A lucid methodology for the design and implementation of integer order PID (IOPID), integer order PID with derivative filter (IOPID-F), fractional order PID (FOPID) and fractional order PID with fractional order filter (FOPID-F) controllers for precisely controlling the position of an unstable Magnetic Ball LevitationSystem (Maglev) is reported in this work. Controller parameter values are obtained by numerically solving a constrained optimization problem incorporating desired performance criteria formulated by judiciously choosing selective transient performance metrics. The recently introduced Atom Search Optimization algorithm, used in this work, is fast, efficient and provides intelligent solutions for such complicated engineering design problems. Physical constraints are imposed on the optimization process when defining the feasible search space for the optimum controller parameter values. Both simulation and experimentation are carried out to establish the efficacy of the proposed technique. It has been observed from both simulation and experimental results that the FOPID-F controller showcases comparatively better performance in terms of transient specifications, stability margins and input reference tracking capability. Robustness to parameter variations for the proposed controllersis established with extensive experimentation on the Maglev set up.