Abstract
A linear mechanical oscillator is non-linearly coupled with an electromagnet and its driving circuit through a magnetic field. The resulting non-linear dynamics are investigated using magnetic circuit approximations without major loss of accuracy and in the interest of brevity. Different computational approaches to simulate the setup in terms of dynamical system response and design parameters optimization are pursued. A current source operating in baseband without modulation directly feeds the electromagnet, which consists commonly of a solenoid and a horseshoe-shaped core. The electromagnet is then magnetically coupled to a mass made of soft magnetic material and attached to a spring with damping. The non-linear system is described by a linearized steady-space representation while is examined for controllability and observability. A controller using a pole placement approach is built to stabilize the element. Drawing upon the fact that coupling works both ways, enabling estimation of the mass position and velocity (state variables) by processing the induced voltage across the electromagnet, a state observer is constructed. Accurate and fast tracking of the state variables, along with the possibility of driving more than one module from the same source using modulation, proves the applicability of the electro-magneto-mechanical transducer for sensor applications. Next, a three-layer feed-forward artificial neural network (ANN) system equivalent was trained using the non-linear plant-linear controller-linear observer configuration. Simulations to investigate the robustness of the system with respect to different equilibrium points and input currents were carried out. The ANN proved robust with respect to position accuracy.
Highlights
Advancements in the field of magnetic materials in terms of better efficiency and energy densities [1], together with the integration of mechanics, electromagnetics, power and control electronics into the system, have enabled intelligent electromagnetic actuators and sensors
We examine a sensor application of an electromechanical oscillator as proposed by Xiros [24,25] (Figure 1)
Responses of the state variables, for different equilibrium points are depicted in Figures 17–19: it is clear that the estimate states converge to the actual state variables while tracking reasonably well the equilibrium value
Summary
Advancements in the field of magnetic materials in terms of better efficiency and energy densities [1], together with the integration of mechanics, electromagnetics, power and control electronics into the system, have enabled intelligent electromagnetic actuators and sensors. Given the joint sensing-actuation functionality, electro-magneto-mechanical devices are a promising solution for multi-agent architectures. Such architectures have a vast application field, such as mechatronics and robotics [10], smart grids [11] as well as sensor networks [12]. The acting force has changed and the mass moves again This iterative sequence repeats, forming a closed loop between the displacement and the magnetic force. In. Section 4, closed-loop simulations are conducted to achieve a higher degree of stability. By designing a state observer for the electromechanical oscillator, position and velocity tracking is achieved. The current input is kept variable yet close to the equilibrium values where the linearization is still valid
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