Dynamic Feedback Control Research Articles

Continuous Growth Monitoring and Prediction with 1D Convolutional Neural Network Using Generated Data with Vision Transformer.

Crop growth information is collected through destructive investigation, which inevitably causes discontinuity of the target. Real-time monitoring and estimation of the same target crops can lead to dynamic feedback control, considering immediate crop growth. Images are high-dimensional data containing crop growth and developmental stages and image collection is non-destructive. We propose a non-destructive growth prediction method that uses low-cost RGB images and computer vision. In this study, two methodologies were selected and verified: an image-to-growth model with crop images and a growth simulation model with estimated crop growth. The best models for each case were the vision transformer (ViT) and one-dimensional convolutional neural network (1D ConvNet). For shoot fresh weight, shoot dry weight, and leaf area of lettuce, ViT showed R2 values of 0.89, 0.93, and 0.78, respectively, whereas 1D ConvNet showed 0.96, 0.94, and 0.95, respectively. These accuracies indicated that RGB images and deep neural networks can non-destructively interpret the interaction between crops and the environment. Ultimately, growers can enhance resource use efficiency by adapting real-time monitoring and prediction to feedback environmental controls to yield high-quality crops.

A novel approach for perfusion process design based on a "Grey-Box" kinetic model.

Perfusion cell-culture mode has caught industrial interest in the field of biomanufacturing in recent years. Thanks to new technology, perfusion-culture processes can support higher cell densities, higher productivities and longer process times. However, due to the inherent operational complexity and high running costs, the development and design of perfusion-culture processes remain challenging. Here, we present a model-based approach to design optimized perfusion cultures of Chinese Hamster Ovary cells. Initially, four batches of bench-top reactor continuous-perfusion-culture data were used to fit the model parameters. Then, we proposed the model-based process design approach, aiming to quickly find out the "theoretically optimal" operational parameters combinations (perfusion rate and the proportion of feed medium in perfusion medium) which could achieve the target steady-state VCD while minimizing both medium cost and perfusion rate during steady state. Meanwhile, we proposed a model-based dynamic operational parameters-adjustment strategy to address the issue of cell-growth inhibition due to the high osmolality of concentrated perfusion medium. In addition, we employed a dynamic feedback control method to aid this strategy in preventing potential nutrient depletion scenarios. Finally, we test the feasibility of the model-based process design approach in both shake flask semi-perfusion culture (targeted at 5 × 107 cells/ml) and bench-top reactor continuous perfusion culture (targeted at 1.1 × 108 cells/ml). This approach significantly reduces the number of experiments needed for process design and development, thereby accelerating the advancement of perfusion-mode cell-culture processes.

Stability analysis and anti-windup design of saturated switching systems based on multiple Lyapunov functions

Abstract In this paper, employing advanced multiple Lyapunov functions (MLF) technology, we conduct a thorough investigation into the fault-tolerant characteristics of actuator saturation-based systems, particularly those prone to failures. Based on this comprehensive analysis, we carefully design an anti-windup (AW) controller, incorporating an efficient AW compensator and precisely calibrated gains for the dynamic state feedback controller, tailored to meet the specific needs of practical control systems. To further demonstrate the effectiveness of our approach, we also provide a detailed numerical example.

Digital sand patch: Using laser scanning and discrete element simulation for rapider pavement texture depth measurement

The sand patch method is one of the most basic methods for measuring pavement texture depth (TD), which is an important reference index for pavement anti-skid performance evaluation and road maintenance. However, manual sand patch method heavily relies on the experience of the operators. The emergence of laser 3D scanning and simulation has made it possible to conduct digital sand patch. This study introduces a digital sand patch framework based on 3D scanning and discrete element simulation for precise TD measurement. We developed a 3D scanner with an accuracy of 0.04 mm to obtain the pavement texture data, along with algorithms for outlier removal and slope correction in point cloud data. The method of 3D reconstruction of triangular meshes was adopted to transform discrete point clouds into continuous 3D models to build 3D pavement models. In addition, the virtual process of rotation-spreading-measurement of the digital sand patch method was constructed by discrete element simulation with reference to the physical principles of the manual sand patch method. At the same time, an adaptive dynamic feedback control logic was proposed to accurately determine the termination conditions of the sand patching process. To validate our method, we collected 126 samples from over 20 km of pavement surfaces with various gradations. The results demonstrated an average relative error of 2.92 % compared to the manual sand patch method, and a correlation coefficient of 0.9926 with the laser scanning Mean Profile Depth (MPD) algorithm. Stability and accuracy tests, including scanning downsampling and volatility assessments, confirmed the robustness of our method. This innovative technique for rapid and precise TD measurement not only offers immediate practical benefits but also sets the stage for future research on pavement skid resistance.

