Synthesis Of Optimal Control Systems Research Articles

Design of Optimal Control Systems in the Frequency Domain by the Functional of the Generalized Work

The paper considers the problem of analytical design of optimal controllers (ADOC) for one-dimensional linear stationary objects according to the functional of generalized work (FGW) A. A. Krasovsky. The use of FGW in comparison with the quadratic performance functional greatly simplifies the calculation of the optimal controller — the calculation of its matrix of coefficients mainly consists in solving the linear matrix Lyapunov equation, which, in contrast to the nonlinear matrix Riccati equation, fundamentally reduces the amount of calculations. In addition, the use of FGW provides the best stability margins of the designed system in terms of amplitude and phase. This work is devoted to the development of a method for solving the ADOC problem A. A. Krasovsky in the frequency (complex) domain, which reduces the determination of the transfer function coefficients of the optimal controller for an object of order n to the solution of the corresponding system of n linear algebraic equations. In this regard, the proposed method for solving the ADOC problem by A. A. Krasovsky differs by a much smaller amount of calculations in comparison with the standard method, in which the Lyapunov equation is solved with the desired matrix of dimensions n * n. The proposed method for the synthesis of optimal control systems, which has an analytical nature, became the basis for solving the inverse problem ADOC A. A. Krasovsky, which consists in determining the values of the weight coefficients of the FGW, which provide the given primary quality indicators of the synthesized control system. Using its relations, a relatively simple method for calculating the FGW coefficients based on the given values of the error coefficients for the designed dynamic system has been developed.

Parametric synthesis of control systems for the steam generator of a nuclear power plant

This paper proposes models and methods of the parametric synthesis of automatic control systems for a steam generator at a nuclear power plant, based on the modification of unconditional optimization methods. A mathematical model of steam generator control systems designed for the synthesis of model parameters has been considered. Algorithms are given for calculating level objective functions that take into consideration the limitations of variable parameters and quality indicators of problems for identifying and optimizing model parameters. The methods of unconditional optimization have been modified by introducing the operation of comparing the values of the level objective functions. Using the information technology of optimization, computational experiments were carried out to synthesize the parameters of the steam generator control systems by optimizing the level objective functions. The values of 54 parameters for the model of the control system in the PGV-1000 steam generator were identified, the value of standard deviation in the processes of 1 % from the experimental processes was achieved in the model. The result of parametric synthesis of optimal control systems for a steam generator produced a minimum control time of 131 seconds while the time of computational experiments did not exceed 10 minutes. The peculiarity of the proposed approach to the parametric synthesis of control system models is that the level objective function as a single mathematical object includes all the information about the synthesis problem. Therefore, a given approach is promising for simplifying software for solving complex problems of parametric synthesis of control systems. The considered technology of parametric synthesis of control systems could increase the degree of scientific validity of technical projects to improve various applied and promising control systems.

Оптимальные системы управления судовыми техническими средствами с неполной информацией и наличием помех

An approach to the synthesis of optimal control systems for ship technical facilities with incomplete initial information and the presence of noise is proposed, based on the use of methods for analytical design of optimal controllers, Kalman filter and Matlab/Simulink package.

Исследование управляемости билинейных систем с ограниченным управлением

Optimal control is closely related to the choice of the most advantageous control modes for complex objects, which are described using ordinary differential systems. The problem of optimal control consists in calculating the optimal control program and synthesizing the optimal control system. This problem arises in the applied field of the optimal control theory, in the case when control is based on the principle of feedback and in automatic control systems. Optimal control problems, as a rule, are calculated by numerical methods to find the extremum of a functional or to solve a boundary value problem for a differential equation system. From a mathematical standpoint, the synthesis of optimal control systems is a nonlinear programming problem in functional spaces. In this study the problem of complete controllability of a bilinear control system on the plane was considered. The controllability of bilinear systems with both unlimited and limited control was studied. The evidences of closed trajectory systems controllability theorems were produced. The authors have defined multiple criteria of complete controllability for bilinear system with limited control. The complete controllability conditions of bilinear control system have been proposed with their algebraic reasoning. In the contemporary context of universal robotization of production, completely controllable systems matter in navigation, as well as in modeling of a number of economic and social processes.

