Phased array antenna for low-orbit satellite communication in motion and control method thereof

Abstract

The present invention discloses a phased array antenna for low-orbit satellites in motion and a control method thereof. The antenna comprises an antenna body, a mechanical steering compensation mechanism, and a controller. The mechanical steering compensation mechanism comprises an antenna mounting platform, a steering actuator, and a base. The antenna body is fixed to the antenna mounting platform, which is connected to the base via a steering actuator. The steering actuator drives the antenna mounting platform and the antenna body to rotate on the base. An azimuth sensing unit and a motion sensing unit are provided on the antenna mounting platform. The antenna body, the steering actuator, the azimuth sensing unit, and the motion sensing unit are electrically connected to the controller. The present invention uses a mechanical steering actuator to perform angle compensation before the antenna body scans according to the direction of satellite movement; performs attitude correction before the antenna body scans to isolate the carrier from shaking; expands the phased array pointing scanning range, achieves fast tracking speed, and meets the requirements of shipborne and low-orbit use.

Description

Technical Field

[0001] The present invention relates to a phased array antenna and a control method thereof, and in particular to a communication-in-motion phased array antenna for a low-orbit satellite and a control method thereof. Background Art

[0002] Existing shipborne dynamic communication antenna products are used for high-orbit geostationary satellite communications. They generally adopt the form of a three-axis servo turntable and a reflector antenna combination. The three-axis rotation is used to isolate the pitch, roll, and heading motion of the ship, so that the reflector antenna can stably point to the geostationary satellite.

[0003] Low-orbit satellites are usually communication satellite constellations composed of hundreds or more communication satellites. When looking at satellites from the ground, high-orbit geostationary satellites are stationary, while low-orbit satellites are moving rapidly. When the satellite tracked by the current ship-borne mobile communication antenna leaves the sky view, it needs to be re-pointed to another satellite in the sky view. Due to the speed limit of the servo turntable, it takes a certain amount of time to point to the new satellite, usually seconds to tens of meters per second, at which time communication will be interrupted.

[0004] Phased array antennas use electronically controlled scanning to adjust their pointing direction, enabling re-pointing in microseconds to milliseconds, effectively preventing communication interruptions. However, the scanning range of a phased array antenna is typically limited to ±60° from the normal. The motion of the carrier ship further reduces this range, making it unsuitable for tracking large-scale movements of low-orbit satellites. Therefore, existing technology needs improvement. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a moving phased array antenna for low-orbit satellites and a control method thereof. A mechanical steering actuator is used to perform angle compensation and attitude correction according to the direction of satellite movement to isolate the shaking of the carrier, thereby expanding the pointing scanning range of the phased array to meet the needs of shipborne and low-orbit use.

[0006] The technical solution adopted by the present invention to solve the above-mentioned technical problems is to provide a moving phased array antenna for low-orbit satellites, including an antenna body, a mechanical steering compensation mechanism and a controller. The mechanical steering compensation mechanism includes an antenna mounting platform, a steering execution unit and a base. The base is fixedly mounted on a moving carrier, and the antenna body is fixed on the antenna mounting platform. The antenna mounting platform is connected to the base through the steering execution unit, and the steering execution unit drives the antenna mounting platform and the antenna body to rotate on the base; an azimuth sensing unit and a motion sensing unit are arranged on the antenna mounting platform, and the antenna body, the steering execution unit, the azimuth sensing unit and the motion sensing unit are electrically connected to the controller.

[0007] Furthermore, the antenna body transmits and receives electromagnetic waves for satellite communications, the azimuth sensing unit and the motion sensing unit obtain the azimuth and attitude information of the antenna body and send it to the controller; the steering execution unit drives the antenna mounting platform and the antenna body to perform pitch and roll movements relative to the base; the controller controls the antenna body to adjust the electronic scanning angle and controls the steering execution unit to adjust the attitude and azimuth of the antenna body through the electromagnetic energy information received by the antenna body; the adjustment range of the electronic scanning angle of the antenna body is ±60° in the normal direction.

[0008] Furthermore, the orientation sensing unit includes a GNSS dual-antenna direction-finding module and / or a gyrocompass, and the orientation sensing unit detects the orientation of the antenna body in real time; the motion sensing unit includes a three-axis accelerometer and a three-axis gyroscope, and the motion sensing unit detects the posture of the antenna body in real time.

