Electromagnetic actuators are very important for scientific and industrial applications. Their use may vary within a wide range of possibilities due to their most important feature: the ability to apply known and controllable forces to elements or structures without contact. In this article, an application within this range is analyzed: a proportional-integral-derivative (PID) controller is used with a pair of actuators to control the dynamic forced response of a flexible cantilever metallic beam and to keep it at a given reference position. In order to achieve this objective, both the actuators and the controller need to be adjusted. For the actuators, the main parameters evaluated consider mounting particularities, such as the differential assembly and the influence of the air-gap distance over the magnetic flux density and the magnetic force provided. Next, a brief review of PID controllers is pre-
| INTRODUCTIONMagnetic actuators are components with a wide range of possibilities whose application field has been growing year after year. [1][2][3] In fact, the main feature of interest in these components is the ability to apply known and controllable forces over many types of elements and structures with no need of contact and no need of any kind of material medium. In this sense, magnetic actuators are a good alternative for common mechanical components. A simple example is a growing field of research and application on magnetic gears. [1,4] These gears offer clear advantages over their mechanical counterparts such as contactless torque transfer, lower maintenance, inherent overload protection, and physical isolation between input and output shafts, being suitable in a market that desires more efficient and reliable gears. Another example of magnetic actuators competing with mechanical devices occurs with magnetic bearings (both active and/ or passive). [1][2][3] These bearings also have some advantages [5] : besides allowing oil-free machines, magnetic bearings are frictionless (and therefore have low-power losses and no wear), allowing high rotational speed. Besides, the bearings can be remotely controlled and are good monitoring devices (because the bearing forces can be properly measured). Therefore, in the field of magnetic bearings, there are some interest applications. Among these, one may find flywheels for kinetic energy storage as peak power buffer units (i.e., for supplying energy on demand peaks) in vehicle applications, [1,6,7] in oil drilling platforms, [8] and even in electric power network applications. [9] Due to its operation characteristics, it is desirable that flywheels rotate at higher speeds and, if a long-term energy storage is needed, low-energy consumption during storage