Collision Avoidance System Synthesis for a Group of Robots in Unsupervised Learning Paradigm

Collision avoidance is very important problem in the domain of multi-robot interaction. In this paper we propose a new approach of collision avoidance in the context of the optimal control system synthesis problem definition with minimal information available. It is assumed that robots have a certain scope within which they can interact with static and dynamic phase constraints. A group of robots is considered to be homogeneous, and control system unit for reaching terminal states already available to robots. The control system which is responsible for collision avoidance is only activated when the nearest neighbor is located in the scope of the considered robot. The first important feature of this work is the fact that the collision avoidance between two robots is reciprocal with joint control system, without assigning priorities. Another key feature of this work is the complete absence of information about the environment and the current state of other robots at given time. Robots only share information with nearest neighbors if they locate in the scope of each other. We also present a computational experiment with mobile robots as control objects. A multilayer perceptron was used to approximate the control function. Weights of the perceptron were optimized in unsupervised paradigm by an algorithm belonging to the evolutionary strategies class. At the beginning of each epoch we generate a sample of collision scenarios for optimization, while the quality criterion of the achieved weights at the end of epoch is evaluated on a fixed test sample. Experimental results demonstrate strong ability of the optimized multilayer perceptron to map the relative state of two mobile robots to controls in order to avoid collisions.

Метод оптимального налаштування пі-регуляторів із врахуванням обмежень

Анотація . Розроблено метод оптимального налаштування ПІ-регуляторів при врахуванні обмежень. Метод ґрунтується на зведенні задачі налаштування до задачі безумовної оптимізації. Для цього було запропоновано спеціальний комплексний критерій, який характеризується бажаними топологічними властивостями. Останні отримані за допомогою вагових коефіцієнтів, що враховують вимоги щодо стійкості системи, обмежень та комплексу критеріїв, які відображають небажані показники регулювання. Наперед задані топологічні властивості критерію дали змогу знайти його глобальний. У роботі для цієї мети була використана модифікація методу рою часточок ME - PSO , яка характеризується переініціалізацією рою при умові його стагнації. Для оцінки ефективності використання методу були виконані розрахунки коефіцієнтів ПІ-регулятора при обмеженні за перерегулюванням (прийнято, що воно повинно бути нульовим). Критерієм оптимізації була швидкодія регулювання. У результаті отримано, що для чотирьох тестових передаточних функцій (другого та третього порядків; одна передаточна функція відповідає об’єкту регулювання із часовою затримкою) швидкодія регулювання значно збільшується при забезпеченні обмеження за перерегулюванням. Отримані результати порівнювались із тими, що відповідають регуляторам, що налаштовані із використанням інших (відомих у інженерній практиці) методів налаштування ПІ-регуляторів (порівнювані методи дають змогу отримати нульове перерегулювання). Крім того, аналіз якості автоматичного регулювання був проведений із використанням показників: середньоінтегральної похибки та середньоінтегрального регулювання. Розроблений підхід доволі універсальний. Він може використовуватись для синтезу оптимальних систем регулювання у тому числі і нелінійних. Ключові слова: регулятор, оптимізація, критерій, обмеження, налаштування, метод рою часточок

To the Issue of Robust Automatic Control Systems

This work is proposed to continue the discussion of the problems, theoretical foundations and practical features of the construction and synthesis of robust control systems with high gain, allowing us to control multidimensional nonlinear dynamic objects of high dimensional with functional uncertainties. If problems could not be solved at the level where they appeared, it is necessary to rise the level of understanding of the laws of nature, or in the words of master Lui-Shi Chun Qiu (China, 3rd century BC): "The boy of five chi growth leads the bull by the bridle and the bull obeys him in everything. This is because the person in this case follows naturalness" (the laws of nature). The judo philosophy ("soft way") is based on the principles of using the power and energy of the opponent to achieve victory. The purpose of this work is to demonstrate the theoretical aspects and practical features of the methods of synthesis of optimal control systems by the criterion of maximum reproduction accuracy using the example of robust systems, which allow to control dynamic objects with functional uncertainties, including unstable objects, no minimal-phase objects, neutral objects and objects with differentiation properties. The simplicity (at the level of the engineer) and universality, mathematical rigor and physical validity of this approach is based on the judo philosophy: suppressing the dynamics of a functionally uncertain object and external disturbances by the infinitely large gain with the finite control signal and at the same time maintaining sustainability. Theoretically exhaustive solution of the problem of robust control is given by the idea of constructing systems that are stable with an unlimited increase of the gain coefficient. The sustainability properties are valid for optimal systems that were synthesized using quadratic quality functionals that do not explicitly depend on the control signal, and using a restriction on the control signal. It is significant that in contrast to continuous systems with un-measurable disturbances and not well known control object (in which the conditions of invariance imply the use of infinitely large gain), in relay (discontinuous) systems the equivalent effect is achieved with the help of finite control signal. A nice bonus is the highest accuracy which leads to mathematically zero error of regulation, thus all error coefficients (of position, speed, acceleration, acceleration derivative, etc.) is also equal to zero in the presence of external and internal interferences. In fact, the optimal accuracy control system is equivalent to a system with astatism of the n-th order: the regulator contains n serial connected integrators.

