Jul 2026· Vestnik of Samara State Technical University. Technical Sciences Series· Vol 34, pp. 7-20· 0 citations· 1 references
Abstract
The development of effective control systems for nonlinear technological processes remains one of the key challenges in modern control theory. Of particular interest are systems for which a complete dynamic model is unavailable, while the static cha-racteristic of the control channel is known and exhibits an extremal nature. In such cases, traditional linear design methods fail to provide satisfactory control performance, necessitating the use of specialized synthesis techniques that account for the structure of the mathematical model and the specific properties of the plant.This paper explores the method of Analytical Design of Aggregated Regulators (ADAR), which enables the synthesis of a control algorithm based on a simplified plant description combining a nonlinear static model and a linear dynamic model. To ensure system stability in the region of the maximum of the static characteristic, a piecewise-constant function is introduced into the control law, allowing the algorithm to adapt to the sign change of the plant’s transfer coefficient.The proposed approach is applied to the control of a chemical reactor. Four variants of control algorithms were synthesized, differing in structure and the inclusion of an integral component. Computational experiments confirmed the operability and effectiveness of the proposed regulators. The results demonstrate that the ADAR method provides a powerful and practical tool for designing control laws for nonlinear systems under conditions of limited information about the plant dynamics.
The study is devoted to the development of a methodology for the synthesis of a control system for the transportation of a long, deformable, elastic material that is subject to external disturbances and variations in internal parameters. To achieve this, the features of flow lines as control objects have been identified, which significantly complicate the achievement of high-quality technological processes. А set of methods for the synthesis of controllers for linear and nonlinear dynamic systems has been determined, as well as the sequence of their application, which allows for the most effective overcoming of the complexity factors of the controlled object while meeting the specified technical requirements. The developed complex four-stage methodology for the synthesis of a two-channel nonlinear control system is based on the joint use of the principles of separating the rates of motion of the " fast" and "slow" subsystems, as well as robust modal control of the specified accuracy, to form the dynamics and ensure the specified static accuracy of the local channels, followed by the use of the method of analytical design of aggregated controllers for the linearization of nonlinear material deformation by feedback and the adaptation of the system to multiple changes in the elastic properties of the moving web. To illustrate the effectiveness of the proposed approach, a step-by-step example of applying the developed methodology for the synthesis of an automatic control system for a real technological object is considered. In the first step, a mathematical model of a section of a production line consisting of a two-channel DC electric drive and a transporting zone for a deformable material with second-order elasticity as a control object is created. Next, a control subsystem for the local channel is synthesized, which has the desired dynamic, static, and robust properties. In the next step, a subsystem is developed to ensure the linearity of the dynamic properties of the transporting process for the processed material. And, finally, an option for adapting the system to changes in the elastic properties of the moving web is proposed. During the study of the ACS, the reduction of mathematical models was applied twice: in the first case, to achieve robust properties, and in the second case, to simplify the procedure for synthesizing the controller. The effectiveness of the proposed approach has been confirmed by the results of digital simulation modeling at each stage of the automatic control system synthesis.
S. Tararykin, I. A. Tikhomirova, V. Tyutikov· Mekhatronika Avtomatizatsiya...· 0 citations
The research paper presents the synthesis of a fuzzy quasi-optimal controller model and an analysis of its effectiveness compared to a known train speed controller for short-term deviations from the specified operating mode. The task of controlling an underactuated system is of particular importance for railway transport, especially for high-speed transportation. Mechanical systems as control objects are essentially nonlinear dynamical systems of high order. In addition, the complexity of optimizing the operating modes of such systems is due to the fact that even detailed modeling does not accurately predict the cumulative effect of all dynamic factors acting on a dynamic system under operating conditions. Traditionally used in practice linear control laws with constant coefficients are designed to stabilize only one specific mode of motion, which makes them ineffective in conditions of control deficit and a priori uncertainty. Using the reduction of the Lagrange optimization problem to the isoperimetric one makes it possible to obtain a quasi-optimal solution to the structural synthesis problem, which increases control efficiency compared to known methods. The use of the fuzzy logic apparatus allows for parametric synthesis of control, providing adaptability to a priori uncertain operating conditions.
V. Zekhtser, A. Kostoglotov, X.-B. Wu et al.· Вестник Ростовского государс...· 0 citations
A new method is presented for synthesising a control algorithm for second-order nonlinear dynamic systems based on the concept of fixed-time stabilisation with output feedback. The study focuses on a broad class of planar nonlinear systems for which full access to state variables is not possible. The proposed methodology is based on a combination of the theory of bi-limit homogeneity and the principles of classical Lyapunov stability analysis. This approach has enabled the development of a continuous observer with a fixed convergence time, which reliably estimates the unmeasurable state of the system regardless of initial conditions and initial estimation errors. Based on this estimation, a continuous controller is constructed that ensures system stabilisation within a predetermined time.
