To the Issue of Robust Automatic Control Systems

In this paper, the problem of robust stability of systems subject to parametric uncertainties is considered. Sufficient conditions for the existence of parameter-dependent Lyapunov functions are given in terms of a criterion which is reminiscent of, but less conservative than, Popov's stability criterion. An equivalent frequency-domain criterion is demonstrated. The relative sharpness of the proposed test and existing stability criteria is then discussed. The use of parameter-dependent Lyapunov functions for robust controller synthesis is then considered. It is shown that the search for robustly stabilizing controllers may be limited to controllers with the same order as the original plant. A possible synthesis procedure and a numerical example are then discussed.

Разработана методика построения робастных регуляторов для линейных систем с запаздыванием, грубых по отношению к параметрической неопределенности и к изменению величины запаздывания.Такие регуляторы реализуют традиционные (ПИ, ПИД, ПД) и связанные с ними законы управления.Методика базируется на критерии апериодической устойчивости

One of the actual problems for the theory and practice of control of dynamic objects is the development of methods for research and synthesis of control systems of multidimensional objects. The paper proposes a universal approach to construct Lyapunov vector functions directly from the equation of state of control system and a new gradient-speed method of Lyapunov vector functions to study aperiodic robust stability of linear control system with m inputs and n outputs. The study of aperiodic robust stability of automatic control systems is based on the construction of Lyapunov vector functions and gradient-speed dynamic control systems. The basic statements of Lyapunov's theorem about asymptotic stability and notions of stability of dynamic systems are used. The representation of control systems as gradient systems and Lyapunov functions as potential functions of gradient systems from the catastrophe theory allow to construct the full-time derivative of Lyapunov vector functions always as a sign-negative function equal to the scalar product of the velocity vector on the gradient vector. The conditions of aperiodic robust stability are obtained as a system of inequalities on the uncertain parameters of the automatic control system, which are a condition for the existence of the Lyapunov vector-function. A numerical example of synthesis of aperiodic robustness of a multidimensional control object is given. The example shows the main stages of the developed synthesis method, the study of the system stability at different values of the coefficients k, confirming the consistency of the proposed method. Transients in the system satisfy all requirements

This paper discusses an application of Robust Model Matching (RMM) to the spill position control of a fuel injection pump. Since the fuel injection servo mechanism is soaked in fuel oil, the parameters of the plant vary due to differences in the viscosity coefficient caused by wide changes in temperature. The invariable fuel injection characteristic is required to meet the demands of the drivability, exhaust emissions and fuel consumption, even though the parameters change. The RMM is an idea which makes up a robust control system against parameter uncertainties.In this paper, we design a robust discrete-time control system based on the RMM: (1) For the low sensitivity, to make small pulse transfer functions from equivalent disturbances to controlled variables. (2) For the robust stability, to increase the margin of pulse transfer functions from conceptual inputs to control variables. The experimental results show that this robust compensator makes up a robust control system against the parameter variations due to the change in temperature. And it is confirmed that the idea of the RMM is effective for the fuel injection pump which includes the variations, identification errors, friction, hysteresis and delay time of the calculation.

The controlled atmospheric re-entry associated with the precision soft-landing of Reusable Launch Vehicles (RLVs) on Earth is very challenging as it depends on multiple parameters [1]. Over the last decade, the cost-effectiveness of such a technology has been finally demonstrated with the successful recoveries of SpaceX’s Falcon 9 first-stage rocket first [2], then followed by other companies such as the Rocket Lab’s Electron micro-launcher [3]. This breakthrough has been made possible by the development of advanced and robust computational methods able to generate in real time the flight conditions and to command the optimal vehicle's deflections accordingly to achieve a safe pinpoint landing. Indeed, during an Earth atmospheric re-entry, the vehicle is subjected to fast system dynamics changes partly induced by external loads associated with the terrestrial environment (e.g., lift, drag, wind and gusts), but also by the actuation commands to answer the landing constraints satisfaction and the vehicle integrity preservation. All those involve uncertainties and nonlinearities, which lead to vehicle’s instability and therefore give reason why for a highly performant Guidance, Navigation and Control system implementation [4]. More particularly, one of the critical aspects is the design of a robust control strategy capable of counteracting the previously defined disturbances and uncertainties while satisfying the strict accuracy requirements associated with the pinpoint landing [5]. As demonstrated by the current state-of-the-art on control design for launchers [6-7], the classical linear control theory represents a rich heritage with a lot of applications. This choice was motivated by its relative easiness of implementation and the possibility to use gain-scheduling techniques to adapt to nonlinear systems. Nevertheless, these techniques are well-adapted to the control system design of single-input single-output systems, such as for example a reusable rocket using a Thrust Vector Control (TVC) system as the unique actuator. The implementation of multiple-input multiple-output control systems becomes then complex since every channel is addressed in a single-loop fashion. This capability is however required for the future generation of reusable rocket, using also aerodynamic steering based on fins in addition to the TVC system for enhancing control authorities. Moreover, model uncertainties are not accurately considered in the design process, developed only with nominal conditions and stability margin requirements. For all these reasons, it results in an extensive (both in terms of time and cost) Verification and Validation campaign with many iterations and Monte-Carlo analyses to assess the performance and robustness of the control system. To overcome these drawbacks, the H-infinity family of methods, introduced a few years ago [8], provides with a powerful solution for robust control design. It relies on defining the control requirements in the frequency domain in terms of weighting functions and minimising the maximum gain of the resulting weighted system from the exogenous inputs to the outputs to be controlled. Moreover, the control-plant interaction is modelled through a Linear Fractional Transformation (LFT) representing the feedback action. Finally, the structured H-infinity method [9] allows to directly impose a specific control structure – like a Proportional-Integral-Derivative (PID), enabling the re-use of gain-scheduling techniques – and to consider parametric uncertainties for enhanced robustness. This paper studies the synthesis of a robust control system via structured H-infinity for the RLV atmospheric re-entry problem. First, the nonlinear 6-Degree-of-Freedom (6-DoF) RLV re-entry dynamics are simplified into a linear model and then linearised along a reference trajectory to get the nominal LFT of the system, then augmented with parametric uncertainties. The model covers the atmospheric re-entry and vertical landing of a first-stage rocket equipped with a TVC system and steerable planar fins. The controllers are built at different points of the re-entry trajectory, using the structured H-infinity framework through PID-like structures. Weighting functions considering the control objectives and requirements of a realistic RLV re-entry scenario are implemented. A robust stability analysis of the obtained system is performed via classical stability margins and structured singular value. Finally, the controllers are gain-scheduled and validated via Monte-Carlo analyses, using a nonlinear 6-DoF RLV re-entry dynamics simulator equipped with successive convex optimisation guidance. The performance of the resulting guidance and control architecture is compared with the baseline developed in previous works [10], using a TVC system only and classical linear feedback control through gain-scheduled PID controllers. This study lies within the ASCenSIon (Advancing Space Access Capabilities - Reusability and Multiple Satellite Injection) project, an innovative training network funded within H2020.