[0009] Furthermore, the steering execution unit includes at least three electric push rods, which are connected to the base and the antenna installation platform through kinematic pairs. The posture of the antenna installation platform can be adjusted by adjusting the length of the electric push rods.

[0010] Furthermore, the steering execution unit includes an external motion frame and an internal motion frame, the external motion frame is connected to the base and is driven by an external frame motor to perform pitch motion relative to the base; the internal motion frame is arranged in the external motion frame to perform pitch motion with the external motion frame, and the external motion frame is provided with an inner frame motor, the inner frame motor and the outer frame motor are perpendicular to each other in the plane where the external motion frame is located, the inner frame motor drives the internal motion frame to rotate to constitute a rolling motion perpendicular to the pitch motion, and the antenna mounting platform is fixed in the internal motion frame.

[0011] Another technical solution adopted by the present invention to solve the above-mentioned technical problems is to provide a control method for a moving phased array antenna for low-orbit satellites, which is characterized in that it includes the following steps: S1: the controller reads the data of the azimuth sensing unit and the motion sensing unit to obtain the current azimuth and attitude information of the antenna body; S2: the controller controls the steering execution unit to perform attitude correction and / or attitude compensation on the antenna body; S3: the controller calculates the azimuth and pitch angle of the satellite in the antenna body coordinate system based on the azimuth information, attitude information and satellite ephemeris information of the antenna body, and controls the radio beam of the antenna body to point to the satellite; S4: after the antenna body receives the satellite signal, the controller controls the antenna body to perform electronic scanning around the satellite to find the azimuth of the electromagnetic energy signal with the strongest signal, and controls the radio beam of the antenna body to always point to the azimuth of the electromagnetic energy signal with the strongest signal, so as to realize continuous tracking of the satellite signal; S5: repeat steps S1, S2 and S4 to enable the antenna body to communicate continuously with the satellite.

[0012] Furthermore, the posture correction of the antenna body in step S2 includes the steering execution unit adjusting the posture of the antenna body so that the antenna body moves in a direction of decreasing pitch and roll angles until the pitch and roll angles of the antenna body detected by the motion sensing unit reach zero. This allows the antenna body to be dynamically controlled to perform posture corrections while the posture of the moving carrier is constantly changing, ensuring that the antenna body remains horizontal.

[0013] Furthermore, the attitude compensation of the antenna body in step S2 includes: the controller predicts the current satellite movement direction based on the satellite ephemeris information, and before the satellite reaches the phased array scanning boundary, presets the attitude compensation angle x of the antenna body, and the steering execution unit adjusts the antenna body attitude so that the attitude angle of the antenna body increases by x, thereby completing the attitude compensation of the antenna body.

[0014] Furthermore, the attitude correction and attitude compensation of the antenna body in step S2 include: the controller predicts the current satellite movement direction based on the satellite ephemeris information, and presets the attitude compensation angle x of the antenna body before the satellite reaches the phased array scanning boundary. The steering execution unit adjusts the attitude of the antenna body so that the attitude of the antenna body moves in a direction close to the attitude compensation angle x, until the attitude angle of the antenna body detected by the azimuth sensing unit and the motion sensing unit is the attitude compensation angle x, thereby dynamically controlling the antenna body to perform attitude compensation and attitude correction when the attitude of the moving carrier is constantly changing, so that the attitude angle of the antenna body is always the attitude compensation angle x.

[0015] Furthermore, the step S3 includes: S31: using the SGP4 algorithm to calculate the azimuth and pitch angles of the satellite relative to the antenna at the current moment based on the azimuth information of the antenna body and the satellite ephemeris information; S32: calculating the coordinates of the satellite in the geodetic coordinate system based on the azimuth and pitch angles of the satellite relative to the antenna calculated in step S31; S33: obtaining the coordinates of the satellite in the antenna coordinate system through coordinate system transformation based on the attitude information of the antenna body; S34: calculating the azimuth and pitch angles of the satellite in the antenna body coordinate system based on the satellite coordinates obtained in step S23.

