A solid rocket first-stage separation body landing area control system and method

Abstract

The present invention relates to a control system and method for a solid rocket first-stage separation body landing area, wherein the control system includes a grid rudder control system and a measurement and control communication system; the grid rudder control system includes an inertial navigation controller, an integrated controller, a steering gear and a battery; the measurement and control communication system includes a GNSS / BD2 receiving device, a collection and editing device, a telemetry transmitting device and a battery; compared with the traditional offline binding standard trajectory method, the integration process of the online trajectory planning method provided by the present invention is based on the actual flight state at the separation moment to perform trajectory planning, and the initial value of the integration is more accurate, so the obtained standard trajectory is closer to the actual flight environment, and the range of the landing area is reduced. The online trajectory planning method can select the nearest target landing point for trajectory planning according to the actual flight state, which can greatly reduce the pressure on the guidance and control system and improve the safety and flight quality of the flight process.

Description

Technical Field

[0001] The invention relates to the field of solid rocket landing area control design, and in particular to a solid rocket first-stage separation body landing area control system and method. Background Art

[0002] After the launch of a traditional multi-stage solid rocket, the first-stage engine separates and falls after the work is completed, and finally falls to the ground or inland. Since most of my country's solid carrier rocket launch bases are inland, the falling sites of the separated bodies are all on land. Although the rocket will consider avoiding the separation body landing area covering railways, roads, villages and cities when planning and designing the trajectory, due to the large distribution range of the landing points, there is still a possibility of threatening the safety of residents' lives and property. At present, the usual practice is to control the separation body landing area by adjusting the rocket's flight trajectory, controlling the first-stage separation height, separation posture, etc. However, the disadvantage of this method is that the rocket will lose some of its carrying capacity, and the ability to control the landing area through this passive control method is limited. When it is really impossible to avoid the first-stage separation body falling in the village, the local relevant departments need to invest a lot of manpower, material and financial resources to evacuate the residents.

[0003] When the flight state of the first stage of the rocket deviates greatly from the standard ballistic state bound before launch, the initial position velocity of the first-stage separation body will have a large deviation. The initial position velocity is used as the initial value of integration, and the deviation of the initial value of integration will be transmitted to the end point of integration through the integration process. Therefore, the traditional offline binding trajectory method will result in a large drop point dispersion. At the same time, the large difference between the actual flight environment and the offline ballistic calculation environment will bring greater pressure to the rocket guidance and control system.

[0004] In order to solve the safety and adaptability problems of the first-stage separation body landing area, and at the same time to address the shortcomings of the passive landing area control method, the present invention proposes a solid rocket first-stage separation body landing area control system and method. Summary of the invention

[0005] The purpose of the present invention is to provide a control system and method for the landing area of ​​a first-stage separation body of a solid rocket, to actively control the landing area of ​​the first-stage separation body, and to improve the safety of rocket launch and adaptability to missions.

[0006] A control system for a landing area of ​​a first-stage separation body of a solid rocket, wherein the first-stage separation body comprises a grid rudder, and the control system comprises a grid rudder control system and a measurement, control and communication system;

[0007] The grid rudder control system includes an inertial navigation controller, an integrated controller, a steering gear and a battery; the inertial navigation controller can sense the attitude information of the first-stage separation body, perform trajectory planning and stability calculation, and output steering control instructions; the integrated controller receives the control instructions sent by the inertial navigation controller, completes steering gear control and timing control, and enables the grid rudder to move as required; the battery is used to power each device;

[0008] The measurement and control communication system includes a GNSS / BD2 receiving device, a data acquisition device, a telemetry transmitting device and a battery; the GNSS / BD2 receiving device is used to receive GPS / BD2 satellite signals and measure the trajectory of the separated body; the data acquisition device mainly functions to unify and frame the position information of the first-level separated body and the information in the inertial navigation controller; the telemetry transmitter and the telemetry transmitting antenna modulate, amplify and transmit the telemetry information; the battery is used to power each device.

[0009] Furthermore, the grid rudder control system adopts a dual-bus architecture, the control bus mainly transmits control instructions, and the test bus mainly transmits control instructions and telemetry information of the control bus. The two buses are redundant hot backups for each other and are completely isolated physically.

