friction torque. Due to this difference in friction torque, physical position control vibration may occur.

5(a) shows a conventional control system, and FIG. 5(b) shows a control system to which the position control method of the embodiment is applied.

The control system of FIG. 5(b) according to the embodiment does not implement a speed controller. The speed information can be obtained from a linear position sensor implemented to detect the valve position, but it is difficult to calculate the motor speed through dynamic sensing of the linear position sensor. In addition, the speed information is a differential element of the position information, and a filter is required to reduce noise, but the linear position sensor has a slow dynamic characteristic, which can deteriorate the bandwidth of the limited controller. The D controller is not used in the embodiment because it is difficult to obtain the differential component of the position error.

In an embodiment, the control system of FIG. 5(b) may include a PI controller. Hereinafter, a method of improving the performance of a general PI controller will be described.

The position control transfer function according to the embodiment may be expressed by Equation (16).

The control dynamic of the current controller is much faster than that of the position controller, and the transfer function Gc(s) of the current controller can approach 1 at the time of position control. Assuming that the spring load torque is completely compensated by the feed forward path, the position control transfer function can be expressed as in Equation 17.

Here, k _m is k _t / J. If the transfer function is applied to the final value theorem, the error of the step response as in Equation 18 can be obtained.

In the above equation, the PI controller for position control may generate an error in a steady state. The corresponding error is derived from hysteresis control. In the control method according to the embodiment, an allowable range of errors may be set to a practical range. When detecting that the linear position enters the boundary, a timer is activated to observe whether the position is stably or temporarily located within the boundary, and the time required to observe this in the embodiment is 200 ms.

6 is a flowchart illustrating a method for controlling a position according to an embodiment.

In step 610, the position controller obtains the output of the P controller and the output of the I controller.

In an embodiment, the output of the P controller is an output for a position detected in real time based on a preset reference position, and the output of the I controller means a value that accumulates errors between a preset reference position and a position detected in real time.

In step 620, the position controller detects the position error of the output of the P controller based on the allowable range for the error of the predetermined reference position.

In step 630, the position controller sets the gain of the I controller to a predetermined value (for example, a minimum value) when the position error of the output of the P controller reaches the boundary of the allowable range.

In an embodiment, if the position error of the output of the P controller is within an allowable range, the gain of the I controller may not be corrected.

In step 640, the position controller outputs the position control transfer function using the output of the P controller and the output by the set gain of the I controller.

The position control transfer function output in the embodiment may be utilized as a current command in combination with a model of spring torque or coulomb friction modeled as in FIG. 2 or 3.

7 is a graph for explaining the operation of the PI controller of the embodiment.

7(a) is a graph showing a reference position and an allowable range.

7(b) is a graph for comparing the output of the existing PI controller and the output of the PI controller of the embodiment.

Fig. 7(c) is a graph for explaining the phenomenon at the Strebeck speed.

Referring to FIG. 7(a), when the real-time sensed position reaches the position reference, the output of the P controller decreases, and the current and the speed of the motor also decrease.

In an embodiment, as shown in Fig. 7(c), when the speed reaches the Strebeck speed to which static friction is applied in Coulomb friction, the static friction torque affects the total load torque and the motor current is static friction torque. If it cannot be overcome, the motor may stop.

At this time, referring to FIG. 7(b), the output of the P controller remains constant based on the point at which the motor stops, but the I controller cumulatively records a small position error when the detected position is not correct. As the motor stops abruptly at the Strebeck speed, the current exceeds the stationary friction torque, and position vibration due to a rapid speed change may occur as shown in FIG. 4.

When general PI control is applied, the small error output from the I controller accumulates over time, so the value output from the PI controller can continue to increase.

In the PI control method proposed in the embodiment, when the output of the P controller reaches the boundary of the allowable range, the I controller can be deactivated by adjusting the gain of the I controller to a minimum value as shown in FIG. 8. For example, as shown in FIG. 8, the gain of the I controller can be set to be close to zero. As described above, since the I controller causes the position vibration and the real-time position is within the allowable range, a position control method that provides proper control performance within the tolerance by using only the output of the P controller at the allowable boundary as an output Can provide.

The output of the PI controller of the embodiment may refer to FIG. 7(b).

9 is a view for explaining a position controller 900 performing a position control method according to an embodiment.

