Guidance And Control Of Lunar Landers For Soft Landing

Navigation, guidance and control are the key techniques for lunar landing plan,moreover the soft landing is the first problem of lunar exploration. This dissertationsystematically studies navigation and guidance and control of the lunar landing byoptimal control, optimization, nonlinear control, linear matrix inequality and switchedsystem methods based on precursors'results.Main works of the paper include the guidance and control law of soft landing,which can be divided into two parts that are the guidance and control of fix-pointsoft landing and that of unfix-point soft landing. The paper use the optimal analyticalguidance law and model reference control method to deal with the unfix-point softlanding problem. For design of the optimal analytical guidance law, the paper devel-ops two kinds of parameterizing guidance law. Considering the exist of disturbance inthe space, a model reference tracking controller is developed to guarantee the landerrobustly to track the normal orbit. For dealing with the fix-point soft landing problem,the paper develops a feedback control method based on the intersecting method. Atlast, STK is used to validate the feasibility and advantage of the proposed method.At first, a recursive piece-wise constant parametric controller is developed byEular equation of the classic optimal control theory in this dissertation, which canbe infinitely approaching the continuous optimal solution. The number of parametersis equal to the system rank. By substituting the controller into the given system, theoriginal optimal control problem is transferred into a parameter selection problem.The analytic gradient functions of the parameters to the cost function and constraintsare developed for some classic optimization methods. Then, the simulating results aregiven based on the genetic algorithm and the BFGS algorithm, respectively.Essence of the parametric control and the enhancing technique is to use thepiece-wise constant value to approach the optimal solution of optimal control prob-lem. Then, the optimal control problem can be transformed into the parameter selec-tion problem by these methods, moreover the optimal parameters can be solved by thecommon mathematic programming. The approximating precision can be enhanced byincreasing the number of parameters so that an acceptable solution is derived. Based on this method, design of the optimal guidance law for soft landing is transferred intothe normal optimal control problem having Canonical form according to the specificfeature of the soft landing through some transformations and deductions. By usingsome mathematic optimization method, the optimal trajectories of soft landing aregiven.Other, a kind of robust switched model reference tracking controller is developedbased on the combination of the model reference control theory, switched system,linear inequality matrix method and H∞control theory. The existing condition ofthe controller is described by the linear matrix inequality. We linearize the kinematcismodel of the lander and the normal trajectory to construct the normal system model theswitched system with uncertainties for lander. Then, we utilize the proposed resultsof model reference control to solve the tracking controller of the soft landing.For the fixed-point soft landing problem, the paper give a method of design-ing the feedback controller based on the intersecting method. The kinematcis modelof the lander is given based on the coordinate of the fixed-point, and transformedinto the linear system by using the rational approximation. The feedback controllersignals include the position and velocity signals of the lander in the fixed-point co-ordinate. Then, we utilize the quadratic linear regulating method of systems withinput constraints to solve the optimal feedback controller. The great advantage of thismethod is that the feedback controller can be directly realized by the RV of landerso that it can greatly reduce the numeration of the navigation system. Other, the pro-posed method transforms the soft landing problem into the stabilization problem ofthe control system, then the complexity of the problem is reduced greatly. At last, thesimulating results illustrate the feasibility and advantage of the proposed method.At last, the feasibility and advantages of the guidance laws including fixed-pointlanding and unfixed-point landing are confirmed by the STK simulating results. At thesame time, an analyzation of the results given by STK are described, which illustratesthe performance of the proposed methods.