[0010] Furthermore, the individual devices of the grid rudder control system and the measurement, control and communication system are all installed in the tail section to avoid the equipment being separated and heated by heat flow during the falling process.

[0011] The present invention also provides a method for controlling the landing area of ​​a first-stage separation body of a solid rocket, which adopts the above-mentioned control system and specifically includes two control stages: Stage 1 is an attitude stabilization stage, in which the flipping of the separation body is controlled by a correction network of a double-loop feedback of an attitude angle and an attitude angular rate in the early stage after the first-stage separation, so that the separation body is restored to a stable flight state;

[0012] Phase 2 is the reentry flight phase, during which the control system effectively controls the flight of the rocket body through attitude angle (i.e., pitch angle, yaw angle, and roll angle) feedback, so that the separated body flies according to the planned reentry trajectory.

[0013] The reference landing point is obtained by integrating the zero attack angle and zero sideslip state of the separation body, and then the distance between the reference landing point and each candidate landing point bound before firing is determined, and the nearest candidate landing point is selected as the target landing point. Based on this, the flight attack angle and sideslip angle required for the separation body to reach the target landing point are calculated, thereby designing the real-time reentry trajectory of the first-stage separation body.

[0014] Furthermore, the method for judging whether to enter stage 2 from stage 1 is as follows: when the three attitude rates of the first-stage separation body sensitive to the inertial navigation controller are less than 5° / s for 2 consecutive seconds, it is judged that the separation body flight enters stage 2 from stage 1.

[0015] Furthermore, the real-time reentry trajectory design method of the first-stage separation body is:

[0016] Since the first-stage separation body has no thrust during flight, and the effect of aerodynamic ablation is ignored, it is assumed that the mass does not change during flight. Therefore, the motion equation during flight is expressed in the launch coordinate system as follows:

[0017]

[0018] Where v is the velocity vector in the launch coordinate system, r is the position vector in the launch coordinate system, is the derivative of v, is the derivative of r;

[0019] g is the earth's gravitational acceleration vector, which is only related to the earth's center vector R, which can be obtained by R = r + Re0;

[0020] C is the acceleration vector caused by aerodynamic force, which is determined by the flight angle of attack α and the sideslip angle β;

[0021] The variable step length fourth-order Long Kutta integration method is used, with the current actual flight speed and position as the initial value of the integration. The integration termination condition is that the flight altitude is zero. According to the control strategy of zero angle of attack and zero sideslip angle, the integration end point coordinates (x0, y0) can be obtained. Assuming that there are n landing points to be selected, the coordinates are: (x1, y1)...(x i ,y i )...(x n ,y n ), then the distance between the reference point and the i-th candidate point can be expressed as Select the point with the shortest distance as the target point (x b ,y b ), according to the current flight status, the attack angle α and sideslip angle β required to reach the target landing point are obtained through iterative solution, thereby determining the target reentry trajectory.

[0022] Furthermore, in stage 1, the attitude angle increment of the separated body is first obtained by the inertial navigation controller. ψ1, γ1 (pitch angle, yaw angle and roll angle), after tool error compensation calculation and navigation calculation, the quaternion corresponding to the attitude angle of the separated body is obtained, and compared with the quaternion corresponding to the program attitude angle to form an angle deviation Δψ1, Δγ1, the angular deviation is corrected by the gain K1 of the correction network; the attitude angular rate of the separated body is obtained by the inertial navigation controller ( They are ψ1, γ1 derivative), the gain K2 of the correction network is used as negative feedback to synthesize the control command with the angle deviation after gain P ψ , P γ , of the following form:

[0023]

[0024]

[0025]

[0026] The output pitch and yaw channel control commands are filtered. The filtering algorithm adopts a combination of notch filter and low-pass filter to attenuate the interference signal of the elastic vibration of the first-stage separation body, thereby outputting the grid rudder yaw command signal. The actual rudder deviation is then output through the grid rudder system. Controlling the posture of the first-stage separation body;

[0027] Furthermore, the notch filter transfer function model is:

[0028]

[0029] where ω j is the notch frequency, is the notch depth, the center frequency of the notch filter is selected according to the natural frequency of the elastic motion of the first-order separation body, and the elastic motion amplitude in a large frequency range near the natural frequency is effectively attenuated by designing multiple notch filters in series near the corresponding order elastic natural frequency. The low-pass filter is directly designed in the discrete domain, so that the amplitude attenuation filtering is achieved in the frequency range above the notch filter design frequency point under the condition of reducing the intermediate frequency phase lag.