A Computer Package for the Synthesis of Optimal Control Systems with Arbitrary Performance Index

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

Root-Locus Methods for Robust Control Systems Quality and Stability Investigations

The issues of expediency of using adaptation tools in robust control systems are discussed. It is stated that purely robust systems without the use of adaptation tools, in principle, cannot provide high efficiency and versatility in solving practical problems. Robust control systems were originally conceived as non-adaptive systems (passive adaptive systems). In view of the emerging problems in solving practical problems, then a mutation occurred and works appeared under the name "Adaptive-robust systems", "Combined robust systems", etc., partially using adaptation algorithms. Setting the problem of control synthesis under conditions of uncertainty without elements of adaptation is figuratively speaking similar to "search for a black cat in a dark room, especially if it is not there" (Confucius). The most adequate from the point of view of compliance with the fundamental principles of the theory of automatic control is an approach based on an increase in the gain of an open loop. Nevertheless, here too a problem arises — an increase in the gain violates the stability of a closed system. All known research is concentrated around the solution of this problem. An integrated gain self-tuning algorithm and the corresponding circuitry and Simulink implementation scheme have been developed. The reliability of theoretical reasoning was verified by simulating a limiting robust system with self-tuning and a parametrically indeterminate object — "peak gyroscope (parametric pendulum)". Computer studies have made it possible to draw a number of positive conclusions that are of great practical importance.

The minimum variance benchmark is too radical, because it only pursues the minimum variance without considering the robustness of control system, resulting in the life of equipment reducing. So other advanced benchmarks are derived. Quadratic Gaussian benchmark and generalized minimum variance benchmark are directing extensions of the minimum variance benchmark. The penalty for the control effect is considered to avoid the phenomenon of extreme minimum variance. The robustness of the system is greatly improved and the evaluation effect is better. Industrial processes often encounter multi-disturbance dynamics, such as the simultaneous existence of tracking disturbance and random disturbance, or the simultaneous existence of two different kinds of disturbance between actuator and controlled object. Therefore, in this paper, the performance evaluation of generalized minimum variance multi-disturbance control system is proposed.

Here, the robustness of the nuclear reactor control system is discussed by its computer simulation results which are obtained respectively from the analysis without the external control system and the analysis with the external control system. After this, the simulation tests both with the classical PID control and with the advanced PID control are also given. And then, the comparative analysis on the robustness of the reactor control system is shown. Finally, the useful approach improving the robustness of the nuclear reactor control system is provided, too.

Synthesis of the Flexible Flight Control Algorithms Via Reflection Onto Integral Auxiliary Surfaces

We propose a robust control system which has robustness for disturbance and can deal with a nonlinear system with partially unknown structure by fusing reinforcement learning and robust control theory. First, we solved an optimal control problem without using unknown part of functions of the system, using neural network and the repetition learning of reinforcement learning algorithm. Second, we built the robust reinforcement learning control system which permits uncertainty and has robustness for disturbance by fusing the idea of H infinity control theory with above system.

This paper proposes a new robust feedforward tracking servo system for optical disk recording systems in the case of a sudden disturbance for the optical disk recording system. In optical recording systems, the tracking servo system must suppress tracking error below its tolerance. This paper designs the robust feedback control system by using the coprime factorization and disturbance observer. The proposed robust feedback control system suppresses the sudden disturbance caused by walking and running. The detecting signal of optical disk recording systems is only a tracking error. Hence, the feedforward controller of the proposed tracking control system is constructed based on both Zero Phase Error Tracking (ZPET) control theory and prediction of tracking error. The experimental results point out that the proposed tracking servo system has a quick and precise tracking response and keeps the residual tracking error below its tolerance. © 2006 Wiley Periodicals, Inc. Electr Eng Jpn, 156(4): 60– 68, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.20257

We consider synthesis and modeling of hierarchical robust magnetic control systems for plasma in tokamaks with adaptation of the magnetic axis' vertical position. The studies were done for ITER (Cadarache, France) and Globus-M (St. Petersburg, Russia) tokamaks. Our original synthesis method ensures an improvement in performance for the shape of the plasma by resolving the contradiction between position and plasma shape via adaptation in a hierarchical system. Numerical modeling of synthesized control systems on multivariable linear models of plasma and nonlinear plasma-physics code DINA that unites basic equations of plasma dynamics in a magnetic field has shown the efficiency of the proposed approach and a possibility to apply it in a physical experiment.