Method for hierarchical study of spacecraft descent controllability in the Martian atmosphere

The problem of determining the degree of controllability of a linear non-stationary system (LNS) is considered and a scalar method of hierarchical controllability study for the integration of a highly dynamic guidance system for an autonomous landing of spacecraft is proposed. A new criterion of the controllability degree (DOC) for the problem of optimal control with minimization of energy consumption by calculating the singular values and the condition number of the Gramian controllability matrix is developed. The proposed DOC criterion allows to measure the degree of controllability of the system and each state variable. In addition, the normalization and modification method has been applied in calculating the degree of controllab ility. Mathematical modeling of the spacecraft guidance process during descent in the Martian atmosphere according to the tracing scheme of the program trajectory using the control algorithm with active disturbance compensation (ADRC) and PID is presented. Based on the results of the simulation, it is possible to evaluate and compare the optimality of various reference trajectories using the DOC criterion. The DOC criterion can function as an indicator to investigate the effect of trajectory parameters on the landing process from a controllability point of view. Keywords criterion of controllability degree, linear unsteady system, spacecraft, atmospheric descent