Linear Plant Research Articles

Event‐triggered model reference adaptive control system design for SISO plants using meta‐learning‐based physics‐informed neural networks without labeled data and transfer learning

SummaryThis paper examines the controllability of a novel Lyapunov‐based model reference adaptive control (MRAC) system designed with a meta‐learning‐based physics‐informed neural network (MLPINN) for linear and nonlinear single‐input and single‐output (SISO) plants without labeled data (MLPINN‐MRAC system). It is devised with the benefits of several techniques: the integration of the identification process in a training mode into an online control mode (straightforward design); no labeled data generation for online identification by a physics‐informed neural network; the prevention of degradation in tracking performance by meta‐learning, as the system triggers a meta‐learning process only when an error threshold detects the deterioration (high efficiency and the reduction of computation cost); quick adaptation to new inputs and an updated control input for each sub‐time span by transfer learning. It is worth noting that the frequency of the meta‐learning event detection significantly affects the step response stability of the nonlinear plant. To achieve a better quality of the stabilization, more frequent event detection is necessary for both beginning and end intervals in control. Sixteen triggering events are enough to shape the acceptable step response of the nonlinear plant, and 44 triggering events achieve the plant's desired step response with its minor modeling error. While, as for the linear plant, a single triggering event is sufficient to attain its tolerable step response and modeling error, implying that intensive event detection is not critical in the identification. It is obvious that the MLPINN‐MRAC system functions well and is more beneficial and efficient for the nonlinear plant.

Formation of productivity of maize hybrids of different ripening groups in the Forest-Steppe region

The relevance of the study is determined by the necessity of scientifically substantiating the rational ratio of maize hybrids of different ripening groups to ensure the realisation of the genetic potential in forming pre-harvest grain moisture at the level of 18-22%. Therefore, the purpose of the study is to identify the most adapted and plastic ripening groups considering biological features and to identify stable hybrids based on economic efficiency through the calculation of the hybrid’s productivity efficiency index. The method of plot division was used to conduct field research in accordance with the requirements of the research methodology. The results revealed that maize hybrids of different ripening groups react differently to temperature conditions, especially during the interphase period – 3-5 leaves. Maize hybrids with FAO (ripening group of the hybrid) 180-250, having a flint grain subtype, are characterised by faster linear plant growth due to higher cold resistance, making them suitable for early sowing when the soil temperature is 6-80C. Hybrids with FAO 300 and above, with a dent grain subtype, exhibit slower initial plant growth and are more thermophilic. Therefore, it is advisable to plant them after the soil has been thoroughly warmed to 8-100C. Studies have established that the highest grain yield was obtained from mid-late maturity maize hybrids (FAO 401-500) – 10.04-10.17 t/ha, with a maximum level of 14.89 t/ha in 2017. However, considering the dynamics of productivity levels over the years, the most plastic hybrids, i.e., those with the smallest difference in yield between years, are phenotypes with FAO 201-300. It was determined that early and mid-early ripening group hybrids had lower pre-harvest grain moisture – 0.6-23.9% compared to 28.7-2.7% in mid-ripening and mid-late ripening groups. This resulted in a higher productivity efficiency index for these hybrids. The materials of the study contain results for further research on optimising the use of maize hybrids with different FAO numbers and are of practical significance for farms of various ownership forms

Robust control of electrohydraulic soft robots.

This article introduces a model-based robust control framework for electrohydraulic soft robots. The methods presented herein exploit linear system control theory as it applies to a nonlinear soft robotic system. We employ dynamic mode decomposition with control (DMDc) to create appropriate linear models from real-world measurements. We build on the theory by developing linear models in various operational regions of the system to result in a collection of linear plants used in uncertainty analysis. To complement the uncertainty analyses, we utilize ("H Infinity") synthesis techniques to determine an optimal controller to meet performance requirements for the nominal plant. Following this methodology, we demonstrate robust control over a multi-input multi-output (MIMO) hydraulically amplified self-healing electrostatic (HASEL)-actuated system. The simplifications in the proposed framework help address the inherent uncertainties and complexities of compliant robots, providing a flexible approach for real-time control of soft robotic systems in real-world applications.