[0030] Further, taking the pitch channel as an example, the stage 2 first obtains the attitude angle increment of the separated body through the inertial navigation controller ψ2, γ2 (pitch angle, yaw angle and roll angle), after tool error compensation calculation and navigation calculation, the quaternion corresponding to the attitude angle of the separated body is obtained, and compared with the quaternion corresponding to the program attitude angle to form an angle deviation Δψ2 and Δγ2 are filtered, and the filtering algorithm adopts the same notch filter and low-pass filter combination design as stage 1; the correction network is a single-loop control, the input is the filtered angle deviation, and the output is the grid rudder command signal Finally, the grid rudder system outputs the actual rudder deviation. Thereby controlling the posture of the first-stage separation body;

[0031] Furthermore, the selection principle of the optional target landing point for pre-shooting binding is: if there are no railways, roads, villages and cities within the landing area of ​​the first-level separation body, and the landing area requirements are fully met, the center point of the landing area is selected as the target landing point; if there are a small number of railways, roads, villages and cities within the landing area of ​​the first-level separation body, the above-mentioned places are avoided as the principle, and multiple target landing points are selected in a dispersed manner within the landing area.

[0032] Compared with the traditional off-line binding standard trajectory method, the integration process of the online trajectory planning method provided by the present invention is based on the actual flight state at the separation moment to perform trajectory planning, and the initial value of the integration is more accurate, so the obtained standard trajectory is closer to the actual flight environment, which can effectively reduce the landing area; on the other hand, the online trajectory planning method can select the nearest target landing point for trajectory planning according to the actual flight state, especially when the actual flight state is greatly different from the standard state, which can greatly reduce the pressure on the guidance and control system and improve the safety and flight quality of the flight process. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 It is a schematic diagram of the primary separation body;

[0034] Figure 2 This is the block diagram of the attitude control principle in stage 1;

[0035] Figure 3 This is the principle block diagram of stage 2 attitude control.

[0036] Explanation of symbols: 1-first stage engine, 2-tail section, 3-grid rudder. DETAILED DESCRIPTION

[0037] The present invention provides a solid rocket first-stage separation body landing area control system, including a grid rudder control system and a measurement and control communication system. The grid rudder control system includes an inertial navigation controller, an integrated controller, a steering gear and a battery, and the measurement and control communication system includes a GNSS / BD2 receiving device, a collection and editing device, a telemetry transmitting device and a battery.

[0038] The first-stage separator is a separator with a grid rudder at the tail section, such as Figure 1 As shown;

[0039] To avoid heat flow heating during separation and fall, the individual devices of the grid rudder control system and the measurement, control and communication system are installed in the tail section;

[0040] The grid rudder control system adopts a dual-bus architecture. The control bus mainly transmits control instructions, and the test bus mainly transmits control instructions and telemetry information of the control bus. The two buses are completely isolated physically, and serve as redundant hot backups for each other. The control system is powered by batteries. The inertial navigation controller has the functions of an inertial group and a central computer. It can sense the attitude information of the first-stage separation body, perform trajectory planning and stability calculations, and output rudder control instructions. The main function of the integrated controller is to receive control instructions from the inertial navigation controller, complete servo control and timing control, and enable the grid rudder to move as required.

[0041] The measurement, control and communication system adopts ground-based telemetry and GPS / BD2 external measurement solutions, and is powered by batteries. The GNSS / BD2 receiving device is used to receive GPS / BD2 satellite signals and measure the trajectory outside the separated body. The main function of the editor is to unify and frame the position information of the first-level separated body and the information in the inertial navigation controller. The telemetry transmitter and telemetry transmitting antenna modulate, amplify and transmit the telemetry information.

[0042] The control includes two stages: Stage 1 is the attitude stabilization stage, which is the initial stage after the first stage separation. In this stage, the separation body is affected by the separation disturbance and the motion state is unstable. Therefore, it is first restored to a stable flight state through attitude control for a period of time; Stage 2 is the reentry flight stage. In this stage, the control capability covers the interference force, and the control system can effectively control the flight of the rocket body so that the separation body can fly according to the planned reentry trajectory. The judgment method for the two stages is: when the three attitude rates (pitch, yaw and roll) of the first stage separation body that the inertial navigation controller is sensitive to are less than 5° / s for 2 consecutive seconds, it is judged that the flight of the first stage separation body has entered stage 2 from stage 1.

