This paper focuses on the on-line compensation of the disturbance rejection rate (DRR) for a platform seeker. The mathematical model of the typical platform seeker based on the inertial space is established, and the line-of-sight (LOS) rate from different signal extraction points is strictly derived. Considering the spring torque disturbance and damping torque disturbance caused by the missile attitude motion, the seeker DRR transfer functions are deduced and the amplitude and phase characteristics at different frequencies are also analyzed. In order to close the engineering practice, the DRR parasitic loop (DRRPL) model of the seeker is rationally simplified and the stable region of the parasitic loop from different extraction points is also obtained. However, to increase the stability and guidance accuracy of the missile terminal flight, the compensation scheme based on the high-gain extended state observer (ESO) is used to estimate the disturbance torques and eliminate the seeker DRR effect. Numerical simulations are conducted to verify the effectiveness of the proposed scheme. The simulation results show that the seeker DRR effect mainly exists in the middle and low frequencies and the stable region of the parasitic loop at different signal extraction points is different. The proposed compensation scheme can effectively eliminate the parasitic loop effect of the seeker and increase the flight stability of the missile. It can reduce the terminal miss distance of the missile and improve the strike accuracy.
Seekers are the tracking and detecting system of missiles, which are well used to acknowledge and track a target [
The DRR represents the ability of the seeker to isolate the disturbance of the missile body. It not only affects the output accuracy of the LOS rate but also forms an extra parasitic loop in the guidance system, which affects the stability and guidance accuracy [
Obviously, the DRRPL effect of the platform seeker cannot be ignored for the missile’s terminal flight. Improving seeker isolation and reducing the DRR effect have also become an important research field. Two effective methods are proposed by researchers, in which one is to improve the machining accuracy and the other is to design improvements to the seeker control system [
As is well known, disturbance observer (DO) method has been introduced to compensate for strong nonlinearity, unmodeled dynamics, and external disturbances of uncertain systems [
Furthermore, Wangze [
The schematic diagram of the platform seeker is as depicted in Figure
The structure of the platform seeker.
Wire disturbance
The angle relationship of the pitch plane
The schematic diagram of the wire disturbance is illustrated in Figure
Another major disturbance named as the damping torque is related to the rotation angular rate of the seeker platform, which can be expressed as
In Equations (
To form a closed loop for the stable platform, the LOS rate in the inertia space feedback is acquired via the rate gyro. The schematic diagram of a typical platform seeker tracking control system is shown in Figure
Schematic diagram of the platform seeker tracking control system.
As shown in Figure
High-frequency dynamics, correction networks, and small values can be neglected in engineering [
In fact, for a perfect seeker, the influence of disturbance
It is obvious from Equation (
The typical parameters of a platform seeker are shown as in Table
Typical parameters of a platform seeker.
Parameter | Value |
---|---|
Tracking loop gain | |
Stable loop gain | |
Inductance | |
Resistance | |
Moment coefficient of servo motor | |
Rotational inertia | |
Back-EMF coefficient |
LOS rate extraction from the C point and S point.
Without any disturbance
Zero deviation of detector
Zero deviation of rate gyro
Zero deviation of servo system
Detector noise
Rate gyro noise
It can be observed from Figure
The DRR represents the capability of the isolation base motion of a missile, which can guarantee a high-precision LOS rate. The smaller the DRR is, the stronger the ability of the isolation base disturbance the seeker has. Thus, the DRR transfer function in Figure
The DRR amplitude ratio of the C point to the S point is
The DRR amplitude ratio of the C point to the S point.
Proportional coordinate
Logarithmic coordinate
By substituting Equations (
Similarly, the DRR transfer functions from the S point can also be obtained as follows:
From Equations (
Based on Equations (
Bode diagrams of the DRR characteristic.
S point under spring torque
S point under damping torque
C point under spring torque
C point under damping torque
According to Figure
In engineering, the seeker DRR model established in Section High-frequency dynamics, correction links, and small values can be neglected in the seeker DRR analysis, i.e., The back-EMF loop is generally small, and thus, it minimally affects seeker control precision Ignoring the rate gyro dynamics and the feedback gain of the stable loop is equal to 1 (i.e., The forward gain of the stable loop is equivalent to
Based on the above assumptions, the schematic diagram of platform seeker shown in Figure
Equivalent block diagram of the DRR.
Defining
Similarly, Equations (
According to Table
First-order DRR transfer function of the seeker.
