Dynamical Control Systems Research Articles

Decision Support for Flexible Manufacturing Systems: The Evaluation of an Ecological Interface and Principles of Ecological Interface Design

The cognitive systems engineering (CSE)/ecological interface design (EID) approach was applied in developing decision support for the flexible manufacturing system (FMS) work domain. Four interfaces were designed via the factorial application/non-application of direct perception (DP) and direct manipulation (DM). The capability of these interfaces to support performance in a simulated FMS was evaluated using a variety of traditional and novel dependent variables. The ecological interface (with DP, DM and an intact perception-action loop) provided clearly superior decision support (32 favorable significant results) relative to the other three interfaces (a combined total of 28 favorable significant results). The novel dependent variables were very sensitive. The results are interpreted from three different perspectives: traditional EID, the quality of constraint matching between triadic system components and closed-loop, dynamical control systems. The rationale for an expanded theoretical framework which complements, but does not replace, the original principles of CSE/EID is discussed. The potential for both specific interface features and novel dependent variables to generalize to real-world FMS applications is addressed. The expanded theoretical framework is universally relevant for the development of decision making and problem solving support in all computer-mediated work domains.

Non-positive barrier function: a new notion of barrier function for state-safety control of nonlinear dynamical systems

The analysis and control of system state safety are a research hotspot in the field of control. This article has thoroughly investigated some issues related to safety criteria with application to the safety analysis, diagnosis, and safety control of a class of dynamical systems with their unique set of available states via a new notion of barrier functions. Inspired by reciprocal barrier functions and zeroing barrier functions, a type of non-positive barrier function (NPBF) is designed and the safety criteria are proposed, guaranteeing that the unique set of available states is forward-invariant to ensure system safety at all times. Then, the control barrier function is established based on NPBFs for a class of dynamical control systems and used to design the safety controller. Conclusively, this is a first-of-its-kind study to apply safety criteria and control barrier functions to safeguard a class of continuously stirred tank reactors.

Reactive and Risk-Aware Control for Signal Temporal Logic

The deployment of autonomous systems in uncertain and dynamic environments has raised fundamental questions. Addressing these is pivotal to build fully autonomous systems and requires a systematic integration of planning and control. We first propose reactive risk signal interval temporal logic (ReRiSITL) as an extension of signal temporal logic (STL) to formulate complex spatiotemporal specifications. Unlike STL, ReRiSITL allows to consider uncontrollable propositions that may model humans as well as random environmental events such as sensor failures. Additionally, ReRiSITL allows to incorporate risk measures, such as (but not limited to) the conditional value-at-risk, to measure the risk of violating certain spatial specifications. Second, we propose an algorithm to check if an ReRiSITL specification is satisfiable. For this purpose, we abstract the ReRiSITL specification into a timed signal transducer and devise a game-based approach. Third, we propose a reactive planning and control framework for dynamical control systems under ReRiSITL specifications.

A Convex Approach to Data-Driven Optimal Control via Perron–Frobenius and Koopman Operators

This article is about the data-driven computation of optimal control for a class of control affine deterministic nonlinear systems. We assume that the control dynamical system model is not available, and the only information about the system dynamics is available in the form of time-series data. We provide a convex formulation for the optimal control problem (OCP) of the nonlinear system. The convex formulation relies on the duality result in the dynamical system’s stability theory involving density function and Perron–Frobenius operator. We formulate the OCP as an infinite-dimensional convex optimization program. The finite-dimensional approximation of the optimization problem relies on the recent advances made in the Koopman operator’s data-driven computation, which is dual to the Perron–Frobenius operator. Simulation results are presented to demonstrate the application of the developed framework.

