Synthesis of Linear Control Systems with Maximum Speed and Given Overshoot

One of the problems of the theory of management of objects with a high degree of uncertainty of behavior is solved: the development of theoretical foundations of analysis, modeling methods and improvement of bio cybernetic systems, their algorithmic and software necessary to improve the efficiency of the management process is proposed. To solve this problem, it is proposed to use the mathematical apparatus of information theory, on the basis of which the information characteristics of the control signal transmission channel from the source to the control object through the external environment are calculated, taking into account the noise of the ecosystem of the control object. The existing systems using monomodal control signals that do not carry a semantic load are analyzed, and the disadvantages and limited possibilities of improving the control systems under consideration are described. Using the example of one of the insect behavior control systems with a trichromic view, a comparison of the results obtained using various technical means used as control signal sources was performed. For improving the efficiency of control systems, which use a multimodal control signal structure, proposed various algorithms for constructing control systems using a multimodal control signal structure are considered, namely: serial and parallel circuits, combined, combining serial and parallel algorithms for using control signal sources. As a method for further improving the efficiency of control systems for biological objects with a high degree of uncertainty, it is proposed to use biological signals containing a large semantic load for the control object, which determines its behavioral response. The directions of further research are formulated in order to maximize the amount of information transmitted to the control object.

This rigorous yet accessible textbook provides broad and systematic coverage of linear multivariable control systems, including several new approaches to design. In addition to standard state space theory, it provides a new measurement-based approach to linear systems, including a generalization of Thevenin's Theorem, a new single-input single-output approach to multivariable control, and analytical design of PID controllers developed by the authors. Each result is rigorously proved and combined with specific control systems applications, such as the servomechanism problem, the fragility of high order controllers, multivariable control, and PID controllers. Illustrative examples solved using MATLAB and SIMULINK, with easily reusable programming scripts, are included throughout. Numerous end-of-chapter homework problems enhance understanding. Based on course-tested material, this textbook is ideal for a single or two-semester graduate course on linear multivariable control systems in aerospace, chemical, electrical and mechanical engineering.

This rigorous yet accessible textbook provides broad and systematic coverage of linear multivariable control systems, including several new approaches to design. In addition to standard state space theory, it provides a new measurement-based approach to linear systems, including a generalization of Thevenin's Theorem, a new single-input single-output approach to multivariable control, and analytical design of PID controllers developed by the authors. Each result is rigorously proved and combined with specific control systems applications, such as the servomechanism problem, the fragility of high order controllers, multivariable control, and PID controllers. Illustrative examples solved using MATLAB and SIMULINK, with easily reusable programming scripts, are included throughout. Numerous end-of-chapter homework problems enhance understanding. Based on course-tested material, this textbook is ideal for a single or two-semester graduate course on linear multivariable control systems in aerospace, chemical, electrical and mechanical engineering.

This rigorous yet accessible textbook provides broad and systematic coverage of linear multivariable control systems, including several new approaches to design. In addition to standard state space theory, it provides a new measurement-based approach to linear systems, including a generalization of Thevenin's Theorem, a new single-input single-output approach to multivariable control, and analytical design of PID controllers developed by the authors. Each result is rigorously proved and combined with specific control systems applications, such as the servomechanism problem, the fragility of high order controllers, multivariable control, and PID controllers. Illustrative examples solved using MATLAB and SIMULINK, with easily reusable programming scripts, are included throughout. Numerous end-of-chapter homework problems enhance understanding. Based on course-tested material, this textbook is ideal for a single or two-semester graduate course on linear multivariable control systems in aerospace, chemical, electrical and mechanical engineering.

This rigorous yet accessible textbook provides broad and systematic coverage of linear multivariable control systems, including several new approaches to design. In addition to standard state space theory, it provides a new measurement-based approach to linear systems, including a generalization of Thevenin's Theorem, a new single-input single-output approach to multivariable control, and analytical design of PID controllers developed by the authors. Each result is rigorously proved and combined with specific control systems applications, such as the servomechanism problem, the fragility of high order controllers, multivariable control, and PID controllers. Illustrative examples solved using MATLAB and SIMULINK, with easily reusable programming scripts, are included throughout. Numerous end-of-chapter homework problems enhance understanding. Based on course-tested material, this textbook is ideal for a single or two-semester graduate course on linear multivariable control systems in aerospace, chemical, electrical and mechanical engineering.

This rigorous yet accessible textbook provides broad and systematic coverage of linear multivariable control systems, including several new approaches to design. In addition to standard state space theory, it provides a new measurement-based approach to linear systems, including a generalization of Thevenin's Theorem, a new single-input single-output approach to multivariable control, and analytical design of PID controllers developed by the authors. Each result is rigorously proved and combined with specific control systems applications, such as the servomechanism problem, the fragility of high order controllers, multivariable control, and PID controllers. Illustrative examples solved using MATLAB and SIMULINK, with easily reusable programming scripts, are included throughout. Numerous end-of-chapter homework problems enhance understanding. Based on course-tested material, this textbook is ideal for a single or two-semester graduate course on linear multivariable control systems in aerospace, chemical, electrical and mechanical engineering.

