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This work describes the modeling and identification of the parameters of an actual under actuated pendulum that uses an inertial wheel to produce the torque that moves the pendulum arm. The results are validated using a prototype constructed in the System and Control Laboratory at Hope College. This mechanical system is a useful tool for teaching and research. This paper describes the parameter identification methodology of the proposed model. A comparison between simulation and experimental data are included to analyze the accuracy of the model. Different models for non-lineal behavior like certain kinds of frictions and dead-zone effect are presented. This work concludes with a simple strategy to control the swing up and catching the pendulum in its inverted position.

Small fixed-wing unmanned aerial vehicles (UAVs) limits the use of heavy, computational and power consuming sensors. To further increase the use of UAVs, their navigation filters must be robust and reliable. This paper focuses on dynamic attitude, heading reference systems (AHRS) that can be applied to small fixed-wing UAVs. Two options of observers are explored, both using a low-cost single inertial measuring unit (IMU) and Global Positioning System (GPS) receiver. The first option utilizes the kinematics of fixedwing aircraft together with individual IMU and GPS properties. This leads to a set of three angle correction equations that can correct the attitude and heading angles prediction by the onboard IMU. The second set of observers use the GPS velocity measurements which are differentiated to obtain the vehicles acceleration, which can be used to estimate the attitude angles.The attitude and heading angles are obtained using two types of navigation filters. Besides the conventional extended Kalman filter (EKF) a different type of algorithm is explored that uses a coordinate transformation matrix as a basis. The algorithm is a particular nonlinear complementary filter that uses the coordinate transformation matrix between a North-East-Down (NED) and body-fixed frame of reference. This transformation matrix is a special type of Lie group called special orthogonal group or SO(3).In this paper four different AHRS options are explored, two sets of possible observers and two integration algorithms. The performance of all four is explored using a simulation of a small fixed-wing UAV together with detailed IMU and GPS receiver modeling. Besides performance, AHRS time synchronization for coupled IMU/GPS configurations applied to highly dynamic platforms is analyzed. The AHRS identification simulations show that all four options can be applied to real-time AHRS, with little difference between the two sets of observers. During the simulations, the passive complementary filter (PCF) based on the SO(3) group shows a significant improvement over conventional EKF with lower computational requirements.

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