The method has a number of advantages: stability and convergence do not depend on the magnitude and sign of the initial conditions; control remains continuous, which eliminates oscillation of the actuators; high robustness to limited external disturbances and measurement noise is achieved. The algorithm can be implemented on microcontrollers without the need for high-frequency sampling, making it attractive for practical use. As an example, the dynamics of a microelectromechanical system (MEMS) mirror are considered, which is a striking example of a highly non-linear electromechanical object. Numerical simulations were carried out, the results of which confirm the effectiveness of the proposed control scheme. Compared to existing finite-time controllers, the transient response time is reduced by more than a factor of four, whilst the system error and energy consumption are reduced by almost half. The results obtained confirm the applicability of the developed method to high-precision control of micro- and macro-mechanical actuators, as well as in intelligent robotic and vibro-optical systems.
Zhansaya Yergazy, K. Alimhan, N. Mukatayev· Bulletin of Shakarim Univers...· 0 citations
This paper examines the robustness of closed-loop digital control systems for objects whose state is described by a state vector, and whose model is a transfer function matrix. The control function is implemented by a configurable computing module operating in sequential cyclic scanning mode, while program instructions are executed therein strictly synchronously with real time, guaranteeing timely deterministic command execution. The sequential interpretation of the control program represents a deterministic program flow, the mathematical modeling of which in terms of semi-Markov processes allows formalizing the time delays of data processing and quantifying their impact on control stability. There is a time delay between the input of state vector elements to the controller and the output of control vector elements from the controller. The mathematical expectation of this delay forms the pure delay in the control loops of the plant. System robustness is defined as the value of the time delay increment that brings the system to the nearest stability boundary, determined by the necessary and sufficient conditions for the existence of negative real parts of the roots of the characteristic equation for the closed-loop system, formed taking into account the pure delay. A method has been developed to calculate the robustness of a digital vector control system with a controller that calculates the control vector based on the state vector of the plant measured in real time. Based on the system's characteristic equation and inverse Hurwitz matrix, analytical expressions are derived for the boundary delay increments. These equations allow for a quantitative assessment of the robustness level for stability and the probability of control failure. The proposed methodology for designing robust digital control systems outlines a sequence of steps, from mathematical modeling of the plant to verifying that the delay time does not exceed specified thresholds during the control system design phase. The effectiveness of this methodology is confirmed by the results of transient simulations in a dual-loop plant control system, both with and without delays in control action generation. Based on these results, priorities for future work include developing a method for determining the robustness of the control system in terms of overshoot and time to reach steady state. This would be followed by the synthesis of vector control systems that are robust to specified parameters.
Unknown authors· Bulletin of the South Ural S...· 0 citations
A specialized methodology was developed, computer modeling was conducted, and a comparative analysis was performed for autonomous control methods for small spacecraft, differing in how the nonlinearity of the initial stabilization problem is taken into account:
— control constructed using a system of linear differential equations (SLDE);
— control constructed using SLDE applied to a more general system of differential equations in which nonlinear terms are taken into account in trajectory calculations;
— control using the SDRE method for a nonlinear system of differential equations. To evaluate the effectiveness of the three control methods under consideration under identical initial conditions, stabilization problems using the quadratic quality criterion (LQR) were considered.
A computational experiment showed that, in most cases, the SDRE method yields the lowest quality functional of the three control methods considered. However, the final quality functional values for control constructed using SLDE with nonlinear terms remain consistently higher than those for SDRE. This is due to the fact that the nonlinear term significantly contributes to the increase in the quality functional in the initial equations. Unlike linear optimal control, the SDRE method used does not provide the necessary condition for a minimum performance functional, but it does not require the linearity of the initial differential equation system, which is a significant advantage. Despite the lack of a mathematical proof of the minimal performance functional for all cases, numerical experiments nevertheless demonstrate the advantages of the SDRE method for calculating control. However, the lack of a proven minimum performance functional allows this method to be considered a suboptimal control method. The described approach, using a mathematical model of suboptimal control for small spacecraft, allows it to be used to solve energy-intensive problems that largely determine the operational life of such spacecraft
M. A. Bubnova, V. Chetverikov, E. Pozhidaev· INFORMACIONNYE TEHNOLOGII· 0 citations
Theoretically, this work belongs to a fairly broad class of articles and books devoted to solving control problems for dynamic objects with constraints on control actions and the Bolza functional. The necessary conditions for the existence of optimal controls for a terminal differential game are described by a two-point boundary value problem and the condition for choosing the control itself as a function dependent on the behavior of the Hamiltonian along the optimal trajectory. The main problem of finding optimal control is associated with finding a solution to the two-point boundary value problem. It should be noted that the existence of an optimal control is not necessary: the set of admissible controls may not even contain controls that transform the object from the initial state to a given set of goals. Typically, numerical methods are used to solve such problems. In this paper, an alternative to numerical methods for solving two-point boundary value problems, applied to the problem of synthesizing controls for nonlinear objects, is proposed. This approach is based on the assumption of the validity of R. Bellman’s inverse optimality principle, which maintains the functional relationship between the components of a two-point boundary value problem not only at the end of the transient process but throughout the entire control interval. Based on this, a new analytical method for constructing control for nonlinear objects, called the pseudo-optimal control synthesis method, is proposed. A condition is formulated for determining the set of initial conditions of the original nonlinear system that ensure the execution of the formulated control problem. Mathematical modeling of a quadcopter control system with synthesized control confirmed the theoretical results of the proposed method for synthesizing pseudo-optimal control for nonlinear dynamic objects.
V. Afanas'ev, K. Khalifekh· Mekhatronika Avtomatizatsiya...· 0 citations