Sliding mode control for disturbance rejection and estimation under measurement delay with PDE‐backstepping predictor

AbstractIn this article, we address the disturbance rejection problem for linear plants with delayed measured output. The output delay is allowed to be time‐varying and of arbitrary duration. The disturbances that may represent actuator faults are generated by an exogenous dynamic system and can be matched or unmatched. A predictor–based observer is designed via the PDE–backstepping (Partial Differential Equation–backstepping) method so that an estimate of the current state vector, as well as that of unmeasured disturbance, can be obtained. These estimates are used in to regulate the output and reject the disturbance by output feedback sliding mode control. In addition, a solution for finite‐time disturbance rejection (rather than exponential only) is also introduced when the sensor delay is constant. Numerical examples illustrate the performance and robustness of the both proposed predictor‐feedback control systems.

Energetically Optimal Finite-Time Stabilization of Generalized Homogeneous Linear Systems

The problem of finite-time stabilization of a linear plant with an optimization of both a settling time and an averaged/weighted control energy is studied using the concept of generalized homogeneity. It is shown that the optimal finite-time stabilizing control in this case can be designed by means of solving a simple linear algebraic equation. Robustness of the obtained control law is studied.

Optimization of Weight Matrices for the Linear Quadratic Regulator Problem Using Algebraic Closed-Form Solutions

This work proposes an analytical gradient-based optimization approach to determine the optimal weight matrices that make the state and control input at the final time close to zero for the linear quadratic regulator problem. Most existing methodologies focused on regulating the diagonal elements using only bio-inspired approaches or analytical approaches. The method proposed, contrarily, optimizes both diagonal and off-diagonal matrix elements based on the gradient. Moreover, by introducing a new variable composed of the steady-state and time-varying terms for the Riccati matrix and using the coordinate transformation for the state, one develops algebraic equationsbased closed-form solutions to generate the required states and numerical partial derivatives for an optimization strategy that does not require the computationally intensive numerical integration process. The authors test the algorithm with one- and two-degrees-of-freedom linear plant models, and it yields the weight matrices that successfully satisfy the pre-defined requirement, which is the norm of the augmented states less than 10−5. The results suggest the broad applicability of the proposed algorithm in science and engineering.

Design of Discrete and Hybrid Nonlinear Control Systems

In this article the new method of discrete control systems design for nonlinear plants with differentiable nonlinearities is suggested. The increasing demands on the quality of control processes and the widespread use of computer technology provide ample opportunities for the design and implementation of digital control systems. However, discrete models of control plants are needed to solve this problem. In the case of linear plants, such models are created on the basis of z-transformation, Euler or Tustin formulas. In the case of nonlinear plants, these transformations are not applicable, so a large number of approximate discretization methods have been developed to date. Euler and Runge-Kutt transformations are used for these purposes most often, but they lead to satisfactory results only with very small period of discretization. In the case of automatic control systems, this requires the use of digital automation tools with very high speed, which is often economically impractical. Methods of discretization with a long period were most often developed on the basis of decomposition into series of the right-hand sides of the differential equations, transformed on Euler. Here, firstly, the problem of selecting the number of the series members, which to be retained arises, and secondly, already in the third or fourth order of the plant, the calculating ratios turn out to be extremely complex. The discretization method suggested below differs in that it is not the equations of nonlinear plants in the Cauchy form that are discretized, but the corresponding quasilinear model. In this case, a modified trapezoid method is used, and the discretization purpose is not the most accurate approximation of the original equations of the plant, but the stability of a closed nonlinear control system with rather big period. This system is designed using the algebraic polynomial-matrix method for designing of the nonlinear control systems. As a result, a hybrid nonlinear system with fairly simple algebraic calculation expressions is formed. The suggested approach makes it possible to create the control systems for nonlinear controlled plants using conventional computational automation tools.

