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In this paper, the spacecraft formation flying using virtual structure algorithm is studied. In spacecraft formations flying, several small spacecraft have been used instead of employing a single one to achieve the same goal. In virtual structure method, the position and orientation of each spacecraft is measured with respect to the position and attitude of a virtual node in every moment. Two robust control methods are proposed to control formation. At first, the robust μ synthesis controller is used to attenuate the influence of the sensor noises, environment disturbances and parametric uncertainties but it is done with heavy computations. The second method is in the standard form of optimization problem. It is composed of state feedback controller and lyapanov stability theory. The LMI controller Computations are very efficient and the controller is robust against parametric uncertainties and most of the disturbances. The implementations of control methods on virtual center guarantees robust stability and performance. Concerning with Actuator constraints, Simulation example is provided to show the effectiveness of the proposed control schemes to track the desired attitude and position trajectories despite system uncertainties.

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In this paper, the adaptive second order sliding mode (SOSM) controller is designed for two input - two output (TITO) uncertain nonlinear systems and the robustness properties are ensured in the presence of uncertainties and bounded external disturbances. The objective is to design a controller that ensure stability and path tracking despite the effects of coupling. To this end, the system model is divided into two subsystems, and the coupling effects between such subsystems are considered as uncertainties. The sliding mode approach with PI sliding surface is used to remove the offset and converge the steady state error to zero. To avoid chattering phenomenon, Second order sliding mode method is proposed. Using adaptive switching gain, a new method is presented which unlike other methods, does not require the upper bound of the system uncertainties in the design procedure. Robustness properties against system uncertainties and external disturbances is shown by the Lyapunov stability theorem. Finally, the proposed method is used to control azimuth and elevation angle of as a laboratory helicopter with two degrees of freedom. Simulation results show performance of the algorithm in the presence of perturbations.