A Fractional-Order Active Disturbance Rejection Controller Design for a PMSM Servo System

This paper proposes a fractional-order active disturbance rejection controller (FOADRC) parameters tuning design method for a permanent magnet synchronous motor (PMSM) servo system with frequency-domain analysis of active disturbance rejection control. In this method, a fractional-order proportional derivative (FOPD) and a fractional-order [proportional derivative] (FO[PD]) controllers design combining with active disturbance rejection control (ADRC) are proposed. A systematic parameter tuning scheme is presented, and a flat phase constraint is applied as a design specification, which guarantees the phase is flat around the gain crossover frequency point, and the closed-loop system is robust to gain variations. The simulation results illustrate that the response of the PMSM servo system using FO[PD]-ADRC has a smaller overshoot, less tracking error, and better resistance to load disturbance than that using FOPD-ADRC.

PHASE CONSTRAINTS IN MATERIAL MEANS SEPARATION MODELS IN MICROECONOMICS

One of the important and urgent tasks of microeconomics is the problems of research of the economic system, in which there are restrictions associated with the planned volume of output or the size of the enterprise production capacity. These constraints are set by the requirement that the analyzed trajectories do not leave some given region of the control existence space. Most often, such restrictions for all time points are set in the form of inequalities, and certain requirements are imposed on the function of the phase coordinates of the object, their value at a given time. This problem is classified as an optimal control problem with mixed and phase constraints. In general, this area is of scientific interest and requires consideration. In this case, we study the microeconomic model of the household economy as the most stable object in the conditions of crises. The accumulated savings are subject to a natural phase constraint of non-negativity. This led to the study of the features of the microeconomic formulation of the problem of finding a method for the optimal division of material resources into consumed and accumulated parts, since the imposition of a natural phase restriction on the non-negativity of accumulated savings makes everything much more complicated. Just as in macroeconomics, consumption is optimized, but not in its pure form, but the integral discounted utility of consumption is maximized. The relation equation in this paper differs from a similar macroeconomic equation, since the household exists and survives in crisis conditions in a different way than do social organisms and large enterprises. That is why the article formulates and proves sufficient conditions for solving the problem with a phase constraint.

Modified Blind Equalization Algorithm Based on Cyclostationarity for Contaminated Reference Signal in Airborne PBR

In airborne passive bistatic radar (PBR), the reference channel toward the opportunity illuminator is applied to receive the direct-path signal as the reference signal. In the actual scenario, the reference signal is contaminated by the multipath signals easily. Unlike the multipath signal in traditional ground PBR system, the multipath signal in the airborne PBR owns not only the time delay but also the Doppler frequency. The contaminated reference signal can cause the spatial-temporal clutter spectrum to expand and the false targets to appear. The performance of target detection is impacted severely. However, the existing blind equalization algorithm is unavailable for the contaminated reference signal in airborne PBR. In this paper, the modified blind equalization algorithm is proposed to suppress the needless multipath signal and restore the pure reference signal. Aiming at the Doppler frequency of multipath signal, the high-order moment information and the cyclostationarity of source signal are exploited to construct the new cost function for the phase constraint, and the complex value back propagation (BP) neural network is exploited to solve the constraint optimization problem for the better convergence. In final, the simulation experiments are conducted to prove the feasibility and superiority of proposed algorithm.