Dynamic error prediction and link strain feedback control for a novel heavy load multi-DOF envelope forming machine

Thin walled and high rib components (TWHRC) are widely used for rocket cabins, aircraft wings, panels and frames in aerospace equipment as critical load bearing structures. This paper is aimed to develop a novel multi-DOF envelope forming machine (MEFM) with parallel kinematic mechanism (PKM) to realize efficient manufacturing of TWHRC with high performance. Since the heavy load MEFM with PKM has many total differences with the light load PKM, such as dynamic error and precision control, this paper conducts research on dynamic error prediction modelling and precision control method for this novel heavy load MEFM.Firstly, the configuration of MEFM is developed and the kinematic model of MEFM is established. Then, a RFC (rigid-flexible coupling) and RFE (rigid finite element) coupling dynamic model of MEFM is established considering time-variation of kinematic configuration caused by large deformation of all the kinematic elements. Based on the dynamic model, the dynamic deformation and error of MEFM are predicted and their generation mechanisms are revealed. It is found that the linear compression deformation of two-force links is the largest among all the kinematic elements, and it is the most sensitive to the heavy forming load and the most insensitive to the installation error of strain gauges, thus suiting for the feedback of large deformation of MEFM. Based on the above findings, a novel link strain feedback and dynamic error compensation control method is proposed. Finally, experiments under different control methods are conducted, showing that the motion precision of envelope tool and forming precision of formed components under the proposed control method are remarkably improved compared with that under the traditional control method (The geometric deviation of formed components under the proposed control method is remarkably reduced to −18 ∼ 32um from −64 ∼ 54um under the traditional control method). The experimental results verify that the proposed dynamic error prediction model and link strain feedback control method for heavy load MEFM are reasonable.

Anti-control of Hopf bifurcation for a chaotic system

Abstract The anti-control of Hopf bifurcation is a method used for bifurcation control. It can be used to realize the occurrence or delay of bifurcation at the specified position to meet the needs of engineering applications. In this study, a 4D chaotic system is studied, and a dynamic state feedback control method is proposed to realize the anti-control of Hopf bifurcation for the system. By adjusting the control parameters of the controller, the system Hopf bifurcation can be generated or delayed at the specified position to realize the anti-control of Hopf bifurcation. This control method avoids complicated calculation processes and has remarkable control effects. Through numerical simulation analysis, the correctness of this control method is verified.

Model-Free Adaptive State Feedback Control for a Class of Nonlinear Systems

This paper investigates state feedback control for a class of discrete-time multiple input and multiple output nonlinear systems from the perspective of model-free adaptive control and state observation. The design of a dynamic state feedback control can be efficiently carried out using dynamic linearization and state observation. The stability of the proposed method is guaranteed by theoretical analysis. Numerical simulation tests and experimentation on a continuous stirred tank reactor are carried out to validate the effectiveness of the proposed approach. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —The growth in the scale of factories and the complexity of associated production processes increases the complexity and time involved in associated mathematical modelling. Data driven approaches to control remove the need to model processes. To the best of the authors’ knowledge, existing approaches to model-free adaptive control (MFAC) of general systems are all based on an input-output control paradigm. These methods thus cannot guarantee the stability of the system state. The purpose of this study is to develop a novel Model-Free Adaptive Control (MFAC) approach to achieve control of the system state. In this paper, the assumptions required to achieve model-free adaptive control by state feedback are presented mathematically. A controller design and the associated stability proof are then presented. Numerical simulation and experimentation is conducted to validate the effectiveness of the proposed approach. In future research, state feedback data control in the presence of random disturbances will be investigated.

