Further Results on Fractional Process Control Systems

Abstract

The paper presents a new algorithms of fractional process control - type which may include iterative learning feedback control (ILC). When the structure of object is not known or when many parameters cannot be determined, iterative learning control may be considered, [1]. Motivated by human learning, the basic idea of iterative learning control is to use information from previous execution of a trial in order to improve performance from trial to trial. This is an advantage, when accurate model of the system is not available as friction and actuator dynamics, though present in the system, are not modeled to reduce the computational complexity. Therefore, iterative learning control requires less a priori knowledge about the controlled system in the controller design phase and also less computational effort than many other kinds of control. ILC is a technique to control systems operating in a repetitive mode with the additional requirement that a specified output trajectory in an interval be followed to a high precision and in order to improve performance from trial to trial in the sense that the tracking error is sequentially reduced. Also, the fractional integro-differential operators-(fractional calculus) is a generalization of integration and derivation to non-integer order (fractional) operators and they provide an excellent instrument for the description of memory and hereditary properties of various materials and processes and, also obtaining more degrees of freedom in the model, [2]. Fractional order controllers can significantly improve static and dynamic control system properties and they are less sensitive to controlled systems and controllers parameters variations and can be used as robust controllers. In this paper different aspects of including the design schemes and control algorithms are covered. The control scheme comprises two types of control laws: a feedback law and a feed-forward control law where the controller provides stability of the system and keeps its state errors within uniform bounds and in the feed-forward path, a learning control rule/strategy is exploited to track the entire span of a reference input over a sequence of iterations,[3]. The discretization of the continuous fractional-order operators and considered systems will be also investigated in detail and presented. Specially, for robust control law, it is also proposed the a variant of Time Delay Control [4]. Also, a finite time stability test procedure is proposed for (non)linear (non)autonomous time-invariant delay fractional order systems. Moreover, we examine the problem of sufficient conditions that enable system trajectories to stay within the a priori given sets for the particular class of (non)linear nonautonomous fractional order time-delay systems. Finally, to demonstrate the benefits of proposed fractional process control of type an mechatronic system, (producing of technical gases), is used for the simulation study.