An MV-algebra G is an abelian monoid (G0+) with the operation * satisfying (x*)* = x x + 0* = 0* and (x *+y)*+y = (y*+x)* = x . Let G be an MV-algebra. A function f :G →G is called homomorphism if f (x + y) = f (x) + f (y) and f (x*) = (f (x)) * for all x and y in G . In this research we study the homomorphism and isomorphism theorem in MV-algebra.

Proportional plus integral controller has been widely used in permanent magnet synchronous motor (PMSM) drive system due to its simple structure while achieving zero steady-state error. However finding out the optimal parameters of the controller is not an easy task. For this reason this paper presents an automated optimization of proportional plus integral controller for permanent magnet synchronous motor drive system using genetic algorithms. Simulation and experimental results verify the effectiveness than ones of the trial and error method.