C point | S point | Equivalent coefficient | |
---|---|---|---|
Damping torque | |||
Spring torque |
In the terminal guidance phase, the seeker provides the guidance signal for the missile. However, if the seeker cannot isolate the body disturbance perfectly, the guidance signal not only includes the real LOS rate but also includes the additional signal
The simple structure of the DRR parasitic loop.
According to Figure
Stable region of the DRRPL.
Damping torque
Spring torque
It can be observed from Figure
Based on the analysis in Section
The specific model of the seeker disturbance torque is ignored, and the influence of the disturbance torque on the tracking control system of the seeker is replaced by the interference angular acceleration
Compensation scheme of DRR.
Based on Figure
Supposing
The error equations between the extended system (see Equation (
Then, considering the following coordinate transformation
Thus, Equation (
Neglecting
Let
According to Definition
Suppose vector field
For any continuous function
If there is a
So there exists
In addition, according to the Routh stability criterion,
Furthermore, to weaken the high-frequency chattering phenomenon in the simulation, the switching functions
As shown in Figure
Analysis of the above compensation process shows that the scheme does not need to pay more attention to the specific form of the disturbance torque model but depends on the accurate dynamic model of the platform seeker. The above compensation scheme is different from that proposed in reference [
In this section, numerical simulations are conducted to validate the effectiveness of the proposed compensation scheme. The DRR compensation effect is analyzed under different disturbance models. Secondly, the proposed DRR compensation scheme is applied to the missile guidance flight process, and its impact on miss distance is also analyzed.
The desired LOS rate which is
Disturbance angular acceleration.
Sinusoidal signal
Color noise signal
LOS rate outputs under sinusoidal disturbance.
C point output with sinusoidal disturbance
S point output with sinusoidal disturbance
LOS rate outputs under colored noise.
C point output with color noise
S point output with color noise
In Figures
In order to analyze the influence of the seeker DRR compensation scheme on the terminal miss distance of a missile, the block diagram of the missile guidance and control system is established, as shown in Figure
Block diagram of the missile guidance and control system.
The typical flight parameters of a missile are listed in Table
Typical flight parameters of missile.
Parameter | Value | Parameter | Value |
---|---|---|---|
Navigation ratio | Missile velocity | ||
Closing velocity | Rate gyro gain | ||
Autopilot time constant | Filtering time constant | ||
Guidance time constant | Angle-of-attack time constant |
Damping torque.
Disturbance torque
LOS rate
The LOS rate outputs from the C point and S point are given in Figure
Spring torque.
Disturbance torque
LOS rate
The missile flight trajectory curves while considering the influences of the initial velocity pointing error and seeker DRR parasitical loop are shown in Figure
Trajectory curves.
Damping torque
Spring torque
In conclusion, all the simulation results above confirm that the seeker DRR compensation scheme based on the high-gain ESO can effectively suppress the negative impact of the DRRPL on the missile terminal flight. The scheme can be compared with reference [
In this paper, the mathematical model of the platform seeker is built and the feasibility of the seeker structure concept is verified, which have laid the theoretical basis for the following research. The DRR model of the seeker is obtained considering different disturbance torques, and the amplitude and phase characteristics at different frequencies are also analyzed. Based on the reasonable assumptions, the DRRPL of the seeker is simplified and the stable region from different signal extraction points is obtained. The guidance and control system model of the missile is established considering the parasitic loop coupling, and a novel compensation scheme is used to eliminate the DRR effect. Through numerical simulation validation, the following conclusions can be drawn:
The output of the LOS rate from the S point lags slightly behind the C point. The outputs of the seeker are at a certain offset relative to the desired LOS rate under the influence of the detector zero deviation, while they chatter when the disturbance is detector noise. The stable region under the damping torque from the C point is wider than that from the S point, whereas the stable region under the spring torque from the C point is less than that from the S point The DRR effect of the seeker mainly manifests in the low and middle frequencies and can be well suppressed by the proposed compensation scheme. The compensation scheme can effectively improve missile guidance accuracy and reduce terminal miss distance
Our future work will focus on a more realistic seeker model and disturbance torque model and then verify the effectiveness of the proposed scheme through mathematical simulation and hardware-in-the-loop simulation.
In reference [
Damping torque.
Disturbance torque
Los rate
Spring torque.
Disturbance torque
Los rate
The data used to support the findings of this study are included within the article.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work is supported in part by research grants from the Aviation Science Foundation, China (20150172001).