Feedback dynamic control for exiting a debt-induced spiral in a deterministic Keen model.

The Keen model is designed to represent an economy as a dynamic system governed by the interactions between private debt, wage share, and employment rate. When certain conditions are met, the model can lead to a debt spiral, which accurately mimics the impact of a financial crisis on an economy. This manuscript presents a recipe for breaking this spiral by expressing Keen's model as an affine nonlinear system that can be modified through policy interventions. We begin by considering critical initial conditions that resemble a financial crisis to achieve this goal. We then locate a desired point within the system's vector field that leads to a desirable equilibrium and design a path towards it. This path is later followed using one-step-ahead optimal control. We illustrate our approach by presenting simulated control scenarios.

A Behavioral Approach to Data-Driven Control With Noisy Input–Output Data

This paper deals with data-driven stability analysis and feedback stabilization of linear input-output systems in auto-regressive (AR) form. We assume that noisy input-output data on a finite time-interval have been obtained from some unknown AR system. Data-based tests are then developed to analyse whether the unknown system is stable, or to verify whether a stabilizing dynamic feedback controller exists. If so, stabilizing controllers are computed using the data. In order to do this, we employ the behavioral approach to systems and control, meaning a departure from existing methods in data driven control. Our results heavily rely on a characterization of asymptotic stability of systems in AR form using the notion of quadratic difference form (QDF) as a natural framework for Lyapunov functions of autonomous AR systems. We introduce the concepts of informative data for quadratic stability and quadratic stabilization in the context of input-output AR systems and establish necessary and sufficient conditions for these properties to hold. In addition, this paper will build on results on quadratic matrix inequalities (QMIs) and a matrix version of Yakubovich's S-lemma.

Observer-based dynamic event-triggered control for distributed parameter systems over mobile sensor-plus-actuator networks

Abstract The objective of this paper is to develop a policy of observer-based dynamic event-triggered state feedback control for distributed parameter systems over a mobile sensor-plus-actuator network. It is assumed that the mobile sensing devices that provide spatially averaged state measurements can be used to improve state estimation in the network. For the purpose of decreasing the update frequency of controller and unnecessary sampled data transmission, an efficient dynamic event-triggered control policy is constructed. In an event-triggered system, when an error signal exceeding a specified time-varying threshold it indicates the occurrence of a typical event. The global asymptotic stability of the event-triggered closed-loop system and the boundedness of the minimum inter-event time can be guaranteed. Based on the linear quadratic optimal regulator, the actuator selects the optimal displacement only when an event occurs. A simulation example is finally used to verify the effectiveness of such a control strategy can enhance the system performance.

New results on dynamic output state feedback stabilization of some class of time-varying nonlinear Caputo derivative systems

In modern control theory applications, input–output feedback often arises and plays a crucial role in stabilizing any target control systems. However, in many practical applications, the knowledge of full information on the state of systems may not be available in general due to measurements. In order to control such types of systems, this paper uses a universal concept of real order calculus to stabilize by the method of dynamic output feedback control. Is it possible to design a dynamic output feedback stabilization for time-varying real order control systems? This work develops a new dynamic output feedback control method and proposes linear homogeneous time-varying control law to stabilize incommensurate nonlinear time-varying real order systems under the action of Caputo derivative with an addendum of ultimate random initial-time. We utilize the ideas of the comparison method and establish order-dependent asymptotic results associated with uniform Lipschitz continuous functions that provide stabilization by means of the dynamic output state feedback control method. We provide three examples that include a practical system and show the importance of some theoretical results in the demonstration to stabilize the problems by means of proposed control method.

