A Method for Assessing the Stability of Digital Automatic Control Systems (ACS) with Discrete Elements. Hypothesis and Simulation Results

The article presents a new approach to the analysis of the stability of automatic systems with discrete links. In almost all modern automatic control systems (ACS), there are links that break signals in time. These are power controlled switches—transistors or thyristors operating in a pulsed mode and digital links in regulators. Time discretization significantly affects the stability of processes in the automatic control system. The theoretical analysis of such systems is rather complicated and requires a significant change in engineering approaches to analysis. With the improvement of digital controllers and a significant increase in their performance, this problem has practically been forgotten. However, its mathematical “content” has not changed since the 1980s when discreteness began to play a major role in hindering the transition to digital automatic control systems. In this paper, we propose a new approach that consists of interpreting the sampling operation by a link with the proposed frequency characteristic, which determines the suppression of input high-frequency signals. This link greatly simplifies engineering calculations and demonstrates the new capabilities of sampling systems. These possibilities include the rational distribution of digitalization resources—the number of bits and the sampling interval between the regulator channels, depending on the frequency range of the efficiency of these channels. We verify and confirm our theoretical statements through simulations and show how this approach makes it possible to formulate new principles of construction of seemingly well-known controllers—PID (Proportional Integral Differential) controllers and variable structure systems (VSS).

MODELS AND DESIGNING METHODS FOR THE DYNAMICALLY RECONFIGURABLE GROUP CONTROL SYSTEM FOR MOBILE ROBOTS

High adaptability is an important requirement for the control system over a group of mobile robots operating in a nondeterministic changing environment. The group control system must ensure that the group task is completed when the structure of the group or the environment changes. Such adaptability can be achieved through dynamic reconfiguration of the control system. The article discusses the mathematical models of a dynamically reconfigurable system from the standpoint of computer-aided design. A review of mathematical models of variable structure system, reconfigurable control systems and their design methods is presented. The paper deals with set-theoretic, analytical, discrete-event models of variable structure systems and methodologies of designing reconfigurable systems. It is shown that the existing design methods do not fully provide the required adaptability of designed group control system. The paper compares the group control system and the reconfigurable multiprocessor computing system and shows how to increase adaptability and autonomy of designed control system using principles of reconfigurable computing systems designing.

A Method for Assessing the Stability of Digital Automatic Control Systems (ACS) with Discrete Elements. Hypothesis and Simulation Results

The article presents a new approach to the analysis of the stability of automatic systems with discrete links.In almost all modern automatic control systems, there are links that break signals in time. These are power controlled switches - transistors or thyristors operating in a pulsed mode and digital links in regulators.Time discretization significantly affects the stability of processes in the automatic control system. The theoretical analysis of such systems is rather complicated and requires a significant change in engineering approaches to analysis. In connection with the improvement of digital controllers and a significant increase in their performance, in recent years this problem has practically not been remembered. However, its mathematical "content" has not changed since the 80s of the 20th century, when discreteness began to play a major role among the problems hindering progress in automatic control systems, in terms of the transition to digital systems.In this paper, a new approach is proposed, which consists in interpreting the sampling operation by a link with the proposed frequency characteristic, which determines the suppression of input high-frequency signals. This link greatly simplifies engineering calculations and demonstrates the new capabilities of sampling systems. These possibilities include the rational distribution of digitalization resources - the number of bits and the sampling interval between the regulator channels, depending on the frequency range of the efficiency of these channels. Theoretical statements have been verified and confirmed by simulation. It is shown how this approach makes it possible to formulate new principles of construction of seemingly well-known controllers - PID controllers and variable structure systems (VSS).

Electrical Drives Control via Discrete-Time Variable Structure Systems with Sliding Mode

Modern control techniques of electrical drives (EDs) use robust control algorithms. One of such algorithms is variable structure control (VSC) with sliding mode (SM). SM control needs more information on the controlled plant than the conventional PI(D) control. Valid mathematical model of the controlled plant is necessary for the SM controller design. Generalized mathematical model of two-phase electrical machine and its adaptation to direct current (DC) and induction motor (IM) are given in this paper, employed in the cascade control structure. Also, the basic SM control theory and discrete-time controller design approach, developed by the authors, are given. Finally, experimentally realized examples of speed and position control of DC and IM are given as an illustration of the efficiency of the promoted EDs controller design via discrete-time VSC.

A Unified Theory of Structure, Synthesis and Analysis of Multibody Mechanical Systems with Geometrical, Flexible and Dynamic Connections. Part 1. Basic Structural Equations and Universal Structure Tables

Multibody mechanical systems (mechanisms and machine drives) are widely used in different fields of modern engineering due to their reliability and simple design. They can be found in robots, manipulators, technological and construction equipment, automatic lines, etc. This paper presents a unified theory of structure, synthesis and analysis of mechanisms and machines with geometrical (single and multiple kinematic pairs), flexible contact (friction or belt) and dynamic contactless (inertial, gravitational, etc.) connections. The theory can be used to construct planar and spatial single- and multi-loop kinematic chains of machines with a given number of closed loops and driving motors. Areas of possible existence of multibody mechanical systems with open, closed and mixed kinematic chain are determined. Based on these findings, various planar and spatial gear and linkage patentable mechanisms are developed that can be used in vibrational drives, variable structure systems requiring precise stoppage during the cycle, lever actuators of multi-axle locomotives, spatial mixers with several mixing tanks, tribometers for measuring the limiting pulling capacity of flexible belts of belt-and-pulley drives, and direct-drive devices for horizontal motion of a suspended load with a low set velocity.

Modelling and Simulation of DC-DC Boost Converter using Sliding Mode Control

DC-to-DC converter is an electronic circuit that converts direct current (DC) from a given voltage to another. DC-DC converters have a broad range of applications, starting from electronic gadgets to household equipment, adapters of mobile phone and laptops, aero plane control frameworks and communication hardware. This paper illustrates the practical application of DC-DC boost converter using Sliding Mode Control (SMC). DC-DC converters can be categorized into different categories in terms of mechanical, electrical and electronic features. SMC DC-DC converters show better performance compared to other converters under certain conditions. This nonlinear control system is especially well suited for Variable Structure Systems. The most significant advantage of Sliding Mode Control over conventional control systems is its robustness against load, line and parametric uncertainties.

Fuzzy sliding mode control of doubly-fed induction generator driven by wind turbine

<span lang="EN-US">This paper present a hybrid nonlinear control based on fuzzy sliding mode to control wind energy conversion system using a doubly fed induction generator (DFIG). Consiting of coupling fuzzy logic control and sliding mode control this technique is introduced to avoid the major disadvantage of variable structure systems, namely the chattering phenomenon. Effectiveness and feasibility of the proposed control strategy are verified by simulation results in Matlab Simulink.</span>