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This study presents a novel integrated guidance and control method for near space interceptor, considering the coupling among different channels of the missile dynamics, which makes the most of the overall performance of guidance and control system. Initially, three-dimensional integrated guidance and control model is employed by combining the interceptor-target relative motion model with the nonlinear dynamics of the interceptor, which establishes a direct relationship between the interceptor-target relative motion and the deflections of aerodynamic fins. Subsequently, regarding the acceleration of the target as bounded uncertainty of the system, an integrated guidance and control algorithm is designed based on robust adaptive backstepping method, with the upper bound of the uncertainties unknown. Moreover, a nonlinear tracking differentiator is introduced to reduce the “compute explosion” caused by backstepping method. It is proved that tracking errors of the state and the upper bound of the uncertainties converge to the neighborhoods of the origin exponentially. Finally, simulations results show that, compared to the conventional guidance and control design, the algorithm proposed in this paper has greater advantages in miss distance, required normal overload, and flight stability, especially when attacking high-maneuvering targets.

The guidance and the control systems of interceptors are complicated because they are nonlinear and coupled with each other. On the one hand, the guidance system guides the interceptor to the target, during which the variation of trajectory parameters intensifies the uncertainty of the attitude model and brings a burden to the control of attitude. On the other hand, the control system adjusts the attitude in order to track the guidance command, during which the action of the actuators exerts influence on the trajectory and the autopilot lag reduces the performance of the guidance system. Conventionally, guidance and control systems are designed separately, which is proved efficient and convenient merely for the interception of nonmaneuvering target. However, the conventional design approach does not make full use of the coupling between guidance and control and hence has great limitations in improving the overall performance of the interceptor. For the near space interceptor, especially when attacking high-maneuvering target, the coupling between guidance and control is significant while the conventional design method may result in deterioration of the overall performance, sometimes even failure of the interception. Therefore, the study of integrated guidance and control, which makes full use of the coupling between the guidance and the control, is of great significance for better overall performance of the interceptor and higher accuracy for near space interception.

Integrated guidance and control design can be mainly classified into two categories: the partial one and the complete one. Partial integrated guidance and control is that the guidance law is designed accounting for autopilot dynamics, by which the negative influence of autopilot lag is compensated. In [

Complete integrated guidance and control is that the guidance and control is designed as a whole and the control command is produced directly according to the interceptor-target relative motion, which breaks through the outline of conventional design scheme entirely. Complete integrated guidance and control has great advantage in making full use of the coupling between guidance and control and improving the overall performance of the system, which is the trend of the guidance and control design. For convenience, most of the complete integrated guidance and control are studied in two-dimensional space [

Based on the idea of complete integrated guidance and control, a novel integrated guidance and control considering the coupling among three channels is proposed in this paper, aiming at three-dimensional near space interception of maneuvering target. Firstly, considering the coupling among the pitch, yaw, and roll channels, three-dimensional integrated guidance and control model is built, which establishes the direct relationship between the interceptor-target relative motion and the deflections of aerodynamic fins. Secondly, regarding the acceleration of the target as bounded uncertainty of the system, an integrated guidance and control algorithm is designed based on robust adaptive backstepping method, with no information of the upper bound of the uncertainties. Thirdly, a nonlinear tracking differentiator is introduced to reduce the “compute explosion” caused by backstepping method. It is proved that tracking errors of the state and the unknown parameters converge to the neighborhoods of the origin exponentially. Finally, simulation and comparison are conducted between the proposed integrated guidance and control method and the conventional guidance and control design. Simulation results show that the proposed algorithm in this paper has greater advantages in miss distance, required normal overload, and flight stability, especially when attacking the high-maneuvering target.

The interceptor-target engagement geometry in three-dimensional space is shown in Figure

Three-dimensional interceptor-target engagement geometry.

According to the above definitions, integrated guidance and control model for near space interceptor in three-dimensional space can be described as the following form [

Before the controller design process, some assumptions are made as follows.

There exist a set of unknown positive constant

Design objective of integrated guidance and control is selected to be zero line-of-sight angular rate. What is more, roll angle of STT interceptor should be kept zero during the whole flight. That is,

The tracking error of state

Let

The tracking error of state

It should be emphasized that, as a common drawback of classical backstepping method, the derivative of the virtual control (e.g.,

To analyze the performance of this differentiator, a numerical simulation is conducted, in which the gain parameter and sampling step are set as

Tracking results of sinusoidal input and its derivative.

Define the candidate Lyapunov function as

(1) For arbitrary

To verify the performance of proposed integrated guidance and control algorithm, numerical simulation is conducted for three-dimensional near space interception.

