Three Dimension Angular Position Stabilization using LQR and Kalman Filter

This paper presents a design and evaluation for controlling a coupled system using a robust Linear Quadratic Regulator (LQR) controller acting on the augmented integral state space matrix model of a coupled system. System under investigation consisted of dual fan module that is interlinked and its axis moving freely in the pitch plan. On the other hand, a counter weight was used to balance the two fans thrust to optimize the controller effort in the elevation plan. The counterweight axe was denoted as the elevation axis. If the fans are not on the same horizontal line, the rotation of the system around itself in clockwise or anti-clockwise direction was carried out around the travel axis. The LQR controller design parameters should be able to stabilize itself at any degree on the travel or elevation axes while maintaining hover level along the pitch axis. Such controller acts by defining the penalty of each type of error in controlling this system. The error was multiplied by relevant penalty, then fed-back to the controller that controls the fan speeds accordingly. The representing model had three axes, each have a proportional, derivative, and integral term for the travel and elevation axes but not the pitch axis, the reasons will be discussed later in the paper. Modeling started by design process through defining a non-linear model of the system, linearizing it, then was transferred to state space format, add integral part to the model, then finally design and testing of an LQR controller.