The location controller 900 may be configured to include, in an embodiment, a memory 610 and one or more processors 620, through one or more programs stored in the memory 610 and executed through the processor 620. A position controller 900 that performs the following position control method may be provided.

In an embodiment, the position controller 900 obtains the output of the P controller and the output of the I controller.

In an embodiment, the output of the P controller is an output for a position detected in real time based on a preset reference position, and the output of the I controller means a value that accumulates errors between a preset reference position and a position detected in real time.

The position controller 900 detects the position error of the output of the P controller based on the allowable range for the error of the predetermined reference position.

In addition, the position controller 900 sets the gain of the I controller to a minimum value when the position error of the output of the P controller reaches the boundary of the allowable range.

In an embodiment, if the position error of the output of the P controller is within an allowable range, the gain of the I controller may not be corrected.

In step 640, the position controller outputs the position control transfer function using the output of the P controller and the output by the set gain of the I controller.

In an embodiment, when the speed reaches the Strebeck speed to which static friction is applied in Coulomb friction, the static friction torque affects the overall load torque and the motor stops when the motor current does not overcome the static friction torque. The output of the P controller remains constant based on when the motor stops, but the I controller accumulates a small position error when the detected position is not correct. The current may exceed the static friction torque while the motor suddenly stops at the Strebeck speed, and positional vibration may occur due to the rapid speed change. Therefore, when the position error of the output of the P controller is within the allowable range, the output of the general PI controller is obtained, and when the position error of the output of the P controller reaches the boundary of the allowable range, the gain of the I controller is the minimum value. By setting to, it is possible to provide a position control method that provides proper control performance within the tolerance by acquiring only the output of the P controller.

The position control transfer function output in the embodiment may be utilized as a current command in combination with a model of spring torque or coulomb friction modeled as in FIG. 2 or 3.

10 shows the settings for the experiment for the Examples.

In an embodiment, a TMS320F28335, a high-performance DSP board 1010, may be used for comparison of the position control method, and performance is measured in connection with a mechanical valve system 1020. In an embodiment, the speed sensor can be implemented immediately in the system 1020. In an embodiment, the sampling frequency and switching frequency of the current controller may be set to 20 kHz, and the position control frequency may be set to 2 kHz.

The motor parameters are shown in Table 1 below.

Parameters Value Unit Rated Power 200 [W] Input voltage 12 [V] Max. Current 20 [A] Rated Speed 500 [rpm]

11 is a graph for position dynamic response.

11(a) shows a case where a 10% position criterion is applied, and FIG. 11(b) shows a case where a 100% position criterion is applied.

Due to the high static friction torque, if the position error is small, the I controller takes some time to generate an output for the proper torque for the static friction torque. When the smallest position criterion is applied, the gain can be set considering the maximum allowable control response time.

As shown, when the 10% criterion is applied, the control response time is longer than the result to which the 100% criterion is applied due to the static friction torque. On the other hand, due to the overshoot (overshoot) limit, the control gain can not be increased to infinity, the setting of the control gain can be compromised considering the two aspects of response time and overshoot.

12 is a graph for comparing the performance of a conventional position control method and a position control method according to an embodiment.

Fig. 12(a) relates to an existing position control method, and Fig. 12(b) shows a result of a position control method for an embodiment.

As shown, due to the large difference between static friction and coulomb friction torque, the controlled position vibrates with the existing PI control method. Since the static friction torque resists movement until the current reaches 2.5A in the forward direction, there is little position movement, but since the current is more than 10A, the position may vibrate due to sudden friction. Vibration may also occur in the reverse direction. This is due to the accumulation of small position errors from the I controller.

The PI controller proposed through the embodiment does not generate an error beyond the allowable range because the position error is integrated within the allowable error range. According to the experiment of the embodiment, the valve position capable of stable control is 83.4%, and has an error of 3.4% in the corresponding standard.

It is possible to propose a position control method that is effective and quick in terms of cost that can be used in a vehicle valve system such as the embodiment. In a low-cost mechanical system, since the difference between static friction and Coulomb friction is large, the control performance is deteriorated in the existing linear controller, but in the control method according to the embodiment, the allowable boundary and selectable motion of the I controller provide appropriate control performance with tolerance. can do.