Application of the Tomtit Flock Metaheuristic Optimization Algorithm to the Optimal Discrete Time Deterministic Dynamical Control Problem

A new bio-inspired method for optimizing the objective function on a parallelepiped set of admissible solutions is proposed. It uses a model of the behavior of tomtits during the search for food. This algorithm combines some techniques for finding the extremum of the objective function, such as the memory matrix and the Levy flight from the cuckoo algorithm. The trajectories of tomtits are described by the jump-diffusion processes. The algorithm is applied to the classic and nonseparable optimal control problems for deterministic discrete dynamical systems. This type of control problem can often be solved using the discrete maximum principle or more general necessary optimality conditions, and the Bellman’s equation, but sometimes it is extremely difficult or even impossible. For this reason, there is a need to create new methods to solve these problems. The new metaheuristic algorithm makes it possible to obtain solutions of acceptable quality in an acceptable time. The efficiency and analysis of this method are demonstrated by solving a number of optimal deterministic discrete open-loop control problems: nonlinear nonseparable problems (Luus–Tassone and Li–Haimes) and separable problems for linear control dynamical systems.

A new result on PD controller design for second order nonlinear uncertain systems

Under what condition a proportional-derivative (PD) controller can stabilize globally second order nonlinear uncertain systems? It is an important and attractive question. This paper will broaden the range of a function space F which is used to describe the uncertainty of nonlinear systems in literature, such that the corresponding result still holds for nonlinear dynamical control systems with more uncertainty. The method is based on some related results in the research about Markus-Yamabe Conjecture.

Automatic gas dynamic volumetric system for aquatic products' MA preservation

As there are many links in the cold chain logistics process, which takes a long time, the processed aquatic products are easily damaged and deteriorated. And the growth and reproduction of microorganisms in aquatic products can be inhibited by MA (Modified Atmosphere) preservation, thus extending the shelf life of aquatic products. In this context, we have developed an automatic gas dynamic volumetric system for aquatic products' MA preservation. It can control the operation platform by a 4G network cell phone client and realize remote monitoring function. Particularly, there are the main contents and conclusions of the study: 1) Combined with MA preservation, intelligent control and network communication technologies, we overcame the difficulties of remote monitoring for gas dynamic volumetric. Then, according to MA preservation and automatic gas dynamic volumetric, we designed a logical structure of the system, including the specific distribution of the sensing layer, network transmission layer and application layer. 2) We established the mathematical model for the system based on the step response method, and designed the analog acquisition, control and gas dynamic volumetric system; In addition, in this system, we realized the gas dynamic volumetric based on the embedded PID control algorithm and mass flow controller; Then, we used 4G network for remote data transmission and 4G DTU as network data transceiver, and realized remote monitoring function of mobile client through cell phone terminal applet software. 3) The results were shown by testing the stability, accuracy and communication of the system: the gas concentration error of the system floated at ± 0.25% when the gas dynamic volumetric system was stable, which was 12 times more accurate than before, and the gas dynamic volumetric speed based on embedded PID control algorithm was increasing by approximately about 50%, which greatly improved the working conditions and production efficiency.

Disconnection-Aware Attack Detection and Isolation With Separation-Based Detector Reconfiguration

This study addresses incident handling during an adverse event for dynamical networked control systems. Incident handling can be divided into five steps: detection, analysis, containment, eradication, and recovery. For networked control systems, the containment step can be conducted through physical disconnection of an attacked subsystem. In accordance with the disconnection, the equipped attack detection unit should be reconfigured to maintain its detection capability. In particular, separating the detection subunit associated with the disconnected subsystem is considered as a specific reconfiguration scheme in this study. This article poses the problem of disconnection-aware attack detection and isolation with the separation-based detector reconfiguration. The objective is to design an attack detection unit that preserves its detection and isolation capability even under any possible disconnection and separation. The difficulty arises from network topology variation caused by disconnection that can possibly lead to stability loss of the distributed observer inside the attack detection unit. A solution is proposed based on an existing controller design technique referred to as retrofit control. Furthermore, an application to low-voltage power distribution networks with distributed generation is exhibited. Numerical examples evidence the practical use of the proposed method through a benchmark distribution network.

