The Design of Fractional I-LQR Controller for Constrained Quadrotor Using Grasshopper optimization Algorithm

In control theory and its applications, the development of high-performance controllers is important. Therefore, this paper describes linear quadratic regulator (LQR), integral-LQR (I-LQR), and fractional integral-LQR (FI-LQR) with grasshopper optimization algorithm for quadrotors in hover mode. At first, the dynamic of a quadrotor is introduced, and the equations are presented to simulate the model, then the constraint of the quadrotor is presented which by this constraint, the structure should be described as a singular model. Then the LQR, I-LQR, and FI-LQR are designed to control the height and angles of the quadrotor. Then, by changing the dynamic of the system and defining the error as a new state, new quadrotor dynamics based on FI-LQR are achieved, and it is designed to eliminate the steady-state error. For optimizing the parameters of FI-LQR, a new optimized grasshopper optimization algorithm is used that the cost function has the lowest value. The input value of the motors is calculated to indicate the capability of the controller. For a more accurate comparison, the cost function is calculated for different values of the Q and R matrices for controllers and, the results are compared. The results show that the FI-LQR with grasshopper optimization algorithm has a higher ability to minimize the cost function rather than LQR and I-LQR.