Control System Identification Research Articles

Stages and main tasks of the century-long control theory and system identification development. Part IV. Methods and problems of designing robust control systems

The article provides a review of the most important methods and problems in the design of robust discrete control systems. In this case, the main attention was focused on the problems of suppressing limited external disturbances, information about which is presented only in the form of a limitation on their maximum value. The use of invariant ellipsoids is considered as the first mathematical apparatus for describing the characteristics of the influence of external disturbances on the trajectory of motion of dynamic systems. Theorems on the representation of invariant ellipsoids in the form of linear matrix inequalities (LMI) are formulated, which are further used to synthesize discrete state controllers that suppress external disturbances. The solution to a more general problem of robust suppression of limited disturbances based on the use of LMI in the presence of system uncertainties in the parameters of the mathematical model of the control object is considered. The use of H∞-control theory is considered as a second mathematical apparatus for suppressing external l2-limited external disturbances. In this case, the optimality criterion consists in minimizing the maximum ratio of the l2-norm of the vector of output stabilized coordinates to the l2-norm of the vector of input disturbances. The problem is solved by reducing it to the problem of robust control of a discrete dynamic system in space H∞ based on the Two-Ricatti approach. The standard H∞-optimization problem is also considered.

THE FREQUENCY METHOD FOR OPTIMAL IDENTIFICATION OF CLOSE-LOOP SYSTEM ELEMENTS

Context. The article is devoted to overcoming the contradictions between the assumptions adopted in known methods of closedloop control system identification and the design and conditions of its operation. The article presents a new method of identifying the transfer functions matrix of a two-level closed-loop control system element, which functions under the conditions of multidimensional stationary centered random influences.
 Objective. The purpose of the study, the results of which are presented in this paper, is to extend the indirect identification method to the case of estimating one of the two-level closed-loop control system elements’ dynamics model based on passive experiment data.
 Method. To solve the optimal identification problem, a variational method for minimizing the quality functional on the class of fractional-rational transfer function matrices was used.
 Results. As a result of the research, the identification problem formulation was formalized, the rules for obtaining experimental information about the input and output signals were determined, the rules for identifying the transfer functions matrix of a two-level closed-loop control system element, which minimizes the sum of the variances of identification errors in the frequency domain, and the verification of these rules was carried out.
 Conclusions. Justified rules allow to correctly determine transfer functions matrices of the closed-loop systems selected element when fulfilling the defined list of conditions. The closed-loop systems control paths signals analysis proves the possibility of the effect of changing these signals statistical means, even under conditions of only centered stationary input influences actions on the system. Based on this, the further development of research can be aimed at overcoming such effects.

Stages and main tasks of the century-long control theory and system identification development. Part III. The problem of complex systems identifying by inaccurate data

The article presents the main most noteworthy research results on the identification problem and methods that are widely used in solving identification problems. The most significant here is the problem of modeling especially complex systems, for which it is impossible, even in general, but in constructive form for identification, to write down a class of models in which the system under study has the most accurate description in which there is one of them adequate to the available data obtained from experiments. If the available knowledge on the object under study does not allow us to write down a suitable class of models in mathematical form, then asymptotic modeling should be used, as is done in computational mathematics. Instead of differential, integral and other equations, for example, algebraic equations approximating them are solved, the solutions of which approach the exact ones with increasing dimension and discretization step. Various forms of asymptotic expansions are used in identification, including rational approximation as applied to irrational and infinite-dimensional systems. However, in the presence of errors in the data, the use of asymptotic modeling leads to the fact that, with intentions to increase the accuracy of the resulting model due to its large dimension, in many cases the identification problems becomes incorrectly posed. Therefore, we have to look for a compromise or trade-off between bias and variance, which should determine the best-quality model. In addition to the modeling problem, the article discusses two concepts on the basis of which most existing methods for solving identification problems are based. Both of them give their own interpretation of the errors present in the data, namely, stochastic and nonstochastic. With the stochastic concept, errors are treated as a random process or sequence. The concept of estimation consistency is introduced, which makes it possible to use widely the theory of statistics in justifying methods for solving identification problems. The nonstochastic identification paradigm allows for arbitrary but bounded uncertainties in the data, i.e. belonging to some bounded sets. The largest number of different methods, as well as algorithms and software implementations, are made within the framework of the stochastic concept. Within the framework of nonstochastic identification, we mainly consider various modifications of the so-called subspace methods. In relation to complex systems, problems were noted that did not allow the development of sufficiently universal and effective methods for solving identification problems. A number of research areas have been pointed out that need further development in order to obtain more accurate models of complex systems.

