Robust Fractional-Order Perfect Control for Non-Full Rank Plants Described in the Grünwald-Letnikov IMC Framework

Abstract

The advanced analytical study in the field of fractional-order non-full rank inverse model control design is presented in the paper. Following the recent results in this matter it is certain, that the inverse model control-oriented perfect control law can be established for the non-full rank integer-order systems being under the discrete-time state-space reference with zero value. It is shown here, that the perfect control paradigm can be extended to cover the multivariable non-full rank plants governed by the more general Grünwald-Letnikov discrete-time state-space model. Indeed, the postulated approach significantly reduces both iterative and non-iterative computational effort, mainly derived from the approximation of the Moore-Penrose inverse of the non-full rank matrices to finally be inverted. A prevention provided by the new method excludes the detrimental matrix behavior in the form of singularity, often avoided due to the observed ill-conditioned sensitivity. Thus, the new defined robust fractional-order non-full rank instance of such control strategy, supported by the pole-free mechanism, gives rise to the introduction of the general unified non-full rank perfect control-originated theory. Numerical algorithms with simulation investigation clearly confirm the innovative peculiarities provided by the manuscript.

Processing characteristics correction of measuring systems by means a differintegral of variable order

“…The fractional calculus have found a range of applications, in particular, modelling of process dynamics and physical effects whose modelling with classic mathematical apparatus has not always been faithful to reality, e.g. modelling of such effects as memory process, PID controllers, robust control, heat transfer process, electrical drive, voltage regulator, charging and discharging of supercapacitors, robot manipulators, cell growth dynamics, biomedical engineering, image processing, chemical reaction processes, dynamics of automatic or electronic systems, photovoltaic systems, hybrid power systems or such non-technical issues as analysis of financial processes [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. The fractional calculus seems an ideal tool for modelling of nonlinear and highly complex effects and processes.…”

Application of Generalized Inverses in the Minimum-Energy Perfect Control Theory

“…speed and accuracy phenomena [6], [7], [8], [9], [10], [11]. The family of IMC-related algorithms constitutes the wellknown and broadly explored stochastic minimum variance (MV) and deterministic perfect control (PC) formulas strictly dedicated to the plants defined in both the transfer function [12], [13], [14], and state-space frameworks [4], [15], [16]. The special peculiarities of such unified control law, i.e., the maximum-speed/maximum-accuracy and robust maintenance, make it desirable in many industrial real-life implementations, for example, in the quadruple tank process [9], wireless autopilot of a quadcopter [17], control of a satellite system [18], power system control [19], water distribution system [20], linear/nonlinear servo control systems [21], [22], nonlinear pendulum system [23], and refrigeration device [24].…”