Using an enhanced homotopy perturbation method in fractional differential equations via deforming the linear part

AbstractConvergence and stability are main issues when an asymptotical method like the Homotopy Perturbation Method (HPM) has been used to solve differential equations. In this paper, convergence of the solution of fractional differential equations is maintained. Meanwhile, an effective method is suggested to select the linear part in the HPM to keep the inherent stability of fractional equations. Riccati fractional differential equations as a case study are then solved, using the Enhanced Homotopy Perturbation Method (EHPM). Current results are compared with those derived from the established Adams–Bashforth–Moulton method, in order to verify the accuracy of the EHPM. It is shown that there is excellent agreement between the two sets of results. This finding confirms that the EHPM is powerful and efficient tool for solving nonlinear fractional differential equations

Control Architectures for Metamaterials in Vibration Control

Metamaterials are artificial structures with properties that are rare or non-existent in nature. These properties are created by the geometry and interconnection of the metamaterial unit cells. In active metamaterials, sensors and actuators are embedded in each unit cell to achieve greater design freedom and tunability of properties after the fabrication. While active metamaterials have been used in vibration control applications, the influence of applied control architectures on damping performance has not been thoroughly studied yet. This paper discusses the relationship between suitable control architectures for increased damping in finite active metamaterials and the number of damped modes. A metamaterial beam consisting of links with measured and actuated joints is considered. Optimal controllers for each of the considered scenarios are designed in the modal domain using linear-quadratic regulator (LQR). We show that, when all modes of a structure should be damped, the optimal solution can be reduced to a decentralised controller. When modes in a smaller range of frequencies are targeted, distributed controllers show better performance. The results are confirmed with experiments.</p

A powered lower limb orthosis to assist the gait of incomplete spinal cord injured patients

This paper addresses the mechanical design and control of a new active stance-control knee-ankle-foot orthosis. The orthosis is intended to provide gait assistance for incomplete spinal cord injured patients with functional hip muscles, but partially denervated knee and ankle muscles. This device consists of a passive compliant joint that constrains ankle plantar flexion, along with a powered knee unit that prevents knee flexion during stance and controls flexion-extension during swing. For this purpose, the knee joint incorporates a controllable mechanical locking system and an electrical DC motor. Based on human walking biomechanics, a hybrid control model is proposed. This model takes into account the parameters of the orthosis and the characteristics of the gait cycle, which is divided in eight different phases. A fractional order controller is designed following decision based control techniques.Postprint (published version

A powered lower limb orthosis to assist the gait of incomplete spinal cord injured patients

This paper addresses the mechanical design and control of a new active stance-control knee-ankle-foot orthosis. The orthosis is intended to provide gait assistance for incomplete spinal cord injured patients with functional hip muscles, but partially denervated knee and ankle muscles. This device consists of a passive compliant joint that constrains ankle plantar flexion, along with a powered knee unit that prevents knee flexion during stance and controls flexion-extension during swing. For this purpose, the knee joint incorporates a controllable mechanical locking system and an electrical DC motor. Based on human walking biomechanics, a hybrid control model is proposed. This model takes into account the parameters of the orthosis and the characteristics of the gait cycle, which is divided in eight different phases. A fractional order controller is designed following decision based control techniques