A Comparative Energy Analysis of Dynamic External Shadings for Office Buildings

Abstract In this paper, the energy performance of dynamic instead of static shading devices is investigated for prototypical US office spaces. Specifically, six dynamic shading systems are considered to assess their ability to reduce heating and cooling thermal loads, total building energy use, and electrical peak demand. The most promising dynamic shading is the rotating overhang and is evaluated further using a wide range of design and operation conditions. It is found that rotating overhangs can provide effective and easily controllable dynamic shading systems for windows to reduce the energy consumption of US office buildings by up to 39% especially for mild US climates. Moreover, the rotating overhangs have the added benefit to support PV panels for on-site electricity generation. A series of sensitivity analysis results indicate that the performance of the dynamic external shading systems depends on its depth and orientation, the location climate, the window size, and the glazing type have significant impacts. For instance, the dynamic shading device can reduce annual heating and cooling energy end-use for an office space located in Boulder, CO, compared to no shading case by 19% for a window-to-wall ratio (WWR) of 15% and by 31% for a WWR of 30%.

Control of a Discrete Dynamical System with Noise

For a discrete dynamical control system with noise, we consider the problem of retaining a phase point in a given family of sets at discrete instants of time. We analyze the case where the control vectogram is a polyhedron defined by a system of linear inequalities. We prove some properties of specific polyhedra satisfying the linearity condition, which allows us to obtain a condition of retention in the explicit form. Necessary and sufficient conditions for the possibility of retention are given. The results obtained are illustrated by an example.

Orbital decompositions and integrable pseudosymmetries of control systems

Local decompositions of nonlinear dynamical control systems are investigated. We use orbital equivalences to transform systems into decomposed forms. In the language of infinite jets, every control system is interpreted as an infinite dimensional manifold. Each orbital decomposition of the system defines an invariant distribution on this manifold. A local basis of this distribution is an integrable pseudosymmetry of the system. An algorithm for constructing orbital decompositions is given and demonstrated by the example of the Kapitsa pendulum system. It is also shown how to use orbital decompositions to plan trajectories.

Technique for optimizing the adaptive control of the output of an enterprise based on a dynamical economic and mathematical model

The article is devoted to the application of dynamic economic and mathematical models for managing the production of an enterprise based on the use of the feedback principle. Formation of a discrete controllable dynamical system is given, which describes the process of production output by a manufacturing enterprise in the presence of a predictable demand function for products. The phase vector of a dynamical system describes the main parameters of production, and the control action vector (control vector) describes the intensity of the use of technological methods of production that are available to the subject of control. It is assumed that in each period of time the subject of control knows the vector function that describes the volume of demand for the company's products in subsequent periods of time, and the given geometric restrictions on the implementation of the phase vector, control vector and demand vector are also known. As the target function of the problem, the value of the discrepancy between the volumes of output by the enterprise relative to the given predicted value of the demand function in the subsequent control period is considered. Using the generated dynamical system, the paper proposes an economic-mathematical model of the studied problem of optimizing the adaptive control of the enterprise's output, which includes a class of admissible strategies for adaptive control and the formulation of the problem. The paper proposes a method for solving the formulated problem of optimizing the adaptive control of the output of an enterprise, which is implemented as a finite sequence of one-step algebraic operations on vectors of a finite-dimensional vector space, a finite set of solutions to problems of linear and convex mathematical programming. The results obtained can be used in the development of intelligent decision support systems for the actual tasks of managing the production of products at industrial enterprises.

On Periodical Damping Ratio of a Controlled Dynamical System With Parametric Resonances

A dynamical system whose damping of oscillation or vibration is directly controlled may manifest a periodically varying damping ratio. In this letter, such a phenomenon is discovered to arise from a new type of parametric resonance, named the “zero-th order parametric resonance,” which is different from the conventional principal parametric resonance. This letter proposes an approach using the method of multiple scales to find approximate, analytical solutions of the system and thus providing an interpretation on damping variations.