[0043] The landing area control method specifically includes an online trajectory planning method and a posture control method.

[0044] The online trajectory planning method is as follows: in stage 1, no online calculation and planning is performed on the trajectory of the separation body. When it is determined that the flight enters stage 2, starting from the starting moment, the reference landing point is calculated in real time based on the current flight position and speed of the first-stage separation body at intervals. The target landing point is selected based on the degree of match between the reference landing point and the candidate landing point bound before shooting, and then the re-entry flight trajectory is planned in real time based on the target landing point.

[0045] The principle for selecting the optional target landing points before shooting is as follows: if there are no railways, roads, villages and cities within the landing area of ​​the first-level separation body, and the landing area requirements are fully met, the center point of the landing area is selected as the target landing point; if there are a small number of railways, roads, villages and cities within the landing area of ​​the first-level separation body, the principle of avoiding the above-mentioned places is adopted, and multiple landing points to be selected are selected in a dispersed manner within the landing area.

[0046] The planning method of the reentry flight trajectory is as follows: after the first-stage separation body resumes stable flight, the current position and flight speed are determined by the inertial navigation controller at regular intervals, and the reference landing point is obtained by integrating the zero attack angle and zero sideslip state of the first-stage separation body. Then, the distance between the reference landing point and each candidate landing point bound before firing is determined, and the nearest candidate landing point is selected as the target landing point. Based on this, the flight attack angle and sideslip angle of the first-stage separation body are calculated, thereby designing the real-time reentry trajectory of the first-stage separation body.

[0047] Specifically, the real-time reentry trajectory design method of the first-stage separation body is:

[0048] The equation of motion during flight is expressed in the launch coordinate system as follows:

[0049]

[0050] Where v is the velocity vector in the launch coordinate system, r is the position vector in the launch coordinate system, is the derivative of v, is the derivative of r;

[0051] g is the earth's gravitational acceleration vector, which is only related to the earth's center vector R, which is obtained by R = r + Re0;

[0052] C is the acceleration vector caused by aerodynamic force, which is determined by the flight angle of attack α and the sideslip angle β;

[0053] Assume that there are n points to be selected, and their coordinates are: (x1, y1)...(x i ,y i )...(x n ,y n ), using the fourth-order Longo Kutta integration method with variable step size:

[0054] Assume that the problem to be solved is

[0055]

[0056] q(t0)=q0

[0057] q is the integral state quantity, is the derivative of q, t is the integration time;

[0058] According to the solution accuracy, a suitable integration step length h is selected, and the iterative process can be expressed as:

[0059]

[0060] The initial condition of integration q0 is the current flight position r, velocity vector v, j represents the time, and the position and velocity at the subsequent flight time can be obtained through the above iteration, thereby determining the flight trajectory. The current actual flight speed and position are used as the initial value of integration, and the integration termination condition is that the flight altitude is zero (that is, the first-stage separation body falls to the ground). According to the control strategy of zero angle of attack and zero sideslip angle, the above integration method can be used to obtain the integration end point coordinates (x0, y0); assuming that there are n landing points to be selected, the coordinates are: (x1, y1)...(x i ,y i )...(x n ,y n ), then the distance between the reference point and the i-th candidate point can be expressed as Select the point with the shortest distance as the target point (x b ,yb ), according to the current flight status, the target landing point coordinates (x b ,y b )’s angle of attack α and sideslip angle β, thereby determining the target’s reentry trajectory.

[0061] The attitude control method is as follows: The main purpose of attitude control in stage 1 is to stabilize the flight attitude of the first-stage separation body. The Mach number is high during separation, and the first-stage separation body is in a statically unstable state. It will flip when disturbed by separation. At this time, the attitude control controls the flipping of the first-stage separation body through the correction network of the double-loop feedback of the attitude angle and the attitude angular rate. As the control ability gradually increases and covers the interference force, the first-stage separation body will return to a stable flight state.