Synthesis of optimal control systems with the change of motion patterns

Synthesis of optimal control systems with the change of motion patterns

Synthesis of Optimal Control-Systems with a Change of the Models of Motion

In this paper, the problem of synthesizing an optimal system controlled with switches is considered. The term switching is understood more broadly than in hybrid systems; i.e., there is a controlled change of the mathematical model of the controlled system at a switching moment: the equations of motion, the state space, and controls are changed. The quality of the control process is estimated by the functional that takes into account both the losses in the continuous motion of the system between switching moments and the cost of each switch. The number of switches and the switching moments themselves are not preassigned and are found during the process of optimization. The sufficient conditions for optimal control are obtained and their application is demonstrated by academic examples of group performance.

ALGORITHMIC PROCEDURES OF SYNTHESIS OF VARIABLE STRUCTURE SYSTEMS FOR MARINE VEHICLES CONTROL

Context. Algorithmic procedures for synthesizing optimal speed systems with variable feedback structure and a given dimension of the vehicle model, required type of stabilization trajectories and constraints on control actions are proposed for solving the tasks of increasing level of automatization control processes of marine vehicles at maneuvering and dynamic positioning. The study object are dynamic processes which stabilize marine mobile objects in conditions of incomplete informative nature of their models and the environment. The subject of the research is automated algorithmic procedures for synthesis of optimal control systems with variable feedback structure.Objective – to increase the level of automation and quality indicators for the control processes of marine mobile objects on the basis of creating automated procedures for the synthesis of robust-optimal systems.Method. To optimize control processes, optimal stabilization trajectories are formed, also the necessary switching moments and the type of control functions are determined for the feed-backs of optimizing control processes. Nonlinear models of marine vehicles with incomplete informativeness of model parameters and external disturbances are considered. The robust correcting control circuit providing compensation of the errors of the actual trajectory of physical object from the optimal trajectories, which arise from a mismatch between the parameters of the model and the physical object and from the effect of uncontrolled disturbances, is proposed. Thus, the control system is invariant for incomplete informativeness of models and minimal values errors of control can be achieved.Results. The algorithmic procedures for synthesizing robust optimal systems of variable structure have been implemented and studied in the simulation of the stabilizing process of a mobile marine object on a given trajectory, the results of which confirmed the correctness and effectiveness of the proposed approach.Conclusions. On the basis of systems with variable feedback structure for the criterion of optimality for the maximum operating speed, algorithmic procedures for the automated synthesis of control functions for multidimensional nonlinear systems describing the dynamics of mobile marine objects have been developed. The software tools for automating the synthesis process and schematic solutions of control systems are practically applicable for a wide class of mobile objects of various technical purposes.

To the Synthesis of Optimal Control Systems

The linear-quadratic optimal control problem subject to linear terminal constraints is considered. An optimal feedback control that is linear in the state variables is constructed.

Metodology of identification parameters of models control objects of automatic trailing sys

The determining factor for the successful solution of the problem of synthesis of optimal control systems of different processes are adequacy of mathematical model of control object. In practice, the options can differ from the objects taken priori, causing a need to clarification of them. In this context, the article presents the results of the development and application of methods parameters identification of mathematical models of control object of automatic trailing system. The stated problem in the article is solved provided that control object is fully controlled and observed, and a differential equation of control object is known a priori. The coefficients of this equation to be determined. Identifying quality criterion is to minimize the integral value of squared error of identification. The method is based on a description of the dynamics of the object in space state. Equation of identification synthesized using the vector-matrix representation of model. This equation describes the interconnection of coefficients of matrix state and control with inputs and outputs of object. The initial data for calculation are the results of experimental investigation of the reaction of phase coordinates of control object at a typical input signal. The process of calculating the model parameters is reduced to solving the system of equations of the first order each. Application the above approach is illustrated in the example identification of coefficients transfer function of control object first order. Results of digital simulation are presented, they are confirming the justice of set out mathematical calculations. The approach enables to do the identification of models of one-dimensional and multidimensional objects and does not require a large amount of calculation for its implementation. The order of identified model is limited capabilities of measurement phase coordinates of corresponding control object. The practical significance of the work is to create a theoretical and methodological basis of identification of parameters of mathematical models of control objects, and then use the results obtained at the processes of synthesis and operation of control systems of various purpose.