Division Linearization Zero-Bias Current Control for AMBs–Rotor System With Uncertainties and Saturation

Traditional constant current sum (CCS) distribution strategy is always employed in the nonlinear active magnetic bearing (AMB) system control for linearization, but the bias current in CCS causes extra power consumption and limits the AMBs' capacity. In this paper, a division linearization zero-bias current (DLZBC) distribution strategy is proposed as a substitution for CCS strategy. Under this strategy, a linear active disturbance rejection controller (LADRC) with a static anti-windup compensator (SAWC) is applied to deal with model uncertainties and current saturation. For different types of AMB-supported machines, a partial normalized nonlinear model is established. Subsequently, the performance of the CCS strategy is analyzed, and a DLZBC strategy is presented to reduce the power consumption and transform the system into a linear plant with a lumped uncertain parameter. Afterward, a LADRC is designed to enhance robustness, whose parameters are chosen according to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mu -$</tex-math></inline-formula> synthesis framework and are convenient for adjustment practically. For anti-saturation, a SAWC is developed to help the system escape quickly from current saturation and enlarge the stability domain of the saturated system. Comparative simulations and experiments results show that the proposed control method can significantly reduce power consumption and achieve good response in AMB-rotor system.

Parameterization of minimal order strongly stabilizing controllers for two-link underactuated planar robot with single sensor

This paper investigates the minimal order of strongly stabilizing controllers for a two-link planar robot moving in a vertical plane with a single actuator and sensor, focusing on stabilizing the robot around its upright equilibrium point where both links are upright. By designing an output as the horizontal displacement of a point along the second link’s straight line, existing literature demonstrates that the robot’s strong stabilization problem is equivalent to that of a fourth-order linear plant, featuring two pairs of symmetric real poles and adjustable zeros. In contrast to an existing second-order strongly stabilizing controller tailored to a pair of symmetric real zeros around the origin within a given range, this paper achieves four main contributions. First, this paper obtains a parameterization of second-order strongly stabilizing controllers allowing the positive real zero in an expanded range. Second, this paper considers the plant with a pair of symmetric real zeros around the origin, a double origin zero, and a pair of conjugate imaginary zeros in a unified manner, and presents a more general parameterization of second-order strongly stabilizing controllers accommodating these three types of zeros in a more expanded range. Third, this paper provides a necessary and sufficient condition on these zeros (equivalently, all ranges of the observation point) for the existence of a second-order strongly stabilizing controller. Fourth, this paper demonstrates that a first-order stabilizing controller does not exist for the plant, regardless of its types of zeros, confirming that the minimal order of the strongly stabilizing controllers is two. This paper obtains all feasible regions for the parameters in each parameterization by explicitly expressing the range of each parameter using inequalities in a cascade structure, which makes the inequalities easy to check and verify. The results are applicable to both the Acrobot and Pendubot. The paper validates the theoretical findings through numerical investigations and simulations.

Fish Swarmed Kalman Filter for State Observer Feedback of Two-Wheeled Mobile Robot Stabilization

Over the past few decades, there have been significant technological advancements in the field of robots, particularly in the area of mobile robots. The performance standards of speed, accuracy, and stability have become key indicators of progress in robotic technology. Self-balancing robots are designed to maintain an upright position without toppling over. By continuously adjusting their center of mass, they can maintain stability even when disturbed by external forces. This research aims to achieving and maintaining balance is a complex task. Self-balancing robots must accurately sense their orientation, calculate corrective actions, and execute precise movements to stay upright. Eliminating disturbances and measurement noise in self-balancing robot can enhance the accuracy of their output. One common technique for achieving this is by using Kalman filters, which are effective in addressing non-stationary linear plants with unknown input signal strengths that can be optimized through filter poles and process covariances. Additionally, advanced Kalman filter methods have been developed to account for white measurement noise. In this research, state estimation was conducted using the Fish Swarm Optimization Algorithm (FSOA) to provide feedback to the controller to overcome the effects of disturbances and noise in the measurements through the designed filter. FSOA mimics the social interactions and coordinated movements observed in fish groups to solve optimization problems. FSOA is primarily used for optimization tasks where finding the global optimal solution is desired. The results show that the use of an optimized Kalman filter with FSOA on a two-wheeled mobile robot to handle system stability reduces noise values by 38.37%, and the system reaches a steady state value of 3.8 s with a steady error of 0.2%. In addition, by using the proposed method, filtering disturbances and measurement noise in self-balancing robot can help improve the accuracy of the self balancing robot’s output. System response becomes faster towards stability compared to other methods which are also applied to two-wheeled mobile robots.