[0016] Compared with the prior art, the present invention has the following beneficial effects: the phased array antenna for low-orbit satellites provided by the present invention performs angle compensation according to the satellite movement direction before the antenna body scans through a mechanical steering actuator; performs attitude correction to isolate the shaking of the carrier before the antenna body scans; expands the pointing scanning range of the phased array while reducing the difficulty of real-time scanning of the antenna body; compensation and correction are completed before scanning, do not occupy scanning follow-up time, and the tracking speed is faster, meeting the needs of ship-borne and low-orbit use. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 This is a schematic structural diagram of a phased array antenna for low-orbit satellite communication in motion according to an embodiment of the present invention;

[0018] Figure 2 This is a schematic diagram of a mechanical steering compensation mechanism according to an embodiment of the present invention;

[0019] Figure 3 A schematic diagram of another mechanical steering compensation mechanism according to an embodiment of the present invention;

[0020] Figure 4 This is a flow chart of a method for controlling a moving phased array antenna for a low-orbit satellite according to an embodiment of the present invention.

[0021] In the picture:

[0022] 1. Base; 2. Antenna mounting platform; 3. Electric push rod; 4. External motion frame; 5. External frame motor; 6. Internal motion frame; 7. Internal frame motor. DETAILED DESCRIPTION

[0023] The present invention will be further described below with reference to the accompanying drawings and examples.

[0024] Figure 1 The figure is a schematic diagram of the structure of a phased array antenna for communication in motion for low-orbit satellites according to an embodiment of the present invention.

[0025] See Figure 1 The phased array antenna for low-orbit satellite communication in motion according to an embodiment of the present invention includes an antenna body, a mechanical steering compensation mechanism and a controller. The mechanical steering compensation mechanism includes an antenna mounting platform, a steering execution unit and a base. The antenna body is fixed on the antenna mounting platform, and the antenna mounting platform is connected to the base via the steering execution unit. The base is fixedly mounted on a moving carrier, and the steering execution unit drives the antenna mounting platform and the antenna body to rotate on the base. An azimuth sensing unit and a motion sensing unit are provided on the antenna mounting platform, and the antenna body, the steering execution unit, the azimuth sensing unit and the motion sensing unit are electrically connected to the controller.

[0026] Specifically, the antenna body transmits and receives electromagnetic waves for satellite communications, the azimuth sensing unit and the motion sensing unit obtain the azimuth and attitude information of the antenna body and send it to the controller; the steering execution unit drives the antenna mounting platform and the antenna body to perform pitch and roll movements relative to the base; the controller controls the antenna body to adjust the electronic scanning angle and controls the steering execution unit to adjust the attitude and azimuth of the antenna body through the electromagnetic energy information received by the antenna body; the adjustment range of the electronic scanning angle of the antenna body is ±60° in the normal direction.

[0027] Specifically, the orientation sensing unit includes a GNSS dual-antenna direction-finding module and / or a gyrocompass, and the orientation sensing unit detects the orientation of the antenna body in real time; the motion sensing unit includes a three-axis accelerometer and a three-axis gyroscope, and the motion sensing unit detects the posture of the antenna body in real time.

[0028] GNSS (Global Navigation Satellite System) refers to the global navigation satellite system. The GNSS dual-antenna direction-finding module carries Beidou antenna and GPS antenna, with high measurement accuracy and accurate positioning and orientation.

[0029] Please also see Figure 2 In one embodiment, the steering actuator unit includes at least three electric push rods 3 connected to the base 1 and the antenna mounting platform 2 via kinematic joints. Adjusting the length of the push rods 3 adjusts the posture of the antenna mounting platform 2. Due to the mechanical limitations of the push rods 3, the steering actuator unit can adjust the angle in each direction within ±90°.

[0030] A kinematic pair is a movable connection between two components that are in direct contact and can produce relative motion. The points, lines, surfaces, and other elements on the two components that are in contact and form the kinematic pair are called kinematic pair elements. Kinematic pairs include ball joints, Hooke's joints, hinges, etc. Kinematic pairs generally include 3-degree-of-freedom kinematic pairs and 6-degree-of-freedom kinematic pairs. The 3-degree-of-freedom kinematic pair connects three electric linear actuators 3, which are connected to the base 1 through a hinge and to the antenna mounting platform 2 through a universal structure such as a ball joint or Hooke's joint. The 6-degree-of-freedom kinematic pair connects six electric linear actuators 3, which are connected to the base 1 through a Hooke's joint and to the antenna mounting platform 2 through a ball joint or Hooke's joint.

