LMIs in Control/Click here to continue/Applications of Linear systems/H∞-based Synthesis of Quadrotor Guidance and Control System

System Dynamics Consider the motion of a quadrotor along a horizontal plane alone. The control law is synthesised for roll motion(rotation wrt. X-axis) coupled with linear motion along Y-axis. The equations of motion governing the 2-D motion are given by(taken from the paper provided below): and are the displacements along X & Y axis, respectively. and are the angular displacement about X & Y axis, respectively. and are constants that depend on the intrinsic properties of the quadrotor. The state space representation of The Quadrotor Guidance is given below, (where is the increment in motor's rotation rate) The Optimization Problem For the above-linearized model of the quadrotor, the linear control would be as below: where V is the voltage input, and The cost function of this controller could be defined as: , where, The LMI < 0 . Solving the above LMI gives the value of for X>0, >0 and Z. Conclusion This LMI can be used in a problem and can be solved using the solvers like Yalmip,sedumi,gurobi etc,. This can be used to analyze the state feedback control and path tracking of a quadcopter.