Proposed Control Method Research Articles

Impacts of legume and cereal based artificial diets on development and reproductive parameters of the armyworm Spodoptera litura (Lepidoptera: Noctuidae)

The development of a viable mass-production technique for the generalist herbivore Spodoptera litura Fabricius (Lepidoptera: Noctuidae), using various artificial diets, is crucial for conducting experiments to study its biology and propose control methods. This study aims to investigate the developmental biology of S. litura fed on three distinct diets: two legume-based diets (chickpea flour, Cicer arietinum L. and common bean flour, Phaseolus vulgaris L.) and a cereal-based diet (corn flour, Zea mays L.). Results on various developmental parameters and total life cycle durations indicated that the chickpea and bean-based diets yielded the superior outcomes, with shorter developmental periods (29.74 and 30.73 days, respectively) compared to the corn flour diet (33.10 days). Growth parameters derived from life tables, such as the net reproductive rate (Ro), intrinsic rate of increase (rm) and finite rate of increase (λ), were also higher on chickpea and bean-based diets than the corn flour diet. These results suggest that legumes such as chickpeas and beans, which are rich in vegetable proteins, fibers, carbohydrates and essential minerals, provide a higher-quality nutritional foundation for the growth of S. litura compared to corn-based diet. Furthermore, these diets are suitable for understanding the phenology of S. litura, especially in relation to the nutritional variations of its host plants.

Neural Network-Based Adaptive Tracking Control for Denitrification and Aeration Processes With Time Delays.

Wastewater treatment process (WWTP), consisting of a class of physical, chemical, and biological phenomena, is an important means to reduce environmental pollution and improve recycling efficiency of water resources. Considering characteristics of the complexities, uncertainties, nonlinearities, and multitime delays in WWTPs, an adaptive neural controller is presented to achieve the satisfying control performance for WWTPs. With the advantages of radial basis function neural networks (RBF NNs), the unknown dynamics in WWTPs are identified. Based on the mechanistic analysis, the time-varying delayed models of the denitrification and aeration processes are established. Based on the established delayed models, the Lyapunov-Krasovskii functional (LKF) is used to compensate for the time-varying delays caused by the push-flow and recycle flow phenomenon. The barrier Lyapunov function (BLF) is used to ensure that the dissolved oxygen (DO) and nitrate concentrations are always kept within the specified ranges though the time-varying delays and disturbances exist. Using Lyapunov theorem, the stability of the closed-loop system is proven. Finally, the proposed control method is carried out on the benchmark simulation model 1 (BSM1) to verify the effectiveness and practicability.

Distributed Estimator-Based Event-Triggered Neuro-Adaptive Control for Leader-Follower Consensus of Strict-Feedback Nonlinear Multiagent Systems.

This article investigates the leader-follower consensus problem for strict-feedback nonlinear multiagent systems under a dual-terminal event-triggered mechanism. Compared with the existing event-triggered recursive consensus control design, the primary contribution of this article is the development of a distributed estimator-based event-triggered neuro-adaptive consensus control methodology. In particular, by introducing a dynamic event-triggered communication mechanism without continuous monitoring neighbors' information, a novel distributed event-triggered estimator in chain form is constructed to provide the leader's information to the followers. Subsequently, the distributed estimator is utilized to consensus control via backstepping design. To further decrease information transmission, a neuro-adaptive control and an event-triggered mechanism setting on the control channel are codesigned via the function approximate approach. A theoretical analysis shows that all the closed-loop signals are bounded under the developed control methodology, and the estimation of the tracking error asymptotically converges to zero, i.e., the leader-follower consensus is guaranteed. Finally, simulation studies and comparisons are conducted to verify the effectiveness of the proposed control method.

Asymptotic Tracking Control With Bounded Performance Index for MIMO Systems: A Neuroadaptive Fault-Tolerant Proportional-Integral Solution.

It is technically challenging to maintain stable tracking for multiple-input-multiple-output (MIMO) nonlinear systems with modeling uncertainties and actuation faults. The underlying problem becomes even more difficult if zero tracking error with guaranteed performance is pursued. In this work, by integrating filtered variables into the design process, we develop a neuroadaptive proportional-integral (PI) control with the following salient features: 1) the resultant control scheme is of the simple PI structure with analytical algorithms for auto-tuning its PI gains; 2) under a less conservative controllability condition, the proposed control is able to achieve asymptotic tracking with adjustable rate of convergence and bounded performance index collectively; 3) with simple modification, the strategy is applicable to square or nonsquare affine and nonaffine MIMO systems in the presence of unknown and time-varying control gain matrix; and 4) the proposed control is robust against nonvanishing uncertainties/disturbances, adaptive to unknown parameters and tolerant to actuation faults, with only one online updating parameter. The benefits and feasibility of the proposed control method are also confirmed by simulations.