Dynamic feedback H ∞ control for discrete singular systems with time–varying delays

This work carefully revisits the topic of dynamic feedback H ∞ control problem for discrete singular systems (DSSs) with time–varying delays. A new state decomposed Lyapunov-Krasovskii functional is presented by a discrete state decomposition method. For the unforced nominal DSSs, delay–dependent sufficient conditions with an H ∞ performance index are derived. Based on these conditions, a closed–loop system being regular and causal is developed via a dynamic feedback controller. As a new discrete state decomposition–reorganization method is proposed, the required admissibility conditions are attained. Through the accurate calculation of each decomposition component of the dynamic feedback controller, the desired dynamic feedback controller settings are determined. The numerical findings demonstrate the superiority of our method over earlier approachers, and the results are less conservative.

Command filter and high gain observer based adaptive output feedback control for stochastic nonlinear systems with prescribed performance and input quantization

SummaryIn this paper, an adaptive output feedback dynamic surface control (DSC) strategy is proposed for strict‐feedback stochastic nonlinear systems with input quantization, prescribed performance and dynamic uncertainties. A new quantizer is used to process the input signal, which can avoid the chattering of the quantization signal and keep the upper bound of the quantization error constant. Radial basis functions are used to approximate unknown smooth functions, unmodeled dynamics are processed by dynamic signals, and unmeasurable states are estimated by high gain observer. Hyperbolic tangent functions are employed to handle prescribed performance. The second order command filter is used to replace the first order filter used in general DSC, and the compensation term is added in each step of DSC. By the Lyapunov stability analysis, all signals in the controlled system are semi‐globally uniformly ultimately bounded (SGUUB) in probability. Two examples further prove that the control scheme designed in this paper is reasonable and effective.

Individual axis control for industrial robots by posture-variant dynamic compensation and feedback control using the FDTD method

Industrial robots experience posture-dependent inertial variation and interference forces between joints, which in turn generates undesired vibrations due to the inherent elasticity of the reduction gears, making it difficult to control each axis independently. Conventionally, dynamic compensation is used to compensate the robot dynamics and decouple each axis, while state feedback control based on a two-inertia model is used for dealing with the vibrations caused by the elasticity of the reduction gears. However, the control design for this approach usually assumes a fixed moment of inertia, so its performance is compromised when large and fast changes in the robot posture occurs. In this paper, a posture-variant approach that takes into account the posture-dependent inertial variation in real time is proposed to achieve exact dynamic compensation and independent control of each axis regardless of the robot posture. The state equations of the posture-variant two-inertia system model for each robot axis are discretized using the finite-difference time-domain (FDTD) method and adapted on both the dynamic compensation and feedback control parts, allowing to easily redesign the whole control system considering the inertial variation at each control cycle. The effectiveness of the method is confirmed by experimental verification on a 6-axis industrial robot.

I&I adaptive fault-tolerant control of a class of nonaffine systems with nonlinearly parameterised faults

This paper provides a novel fault-tolerant control scheme for a class of nonaffine systems with nonlinearly parameterised (NLP) faults. The nonaffine system is firstly transformed into an augmented one via dynamic feedback control. A fault-tolerant controller with Immersion and Invariance (I&I) adaptation law is designed for the transformed system through dynamic surface control. The controller avoids complexity due to the explosion of terms in backstepping design. The I&I adaptation law is developed to recover the unknown parameters of NLP faults in the system. The proposed scheme can shape the transient performance of the parameter estimation error and tracking error. In the tracking problem, all the signals and tracking error converge exponentially to a small neighbourhood of the origin. In the regulation problem, the system output converges exponentially to zero. A numerical simulation is carried out to verify the effectiveness of the proposed scheme.

An Analytic Investigation of Hopf Bifurcation Location Control for the Rulkov Map Model

From the point of view of nonlinear dynamical systems, some neurological disorders can be indicated by bifurcations because bifurcations change the firing patterns of neurons; therefore, it is essential to control the bifurcations. We can avoid undesirable dynamical behaviors such as the behaviors of the Rulkov map model by controlling bifurcation which, then, can assist in modeling neuronal diseases. In this paper, we investigate the existence of Hopf bifurcation and analytically identify the type of bifurcation for the Rulkov map model; then, we apply a dynamic feedback controller using a washout filter to control the onset of Hopf bifurcation. Also, we can control the behaviors of the neurons, such as spiking or spiking-bursting behavior of neurons, and create the Hopf bifurcation for some parameters. The results analytically obtained in this paper can be applied to control some epileptic seizures.

