Optimal Attitude Control For Three-axis Stabilized Spacecrafts

The spacecraft attitude control system is a very important subsystem of the whole spacecraft system, the design of which impacts on satisfaction of holistic performance index directly. For any on-orbit spacecraft, it takes on the assignments such as exploration, space exploiture and so on. In general, when the attitude attains stability or tracking, it may be expected to achieve certain performance objective such as minimal time or minimal control energy in the assignments. The optimal control has played significant roles in the attitude control and attracted considerable attention in recent years.Because spacecraft attitude control system is a multi-input multi-output coupled uncertain nonlinear system, it makes quite difficulty and complexity on the solution to the problems using optimal control method. At the same time, for any on-orbit satellite, it is inevitable to be influenced by some kinds of disturbance torques. This makes achieving approved optimal control performance more difficult practically. On this background, this thesis investigates optimal control algorithms for spacecraft attitude control system in detail, from both theoretical and applicable aspects, and applies the proposed control schemes to certain spacecraft control system. The main contents of this thesis are as follows.A time-optimal controller based on the pseudospectral method is proposed to solve the spacecraft attitude maneuver time-optimal control problem. Firstly, the open-loop time-optimal controller based on the Legendre pseudospectral method and Gauss pseudospectrol method are designed respectively, the optimality of which are proved by the Pontryagin's Minimum Principle. Then, the closed-loop real-time optimal controller is proposed using Bellman's Principle, which fulfills the maneuver mission while being robust to external disturbances and plant uncertainties.A new nonlinear synthesized technique called theθ-D method is presented for the spacecraft attitude tracking optimal control problem with quadratic performance index. Based on the solution of HJB equation, by introducing intermediate variableθ, the performance index, the optimal cost can be expanded as a power series in terms ofθ. The HJB equation is then reduced to a set of recursive algebraic equations and yields a closed-loop controller with a finite number of terms. By adding perturbations to the cost function and manipulating them, we are able to ensure convergence of the series and achieve semi-global asymptotic stability. In addition, this technique can overcome the problem of large-control-for-large-initial-states encountered by some other power series expansion based control laws. Tuning the parameters in perturbation terms also enables us to modulate the system transient performance in a flexible way.The synergetic optimal problem of an affine nonlinear dynamics referring to the design of sliding surface in the variable structure control is studied and the synergetic optimal control scheme is proposed. Then it is proven to have optimality property with respect to a meaningful cost functional. The control technique combines the advantages of variable structure control and optimal control. At the same time, it avoids the chattering phenomenon caused by discontinuity in the variable structure control and fulfills the control mission of spacecraft attitude tracking time-varying signal with good robustness.