이차 불확실 플랜트의 출력 예측 성능을 갖는 적분 터미널 슬라이딩 모드 제어를 위한 Utkin 정리의 증명

In this paper, a complete proof of Utkin"s theorem is presented for the ITSMC(integral terminal sliding mode control) of second order uncertain linear plants when Δb≠0. The addition of integral action to the TSMCs so called the ITSMC enhances performance in both transient and steady states. Therefore, proof of Utkin’s theorem is essential for ITSMC systems. There are five approaches to designing ITSMCs; control input transformation, sliding surface full transformation, and three sliding surface part transformations, which is for first time pointed out in this paper. The invariance property of the Utkin’s theorem applies only to the first two transformations. Specifically, the sliding mode equation, i.e., the sliding surface, remains invariant for the first two transformations. However, the invariance property of Utkin’s theorem can not apply to the three additional sliding surface part transformations, although they serve as design and stabilization approaches. The sliding surface full transformation first appears in the TSMCs, except in [32], while the three sliding surface part transformations appear for the first time in the TSMCs. This paper includes research on the first three transformations, and further studies will cover the last two sliding surface part transformations. This paper presents three transformation methods that achieve the same performances as those obtained through output prediction, predetermination, and predesign. Through an illustrative example and simulation study, the usefulness of the main results is verified.

Effect of antigibberellins on morphogenesis, photosynthetic apparatus, productivity and their residual content in tomato fruits

The application of growth and development regulators on crops in order to optimize their production process is one of the leading tasks of modern plant physiology. Retardants – gibberellin inhibitors are widely used for this purpose. We investigated the effect of foliar treatment with EW-250, ССС-750 and 2-СEPA on morphogenesis, leaf apparatus, content of photosynthetic pigments, indices of chlorophyll fluorescence induction, CO2 gas exchange, and residual amounts of drugs in the fruits of tomato (Lycopersicon esculentum Mill.) Bobcat hybrid. The field experiment was laid on plots with an area of 33 m2. The treatment of the plants was carried out at the budding stage. Morphometric indices were determined at the stages of flowering and fruit formation. The chlorophylls content was determined in the raw material by the spectrophotometric method. Indices of photosystem II (PSII) photochemical activity were determined according to the parameters of chlorophyll fluorescence induction after a half-hour exposure of plants in the dark using a portable single-beam fluorimeter "Floratest". The determination of the residual content of retardants in the fruits was carried out on a Shimadzu GC gas chromatograph with a mass spectrometric detector – GCMS- QP2020 EI. All gibberellin inhibitors reduced linear plant size. The number of leaves on the plants decreased under 2-CEPA treatment, and increased after the application of EW-250. Treatment with 2-CEPA decreased, EW-250 significantly increased, and CCC-750 practically did not change the leaves’ fresh and dry weight. Leaf area and leaf index decreased under 2-CEPA treatment, but practically did not change when EW-250 and ССС-750 were applied. All antigibberellin drugs increased the leaf specific leaf weight and thickened the leaf lamina due to the growth of chlorenchyma cells. At the same time, growth inhibitors increased the volume of columnar parenchyma cells and practically did not change the size of spongy parenchyma cells. Retardants increased the chlorophylls content in leaves, while the ethylene producer 2-CEPA did not change this index. The plants’ chlorophyll index after treatment with drugs increased significantly. The whole plant dry weight increased under EW-250 treatment, decreased after 2-CEPA application, and did not change under CCC-750. It was established that the photosynthetic rate increased under the EW-250 treatment, both in the flowering stage and in the stage of fruit formation, while when using 2-CEPA and CCC-750, it occurred only at the stage of fruit formation. The most significant positive changes of PSII photochemical activity indices were observed under the use of EW-250. Under the action of the drug, the maximum and actual quantum efficiency of PSII increased, the linear electron transport accelerated, and the fraction of reaction centers that did not transfer electrons from the primary acceptor QA to QB decreased, at the same time the chlorophyll fluorescence decay coefficient significantly increased, which indicates an increase in the CO2 assimilation intensity. Retardants increased the proportion of the fruit in the whole plant dry weight. All growth regulators increased net photosynthetic efficiency. A significant increase in fruit yield occurred under EW-250 treatment. When using CCC-750, the index tended to increase, while under the influence of 2-CEPA the yield decreased. The residual amounts of EW-250 and CCC-750 in the fruits did not exceed the maximum permissible concentrations.

