Evaluation and optimization of strapdown velocity numerical integration algorithms for SINS in spinning ballistic missiles

The error of the conventional velocity numerical integration algorithm was evaluated through the Taylor series expansion. It is revealed that neglecting the second- and higher-order terms of attitude increments will lead to the velocity numerical integration error, which is proportional to the triple cross product of the angular rate and specific force. A selection criterion for the velocity numerical integration algorithm was established for strapdown inertial navigation system (SINS) in spinning missiles. The spin angular rate with large amplitude will cause the accuracy of the conventional velocity numerical integration algorithm in SINS to decrease dramatically when the ballistic missile is spinning fast. Therefore, with the second- and higher-order terms of attitude increments considered, based on the rotation vector and the velocity translation vector, the velocity numerical integration algorithm was optimized for SINS in spinning ballistic missiles. The superiority of the optimized algorithm over the conventional one was analytically derived and validated by the simulation. The optimized algorithm turns out to be a better choice for SINS in spinning ballistic missiles and other high-precision navigation systems and high-maneuver applications.

Second order sliding mode control with back stepping approach for moving mass spinning missiles

An attitude controller using the second order sliding mode control methodology with a backstepping approach（SOSMCB）is designed and implemented for a spinning missile with two internal moving mass blocks.The system consists of a rigid body and two radial internal moving mass blocks and its mathematical model is established based on Newtonian mechanics.The control scheme integrates a second order sliding mode control algorithm into the last step of the backstepping approach,and its stability is proved by means of a Lyapunov function.The performance of the controller is demonstrated by numerical simulations,the results show that the attitude controller is stable and effective.

Coning motion instability of spinning missiles induced by the delay of strap-down seeker

The strap-down seeker,which combines the seeker's and the onboard gyro's measurements to obtain the target information,has been extensively applied by spinning missiles.The response delay of the strap-down seeker,a novel factor that could result in crosscoupling between the acceleration commands in the pitch and yaw channels and subsequently cause the significant deterioration in dynamic stability of the spinning missile equipped with a rate loop,is noted in this paper.The sufficient and necessary stability conditions are also analytically established based on the system equation with complex coefficient,which are further verified by numerical simulations.It could be indicated that the response delay of the strap-down seeker will greatly deteriorate the dynamic stability of the whole guidance system designed by the conventional method.It is also noticed from analysis that the stable region of the combined guidance coefficient is shrunken significantly with the increase of the spinning rate.