[0062] Specifically, the dual-loop feedback correction network and control principle, taking the pitch channel as an example, the control principle block diagram is as follows Figure 2 As shown in the figure, when the pitch angle rate is large (>5° / s), the pitch angle increment of the separated body is sensitive to the inertial navigation controller. After tool error compensation calculation and navigation calculation, the quaternion corresponding to the attitude angle of the first-level separation body is obtained and compared with the quaternion corresponding to the program attitude angle to form an angle deviation The angular deviation is corrected by the gain K1 of the correction network; the pitch rate of the separated body is sensed by the inertial navigation controller The gain K2 of the correction network is used in the form of negative feedback to the pitch angle deviation after gain The synthetic control instruction is as follows:

[0063]

[0064] The filtering algorithm adopts a combination of notch filter and low-pass filter to attenuate the interference signal of the elastic vibration of the first-stage separation body, so as to output the control command as the grid rudder deflection command signal. The actual rudder deviation is then output through the grid rudder system. Control the posture of the first-stage separation body.

[0065] Specifically, the notch filter transfer function model is:

[0066]

[0067] where ω j is the notch frequency, is the notch depth (ξ1 is the inherent elastic damping ratio of the separation body, ξ2 is the design damping ratio, and the difference is the notch depth). The center frequency point of the notch filter is selected according to the natural frequency of the elastic motion of the first-order separation body. By designing a plurality of notch filters in series near the corresponding order elastic natural frequency, the elastic motion amplitude in a large frequency range near the natural frequency is effectively attenuated. The low-pass filter is directly designed in the discrete domain, so that under the condition of reducing the intermediate frequency phase lag, amplitude attenuation filtering is realized in the frequency range above the design frequency point of the notch filter.

[0068] The main purpose of the attitude control in stage 2 is to adjust the attitude of the separated body to follow the online planned reentry trajectory so as to achieve control of the landing area. This stage adopts attitude angle feedback control. Taking the pitch channel as an example, the control principle block diagram of the attitude angle feedback is as follows: Figure 3 As shown, the pitch angle increment is output by the inertial navigation controller After tool error compensation calculation and navigation calculation, the quaternion corresponding to the attitude angle of the first-level separation body is obtained, and compared with the quaternion corresponding to the program attitude angle to form an angle deviation The filtering algorithm also adopts the combination of notch filter and low-pass filter; the correction network is single-loop control, and the input is the filtered Output is grid rudder command signal Finally, the grid rudder system outputs the actual rudder deviation. Thereby the posture of the first-stage separation body is controlled.

Claims

1. A method for controlling the landing area of ​​a first-stage separation body of a solid rocket, wherein the first-stage separation body includes a grid rudder, characterized in that: A solid rocket first-stage separation body landing area control system is used, and the control system includes a grid rudder control system and a measurement, control and communication system; The grid rudder control system includes an inertial navigation controller, an integrated controller, a steering gear and a battery; the inertial navigation controller can sense the attitude information of the first-stage separation body, perform trajectory planning and stability calculation, and output steering control instructions; the integrated controller receives the control instructions sent by the inertial navigation controller, completes the steering gear control and timing control, so that the grid rudder moves as required; the battery is used to power each device; The measurement and control communication system includes a GNSS / BD2 receiving device, a collection and editing device, a telemetry transmitting device and a battery; the GNSS / BD2 receiving device is used to receive GPS / BD2 satellite signals to measure the trajectory of the separated body; the collection and editing device aggregates and frames the position information of the first-level separated body and the information in the inertial navigation controller; the telemetry transmitter and the telemetry transmitting antenna modulate, amplify and transmit the telemetry information; The control method includes two control stages: Stage 1 is an attitude stabilization stage, in which the flipping of the separated body is controlled by a correction network of a double-loop feedback of attitude angle and attitude angular rate in the early stage after the first stage separation, so as to restore the stable flight state; Phase 2 is the reentry flight phase, during which the control system effectively controls the flight of the rocket body through attitude angle feedback, so that the separated body flies according to the planned reentry trajectory; The reentry trajectory planning method is as follows: a reference landing point is obtained by integrating the zero attack angle and zero sideslip state of the separation body, and then the distance between the reference landing point and each candidate landing point bound before firing is determined, and the candidate landing point with the closest distance is selected as the target landing point. Based on this, the flight attack angle and sideslip angle required for the first-stage separation body to reach the target landing point are calculated, thereby designing the real-time reentry trajectory of the first-stage separation body; The real-time reentry trajectory design method of the first-stage separation body is: The equation of motion during flight is expressed in the launch coordinate system as follows: Where v is the velocity vector in the launch coordinate system, r is the position vector in the launch coordinate system, is the derivative of v, is the derivative of r; g is the earth's gravitational acceleration vector, which is only related to the earth's center vector R. The earth's center vector R is obtained by R = r + Re0, where Re0 is the earth's center vector diameter at the launch point; C is the acceleration vector caused by aerodynamic force, which is determined by the flight angle of attack α and the sideslip angle β; The variable step length fourth-order Long Kutta integration method is used, the current actual flight speed and position are used as the initial value of the integration, the integration termination condition is that the flight altitude is zero, and according to the control strategy of zero angle of attack and zero sideslip angle, the integration end point coordinates (x0, y0) are obtained; assuming that there are n landing points to be selected, the coordinates are: (x1, y1)...(x i ,y i )...(x n ,y n ), then the distance between the reference point and the i-th candidate point is expressed as Select the one with the shortest distance as the target point (x b ,y b ), according to the current flight status, the target landing point coordinates (x b ,y b )’s angle of attack α and sideslip angle β, thereby determining the target’s reentry trajectory.