Model predictive control of an active ankle-foot orthosis with non-linear actuation constraints

The goal of active ankle-foot orthoses (AAFO) is to assist the user in recreating a nominal gait motion. Previously proposed control systems for AAFOs have been reactive, with controllers based on the current tracking error. However, the optimal AAFO controller must ensure adequate trajectory tracking while minimizing the amount of assistance provided to the user. To this end, a model predictive controller (MPC) can be considered to determine the optimal control sequence for a given trajectory. The MPC minimizes the control effort, thereby determining the minimal assistance required for a user to regain a natural gait. This work outlines the formulation of a non-linear MPC for an AAFO and its combination with an extended state observer (ESO) for tracking of an AAFO.In this work, a MPC controller is proposed for optimal control of an AAFO, a linear plant subject to non-linear actuation constraints. A novel method is expressed to determine the initial control horizon selection in combination with variable step Newton-based optimization to enable real-time implementation. The MPC control effort is then combined with the estimated disturbance from an ESO to accurately track the desired gait.Simulations and experimental results prove the tracking capabilities of the proposed method. Compared to a tuned proportional–derivative controller, the simulated controller reduced the trajectory tracking error by up to 65.1% and 15.3% in an undisturbed and disturbed environment, respectively. The MPC and ESO combination allows the controller to identify the optimal control action for accurate trajectory tracking. Concurrently, the ESO rejects both external and internal disturbances, with superior tracking capabilities in both undisturbed and heavily disturbed systems, making it the optimal choice for AAFO control.

Effects of Jamming Attacks on Wireless Networked Control Systems Under Disturbance

Jamming attacks on wireless networked control systems are investigated for the scenarios where the system dynamics face exogenous disturbance. In particular, the control input packets are assumed to be transmitted from a controller to a remotely located linear plant over an insecure wireless communication channel that is subject to jamming attacks. The time-varying likelihood of transmission failures on this channel depends on the power of the jamming interference signal emitted by an attacker. We show that jamming attacks can prevent stability when the system faces disturbance, even if the attacked system without disturbance is stable. We also show that stability under jamming and disturbance can be achieved if the average jamming interference power is restricted in a certain way that we characterize in this article. We illustrate our results on an example networked control system with a fading wireless channel, where the outage probability is affected by jamming attacks.

Limitations of FxLMS in Feedforward Active Vibration Control of a Nonlinear Two-Degree-of-Freedom System

Active control systems are often used to surmount the challenges associated with passive noise and vibration control measures to control low frequency disturbances, since they achieve control without the application of large or heavy control treatments. Historically, linear active control strategies have been used in feedforward control systems to drive the control source to minimise the signal measured at the error sensor. Amongst the various control algorithms available, the Filtered-reference Least Mean Squares (FxLMS) algorithm has become extremely popular in the last few decades due to its relatively good performance and high level of robustness, as well as simplicity in both design and application. However, when the system under control contains nonlinearities, either in the primary or secondary paths, the performance of the FxLMS algorithm can degrade dramatically. This paper explores the performance limitations of the FxLMS algorithm when applied to the control of a two degree of freedom mass-spring-damper system with linear and cubic nonlinear stiffness terms. The aim of this study is to improve understanding of and inspire better design of nonlinear control systems. The statistical uncertainty present in the linear plant model and control filter is discussed, as well as the effect of this on control performance and control effort. The effect of nonlinearity on the maximum convergence parameter of the algorithm is also discussed.

Improved Model-Free Adaptive Control for Integral Plants

In this paper, an application of a model-free adaptive control (MFAC) to integral plants, which are linear plants with poles at the origin, is discussed. It is well known that an MFAC gives excellent performance for nonlinear plants and stable linear plants. However, for integral plants that are widely used in industrial robots, an MFAC fails in control. Therefore, we firstly investigate the stability of an MFAC for an integral plant, and it is shown that a system of an MFAC with an integral plant becomes unstable. Then, we propose a structure to improve an MFAC by adding a PID controller. The stability of the proposed method with an integral plant is confirmed by the Jury stability criterion and a root locus method. The validity of our method is confirmed by simulations and actual experiments.

