Beneficially combining LQR and PID to control longitudinal dynamics of a SmartFly UAV

Abstract

The problem of control system design for longitudinal axis of a small-size flying wing is studied. The new controller proposed is comprised of two controllers working together to provide robust stability and step reference tracking for the nonlinear dynamics of SmartFly UAV. More precisely, Linear Quadratic Regulator (LQR) is used together with Proportional, Integral, Derivative (PID) controller. The inspiration comes from the fact that each of the mentioned controllers have advantages and disadvantages that cannot be neglected. LQR, as an optimal in terms of energy-like regulator, provides robust stability with a minimized energy-like performance index. It is also very computationally efficient. But, when it comes to the transient of particular output, LQR is not the best solution. On the other hand, PID has the advantage of a possibility to tune the gains for optimized transient behavior, especially for well-behaving plants. Furthermore, PID controller is particularly useful for tracking problems. However, PID is often not robust (in terms of parameter uncertainties) and it is also difficult to tune PID parameters for unstable systems. By differentiating between system stability and performance in the controller design process, it is possible to benefit from both controllers, using them along side together in one system. Functionality of this method was verified through computer simulation in MATLAB/SIMULINK for a nonlinear model of SmartFly UAV. Closed-loop system performance was evaluated in terms of robustness and step reference tracking.