# State estimation algorithms enabling sensor fusion for an under-actuated mechanical system

OData: XML JSON What's this?The application of state feedback control often requires state estimation since the number of measured variables is less than the state dimension. Roughly speaking, the problem of state estimation results in sensor fusion if there is more than one variable measured, i.e. the system has more than one output. Supposing sampled measurements, the time offset between the sampling instances or the sample times of the sensors may differ considerably. In this thesis we consider a sensor fusion problem such that some of the measurements are obtained randomly, at unpredictable time instances. The suggested solution is based on Kalman filtering techniques. Its effectiveness is demonstrated on the measured signals of a nonlinear overhead crane. The algorithm's feasibility is shown by proving that the crane system is observable.

The load of overhead cranes is attached to the mechanical structure with a rope, consequently the trajectory of the load cannot be actuated directly. This results in an unwanted oscillatory behaviour, which needs to be damped for the effective and safe transportation. In existing automated cranes, control solutions suggest state-feedback law. In previous work we proposed an estimation algorithm employing the unscented Kalman filter for the calculation of the unmeasured states. Because of the stiction, this method becomes inaccurate when the trolley does not move, or moves at low velocities only. In this thesis the suggested method is based on the application of a pair of laser slot sensors for detecting when the rope is close to the vertical. Incremental encoders are used to measure the displacement of the trolley and the length of the rope. Since the detection of the vertical rope angle is asynchronous w.r.t. the sampling instant, an appropriate sensor fusion technique is required.

Three sets of experimental and simulation data are provided to present estimation results. The measured and estimated signals are evaluated in a manually controlled and in a closed-loop scenario. In the latter case we employ an energy-based controller, which does not utilizes the estimated states as feedback information. We also conducted a simulation with linearising feedback controller, where the estimator was part of the closed-loop.