The initial position and velocity vectors of the interceptor with respect to inertial coordinate system are set as

(1) The proposed integrated guidance and control algorithm is denoted by IGC. The gain parameters of the IGC algorithm are set as

(2) The proportional navigation guidance law combined with PID control law is denoted by PN+PID. Using PN law, we can get the commanding normal overload with respect to half velocity coordinate system; that is [

The PID law is used to track the commanding normal overload, which is given by the following [

(3) The sliding mode guidance law combined with active disturbance rejection control law is denoted by SMG+ADRC. Using SMG law, we can get the commanding normal acceleration with respect to line-of-sight coordinate system [

The ADRC law is used to track the guidance command, which is given by the following [

Under conditions above, numerical simulations are carried out in two typical engagement scenarios. For better illustration of proposed methods performance when there are aerodynamic uncertainties, 100 Monte-Carlo runs are performed in each engagement scenario, in which the random variables are the deviation of the aerodynamic parameters from their nominal design values, uniformly distributed in the interval [−20%, +20%].

Suppose that the target does not maneuver; the mean miss distance and interception time of the three schemes resulting from Monte-Carlo runs are summarized in Table

Mean miss distance and interception time of the three schemes in Scenario

Scheme | Mean miss distance | Mean interception time |
---|---|---|

IGC | 0.63 m | 37.1 s |

PN+PID | 1.21 m | 38.2 s |

SMG+ADRC | 0.95 m | 37.7 s |

The interceptor-target relative motion in Scenario

The range of attack angle, sideslip angle, and roll angle with respect to time in Scenario

The range of rotational angular velocity with respect to time in Scenario

The range of deflections of aerodynamic fins with respect to time in Scenario

Assume that the target escapes with acceleration of

Mean miss distance and interception time of the three schemes in Scenario

Scheme | Mean miss distance | Mean interception time |
---|---|---|

IGC | 0.71 m | 22.2 s |

PN+PID | 2.32 m | 23.2 s |

SMG+ADRC | 1.45 m | 22.7 s |

The interceptor-target relative motion in Scenario

The range of attack angle, sideslip angle, and roll angle with respect to time in Scenario

The range of rotational angular velocity with respect to time in Scenario

The range of deflections of aerodynamic fins with respect to time in Scenario

Simulation results above indicate that, comparing to conventional design methods, the integrated guidance and control algorithm is more effective with the following advantages:

less miss distance and interception time, which is not obvious when attacking nonmaneuvering target while it is rather remarkable when attacking maneuvering target;

smaller attack angle and sideslip angle, hence reduced required normal overload and less fluctuation of trajectory; therefore, the integrated design excels in maneuvering target interception especially when the available normal overload is limited;

higher flight stability, with the attack angle, sideslip angle, roll angle, rotational angular velocity, and deflection of aerodynamic fins remaining stable during the whole flight, while those of conventional design schemes tend to diverge when the interceptor approaches the target.

Aiming at three-dimensional near space interception of maneuvering target, a novel integrated guidance and control method considering the coupling among three channels is proposed in this paper. Firstly, considering the coupling among the pitch, yaw, and roll channels, three-dimensional integrated guidance and control model is employed by combining the interceptor-target relative motion model with the nonlinear dynamics of the interceptor, in which the direct relationship between the interceptor-target relative motion and the deflections of aerodynamic fins is established. Secondly, regarding the acceleration of the target as bounded uncertainty of the system, an integrated guidance and control algorithm is designed based on robust adaptive backstepping method, with the upper bound of the uncertainties unknown. Moreover, a nonlinear tracking differentiator is introduced to reduce the “compute explosion” caused by backstepping method. It is proved that tracking errors of the state and the upper bound of the uncertainties converge to the neighborhoods of the origin exponentially. Finally, simulation and comparison are carried out under three guidance and control schemes. In contrast to conventional design methods, the integrated guidance and control algorithm leads to higher flight stability, less miss distance, and required normal overload, especially when attacking the high-maneuvering target.

Line-of-sight distance (m)

Velocity of interceptor (m/s)

Elevation angle of the line-of-sight (rad)

Azimuth angle of the line-of-sight (rad)

Flight path angle (rad)

Pitch angle (rad)

Angle of attack (rad)

Angle of sideslip (rad)

Roll angle (rad)

Roll, yaw, and pitch rates (rad/s)

Aileron, rudder, and elevator deflections (rad)

Mass of interceptor (kg)

Dynamic pressure (Pa)

Reference area (m^{2})

Reference length (m)

Roll, yaw, and pitch moments of inertia (kg·m^{2})

Partial derivative of lift force coefficient with respect to

Partial derivative of lateral force coefficient with respect to

Partial derivatives of rolling moment coefficient with respect to

Partial derivatives of yawing moment coefficient with respect to

Partial derivatives of pitching moment coefficient with respect to

The authors declare that there are no competing interests regarding the publication of this paper.

This work was partially supported by the National Natural Science Foundation of China (Grant no. 11572097).

_{1}adaptive state feedback controller for three-dimensional integrated guidance and control of interceptor