Stages and main tasks of the century-long control theory and system identification development

The article provides a review of the mathematical description of the dynamics of continuous and discrete linear stationary systems and objects, used at the development stage of the classical theory of automatic control in the form of mathematical models of the «input-output» type. The time and frequency characteristics of continuous and discrete control systems are described, typical links of stationary systems are considered, parametric discrete models of objects as part of typical digital control loops are presented. Stochastic discrete autoregressive models of stationary time series used to describe the dynamic objects in the synthesis of digital control systems are considered. A review of standard control laws for the implementation of continuous and discrete controllers has been completed. A method for synthesizing discrete controllers for multidimensional controlled objects with different, unknown and changing delays is considered, through which variable delays are compensated in the characteristic equation of a closed-loop control system. A common technique for synthesizing one-dimensional and multidimensional controllers for stochastic objects with delays based on ARMAX models is considered. An analysis of approaches to identifying delays in controlled objects is carried out and a method for identifying delays when using input-output models is considered, based on the calculation and comparison of impulse responses for extended and non-extended models of the controlled object. An analysis of the advantages and disadvantages of «input-output» type models is given, as well as the possibilities of their application for solving various classes of control theory problems.

Parameters identification of the satellite attitude control system with large inertia rotating components

This paper investigates the unbalance parameter identification of the large inertia rotating component of satellite. Firstly, the dynamics model with unbalance parameter of the large inertia rotating component is established. Then, based on the principle of parameter separation and decoupling, a modified two-stage exogenous Kalman filter (TSXKF) algorithm is proposed. This method works directly on nonlinear system, estimates the centroid position, the centroid velocity, attitude angular, attitude angular velocity, and identifies the nonlinear unknown static unbalance parameter, which is the centroid offset. Finally, the simulation results verify the effectiveness of the method.

Stages and main tasks of the century-long the control theory and system identification development. Part I. State space method in the theory of linear automatic control systems

This article opens a series of publications dedicated to the scientific and technical achievements of the century-long development of control theory and methods. Problems that could not be fully resolved based on one approach or another are also noted. The first of these articles is devoted to the state space method, which began to actively develop somewhere in the 70-80s of the last century within the framework of systems theory and general systems theory. A description of the method is given in relation to linear automatic control systems. A generally accepted description of controlled and observable dynamic processes in such systems is given. The problems of synthesis of stabilizing control in closed loop systems with feedback based on the theory of stability formulated by Lyapunov are mainly considered. In addition to stability, within the framework of the state space method, such important qualitative properties as controllability and observability are formulated. The most developed method is the synthesis of state-based linear controllers. Among them, a special pole placement by method of modal control synthesis occupies a special place which is considered within the framework of the Jordan implementation and various modifications of the method depending on the dimension of the control vector. The synthesis of an optimal controller with a quadratic criterion of a fairly general form is considered. In case of incomplete measurements, when the dimension of the output is less than the dimension of the state vector, in order to implement synthesized control laws based on the state, it becomes necessary to include a state estimator in the control system. In the deterministic case, you can use the Luenberger estimator described in the article, and in the presence of measurement errors in the form of zero-mean white noise, the widely used Kalman filter, also presented in the article. The output control method was not left unattended in the work. The conclusions give the advantages and disadvantages of control methods based on state-space descriptions.