PID Control System Design and Automatic Tuning Using MATLAB/SIMULINK [Bookshelf

Proportional-integral-derivative (PID) controllers are undoubtedly the most employed controllers in industry, and they have significantly contributed to the impact of control systems in society. This book is a very welcome addition to the PID control literature as it aims to reduce the gap between theory and practice and foster technology transfer from academia to industry. Indeed, the topics included in the book are useful for students and practitioners in different fields to better understand how to design a PID controller and address the many issues that are faced in practice. The only prerequisites that are assumed of the reader are a basic knowledge of feedback control systems and dynamic systems (for example, transfer functions, frequency response, and state space models). The main feature of this book is the presence of many detailed worked examples that help the reader understand the underlying concepts. The reader is guided in developing Matlab scripts (also available from the book’s associated website) that help to clearly outline the sequence of steps associated with each design technique. There are also study questions, provided after each section, designed to evaluate whether the reader fully understands the chapter topics. Numerical and simulation problems are also presented at the end of each chapter. Overall, the pedagogical approach followed in this text is appreciated and commendable. This book is suitable for those students and practitioners who have been exposed to a single control course and want to learn more about PID controllers or are asked to work with them in an industrial setting. It is worth emphasizing that, due to the inclusion of resonant controllers and a chapter dedicated to unmanned aerial vehicles, this book addresses general areas of application and is not only limited to process control problems. In summary, this book is a very good reference for those who want to deepen their knowledge about PID control without requiring a strong background in control theory. Further advancements in the field can then be learned from other more advanced books once the basic concepts have been mastered.

Reinforcement learning control of constrained dynamic systems with uniformly ultimate boundedness stability guarantee

Reinforcement learning (RL) is promising for complicated stochastic nonlinear control problems. Without using a mathematical model, an optimal controller can be learned from data evaluated by certain performance criteria through trial-and-error. However, the data-based learning approach is notorious for not guaranteeing stability, which is the most fundamental property for any control system. In this paper, the classic Lyapunov’s method is explored to analyze the uniformly ultimate boundedness stability (UUB) solely based on data without using a mathematical model. It is further shown how RL with UUB guarantee can be applied to control dynamic systems with safety constraints. Based on the theoretical results, both off-policy and on-policy learning algorithms are proposed respectively. As a result, optimal controllers can be learned to guarantee UUB of the closed-loop system both at convergence and during learning. The proposed algorithms are evaluated on a series of robotic continuous control tasks with safety constraints. In comparison with the existing RL algorithms, the proposed method can achieve superior performance in terms of maintaining safety. As a qualitative evaluation of stability, our method shows impressive resilience even in the presence of external disturbances.

High-order fully actuated system approaches: part VII. Controllability, stabilisability and parametric designs

In this paper, high-order fully actuated (HOFA) models with multiple orders for general dynamical control systems are firstly proposed, for which controllers can be easily designed such that the closed-loop systems are constant linear ones with completely assignable eigenstructures. Based on this special feature of the type of HOFA models, controllability of general dynamical control systems is proposed. It is revealed that a general dynamical control system can be represented by a controllable subsystem described by a HOFA model, and an extra uncontrollable one or supplementary one. While a general dynamical control system is called stabilisable if its uncontrollable (autonomous) subsystem does not exist, or is stable in a certain sense. Finally, two parametric design approaches for control of the type of general HOFA models are proposed, which provide all the design degrees of freedom. Several examples, including ones of sub-fully actuated systems, are treated, which demonstrate the effect of the proposed theories.

