Research On Nonlinear Guaranteed Cost Attitude Control Methods Of Spacecraft

The rapid development of aerospace engineering and technologies imposes higher requirements on spacecraft attitude control methods.On one hand,the principle of reduc-ing energy consumption and the space missions such as rapid maneuvering and precise orientation require spacecraft to complete maneuvering control with maximal control ac-curacy and in the shortest time.On the other hand,the complex space environment leads to a variety of control problems,such as parameter uncertainty,control saturation,external disturbance,etc.,that decrease system performance and even endanger system stability.Therefore,reliable and cost-efficient attitude control methods will play a more important role in future aerospace applications.This thesis starts from the the perspective of engi-neering and applications,aims to make a breakthrough compared with the existing the-oretical framework of optimal attitude control,carries systematically out the research of spacecraft guaranteed cost attitude control（GCAC）under various control problems,and analyzes in a quantitative way the constraint relationship between system performance index and control problem.Consider the nonlinear guaranteed cost attitude control of rigid spacecraft.The ex-isting results of GCAC at home and abroad are summarized,and a novel GCAC method based on dynamic gain design technology is proposed,of which the main contributions are as follows:i)The more complex but accurate nonlinear attitude dynamics is explicitly considered,which avoids the dependence on model linearization of the traditional opti-mal attitude control and the resulting modeling error.Therefore,the proposed method is more applicable for large-scale rapid attitude maneuvering tasks and can overcome the influence of parameter uncertainty;ii)The proposed GCAC method applies linear matrix inequality（LMI）,a classical linear system control tool,to the control of nonlinear attitude systems without resorting to model linearization.This is one important distinction from the existing attitude control methods based on LMIs.By solving the controller existence conditions in off-line,a simple proportional-differential controller is obtained.Further-more,by the dynamic gain technique,the existence conditions are of special structure,which can be transformed into tractable optimization problems and ensure the optimal solution.This is the second important difference between the existing results.Consider the GCAC problem for spacecraft with time-varying parameter uncertain-ty.Take into account the change of inertia parameters caused by fuel consumption or load motions,and the uncertainties of input matrix caused by actuator installation deviation or failures,they are modeled as polyhedral uncertainties in a general case.By exploring the features of spacecraft attitude system described by quaternion,the controller existence is cast into a series of LMI/bilinear matrix inequality（BMI）conditions by using some special analysis techniques.The conditions are further improved to LMIs by combining with some scaling techniques for matrix inequalities.Finally,the optimal GCAC method is formed based on these conditions that ensures the optimal cost index and trajectory of the uncertain spacecraft attitude system.In views of avoiding modeling error,the pro-posed method follows the advantages of the last proposed method,and then it is suitable to the applications in large-angle attitude maneuvering missions,which is superior to the traditional GCAC methods.The GCAC problem for spacecraft with limited control input is studied.The trade-off relationship between system performance and control input constraint is analyzed.The constraints between cost index and maximal control effort are established in both qualitative and quantitative manner.By exploring the characteristics of attitude dynam-ics described by quaternion and using special analysis techniques,the control saturation problem,together with the requirements on system stability and cost index,is transformed into some conditions in the form of LMI/BMIs.Through the conditions,the allowable op-timal system performance can be obtained under the given limit of control torques,and the minimal control torque can be determined under the prescribed system performance index.Furthermore,by the controller existence conditions,the optimal control methods based on BMIs and LMIs are designed respectively,and the corresponding algorithms are given for solving,by which the advantages and disadvantages of the two kinds of optimal methods are analyzed theoretically.For the spacecraft nonlinear attitude system with energy-bounded disturbances,a novel state feedback based multi-objective optimal attitude control（SFMOOAC）method is proposed,which combines H_∞,generalized H₂（GH₂）and guaranteed cost perfor-mance.This method can not only achieve the integrated optimization on the multiple performance indices,but also ensure one certain index of the multiple performance.On this basis,considering the case of unmeasurable system states,the SFMOOAC method is extended to the case of designing controller with output feedback,where the disturbed measurement is used for the optimal controller design.In addition,the accurate non-linear attitude models are considered in the proposed method that is different from the traditional nonlinear H_∞control methods in the following aspects.First,the analysis and synthesis techniques of the proposed method are different and the controller structure is also different;Second,the controller existence of the proposed method does not depend on the nonlinear Hamilton-Jacobian inequality（HJI）conditions,but is cast into BMI/LMI conditions that ensure a suboptimal solution in a tractable way.For the spacecraft nonlinear attitude system with magnitude-bounded disturbances,a novel tube-based control framework is proposed.First,a GCAC method is proposed for the disturbance-free case,which handles the general case where full information of iner-tia parameters is unavailable except an upper bound.The proposed GCAC method sets itself apart from previous GCC and LQR results in that the stability analysis is performed without resorting to model linearization and the controller existence is cast into LMI/BMI conditions,by which some tractable optimizations are formed to plan the optimal nominal trajectory.When disturbance is considered,an adaptive robust error control scheme for disturbance attenuation is added,which,together with the nominal controller,constructs an integrated tube-based control scheme that attains a trajectory tube for bounding origi-nal attitude states.Specifically,the optimal nominal trajectory serves as the central path of the tube,and an error set is derived under the error control scheme to serve as the cross section of the tube.