[0031] Please also see Figure 3 In another embodiment, the steering execution unit includes an external motion frame 4 and an internal motion frame 6. The external motion frame 4 is connected to the base 1 and is driven by the external frame motor 5 to perform pitch motion relative to the base 1. The external motion frame 4 is provided with an internal frame motor 7. The internal frame motor 7 and the external frame motor 5 are perpendicular to each other in the plane of the external motion frame 4. The internal frame motor 7 drives the internal motion frame 6 to rotate, forming a rolling motion perpendicular to the pitch motion. The antenna mounting platform is fixed in the internal motion frame 6. The rotation range of the internal motion frame 6 and the external motion frame 4 is 0°-360°.

[0032] See Figure 4 The control method of the phased array antenna for low-orbit satellite communication in motion according to the embodiment of the present invention includes the following steps:

[0033] S1: The controller reads the data of the orientation sensor unit and the motion sensor unit to obtain the current orientation and posture information of the antenna body;

[0034] S2: The controller controls the steering execution unit to perform posture correction and / or posture compensation of the antenna body;

[0035] S3: The controller calculates the azimuth and elevation angles of the satellite in the antenna body coordinate system based on the antenna body's azimuth information, attitude information, and satellite ephemeris information, and controls the antenna body's radio beam to point toward the satellite.

[0036] S4: After the antenna body receives the satellite signal, the controller controls the antenna body to perform electronic scanning around the satellite to find the direction of the strongest electromagnetic energy signal, and controls the radio beam of the antenna body to always point to the direction of the strongest electromagnetic energy signal, so as to achieve continuous tracking of the satellite signal;

[0037] S5: Repeat steps S1, S2 and S4, so that the antenna body continues to communicate with the satellite.

[0038] Specifically, the antenna body's posture correction in step S2 includes the following: the steering execution unit adjusts the antenna body's posture so that the antenna body moves in a direction that reduces the pitch and roll angles until the pitch and roll angles detected by the motion sensing unit reach zero. This dynamically controls the antenna body for posture correction as the motion carrier's posture continuously changes, ensuring that the antenna body remains horizontal, isolating the impact of the ship's swaying.

[0039] Specifically, step S2 of antenna body attitude compensation involves: a controller predicting the current satellite movement direction based on satellite ephemeris information and, in combination with the current ship motion, presetting the antenna body's attitude compensation angle x before the satellite reaches the phased array scanning boundary. The steering execution unit then adjusts the antenna body's attitude to increase the antenna body's attitude angle by x, completing the antenna body attitude compensation. Since the antenna body's electronic scanning angle adjustment range is ±60° from the normal, the phased array scanning boundary is ±60° from the normal to the antenna body.

[0040] Specifically, the attitude correction and attitude compensation of the antenna body in step S2 include: the controller predicts the current satellite movement direction based on the satellite ephemeris information, and combines the current ship shaking situation to preset the attitude compensation angle x of the antenna body before the satellite reaches the phased array scanning boundary. When the hull shaking angle is y, that is, the antenna body attitude is x+y and thus deviates from the compensation angle x, the steering execution unit adjusts the antenna body attitude so that the attitude of the antenna body moves in a direction close to the attitude compensation angle x, until the attitude angle of the antenna body detected by the azimuth sensing unit and the motion sensing unit is the attitude compensation angle x, thereby isolating the ship shaking angle y, and thus dynamically controlling the antenna body to perform attitude compensation and attitude correction when the attitude of the moving carrier is constantly changing, so that the attitude angle of the antenna body is always the attitude compensation angle x.

[0041] Specifically, step S3 includes:

[0042] S31: Calculate the azimuth and elevation angles of the satellite relative to the antenna at the current moment using the SGP4 algorithm based on the antenna's position information and satellite ephemeris information.

[0043] The location information of the antenna body, i.e., the longitude and latitude information, is obtained through GPS, the two satellite ephemeris is obtained, and the SGP4 algorithm is used to calculate the azimuth and pitch angle of the satellite relative to the antenna at the current moment.