Algorithm for solving optimal open-loop terminal control problem for spacecraft rendezvous with account of constraints on the state

The paper proposes an algorithm for solving the optimal open-loop terminal control problem of two spacecraft rendezvous with constraints on their states. A system of nonlinear differential equations that describes the dynamics of the active (maneuvering) spacecraft relative to the passive spacecraft (station) in the central gravitational field of the Earth in the orbital coordinate system of coordinates related to the passive spacecraft center-of-mass is considered as an initial model. The obtained nonlinear model of the active spacecraft dynamics is linearized relative to the specified reference state trajectory of the passive spacecraft, and then it is discretized and reduced to linear recurrence relations. Mathematical formalization of the spacecraft rendezvous problem under consideration is carried out at a specified final moment of time for the obtained discrete-time controlled dynamical system. The quality of solving the problem is estimated by a convex functional taking into account the geometric constraints on the active spacecraft states and the associated control actions in the form of convex polyhedral-compacts in the appropriate finite dimensional vector space. We propose a solution of the problem of optimal terminal control over the approach of the active spacecraft relative to the passive spacecraft in the form of a constructive algorithm on the basis of the general recursive algebraic method for constructing the availability domains of linear discrete controlled dynamic systems, taking into account specified conditions and constraints, as well as using the methods of direct and inverse constructions. In the final part of the paper, the computer modeling results are presented and conclusions about the effectiveness of the proposed algorithm are made.

Dynamic Control of Integrated Wind Farm Battery Energy Storage Systems for Grid Connection

The intermittent nature of wind power is a major challenge for wind as an energy source. Wind power generation is therefore difficult to plan, manage, sustain, and track during the year due to different weather conditions. The uncertainty of energy loads and power generation from wind energy sources heavily affects the system stability. The battery energy storage system (BESS) plays a fundamental role in controlling and improving the efficiency of renewable energy sources. Stochasticity of wind speed and reliability of the main system components are considered. This paper presents a dynamical control system based on model predictive control (MPC) in real time, to make full use of the flexibility and controllability of energy storage to mitigate problems of wind farm variability and intermittency. The control scheme first plans the expected output, then stochastic optimization is used to optimize grid integrated wind farm BESS output power, develop an optimal operation strategy for BESS, and prevent some unpredictable conditions that may have impacts on the stability of the system. The results show that the proposed method can reduce grid-connected wind power fluctuations, limit system faults, control command for the BESS in the dispatching period, and ensure system stability for grid connection.

Optimization of Right-Hand Sides of Nonlocal Boundary Conditions in a Controlled Dynamical System

We study an optimal control problem described by a system of linear ordinary differential equations with boundary conditions containing point and integral values of the state variable. The controls occurring in the differential equations and the values of the right-hand sides of the nonlocal boundary conditions are determined in this problem. Necessary conditions for the existence and uniqueness of a solution of the boundary value problem and for the convexity of the objective functional, as well as necessary conditions for the optimality of the parameters to be optimized in the control problem, are studied. The formulas obtained for the gradient of the objective functional of the problem are used in the numerical solution of an illustrative problem. The results of numerical experiments are provided.

Closed-loop online harmonic vibration estimation in DC electric motor systems

In this article, an active vibration control technique for direct-current electric motors subjected to harmonic mechanical load torque is introduced. Formulae to compute uncertain parameters of amplitude, frequency and phase angle of harmonic torque disturbances for angular velocity reference trajectory tracking are proposed. Vibrating torque disturbances are actively suppressed by the control voltage input. Mathematical modelling based on vibrating systems is adopted for purposes of online parameter estimation of oscillating signals. In this fashion, accurate estimation can be performed using measurements of the output signal only. Online parameter estimation is extended for a class of controllable dynamical engineering systems subjected to harmonic disturbances. Formulae for closed-loop online parameter estimation of harmonic vibrations on differentially flat linear dynamical systems of n degrees of freedom for efficient tracking of desired time-varying motion reference profiles are then presented. Analytical and numerical results prove that proposed formulae can be used to accurately determine the parameters of unknown harmonic vibrations, which is an excellent feature for high-efficiency active vibration control strategies.