Adaptive Multi-Switching-Based Global Tracking Control for Switched Nonlinear Systems With Prescribed Performance

This paper is concerned with the tracking control for a class of switched nonlinear systems subject to prescribed performance. Firstly, a barrier function and a normalized function are introduced to achieve prescribed performance control, which ensures that the tracking error evolves within prescribed boundary. Then, multi-dimensional Taylor network provides a new approach for how to estimate the nonlinearity arising from the backstepping control process. Significantly, the proposed multi-switching-based adaptive controller realizes that all signals in the closed-loop system are globally uniformly ultimately bounded while ensuring asymptotic tracking. Different from most existing network-approximation-based control strategies, the developed method in this paper is not only independent of the initial state, but also can achieve global stability. Finally, it is easy to verify the effectiveness of the proposed control method through two simulations. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This research is motivated by the fact that the control ideas of many practical engineering systems can be provided by making a profound study on switched nonlinear systems. However, most of the existing results focused on semi-global stability of systems. Therefore, this study devotes to develop a novel adaptive prescribed performance control strategy, which can not only ensure global stability of closed-loop system but also realize the asymptotic tracking of the switched nonlinear systems. It is worth noting that the proposed control approach has great significance for many practical systems, such as circuit systems and single-link inverted pendulum systems.

Security control of direct current microgrids under deception attacks—A dynamic event‐triggered approach

AbstractThis paper studies the security control of direct current (DC) microgrids under deception attacks, and a dynamic event‐triggered mechanism (DETM) is proposed to save constrained network bandwidth. The DETM can reduce the frequency of data communications and exclude Zeno behavior inherently. Then, a time‐delay closed‐loop system model is built, which integrates parameters of the DC microgrid, the DETM, deception attacks, injection current controller, and network‐induced delays in one unified framework. Sufficient conditions are derived for globally exponentially ultimately bounded stability in mean square, which establish the relationship between system performance and the contributing factors such as the DETM, deception attacks, and network delays. Further, a co‐design method is presented to derive the parameters of the controller and the DETM in just one step. Simulation results confirm the effectiveness of the proposed method for security control of DC microgrids, achieving 21.5% savings of communication resources while effectively stabilizing the system even 10.7% of the transmitted data that are manipulated by the deception attacks.

Modulation of wetting state switching of droplets on superhydrophobic microstructured surfaces by external electric field

HypothesisElectrowetting on conventional dielectrics requires direct fluid-electrode contact to generate strong electric fields at the three-phase contact line to modulate the wetting. Since the electric field alters wetting, the modulation of wetting can be achieved by applying an external electric field through insulated electrodes, preventing the liquid from contacting the electrodes. ExperimentA simple and efficient method for non-contact between the fluid and the electrode external electric field modulation of fluid wetting was proposed. The switching ability of droplets on microgroove surfaces from Cassie-Baxter to Wenzel wetting state under an external electric field was used to drive and quantify the relationship between wetting, contact angle, and the applied voltage. FindingsApplying an external electric field modulates the wetting of deionized water, ionic liquids, and high-viscosity liquids on microgrooves. The wetting degree of liquid can be controlled by adjusting the external voltage parameters. The finite element simulations revealed that the Maxwell force drove this process. The effects of substrate size and liquid properties on wetting behavior were also examined. Post-application cross-sectional imaging showed the formation of a conformal interface, highlighting the relevance of the proposed method in advanced adaptive shape fabrication and microfluidic control, among other applications.

Analysis of influencing factors of seawater intrusion in the Yangtze River Estuary and control for water supply security

Seawater intrusion poses a significant threat to the water supply of coastal cities both presently and in the future. It is crucial to identify the controllable factors influencing seawater intrusion, both natural and anthropogenic, in order to ensure water supply security. This study examined seawater intrusion characteristics using monitoring data from 1994 to 2019. Factors such as daily flow rate, duration of intrusion, water quality, and tidal level were analyzed to establish correlations and identify the primary influencing factors in the Yangtze River Estuary. The findings reveal that seawater intrusion in this area is most prevalent from November to April, peaking in February and March. The key controllable factors affecting chloride levels at the intake are the daily flow rate at Datong Station and the tidal range at Xuliujing Station. Additionally, the study proposes control methods to safeguard water supply, including providing daily flow rate values for flushing seawater intrusion at Datong Station under different tidal ranges and intrusion durations. These research results provide valuable guidance for the emergency operation of the Three Gorges-centered reservoir group against seawater intrusion.

