1. A hierarchical control system for a Pulsed Laser Deposition (PLD) growth process in which a target of a given material and a substrate are located within a vacuum chamber, and a laser transmits a laser beam, beam control means for controlling the direction of the laser beam to scan the target to produce a plasma which coats the substrate, wherein there are sensors for the vacuum chamber, with data acquisition means coupled to at least one of the sensors; a process control computer coupled via a bus to the laser, the beam control means, the data acquisition means, and at least some of the sensors; wherein said hierarchical control system comprises a multifeatured control system for the growth process, utilizing said sensors for sub process control, combined with a dynamical feedback control PLD process, having first, second and third levels of feedback control; wherein the first level of feedback control includes means to improve the precision and tracking of sub process variables by linear observer based compensator control, wherein a plume species density per laser pulse and bulk substrate thickness from the sensors provide real time sub process data to an observer; and an observer based compensator means then directly calculates laser energy density per pulse and pulse repetition rate based on current values predicted by the linear model; wherein the second level of feedback control provides the observer with a linear controller design, the second level of feedback control comprising a dynamical system design means and nonlinear process map, nonlinear mapping being used to design a new observer based compensator for each linearization point chosen by the third level of feedback control, wherein the second level of feedback control relies on a nonlinear first order multidimensional differential mapping of the process, this nonlinear dynamical model of the process being updated using automatic process identification experiments; wherein the third level of feedback control comprises an expert system rulebase and command input means to achieve a desired product goal, the rulebase being general enough to be the basis of an expert system that deals with the interaction of any controller and process, wherein an expert controller decides whether or not the process linearized model used by the first level of feedback control is accurate enough to achieve the desired process goals, and based on controller-process performance, a controller re-design is commanded by the third level of feedback control to the second level of feedback control, and then implemented by the first level of feedback control.