[0044] S32: Calculate the coordinates of the satellite in the geodetic coordinate system based on the azimuth and elevation angles of the satellite relative to the antenna calculated in step S21;

[0045] S33: Obtain the coordinates of the satellite in the antenna coordinate system through coordinate system transformation according to the attitude information of the antenna body;

[0046] S34: Calculate the azimuth and elevation angles of the satellite in the antenna coordinate system based on the satellite coordinates obtained in step S23.

[0047] In one specific embodiment, the antenna's scanning range along the pitch axis is ±60° normal to the normal, meaning a pitch angle of 30°-150°. When the carrier is a ship, when the ship undergoes long-term pitch motion of ±10° (a ship's motion period is typically several seconds), the antenna's scanning range is superimposed on the ship's motion, resulting in the antenna's output pitch angle being between 40°-160° and 20°-140°. If the satellite's elevation angle is 35°, the antenna will be unable to maintain continuous communication with the satellite.

[0048] Perform attitude correction on the antenna body, control the steering execution unit to adjust the antenna body attitude to move in the direction of zero pitch angle, isolate the impact of ship shaking, and the final output pitch angle of the antenna body is 30°-150°. At this time, the antenna body can maintain continuous communication with the satellite at an elevation angle of 35°.

[0049] To perform attitude compensation for the antenna body, the controller predicts the current satellite movement direction based on the satellite ephemeris information, and presets the attitude compensation angle of the antenna body to a pitch angle of -20°, and the pitch angle of the antenna body to 30°-150°. After controlling the steering execution unit to superimpose the attitude compensation angle, the pitch angle of the antenna body is 10°-130°, and the pitch angle of the ship pitch motion is superimposed by ±10°. Finally, one boundary of the pitch angle is 20°-140°, and the other boundary is 0°-120°. At this time, the antenna body can maintain continuous communication with the satellite at an elevation angle of 35°.

[0050] Perform attitude compensation and attitude correction on the antenna body. The controller predicts the current satellite movement direction based on the satellite ephemeris information, presets the attitude compensation angle of the antenna body to a pitch angle of -20°, and the pitch angle of the antenna body is 30°-150°. After the steering execution unit is controlled to superimpose the attitude compensation angle, the pitch angle of the antenna body is 10°-130°. The steering execution unit is controlled to adjust the antenna body attitude to move in the direction of a pitch angle of -20° to isolate the impact of ship shaking. The final pitch angle output by the antenna body is 10°-130°. At this time, the antenna body can maintain continuous communication with the satellite at an elevation angle of 35°.

[0051] When the currently tracked satellite leaves the sky field of view and a new satellite is tracked, the steering execution unit makes a prediction based on the ephemeris, outputs a new attitude compensation angle in advance, and then further communicates.

[0052] In summary, the moving phased array antenna for low-orbit satellites and the control method thereof of the embodiments of the present invention use a mechanical steering actuator to perform angle compensation according to the satellite's movement direction before the antenna body scans; perform attitude correction to isolate the shaking of the carrier before the antenna body scans; expand the pointing scanning range of the phased array while reducing the difficulty of real-time scanning of the antenna body; compensation and correction are completed before scanning, do not occupy scanning follow-up time, and have a faster tracking speed, meeting the needs of shipborne and low-orbit use.

[0053] Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art may make some modifications and improvements without departing from the spirit and scope of the present invention. Therefore, the scope of protection of the present invention shall be based on the definition of the claims.

