State estimator based on an indirect Kalman filter for a hydraulically actuated multibody system

In multibody system dynamics, the equations of motion are often coupled with systems of other physical nature, such as hydraulics. To infer the real dynamical state of such a coupled multibody system at any instant of time, information fusing techniques, such as state estimators, can be followed. In this procedure, data is combined from the coupled multibody model and the physical sensors installed on the actual machine. This paper proposes a novel state estimator developed by combining a multibody model with an indirect Kalman filter in the framework of hydraulically driven systems. An indirect Kalman filter that utilizes the exact Jacobian matrix of the plant at position and velocity level is extended for hydraulically actuated systems. The structures of the covariance matrices of the plant and measurement noise are also studied. The multibody system, described using a semi-recursive formulation, and the hydraulic subsystem, described using lumped fluid theory, are coupled using a monolithic approach. As a case study, the state estimator is applied to a hydraulically actuated four-bar mechanism. The state estimator considers modeling errors in the force model because of its uncertainty in modeling. The measurements are obtained from a dynamic model which is considered as the ground truth, with an addition of white Gaussian noise to represent the noise properties of the actual sensors. The state estimator uses four sensor configurations with different sampling rates. For the presented case study, the state estimator can accurately estimate the work cycle and hydraulic pressures of the coupled multibody system. The results demonstrate the efficacy of the proposed state estimator.