The embodiments described above may be implemented as hardware components, software components, and/or combinations of hardware components and software components. For example, the devices, methods, and components described in the embodiments include, for example, processors, controllers, arithmetic logic units (ALUs), digital signal processors (micro signal processors), microcomputers, and field programmable gates (FPGAs). It can be implemented using one or more general purpose computers or special purpose computers, such as arrays, programmable logic units (PLUs), microprocessors, or any other device capable of executing and responding to instructions. The processing device may run an operating system (OS) and one or more software applications running on the operating system. In addition, the processing device may access, store, manipulate, process, and generate data in response to the execution of the software. For convenience of understanding, a processing device may be described as one being used, but a person having ordinary skill in the art, the processing device may include a plurality of processing elements and/or a plurality of types of processing elements. It can be seen that may include. For example, the processing device may include a plurality of processors or a processor and a controller. In addition, other processing configurations, such as parallel processors, are possible.

The software may include a computer program, code, instruction, or a combination of one or more of these, and configure the processing device to operate as desired, or process independently or collectively You can command the device. Software and/or data may be interpreted by a processing device, or to provide instructions or data to a processing device, of any type of machine, component, physical device, virtual equipment, computer storage medium or device. , Or may be permanently or temporarily embodied in the transmitted signal wave. The software may be distributed over networked computer systems, and stored or executed in a distributed manner. Software and data may be stored in one or more computer-readable recording media.

The method according to the embodiment may be implemented in the form of program instructions that can be executed through various computer means and recorded on a computer-readable medium. The computer-readable medium may include program instructions, data files, data structures, or the like alone or in combination. The program instructions recorded on the medium may be specially designed and configured for the embodiments or may be known and usable by those skilled in computer software. Examples of computer-readable recording media include magnetic media such as hard disks, floppy disks, and magnetic tapes, optical media such as CD-ROMs, DVDs, and magnetic media such as floptical disks. Includes hardware devices specifically configured to store and execute program instructions such as magneto-optical media, and ROM, RAM, flash memory, and the like. Examples of program instructions include high-level language code that can be executed by a computer using an interpreter, etc., as well as machine language codes produced by a compiler. The hardware device described above may be configured to operate as one or more software modules to perform the operations of the embodiments, and vice versa.

As described above, although the embodiments have been described by the limited drawings, those skilled in the art can make various modifications and variations from the above description. For example, the described techniques are performed in a different order than the described method, and/or the components of the described system, structure, device, circuit, etc. are combined or combined in a different form from the described method, or other components Alternatively, even if substituted or substituted by equivalents, appropriate results can be achieved. Therefore, other implementations, other embodiments, and equivalents to the claims are also within the scope of the following claims.

Claims (10)

In the position control method performed in the position controller,
Obtaining the output of the P controller and the output of the I controller;
Detecting a position error of the output of the P controller based on an allowable range for an error of a predetermined reference position;
Setting the gain of the I controller to a predetermined value when the position error reaches the boundary of the allowable range; And
Outputting a position control transfer function using the output of the P controller and the output of the set gain of the I controller.
Containing,
Position control method.
According to claim 1,
The predetermined value is
A value that reduces the gain of the I controller,
Position control method.
According to claim 1,
Maintaining the gain of the I controller when the position error is within the allowable range
Further comprising,
Position control method.
According to claim 1,
The position transfer function is modeled by current command,
Position control method.
According to claim 1,
The friction torque applied to the position controller is
Coulomb friction torque of gears and joints included in the controlled system;
Static friction torque of the gear and joint; And
Strebeck speed
Modeled based on at least one of the
Position control method.
The method of claim 5,
The friction torque applied to the position controller is

-T _{ge _ col} is coulomb friction torque of gear and joint, T _{ge _ sta} is static friction torque of gear and joint ,

_s is the Strebeck speed ,

_r is the current speed
Modeled as,
Position control method.
A computer program stored in a computer readable recording medium in combination with hardware to execute the method of claim 1.
One or more processors;
Memory; And
One or more programs stored in the memory and configured to be executed by the one or more processors,
The above program,
Obtaining the output of the P controller and the output of the I controller;
Detecting a position error of the output of the P controller based on an allowable range for an error of a predetermined reference position;
Setting the gain of the I controller to a predetermined value when the position error reaches the boundary of the allowable range; And
Outputting the position control transfer function using the output of the P controller and the output of the set gain of the I controller,
Position controller.
The method of claim 8,
The predetermined value is
A value that reduces the gain of the I controller,
Position controller.
The method of claim 8,
The above program,
Maintaining the gain of the I controller when the position error is within the allowable range,
Position controller.

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