Algebraic Design of a Discrete-Time Angle Tracking Observer

This paper presents a discrete-time design methodology for an angle tracking observer based on algebraic controller tuning techniques. A piecewise model of the estimated angular velocity is first introduced to approximate its dynamic behavior across sampling intervals. The corresponding angular position is then obtained analytically through integration, leading to a discrete-time system that captures the relationship between the velocity and the angle. A one-step delay is incorporated into the feedback path and compensated by a one-step angle prediction to avoid algebraic loops in the closed-control structure. Finally, an algebraic controller is designed to assign the closed-loop poles to the selected positions, ensuring desirable dynamics and filtering of the observer. The designed observer is experimentally validated and benchmarked against the conventional structures.