A Nonlinear Magnetic Stabilization Control Design for an Externally Manipulated DC Motor: An Academic Low-Cost Experimental Platform

The main objective of this paper is to present a position control design to a DC-motor, where the set-point is externally supplied. The controller is conceived by using vibrational control theory and implemented by just processing the time derivative of a Hall-effect sensor signal. Vibrational control is robust against model uncertainties. Hence, for control design, a simple mathematical model of a DC-Motor is invoked. Then, this controller is realized by utilizing analog electronics via operational amplifiers. In the experimental set-up, one extreme of a flexible beam attached to the motor shaft, and with a permanent magnet fixed on the other end, is constructed. Therefore, the control action consists of externally manipulating the flexible beam rotational position by driving a moveable Hall-effect sensor that is located facing the magnet. The experimental platform results in a low-priced device and is useful for teaching control and electronic topics. Experimental results are evidenced to support the main paper contribution.

Vibrational Control of a 2-Link Mechanism

This paper describes vibrational control and stability of a planar, horizontal 2-link mechanism using translational control of the base pivot. The system is a 3-DOF two-link mechanism that is subject to torsional damping, torsional stiffness, and is moving on a horizontal plane. The goal is to drive the averaged dynamics of the system to a desired configuration using a high-frequency, high-amplitude force applied at the base pivot. The desired configuration is achieved by applying an amplitude and angle of the input determined using the averaged dynamics of the system. We find the range of stable configurations that can be achieved by the system by changing the amplitude of the oscillations for a fixed input angle and oscillation frequency. The effects of varying the physical parameters on the achievable stable configurations are studied. Stability analysis of the system is performed using two methods: the averaged dynamics and averaged potential.

Vibrational control: A hidden stabilization mechanism in insect flight

It is generally accepted among biology and engineering communities that insects are unstable at hover. However, existing approaches that rely on direct averaging do not fully capture the dynamical features and stability characteristics of insect flight. Here, we reveal a passive stabilization mechanism that insects exploit through their natural wing oscillations: vibrational stabilization. This stabilization technique cannot be captured using the averaging approach commonly used in literature. In contrast, it is elucidated using a special type of calculus: the chronological calculus. Our result is supported through experiments on a real hawkmoth subjected to pitch disturbance from hovering. This finding could be particularly useful to biologists because the vibrational stabilization mechanism may also be exploited by many other creatures. Moreover, our results may inspire more optimal designs for bioinspired flying robots by relaxing the feedback control requirements of flight.