The Unscented Kalman Filter for Nonlinear Parameter Identification of Adaptive Cruise Control Systems

This paper develops and investigates a dual unscented Kalman filter (DUKF) for the joint nonlinear state and parameter identification of commercial adaptive cruise control (ACC) systems. Although the core functionality of stock ACC systems, including their proprietary control logic and parameters, is not publicly available, this work considers a car-following scenario with a human-driven vehicle (leader) and an ACC engaged ego vehicle (follower) that employs a constant time-headway policy (CTHP). The objective of the DUKF is to determine the CTHP parameters of the ACC by using real-time observations of space-gap and relative velocity from the vehicle's onboard sensors. Real-time parameter identification of stock ACC systems is essential for assessing their string stability, large-scale deployment on motorways, and impact on traffic flow and throughput. In this regard, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\mathfrak {L}}_{2}$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\mathfrak {L}}_\infty$</tex-math></inline-formula> string stability conditions are considered. The observability rank condition for nonlinear systems is adopted to evaluate the ability of the proposed estimation scheme to estimate stock ACC system parameters using empirical data. The proposed filter is evaluated using empirical data collected from the onboard sensors of two 2019 SUV vehicles, namely Hyundai Nexo and SsangYong Rexton, equipped with stock ACC systems; and is compared with batch and recursive least-squares optimization. The set of ACC model parameters obtained from the proposed filter revealed that the commercially implemented ACC system of the considered vehicle (Hyundai Nexo) is neither <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\mathfrak {L}}_{2}$</tex-math></inline-formula> nor <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\mathfrak {L}}_\infty$</tex-math></inline-formula> string stable.

Comparing multivariable uncertain model structures for data‐driven robust control: Visualization and application to a continuously variable transmission

AbstractThe selection of uncertainty structures is an important aspect of system identification for robust control. The aim of this paper is to provide insight into uncertain multivariable systems for robust control. A unified method for visualizing model sets is developed by generating Bode plots of multivariable uncertain systems, both in magnitude and phase. In addition, these model sets are compared from the viewpoint of the control objective, allowing a quantitative analysis as well. An experimental case study on an automotive transmission application demonstrates these connections and confirms the importance of the developed framework for control applications. In addition, the experimental results provide new insights into the shape of associated model sets by using the presented visualization procedure. Both the theoretical and experimental results confirm that a recently developed robust‐control‐relevant uncertainty structure outperforms general dual‐Youla‐Kučera uncertainty, which in turn outperforms traditional uncertainty structures, including additive uncertainty.

A novel approach to determining the hydrodynamic resistance of droplets in microchannels using active control and grey-box system identification

Inaccurate prediction of droplet hydrodynamic resistance has a profound impact on droplet chip performance and lengthens the iterative design process. Previous studies measuring droplet resistance use various approaches such as interface comparison to quantify flow rate, and pressure taps; all these methods are classified as passive. Although each study supports well their own findings, the wide variety of conditions such as channel geometry and use of surfactant in combination with the difficulty in quantifying the droplet resistance leads to poor consensus across the different studies. Overall guidelines would be broadly beneficial to the community, but are currently fairly crude, with a rule of thumb of 2 to 5 times resistance increase. The active droplet control platform previously developed enables a novel approach that is herein confirmed as promising. This proof-of-concept study focuses on verifying this approach that employs a system identification method to determine the hydrodynamic resistance of a channel containing a single droplet, from which the droplet resistance is retrieved. This method has the potential to be further applied to a large variety of conditions, and most importantly, to non-Newtonian fluids once key limitations are overcome to improve measurement resolution. The current results qualitatively agree with the literature and demonstrate the promising future for this novel active approach to quantifying droplet resistance.