This rigorous yet accessible textbook provides broad and systematic coverage of linear multivariable control systems, including several new approaches to design. In addition to standard state space theory, it provides a new measurement-based approach to linear systems, including a generalization of Thevenin's Theorem, a new single-input single-output approach to multivariable control, and analytical design of PID controllers developed by the authors. Each result is rigorously proved and combined with specific control systems applications, such as the servomechanism problem, the fragility of high order controllers, multivariable control, and PID controllers. Illustrative examples solved using MATLAB and SIMULINK, with easily reusable programming scripts, are included throughout. Numerous end-of-chapter homework problems enhance understanding. Based on course-tested material, this textbook is ideal for a single or two-semester graduate course on linear multivariable control systems in aerospace, chemical, electrical and mechanical engineering.

This article is devoted to the development of a new method of synthesis a regulators’ transfer functions matrix of an optimal multivariable open-loop control system. The regulator is designed to maximize an accuracy of a nonlinear multivariable control object transition from one steady state to another. It is assumed that disturbances act on the control object and sensors measuring data has inertia and noise. Both disturbances and noises are an additive combination of regular and random components. Random components belong to a class of interconnected stationary processes with rational spectral density matrices. A substantiated method differs from the known one by the fact that during formulation and solution of the problem somebody uses a new block diagram of the control system, which takes into account the results of metrological certification of a sensor dynamics. Synthesis of the regulator is carried out in the frequency domain by the Wiener-Kolmogorov method. A new algorithm, which is obtained as a result of synthesis problem solution, allows you to find the matrix of regulator transfer functions , which provides a minimum of corresponding quadratic quality criteria’s. The first of them is equal to the sum of certain way weighted squared deviations regular repetition errors of the object path and control signals. The second criterion is equal to the sum of the weighted variance of the random error components and the control signals. To execute the proposed algorithm it is necessary to perform the operations of Wiener factorization and separation of rational matrices. The corresponding functions are contained in the freely distributed software package SciLab.

This research work involves the speed control of a mobile robot where stabilization is provided by Non-linear controller. A Mobile Robot capable of following human target, assisted by various sensors that detects the clearance distance between the target and the robot to avoid collision or to maintain constant distance needs a robust control system. A robot in order to follow a human or target which has variable speed must have decision capabilities to decide when to speed up or slow down according to the situation. This decision can be obtained by the use of Artificial Neural Network (ANN) which reduces the burden on the controller reducing the complexity of calculation involved to control the speed of the motors. All these above sensors and actuators provide values as input to the Neural Network database for learning stage providing classification into several actions. The classes and weights obtained by the Neural Network learning phase is then used to vary the speed of the Robot. The speed however being unstable and providing several unnecessary movements will then be stabilized by using Linear Quadratic Regulator control algorithm. Thus, providing a complete solution to setting a fluent and stable Mobile Robot that can track and follow and target under any conditions.

The question addressed is placed in the broad context of fuzzy control, based on fuzzy PI controller, of industrial processes, the equivalence of fuzzy PI controllers with linear PI controllers, tuned with given methods, for the improvement of performance of control systems. The purpose of the study is to analyze the possibility of these implementation and to find the behavior of the resulted fuzzy control systems to compare with the linear control systems. The tuning criteria chosen are the modulus criterion in Kessler’s variant for second-order processes with two time constants, the symmetric criterion in Kessler’s variant, for the second order processes with purely integrator character and Ziegler-Nichols criterion for slow processes. The equivalence of the fuzzy controllers with the linear controllers was made using the input-output transfer characteristics of the fuzzy block and its linearization in the origin to obtain the gain in the origin. The results consist of an equivalence formula for the controller, simulation characteristics for the control systems, comparisons and analyses. The main conclusions are that fuzzy regulators can be designed by equating linear regulators with the presented method and better regulation performances can be obtained.

Performance limits and deconstraints of linear feedback control systems disturbed by random noise are studied from the viewpoint of information theory. By using Bode integral formulas, information transmission in such systems is connected to unstable poles and nonminimum phase zeros of open-loop transfer functions. Performance limits of disturbance rejection are discussed by using such connection, and the conservation law of variety is revised based on a new extended definition of variety. Meanwhile, a necessary information condition which implies a new kind of design constraints of linear tracking problem is proposed with the concept of mutual information rate, and the law of requisite variety is derived from this condition.

Let G be a connected Lie group with Lie algebra g. This review is devoted to studying the fundamental dynamic properties of elements in the normalizer NG of G. Through an algebraic characterization of NG, we analyze the different dynamics inside the normalizer. NG contains the well-known left-invariant vector fields and the linear and affine vector fields on G. In any case, we show the shape of the solutions of these ordinary differential equations on G. We give examples in low-dimensional Lie groups. It is worth saying that these dynamics generate the linear and bilinear control systems on Euclidean spaces and the invariant and linear control systems on Lie groups. Moreover, the Jouan Equivalence Theorem shows how to extend this theory to control systems on manifolds.

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.

The problem of analyzing the tuning parameters of linear continuous controllers related to the class of state models is studied. To do this, algorithms for adjusting the controller are used, which are based on estimates of the plant parameters. Within the framework of this study, the adaptability property of the system is considered, and the primary goal is to determine the possibility of finding an exact solution to the problem of tuning the control loop for a given reference transient. Moreover, the study extends to a whole class of input actions, such as piecewise continuous functions of time. Based on the analysis of the convergence properties of the identification residual in a closed control system, additional simplified conditions for the adaptability of control systems using an identifier and a reference model are put forward, which supplement the already existing knowledge on this topic.

Essential Linearization: A Synthesis Technique for P.W.M. Control System