Comparison of the performance of PID and TVLQR controllers for nonlinear modelling of a freedom flying body

The aim of the research was to enhance the trajectory control of a nonlinear freedom flying body model by comparing time-varying linear quadratic regulator (TVLQR) controller with proportional–integral–derivative (PID) control. The nonlinear behavior of the flying body is represented using a linear time-varying (LTV) approach, accounting for parameter variations over time. The equations of motion for the LTV model and the nonlinear flying body were elaborated within the Matlab-Simulink environment. The optimization method was utilized to adapt the PID gains for the simulation of the nonlinear flying body. Their response was then compared to that of identical PID gains implemented on the LTV model. TVLQR optimal controller was generated by solving the Riccati Equation. A comparison between the performance of TVLQR and PID controllers was conducted using a nonlinear flying body. Additionally, the study examined the impact of wind by introducing wind velocity to the velocity of the flying body. In conclusion, we found that the TVLQR controller had better tracking performance, it excelled in actuator deflection, was wind resistant, and effectively dealt with dynamics and actuator uncertainties.