Nonlinear neural control using feedback linearization explains task goals of central nervous system for trunk stability in sitting posture

Objective. Characterizing the task goals of the neural control system for achieving seated stability has been a fundamental challenge in human motor control research. This study aimed to experimentally identify the task goals of the neural control system for seated stability. Approach. Ten able-bodied young individuals participated in our experiments, which allowed us to measure their body motion and muscle activity during perturbed sitting. We used a nonlinear neuromechanical model of the seated human, along with a full-state feedback linearization approach and optimal control theory for identifying the neural control system and characterizing its task goals. Main results. We demonstrated that the neural feedback for trunk stability during seated posture uses angular position, velocity, acceleration, and jerk in a linearized space. The mean squared error between the predicted and measured motor commands was less than 0.6% among all trials and participants, with a median correlation coefficient of more than 0.9. Our identified optimal neural control primarily used trunk angular acceleration and near-minimum muscle activation to achieve seated stability while keeping the deviations of the trunk angular position and acceleration sufficiently small. Significance. Our proposed approach to neural control system identification relied on a performance criterion (e.g. cost function) explaining what the functional goal is and subsequently, finds the control law that leads to the best performance. Therefore, instead of assuming what control schemes the neural control might utilize (e.g. proportional-integral-derivative control), optimal control allows the motor task and the neuromechanical model to dictate a control law that best describes the physiological process. This approach allows for a mechanistic understanding of the neuromuscular mechanisms involved in seated stability and for inferring the task goals used by the neural control system to achieve the targeted motor behavior. Such neural control characterization can contribute to the development of objective balance evaluation tools and of bio-inspired assistive neuromodulation technologies.

Adaptive behavior in sonar prey tracking tasks: Empirical data and modeling

Echolocating bats can discriminate small differences in target range (Simmons, 1973) and show a clutter interference zone along the range axis of 8–9 cm (Simmons et al., 1988). Because bats use an active sensing system, they can employ various strategies to mitigate the effects of clutter. We studied clutter rejection behaviors of the big brown bat, Eptesicus fuscus, as it tracked a moving target under controlled conditions. We also created data-driven models using control theory and system identification techniques to evaluate oscillating target motion tracking strategies. We trained bats to rest on a stationary platform and track a moving tethered mealworm in two conditions (1) approaching and passing by stationary clutter objects at varying distances and angular offsets, and (2) moving in sinusoidal patterns in an open room. Data from the first experimental condition revealed adaptive echolocation call features and head movements that enabled target tracking in the presence of clutter. Under the oscillating target condition, we analyzed adaptive echolocation behavior to create a data-driven model that maps changes in target motion with sonar call rate. The results of this study demonstrate the bat’s use of active motor control that separates targets from clutter and to track complex motion trajectories.

A New Residual Generation-Based Fault Estimation Approach for Cyber-Physical Systems

This article investigates the problem of data-driven actuator fault estimation for cyber-physical systems (CPSs). First, a stable kernel representation (SKR)-based residual generator is constructed to achieve online detection for actuator fault using the system inputs–outputs (I/O) data. Then an iterative learning fault estimation (ILFE) algorithm is designed to reconstruct the actuator fault in real time. The proposed method realizes the actuator fault estimation when the model parameters are unknown, which avoids much time spent in the modeling process. Moreover, compared with the existing model-based approaches, the presented method still has better transient performance, steady-state performance, and computational efficiency, which is more suitable for the fault identification of practical control systems. Finally, the application to a servo motor demonstrates the superiority of the designed fault estimation method.

Optimal Signal Design in System Identification for Model Predictive Control (MPC)

Optimal Signal Design in System Identification for Model Predictive Control (MPC)

Identification of Engine Rotation Speed Control System Installed in Research Aircraft “Hisho''

Identification of Engine Rotation Speed Control System Installed in Research Aircraft “Hisho''

Design of an E-Learning Course on control systems modeling for students in applied physics

