Model-based control of building energy offers an attractive way to minimize energy consumption in buildings. Model-based controllers require mathematical models that can accurately predict the behavior of the system. For buildings, specifically, these models are difficult to obtain due to highly time varying, and nonlinear nature of building dynamics. Also, model-based controllers often need information of all states, while not all the states of a building model are measurable. In addition, it is challenging to accurately estimate building model parameters (e.g. convective heat transfer coefficient of varying outside air). In this paper, we propose a modeling framework for “on-line estimation” of states and unknown parameters of buildings, leading to the Parameter-Adaptive Building (PAB) model. Extended Kalman filter (EKF) and unscented Kalman filter (UKF) techniques are used to design the PAB model which simultaneously tunes the parameters of the model and provides an estimate for all states of the model. The proposed PAB model is tested against experimental data collected from Lakeshore Center building at Michigan Tech University. Our results indicate that the new framework can accurately predict states and parameters of the building thermal model.

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This article compares the three-dimensional angles of the ankle during step turn and straight walking. We used an infrared camera system ( Qualisys Oqus ®) to track the trajectories and angles of the foot and leg at different stages of the gait. The range of motion (ROM) of the ankle during stance periods was estimated for both straight step and step turn. The duration of combined phases of heel strike and loading response, mid stance, and terminal stance and pre-swing were determined and used to measure the average angles at each combined phase. The ROM in Inversion/Eversion (IE) increased during turning while Medial/Lateral (ML) rotation decreased and Dorsiflexion/Plantarflexion (DP) changed the least. During the turning step, ankle displacement in DP started with similar angles to straight walk (−9.68° of dorsiflexion) and progressively showed less plantarflexion (1.37° at toe off). In IE, the ankle showed increased inversion leaning the body toward the inside of the turn (angles from 5.90° to 13.61°). ML rotation initiated with an increased medial rotation of 5.68° relative to the straight walk transitioning to 12.06° of increased lateral rotation at the toe off. A novel tendon driven transtibial ankle-foot prosthetic robot with active controls in DP and IE directions was fabricated. It is shown that the robot was capable of mimicking the recorded angles of the human ankle in both straight walk and step turn.

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