The Optimal Control Method of Test Power Supply for DC Distribution Network

Background:: The test power supply is one of the key devices in the DC distribution network, which is necessary to supply power with high quality for testing other devices' performance. The double active bridge (DAB) converter is a common circuit topology for test power supply, which has the advantages of high-frequency electrical isolation, bi-directional power flow, and high power density. For the converter, control methods, such as single-phase-shift (SPS) control, and single-current stress or single-return power optimization under extended-phase-shift (EPS) control, have their limitations, which influences efficiency. Objective:: This paper aims to propose a dual-objective optimal control method, which can effectively improve efficiency of the test power supply. Methods:: This paper addresses the limitations of SPS control, and single-current stress or singlereturn power optimization under EPS control of the DAB converter, and proposes a dual-objective optimal control method based on the idea of using objective planning in the full power range under the condition of satisfying soft switching, which effectively improves efficiency of the test power supply. Results:: With the proposed dual-objective optimal control method, the converter achieves a smaller current stress similar to that with the single-current stress optimal control, and the return power is also reduced by 29.51%. Efficiency of the test power supply reaches 86.9%, which is better than 82.5% with SPS control and 85.3% with single-current stress optimization under EPS control. The experimental results fully verify the effectiveness of the proposed control method. Conclusion:: A dual-objective optimal control method is proposed. By using the presented method, current stress and return power are both optimally designed, so the efficiency of the test power supply can be effectively improved.

Chattering Free Sliding-Mode Controller Design for Underactuated Tower Cranes With Uncertain Disturbance

Tower cranes are widely used in various industrial sites and require a high level of anti-disturbance performance from the crane controller due to the variability of the application environment. Although sliding mode control is a typical anti-disturbance control method, most sliding mode controllers suffer from output chattering and do not reflect well under severe external disturbances. To address these issues from a practical application perspective, a finite time sliding mode control method using the super-twisting algorithm (STA) is proposed for underactuated tower cranes operating in the presence of external disturbances. The proposed method includes a finite-time chattering-free sliding mode controller that eases the output torque chattering problem and a finite-time sliding mode observer based on STA to observe the uncertain disturbances. The observed values are then applied to the controller through feedforward compensation. Experimental results show that the proposed control method effectively weakens output torque chattering, compensates for disturbance quickly, and accurately completes control tasks.

Real-Time Hardware Emulation of Microgrid Forming Wireless Power Transfer Systems

The prevalence of wireless charging approaches has manifested a grid-supporting potential which can be evaluated by hardware-based methodologies. In this work, real-time emulation of a bidirectional wireless power transfer (WPT) system capable of DC microgrid formation is investigated on the field-programmable gate array (FPGA). Following a detailed analysis of the transfer characteristics of the dual-active bridge with a series-compensated resonant tank in between, a unified control scheme utilizing a phase-shift strategy is proposed for a flexible voltage or current regulation, thereby enabling the DC microgrid-forming capability. Electromagnetic transient modeling is then carried out so that an accurate digital emulation platform is feasible for prototyping. The fact that the WPT has a high frequency compels a small computation step size, which poses a dramatic challenge to real-time execution. A partition-iteration approach is therefore proposed for matrix dimension reduction which ultimately results in an alleviated processing burden. In the meantime, the parallelism of configurable logic blocks and the pipelined architecture of the FPGA are explored to achieve a low hardware latency. The analytical models, as well as the proposed control method, are validated experimentally, and then real-time hardware emulation of a DC microgrid consisting of WPT systems is performed for an integration study.