Data-driven optimal output regulation for unknown linear discrete-time systems based on parameterization approach

The output regulation problem has been studied based on a parameterization approach. Different from existing literature, the proposed method does not rely on prior knowledge of the system dynamics. Instead, it leverages state and input data to address the absence of information regarding unmodeled dynamics. Firstly, the output regulation problem is transformed into a stabilization problem by using coordination transformation. The feedback control gain is computed directly by solving an optimization problem using input and state data. The feedforward control gain is obtained by using data-based solutions of regulator equations. Secondly, the design of a dynamic feedback controller is also explored within the framework of a data-driven strategy. Thirdly, two algorithms corresponding to the optimal and dynamic data-driven output regulation problems are developed to implement the proposed data-driven method. Finally, a simulation example is carried out to illustrate the effectiveness of the developed data-driven approach.

Adaptive Containment Control of Multiple Underactuated Hovercrafts Subjected to Switching and Directed Topologies

This article addresses the containment control for a group of uncertain underactuated hovercrafts with multiple leaders and switching directed topologies. The underactuated hovercrafts in question are underactuated, nonholonomic, and passively unstable. For such nonlinear systems, we apply the reduced-order method, time-varying approach, adaptive tool, and state transformation technique to derive a novel dynamic feedback control strategy that guarantees all hovercrafts in the group globally converge into the convex hull spanned by leaders. In particular, the proposed containment control algorithm allows the leader trajectories to be either feasible or nonfeasible, and either dynamic or stationary. The Lyapunov stability theory is applied to the closed-loop analysis. Numerical simulations illustrate the control design.

An experimental study on hybrid control of a solar tracking system to maximize energy harvesting in Jordan

Due to its capacity to maximize the power produced by photovoltaic (PV) panels, solar tracking systems have grown in popularity. However, erratic weather conditions, like cloudy or overcast days, change the panel's preferred orientation. On sunny days, the panel is turned to face the sun's radiation; however, on cloudy or overcast days, diffused radiation alters the optimal position. This has increased the necessity for new search algorithms that control the orientation of the panel to generate the most power feasible regardless of the weather conditions. This study aims at developing a sun-tracking system that can adjust the solar panel's orientation to generate the maximum possible electrical output from solar energy in Jordan, regardless of the local climate. To achieve this; a hybrid controller has been created that combines an open-loop sun monitoring system with a dynamic feedback controller built on an active search algorithm. The suggested algorithm is built on the real-time measurement of the PV panels' waning solar irradiance by using small solar cell 0.6 W. The system switches to the recently proposed circular path finding method to locate the Maximum Power Point Tracking (MPPT) if the instantaneous irradiance level falls below a predetermined threshold (DNI irradiance). As a result of the testing phase, the generated power of a solar panel increased by about 35%, confirming the effectiveness of the newly proposed sun tracker hybrid control system. During experimental test, positive irradiance current noises are appeared, using average filter taking the mean of 100 values for one measurement.

Adaptive Prescribed-Time Control of Time-Delay Nonlinear Systems via a Double Time-Varying Gain Approach.

This article studies the global prescribed-time stabilization problem for a class of time-delay nonlinear systems with uncertain parameters. First, we design two time-varying gains with special properties, in which one is introduced into virtual controllers to achieve prescribed-time convergence and the other one is used to construct the Lyapunov-Krasovskii (L-K) functional and Lyapunov function to handle the nonlinear time-delay term and unknown parameters, respectively. Then, by utilizing double time-varying gains and the scaling-free backstepping design approach, a dynamic state feedback controller is constructed, which guarantees that all state variables reach zero within a prescribed time, and the prescribed time can be specified in advance. Then, based on new functionals and regular differential inequality, we figure out the explicit expression for the upper bound of all variables, which plays an important role in proving the boundedness of all system variables. Final, a simulation example is given to demonstrate the effectiveness of the proposed method.