Variational Genetic Programming for Optimal Control System Synthesis of Mobile Robots

The paper focuses on the problem of autonomous control system synthesis for the mobile robot. The proposed numerical solution is based on a new method of symbolic regression called variational genetic programming. This method uses the principle of variations of the basic solution. An optimal solution is searched over the set of small variations of the given basic solution. Such approach allows to generate automatically a control function that describes the feedback controller. In the given example the control system is synthesized using variational genetic programming for the unmanned mobile robot that has to move to some terminal position from the different initial states avoiding obstacles.

Lyapunov problem and synthesis of optimal control systems

The direct (first) Lyapunov method is an efficient method for the analysis and synthesis of dynamic control systems. Constructing the Lyapunov function holds a central position in this method and is a challenge for nonlinear dynamic systems. In the paper, the Lyapunov function is constructed as a solution of the Hamilton---Jacoby equation, which is reduced to a Fredholm-type equation.

The Synthesis of Optimal Control System by the Network Operator Method

The problem of synthesis of optimal control system is considered. It is proved that generally it is necessary to search for control as function of not only coordinates of space of conditions, but of velocities of changes of these coordinates. To solve the problem of synthesis it is offered to use the network operator that allows to present mathematical expression of functional dependence in the form of the directed graph. Properties of the network operator are given. For the search of optimal functional dependence on the set of network operators the genetic algorithm is used. The practical example of the solution of a problem of synthesis is given.

New Approach to Optimal Control Theory

Abstract A view on the synthesis of optimal control systems is presented here. It stems from a newly outlined system theory and leads to a general optimizing recursion. Some interesting and fundamental results for general type of loss function and their connection to the usual solution are shown.

On optimal position control of mechanisms in rolling processes

The paper deals with a feedback system created with the use of the method of regular synthesis of optimal control system which should bring a non-linear and discontinuous planar object to a moving target in a minimum time. In real, practical circumstances, on this system there impinge perturbations such as unexpected and undefined motion resistances variations, parameter changes and errors in measurements of states, which cause that the created time-optimal closed-loop system may generate limit-cycles and may be stopped in other state than the required final one (target). There is shown that while using adequately so called F-solution of discontinuous differential equation, the synthesised closed-loop system may become insensitive towards above mentioned perturbations. Some suggestions are made as to practical application in position devices in reversing rolling mills

An optimal speed controller for permanent-magnet synchronous motor drives

An optimal control system synthesis method which can achieve vector and speed control simultaneously for permanent-magnet synchronous motor (PMSM) drives is proposed in this paper. A state-space multiple-input-multiple-output (MIMO) model for PMSM is first developed and the compensation for the nonlinearities in this model is discussed. A pseudo-linearized PMSM model is dynamically constructed through the state detection, and subsequently an optimal speed controller is developed based on this linearized model. The integral control technique is incorporated to eliminate possible speed offsets. A speed observer is further developed to eliminate the speed sensor from the drive.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Synthesis of optimal control systems for non-minimum phase plants

The features of the synthesis of a determinate system for non-minimum phase plant control by the polynomial equation method are considered. Results of the synthesis are compared according to the square (H2) and minimax (H∞) criteria for the various types of reference models complying with the requirements specified for a synthesized system. The rational structure of the reference models is ascertained.

Mathematical models of synchronous electrical machines

AbstractThis paper is concerned with developments in mathematical modelling of turbo‐generator units for use in the dynamic analysis of electrical power systems. Emphasis is placed on an over‐all reduction in computing time, whilst retaining a high order of accuracy of transient response. Accurate linear models are then derived and provide an alternative to the piecemeal formulations hitherto employed in small signal analysis. These equations form a practical basis for the synthesis of optimal control systems for large alternators.