LMIs in Control/Click here to continue/Applications of Linear systems/Mixed H2-H∞ LMI Satellite Attitude Control

Satellite attitude control helps control the orientation of a satellite with respect to an inertial frame of reference mostly planets. In this section an LMI for Mixed - Satellite Attitude Control is given. The System The system described below for Mixed H Satellite Attitude Control is the same as the one used for separate and Satellite Attitude controls. and are the flywheel torque and the disturbance torque respectively. , , and are the diagonalized inertias from the inertia matrix . is the rotational angular velocity of the Earth, and , , and are the three Euler angles. The state space representation of The Mixed Satellite Attitude Control system is given below, which is the same as the one described on the and Satellite Attitude Control pages. These formulations are found in Duan, page 374-375, steps 12.10 to 12.15. The Data Data required for this LMI include moments of inertia of the satellite being controlled and the angular velocity of the earth. Any knowledge of the disturbance torques would also facilitate solution of the problem. The Optimization Problem There are two requirements of this problem: Closed-loop poles are restricted to a desired LMI region Where , L and M are matrices of correct dimensions and L is symmetric Minimize the effect of disturbance d on output vectors z2 and zinf. Design a state feedback control law such that The closed-loop eigenvalues are located in , That the H2 and Hinf performance conditions below are satisfied with a small and : The LMI: Mixed H2-H∞ Satellite Attitude Control Solving the above LMI gives the value of , , and and , where is equal to . Conclusion Once the solutions are calculated, the state feedback gain matrix can be constructed as , and = Implementation This LMI can be translated into MATLAB code that uses YALMIP and an LMI solver of choice such as MOSEK or CPLEX. Related LMIs H2 LMI for Satellite Attitude Control Hinf LMI for Satellite Attitude Control External Links LMI Methods in Optimal and Robust Control - A course on LMIs in Control by Matthew Peet. - LMIs in Control Systems: Analysis, Design, and Applications - Duan and Yu