Deep Learning for Scalable Optimal Design of Incremental Volt/VAR Control Rules

Volt/VAR control rules enable distributed energy resources (DER) to autonomously regulate voltage in distribution grids. The Volt/VAR rules provisioned by the IEEE Standard 1547 take on a piecewise-linear shape. However, its maximum slope is upper bounded to ensure stability, and that may hamper its voltage regulation performance. This limitation can be surpassed by adding a memory term to the control rule, and thus, obtaining a so-termed incremental control rule. This letter aims to optimally customize the shape of incremental rules across buses to attain desirable voltage profiles. Albeit this task can be posed as a bilevel program, we pursue a more scalable approach by reformulating it as a deep learning task. The idea is that Volt/VAR dynamics can be captured by a recursive neural network (RNN). Interestingly, the RNN weights correspond to the parameters of the control rule; the RNN input to the grid loading conditions; and the RNN output to the equilibrium voltages. Therefore, the optimal rule parameters can be found upon training the RNN so its output (equilibrium voltages) approach unity. Training is performed by feeding the RNN with representative scenarios of the anticipated grid loading conditions. The RNN depth depends on the settling time of Volt/VAR dynamics. Because the discrete-time Volt/VAR dynamics can be viewed as iterations of a proximal gradient descent (PGD) algorithm, we also leverage Nesterov’s accelerated PGD iterations to reduce the RNN depth. The RNN is never implemented in the field. Training this RNN is equivalent to solving the optimal rule design in a more computationally efficient manner. Analytical findings and numerical tests corroborate that the proposed solution can be neatly adapted to single-and multi-phase feeders. The proposed approach could be of general interest in designing piecewise-linear controllers acting on linear plants.

Distributed Hybrid Observer With Prescribed Convergence Rate for a Linear Plant Using Multi-Hop Decomposition

With a continuous-time formulation of the multihop decomposition, we propose a distributed hybrid observer for a sensor network where the plant and local observers run in continuous time and the information exchange among the sensing nodes is sampled-data. Process disturbances, measurement noise and communication noise are considered, and we prove that under some necessary detectability assumptions the observer gains can be tuned to guarantee exponential ISS with a prescribeda convergence rate. Simulations illustrate the performance of the proposed observer.

Strong Stabilization of the Acrobot at the Down–Up Equilibrium Point⋆

In this paper, the strong stabilization of the Acrobot at the Down-Up equilibrium point is addressed, with the first link being downward and the second link being upright. By converting the strong stabilization of the Acrobot at the Down–Up equilibrium point equivalently to the existence and design of a stable stabilizing controller for a fourth-order single-input single-output linear plant with adjustable zeros, a pair of poles on the imaginary axis, and a pair of real poles located symmetrically with respect to the origin, this paper has three main contributions. Firstly, the existence of a stable stabilizing controller for any Acrobot which is linearly controllable at the Down–Up equilibrium point is proved by showing the range of the adjustable zero via adjusting a parameter of the output signal. Secondly, a necessary and sufficient condition on the mechanical parameters of the Acrobot is provided to guarantee the existence of a second-order stable stabilizing controller for the Acrobot around its Down– Up equilibrium point. Thirdly, a direct method is presented to design a second-order stable controller, whose transfer function is preset with three parameters. By utilizing the Liénard– Chipart criterion for a fourth-order polynomial, the necessary and sufficient conditions on these parameters for achieving the strong stabilization are obtained, which are expressed in a cascade form for obtaining these parameters conveniently. A numerical example is presented to validate the effectiveness of the proposed method.

Remote State Estimation with Privacy Against Eavesdroppers

We study the problem of remote state estimation in the presence of a passive eavesdropper, under the challenging network environment of no packet receipt acknowledgments. A remote legitimate user estimates the state of a linear plant from the state information received from a sensor via an insecure and unreliable network. The transmission from the sensor may be intercepted by the eavesdropper. To maintain state confidentiality, we propose an encoding scheme. Our scheme transmits noise based on a pseudo-random indicator, pre-arranged at the legitimate user and sensor. The transmission of noise harms the eavesdropper's performance, more than that of the legitimate user. Using the proposed encoding scheme, we impair the eavesdropper's expected estimation performance, whilst minimising expected performance degradation at the legitimate user. We explore the trade-off between state confidentiality and legitimate user performance degradation.