The research aims to prepare an e-learning course on ‘Identification and Mathematical Modeling of Control systems’ for students in Applied Physics. The software systems Matlab/Simulink, SciLab/Xcos are used for working mastering of the tutorial. The training is based on scaffolding principles, i.e. gradual complication of tasks. The e-learning course is designed in Moodle. It provides easy input and output (import and export) of the course content. The paper presents characteristic properties of the offered course development, which involves many constituent elements and resources of the platform: Page, Glossary, File, Chat, Forum, Presentation, Video lecture, Assignment, Comment, Test, Book, Interactive content, Hyperlink, and Database. The piloting was conducted at Almetyevsk State Oil Institute and Sholom-Aleichem Priamursky State University, Pacific National University, and Far Eastern State Transport University in 2020-2021. The designed online course is introduced in learning based on the distance learning system of Almetyevsk State Oil Institute Digital University. The student’s knowledge and skills assessment over the above-mentioned length of studies prove the effectiveness of the electronic learning resource applied for different kinds of learning. The electronic learning resource is turned out to be useful when changing to distance learning and in the blended learning model.

Research on Identification Algorithm of Cascade Control System

Aiming at the problem of object model identification of modern industrial process control systems, a new closed-loop moment parameter identification online method based on the data of normal operation of the running system is proposed. In this method, only one step response data of the system is required, and appropriate convergence factors are introduced into the Laplace formula, the trapezoidal integral method is used to calculate the values of two derivatives of the transfer function, then the four unknown parameters of the second-order model can be solved by fitting the data with the least square method, and the target model can be identified. Finally, the simulation results of building different objects through Matlab show that the identification method has general applicability and good robustness with high recognition, and it is not sensitive to noise signals.

Cascade tanks system identification for robust predictive control

Cascade tanks system identification for robust predictive control

New Results of Some of the Conformable Models Arising in Dynamical Systems

This article investigates the new results of three nonlinear conformable models (NLCMs). To study such varieties of new soliton structures, we perform the generalized Kudryashov (GK) method. The obtained new results are defined in the styles of the exponential and rational functions. The derived new soliton structures are stable, serviceable, and fitting to embrace the conformable dynamics, chaotic vibrations, global bifurcations, optimal control problems, fluid mechanics, plasma physics, system identification, local bifurcations, control theory and resonances, and so many. The outcomes declare that the process is hugely valuable and accessible for investigating nonlinear conformable order models treated in theoretical physics.

Design of FOPID Controller for Pneumatic Control Valve Based on Improved BBO Algorithm.

Aiming at the problems of nonlinearity and inaccuracy in the model of the pneumatic control valve position in the industrial control process, a valve position control method based on a fractional-order PID controller is proposed. The working principle of the pneumatic control valve is analyzed, and its mathematical model is established. In order to improve the accuracy of the model, an improved biogeography-based optimization algorithm is proposed to tune the parameters of the fractional-order PID controller in view of the wide range and high complexity of the fractional-order PID controller. The initialization of the chaotic graph, the adjustment of the migration model, and the improvement of the migration operator and the mutation operator are introduced to improve the algorithm optimization ability, which is used for the model identification of the control valve control system. The simulation and experimental results clearly show that, compared with the integer-order PID controller, the designed fractional-order PID controller has faster response speed and control accuracy, which can better meet the requirements of pneumatic control valve position control.

System identification and mechanical resonance frequency suppression for servo control used in single gimbal control moment gyroscope.

Effective identification of the control model is one of the key aspects in improving the performance of the single gimbal control moment gyroscope (SGCMG) servo system. The accuracy and stability of the servo system can be improved by studying system identification and mechanical resonance frequency. In this study, firstly, the SGCMG gimbal servo system was simplified to a two-mass block model. The theoretical mathematical model of the system's transfer function and mechanical resonance frequency was derived. Secondly, this paper studied the effective suppression method for mechanical resonance. Thirdly, the mathematical model of the orthogonal correlation analysis method was deduced for system identification. Then, an experimental platform was investigated to obtain the frequency characteristic curve and the transfer function. Finally, the frequency characteristic curve obtained using the transfer function model was plotted and compared with the frequency characteristic curve obtained experimentally. Our results indicate that the orthogonal correlation analysis has a high identification accuracy.