2. A method for controlling the landing area of ​​a first-stage separation body of a solid rocket according to claim 1, characterized in that: The grid rudder control system adopts a dual-bus architecture, wherein the control bus transmits control instructions, and the test bus transmits control instructions and telemetry information of the control bus, and the two buses serve as redundant hot backups for each other.

3. A method for controlling the landing area of ​​a first-stage separation body of a solid rocket according to claim 1, characterized in that: The individual devices of the grid rudder control system and the measurement, control and communication system are all installed in the tail section.

4. A method for controlling the landing area of ​​a first-stage separation body of a solid rocket according to claim 1, characterized in that: The method for judging whether to enter stage 2 from stage 1 is as follows: when the three attitude angular rates of the first-stage separation body sensitive to the inertial navigation controller are less than 5° / s for 2 consecutive seconds, it is judged that the first-stage separation body flight enters stage 2 from stage 1.

5. A method for controlling the landing area of ​​a first-stage separation body of a solid rocket according to claim 1, characterized in that: In the second stage, the attitude angle increment of the separated body is first obtained by the inertial navigation controller. ψ2, γ2, is the pitch angle increment, ψ2 is the yaw angle increment, and γ2 is the roll angle increment. After tool error compensation calculation and navigation calculation, the quaternion corresponding to the attitude angle of the separated body is obtained, which is compared with the quaternion corresponding to the program attitude angle to form an angle deviation. Δψ2, Δγ2, is the pitch angle deviation, Δψ2 is the yaw angle deviation, Δγ2 is the roll angle deviation, and then the pitch and yaw channel signals are filtered. The filtering algorithm is the same as that of stage 1; the correction network is a single-loop control, the input is the filtered angle deviation signal, and the output is the grid rudder command signal Finally, the grid rudder system outputs the actual rudder deviation. Thereby the posture of the first-stage separation body is controlled.

6. A method for controlling the landing area of ​​a first-stage separation body of a solid rocket according to claim 1, characterized in that: The selection principle of the target landing point that can be selected before shooting is: if there are no railways, roads, villages and urban buildings within the landing area of ​​the first-level separation body, and the landing area requirements are fully met, the center point of the landing area is selected as the target landing point; if there are a small number of railways, roads, villages and urban buildings within the landing area of ​​the first-level separation body, the above-mentioned places are avoided as the principle, and multiple target landing points are selected in a dispersed manner within the landing area.

7. A method for controlling the landing area of ​​a first-stage separation body of a solid rocket according to claim 1, characterized in that: The transfer function model of the notch filter is: where ω j is the notch frequency, ξ1 and ξ2 are the notch depths, the center frequency point of the notch filter is selected according to the natural frequency of the elastic motion of the first-order separation body, and the elastic motion amplitude within the frequency range near the natural frequency is effectively attenuated by designing multiple notch filters in series near the corresponding order elastic natural frequency; The low-pass filter is directly designed in the discrete domain, so that the amplitude attenuation filtering can be realized in the frequency range above the design frequency point of the notch filter under the condition of reducing the intermediate frequency phase lag.

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