Claims

1. A control method for a moving phased array antenna for a low-orbit satellite, characterized in that: The mobile communication phased array antenna includes an antenna body, a mechanical steering compensation mechanism, and a controller. The mechanical steering compensation mechanism includes an antenna mounting platform, a steering execution unit, and a base. The antenna body is fixed to the antenna mounting platform, and the antenna mounting platform is connected to the base via the steering execution unit. The base is fixedly mounted on a moving carrier, and the steering execution unit drives the antenna mounting platform and the antenna body to rotate on the base. An azimuth sensing unit and a motion sensing unit are provided on the antenna mounting platform. The antenna body, the steering execution unit, the azimuth sensing unit, and the motion sensing unit are electrically connected to the controller. The steering execution unit includes at least three electric push rods, which are connected to the base and the antenna installation platform through kinematic pairs. The posture of the antenna installation platform can be adjusted by adjusting the length of the electric push rods. Alternatively, the steering execution unit includes an external motion frame and an internal motion frame, the external motion frame being connected to the base and driven by an external frame motor to perform pitch motion relative to the base; the internal motion frame being arranged in the external motion frame and performing pitch motion along with the external motion frame, the external motion frame being provided with an internal frame motor, the internal frame motor and the external frame motor being perpendicular and orthogonal within the plane where the external motion frame is located, the internal frame motor driving the internal motion frame to rotate to form a rolling motion perpendicular to the pitch motion, and the antenna mounting platform being fixed in the internal motion frame; The control method comprises the following steps: S1: The controller reads the data of the orientation sensor unit and the motion sensor unit to obtain the current orientation and posture information of the antenna body; S2: The controller controls the steering execution unit to perform attitude correction and / or attitude compensation on the antenna body; S3: The controller calculates the azimuth and elevation angles of the satellite in the antenna body coordinate system based on the antenna body's azimuth information, attitude information, and satellite ephemeris information, and controls the antenna body's radio beam to point toward the satellite. S4: After the antenna body receives the satellite signal, the controller controls the antenna body to perform electronic scanning around the satellite to find the direction of the strongest electromagnetic energy signal, and controls the radio beam of the antenna body to always point to the direction of the strongest electromagnetic energy signal, so as to achieve continuous tracking of the satellite signal; S5: Repeat steps S1, S2, and S4 to ensure continuous communication between the antenna body and the satellite; The posture correction of the antenna body in step S2 includes: the steering execution unit adjusting the posture of the antenna body so that the posture moves in a direction of decreasing pitch angle and roll angle until the pitch angle and roll angle of the antenna body detected by the motion sensing unit are zero, thereby dynamically controlling the antenna body to perform posture correction when the posture of the moving carrier is constantly changing, so that the antenna body is always in a horizontal state; The attitude correction and attitude compensation of the antenna body in step S2 include: the controller predicts the current satellite movement direction based on the satellite ephemeris information, and presets the attitude compensation angle x of the antenna body before the satellite reaches the phased array scanning boundary. The steering execution unit adjusts the attitude of the antenna body so that the attitude of the antenna body moves in a direction close to the attitude compensation angle x, until the attitude angle of the antenna body detected by the azimuth sensing unit and the motion sensing unit is the attitude compensation angle x, thereby dynamically controlling the antenna body to perform attitude compensation and attitude correction when the attitude of the moving carrier is constantly changing, so that the attitude angle of the antenna body is always the attitude compensation angle x.

2. The control method for a phased array antenna for low-orbit satellite communication in motion according to claim 1, wherein: The antenna body transmits and receives electromagnetic waves for satellite communications, the azimuth sensing unit and the motion sensing unit obtain the azimuth and attitude information of the antenna body and send them to the controller; the steering execution unit drives the antenna mounting platform and the antenna body to perform pitch and roll movements relative to the base; the controller controls the antenna body to adjust the electronic scanning angle and controls the steering execution unit to adjust the attitude and azimuth of the antenna body through the electromagnetic energy information received by the antenna body; the adjustment range of the electronic scanning angle of the antenna body is ±60° in the normal direction.

3. The control method for a phased array antenna for low-orbit satellite communication in motion according to claim 1, wherein: The orientation sensing unit includes a GNSS dual-antenna direction-finding module and / or a gyrocompass, and the orientation sensing unit detects the orientation of the antenna body in real time; the motion sensing unit includes a three-axis accelerometer and a three-axis gyroscope, and the motion sensing unit detects the posture of the antenna body in real time.

4. The control method for a phased array antenna for low-orbit satellite communication in motion according to claim 1, wherein: The step S3 comprises: S31: Calculate the azimuth and elevation angles of the satellite relative to the antenna at the current moment using the SGP4 algorithm based on the antenna body's azimuth information and satellite ephemeris information; S32: Calculate the coordinates of the satellite in the geodetic coordinate system based on the azimuth and elevation angles of the satellite relative to the antenna calculated in step S31; S33: Obtaining the coordinates of the satellite in the antenna coordinate system through coordinate system transformation according to the attitude information of the antenna body; S34: Calculate the azimuth and elevation angles of the satellite in the antenna body coordinate system based on the satellite coordinates obtained in step S23.

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