Nonlinear optimal and multi-loop flatness-based control of the attitude of reentry space vehicles

Purpose The purpose of this paper has been to present new solutions to the nonlinear control problem of the degrees of freedom (6-DOF) attitude dynamics of reentry space vehicles. Among eligible control methods for the spacecraft’s attitude dynamics one can distinguish some sliding-mode control schemes. Besides there are several backstepping control approaches. In addition, one can find results on model predictive control concepts and optimal control-type concepts. Furthermore, one can distinguish methods which perform disturbance estimation and disturbance compensation thus improving the robustness of the reentry space vehicles’ control loop. Besides, this control problem is often treated with use of methods which rely on state-space model transformations and on changes of state variables. The aim of the present paper has been to achieve control and stabilization for the attitude dynamics of reentry space vehicles without forth and back state-space model transformations, changes of state variables (diffeomorphisms), and without the associated singularity issues. To this end, two new nonlinear control methods have been proposed: (i) nonlinear optimal control and (ii) flatness-based control in successive loops. Design/methodology/approach In this paper, the control problem for the multivariable and nonlinear 6-DOF dynamics of the attitude of autonomous reentry space vehicles is solved with the use of (i) a nonlinear optimal control method and (ii) a flatness-based control approach which is implemented in successive loops. To apply method (i) that is nonlinear optimal control, the dynamic model of the reentry space vehicle undergoes approximate linearization at each sampling instant with the use of first-order Taylor series expansion and through the computation of the associated Jacobian matrix. The linearization point is defined by the present value of the system’s state vector and by the last sampled value of the control inputs vector. To compute the feedback gains of the optimal controller an algebraic Riccati equation is repetitively solved at each time-step of the control algorithm. The global stability properties of the nonlinear optimal control method are proven through Lyapunov analysis. To implement control method (ii), that is flatness-based control in successive loops, the state-space model of the 6-DOF attitude dynamics of the autonomous reentry space vehicles is separated into two subsystems, which are connected between them in cascading loops. Each one of these subsystems can be viewed independently as a differentially flat system and control about it can be performed with inversion of its dynamics as in the case of input-output linearized flat systems. The state variables of the second subsystem become virtual control inputs for the first subsystem. In turn, exogenous control inputs are applied to the second subsystem. The whole control method is implemented in two successive loops and its global stability properties are also proven through Lyapunov stability analysis. The proposed method achieves stabilization of the attitude dynamics of the space vehicle without the need of diffeomorphisms and complicated state-space model transformations. Findings In the first control method that the article proposes, the dynamic model of the attitude of the reentry space vehicle undergoes approximate linearization around a temporary operating point which is updated at each sampling period. For the approximately linearized state-space description of the system, an H-infinity feedback controller is designed. To select the controller’s gains, an algebraic Riccati equation is repetitively solved at each time-step of the control method. The global stability properties of the control scheme are proven through Lyapunov analysis. In the second control method of the paper, the dynamic model of the reentry space vehicle is decomposed into a series of subsystems which are connected in chained form. It is proven that these subsystems if viewed independently, are differentially flat. In the chained subsystems, the state vector of the subsequent subsystem becomes virtual control input to the preceding subsystem. From the last subsystem, the real control inputs vector is found. The global stability properties of the flatness-based control method are also proven through Lyapunov analysis. Research limitations/implications There are no research limitations about the proposed control methods for the attitude dynamics of reentry space vehicles. On the contrary, a benefit from using either the nonlinear optimal control approach or the flatness-based control in successive loops for the attitude dynamics of the reentry space vehicle is that a solution of the control and stabilization problem for this nonlinear system can be reached without state-space model transformations and complicated changes of state variables. Practical implications A significant part of the research on nonlinear control for aerospace systems has been on the application of state-space model transformations which allow for writing these systems’ dynamics into an equivalent representation where the solution of the control and state estimation problems can be significantly simplified. In this regard, Lie algebra-based control methods and flatness-based control with transformation into canonical forms pursue the application of diffeomorphisms which allow for writing the initial nonlinear state-space model into an equivalent input-output linearized state-space form. These transformations often precede also the application of sliding-mode control, because it is only for systems in the input-output linearized form that one can follow a systematic procedure for selecting sliding surfaces. The nonlinear optimal and the flatness-based control method in successive loops, which are proposed in this paper, achieve solution for the control and stabilization problem of the attitude dynamics of reentry space vehicles without needing to apply any transformations for these spacecrafts’ state-space model and without imposing any changes of state variables. Social implications Control for autonomous reentry space vehicles has been a nontrivial research topic in the area of aerospace science and technology. Obviously, there is significant benefit from solving the attitude control problem for reentry space vehicles These aerospace systems become more reliable and the success of the associated missions is ensured. Space exploration and exploitation with the use of reentry space vehicles is carried out for civilian or defense purposes and affects the quality of living, prosperity, peace and international cooperation at a worldwide scale. Originality/value The results of this study are genuine and novel. The first method that the paper proposes for the 6-DOF attitude dynamics of reentry space vehicles is a nonlinear optimal (H-infinity) control scheme. The second method that the paper proposes for the attitude dynamics of reentry space vehicles is flatness-based control implemented in successive loops. The proposed methods achieve stabilization of the attitude dynamics of the space vehicle without the need of diffeomorphisms and complicated state-space model transformations.