Adaptive Multi-step Correction Algorithm Based On QSS And Application In Spacecraft Dynamics

Modeling and simulation are the core contents of dynamics analysis in military industry,mechanical arm,aerospace,civil engineering and other fields.A part of the mathematical models established in the analysis of dynamic problems are ordinary differential equations or differential-algebraic equations,which are characterized by strong coupling,non-linearity and strong stiffly,this dynamic equation is generally called "stiff problem".The traditional numerical integration method is usually used in simulation solution of such problems.The traditional methods are generally based on time discretization,when solving stiff problems,it is difficult to ensure the solution precision and efficiency at the same time,and even it may be impossible to figure them out.Quantized State System(QSS)is a new numerical integration method,which discretizes all state variables and replaces "step size" with "quantum".By comparing the time required for each quantized state variable to complete the transition,the shortest transition time is selected to advance the next step of integration.Compared with the traditional numerical integration method,QSS algorithm can ensure higher precision and efficiency in solving non-stiff differential equations,but QSS algorithm is not suitable for solving stiff problem.In order to solve stiff problem in dynamics,this paper proposes an adaptive multi-step correction algorithm based on QSS(AMCQSS),which can effectively improve the simulation solution precision while ensuring the solution efficiency,and expand the application range of QSS algorithm for solving stiff problems.This algorithm is based on QSS algorithm and combined with the idea of implicit multi-step method.In the calculation process,two-step method or three-step method can be adaptively selected to effectively improve the precision and efficiency of solving stiff problems.In this paper,several typical examples of stiff problems are simulated and analyzed.AMCQSS algorithm is compared with QSS,LIQSS and traditional numerical integration methods(ODE15s,ODE23 s,ODE45,etc.)in terms of solution efficiency and precision.the results show that AMCQSS algorithm can not only ensure the solution efficiency and precision,but also has good convergence property and stability.In order to further verify the effectiveness and engineering practicability of the adaptive multi-step correction algorithm,this paper selects a typical flexible spacecraft dynamic model in this kind of dynamic problems for simulation solution.Firstly,the dynamic mathematical model of flexible spacecraft is established by Lagrange method,then the second-order ordinary differential equations are obtained by substituting it into Euler—Lagrange equation,and finally the first-order ordinary differential equations are simplified to be suitable for this algorithm.Compared with QSS algorithm,and traditional numerical integration method,the results show that the proposed algorithm can ensure the stability and convergence property of the solution process when solving the dynamic equations of flexible spacecraft,and has certain advantages in solving efficiency and precision.Therefore,the algorithm in this paper provides ideas and reference for solving complex dynamic problems in engineering field.