Vibration isolation systems based on hybrid electromagnets, consisting of electromagnet and permanent magnet, have a potential usage in many industrial areas, such as clean room design, transportation, semiconductor manufacturing, suspension systems, and robotic surgery due to providing mechanical contact free vibration isolation. Using permanent magnets in the electromagnet structure has some crucial advantages, such as a minimized volume and a more compact structure. Furthermore, the essential force for levitation of vibration isolation stage can be generated by only the permanent magnet(s), which means, by using hybrid electromagnets, magnetic levitation can be achieved with considerably low energy consumption against possible vibrations. This property is called zero-power behavior. However, the main problems of magnetic levitation process are as follows: it has highly nonlinear nature even if it can be linearized; it has unstable pole(s), which makes the system vulnerable in terms of stability. In recent years, linear matrix inequality-based design of controllers has received considerable attention and become very popular due to their ability to satisfy multiobjective design requirements. However, an observer-based H2 controller design for a vibration isolation system having hybrid electromagnets has not been considered yet. Therefore, the linear matrix inequality-based controller is employed to minimize the effect of disturbances on the following objectives, such as vibration isolation, zero-power property, and protection of the levitation gap. The effectiveness of the proposed method is shown with the numerical simulation studies and compared with classical Linear Quadratic Regulator (LQR) approach.
Fuzzy Stabilization for Nonlinear Discrete Ship Steering Stochastic Systems Subject to State Variance and Passivity Constraints
