Toward Optimal Control of a Multivariable Magnetic Levitation System

Abstract

In the paper, a comparative case study covering different control strategies of unstable and nonlinear magnetic levitation process is investigated. Three control procedures are examined in order to fulfill the specified performance indices. Thus, a dedicated PD regulator along with the hybrid fuzzy logic PID one as well as feed-forward neural network regulator are respected and summarized according to generally understood tuning techniques. It should be emphasized that the second PID controller is strictly derived from both arbitrary chosen membership functions and those ones selected through the genetic algorithm mechanism. Simulation examples have successfully confirmed the correctness of obtained results, especially in terms of entire control process quality of the magnetic levitation system. It has been observed that the artificial-intelligence-originated approaches have outperformed the classical one in the context of control accuracy and control speed properties in contrary to the energy-saving behavior whereby the conventional method has become a leader. The feature-related compromise, which has never been seen before, along with other crucial peculiarities, is effectively discussed within this paper.

The Application of Integration of EEG Signals for Authorial Classification Algorithms in Implementation for a Mobile Robot Control Using Movement Imagery—Pilot Study

“…Input and output training patterns included the same number of elements n = 250. The form of the data presented may be supported by the formulae [37]:…”

“…They can be found in the front layers. An output signal of the designed neural network classifying a signal will be according to formulae [37][38][39]: y = W (5) f (4) (W (4) f (3) + b (4) )(W (3) f (2) + b (3) ) (W (2) f (1) + b (2) )(W (1) u + b (1) ) + b (5) .…”

BCI Wheelchair Control Using Expert System Classifying EEG Signals Based on Power Spectrum Estimation and Nervous Tics Detection

“…Artificial intelligence has also successfully been used in the regulation of automation systems. The works [48][49][50] proposed an approach based on an algorithm using an artificial neural network in the task of controlling a magnetic levitation object, music notation classification and a robot.…”

“…It was necessary to distinguish it in the signal to avoid distortions in the classification of traffic commands. Hidden layers consisting of hyperbolic tangent activation functions (tansig) as represented by the following relationship [48]:…”

“…The network output is y. [4,48]: y = W (5) f (4) (W (4) f (3) + b (4) )(W (3) f (2) + b (3) ) (W (2) f (1) + b (2) )(W (1) u + b (1) ) + b (5) . (8) The neural network was trained with IT (input tics) (Equation ( 9)) and with output OT (output tics) (Equation ( 10)).…”