Study On Guidance And Control Problems For Tactical Ballistic Missile Interceptor

This dissertation proposes novel approaches to the development of guidance and control systems for tactical ballistic missile (TBM) interceptor. It is well acknowledged that the guidance and control systems play an important role in precise guidance area, especially the former one. However, the prior work on this subject usually suffers from the following problems. Firstly, the unrealistic/unreasonable assumptions are usually introduced in the development of the guidance algorithms. Secondly, the derived guidance law may show its advances in theory versus proportional navigation (PN) guidance law, but it always fails in practical implementation. In regarding of this, this dissertation focuses on the application of differential geometric (DG) guidance command to the development of new guidance algorithm, which could satisfy the interception of highly maneuverable target, as well as not loss its interest in implementation. Moreover, in order to guarantee a stable and fast attitude tracking, a three-channel flight control system has also been developed in this dissertation using PID and adaptive backstepping techniques.The definitions of the common used frames throughout this dissertation are presented firstly in this paper, as well as the transition matrices among them. Furthermore, the dynamics and kinematics equations in the launch inertial frame are developed so as to describe the motion of TBM in space. It should be pointed out that, in order to avoid the singularity occurring in large-angle slew maneuver of TBM, the quaternions is introduced in the development of kinematics equations instead of the traditional Euler angles.The DG guidance curvature and torsion commands are proposed using classical differential geometry theory. Also, the initial condition is developed so as to avoid singularity of the guidance command as well as to guarantee the capture. However, the proposed guidance command is developed in the arc-length system, which means all the derivations in the guidance commands are taken with respect to the arc-length, not the time. In order for practical implementation, the derived DG guidance commands shall be transformed to the time domain so as to formulate the DG guidance law. It should be pointed out that the output of DG guidance law is the guidance angles (i.e., angle-of-attack, sideslip angle, roll angle), not the load factor. Moreover, the new initial condition is deduced based on a more realistic assumption in anti-TBM scenario. Simulation results show that the proposed guidance law works well and effectively in the proposed engagement, and it performs better than PN guidance law.In order to render the DG guidance command for practical implementation, as well as to develop a new guidance law against the highly-maneuverable target, the DG guidance curvature command is modified to facilitate the practical implementation, as well as to determine the magnitude of the commanded acceleration of the new guidance law, while the direction of the new guidance law is complied with the direction of 3D PPN guidance law. The derived guidance law is a generation of gain-varying PPN guidance law, and compared with other gain-varying algorithms, it does not need the evaluation of the time-to-go information or the target's acceleration, thus facilitates the onboard computation, and improves its effectiveness. Simulation results demonstrate that the proposed guidance scheme is effective in capturing a highly-maneuverable target, and exhibits a better performance than PN guidance law in Monte-Carlo sense.Moreover, based on DG dynamics formulations, the post-launch capturabilities of PPN and TPN guidance laws are presented in the arc-length system, and a unified capture condition for all PN-type guidance law is developed in terms of in-flight information. Compared with prior work on this field, the proposed condition is no longer the function of initial conditions or speed ratio, it demonstrates the quantitively relation between the capture and the acceleration/deceleration of the interceptor, target's maneuver, etc. Simulation results indicate that the proposed condition is a necessary condition, and it becomes more conservative at the end of the engagement.The fuzzy Set-Point weighting PID controller is introduced to develop a 2D flight control system incorporating with 2D DG guidance law. The main function of the flight control system is to track the commanded guidance angle produced by DG guidance curvature command. In particular, the Lyapunov second theory is utilized to study the relation between global stability and the output of the fuzzy inference system. The results show that the proposed control system works well in this case, and performs better than other PID controllers.Furthermore, the adaptive backstepping control system incorporating with constrained command filter is introduced to develop a three-channel flight control system. The propose control scheme overcomes the disadvantages associated with classical backstepping technique, such as overparameterization, taking derivation of uncertainty terms, etc, and most importantly, it could guarantee the convergence of the parameter update law and the global stability of the system, even in the presence of the control saturation.