Event-Triggered Adaptive Saturated Fault-Tolerant Control for Unknown Nonlinear Systems With Full State Constraints

This paper investigates the issue of event-triggered adaptive saturated fault-tolerant control (ESFC) for uncertain nonlinear systems with time-varying full state constraints (TFSCs), actuator saturation and faults as well as unknown control direction. A bounded function with an auxiliary variable is constructed by utilizing a novel dynamics of the auxiliary system, which contributes to reducing the adverse impact of actuator saturation. Different from the previous backstepping-based event-triggered control methods such specifications by either using fuzzy approximation or by employing neural approximation techniques, this paper skillfully addresses the unknown nonlinearities, actuator saturation and faults without involving any approximation structures, and thus, we proposes the ESFC on the basis of low-complexity design framework as contributing to communication and computational resource reduction. A rigorous theoretical analysis shows that the proposed control method is an effective way to handle with the problems of actuator saturation and faults, full state constraints, and unknown system uncertainties, while simultaneously simplifying the backstepping design and avoiding the issue of explosion of complexity. The asymptotic stability of the closed-loop system is guaranteed and the Zeno behavior can be effectively removed. We present an application example of a linear motor scenario to illustrate the effectiveness of the method. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Since state constraints, actuator saturation and faults, unknown mechanism model, and limited bandwidths exist extensively in practical engineering systems, which constantly degrade the operation performance of the plant. To handle these disadvantages, this paper is focus on providing simple but effective ESFC methods to ensure the asymptotic stability and enhance reliability. Compared to existing results, the presented method only uses the state signals of system without using system dynamic functions under mild conditions, which provides a theoretical basis, and has the advantages of low-complexity design, and easy implementation in practical engineering. Preliminary physical experimental comparisons demonstrate that this method is applicable to practical liner-motor platform, and achieves satisfactory control performance.

Model Predictive Control of Magnetic Helical Swimmers in Two-Dimensional Plane

Magnetic micro/mini-swimmers have a great potential application in biomedical research and have gained broad attention. Recent research studies focus on the automatic control methods of magnetic micro/mini-swimmers, such as artificial intelligence methods. However, their autonomous manipulation remains a challenge since they are subject to various disturbances from the external environment and model uncertainties. The current methods employ a status observer to estimate these disturbances and uncertainties. In this paper, we apply a data-driven technique that utilizes the nonlinear approximation ability of neural networks (NNs). To be specific, a flexible structure of NNs, Broad Learning System (BLS), is employed to model the input-output mapping relationship between the direction of the rotating magnetic field and the swimming direction of the helical miniature swimmer. Then, according to the dual-variable decoupling control, a levitation controller is formulated and a path following controller is proposed based on a planar three-degree-of-freedom model of magnetic helical swimmers, which is inspired by the model of wheeled mobile robots. Simulations and experiments are conducted to quantitatively validate the proposed control method using different planar paths. The experiment results show that the mean absolute error of the path following control is about 3 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\%$</tex-math> </inline-formula> of the body length which is less than 0.5 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$mm$</tex-math> </inline-formula> . Our proposed control method provides a preliminary study to alleviate the impact of disturbances and uncertainties on the control performance of magnetic micro/mini-swimmers. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper is mainly motivated by the potential application of artificial intelligence methods in magnetic micro/mini-robot community, especially for the applications that reject disturbances and uncertainties. In practice, a path planner is employed to compute a pre-defined reference path that connects the start and the targeted locations. Then our control method is applied to the magnetic helical swimmer and it is guided to follow the reference path. Tackling external disturbances and model uncertainties is still challenging during the control progress. Neural network-based technique is an intuitive approach since their nonlinear modeling ability and generalization are suitable for estimating these disturbances and uncertainties. As for training the neural-network model, the training data about the angle parameters should be recorded by manual control of the helical swimmer. These angle parameters define the rotating axis of the uniform rotating magnetic field and the self-rotating axis of the magnetic helical swimmer. According to the planar motion model, the optimal controller is formulated using the feedback distance error and angle error, and the sum of the control signal and the prediction of the compensating model is used as the final control input. Our electromagnetic coil system features easy operation and configuration of cameras or other sensors. Simulations and experiments validate the performance of the neural network-based compensating method and the proposed optimal control method using magnetic micro/mini-swimmers.

A Cloud-Connected Digital System for Type-1 Diabetes Prediction using Time Series LSTM Model

Abstract Millions of people worldwide suffer from diabetes, a medical condition that is spreading at an accelerating pace. Numerous studies show that risk factors that may arise from diabetes can be avoided if the disease is detected early. The health-care monitoring system has benefited greatly from early diabetes prediction made possible by the integration of Deep Learning (DL) and Machine Learning (ML) algorithms. The objective of many early studies was to increase the prediction model accuracy. However, DL algorithms often cannot fully exploit the potential of the available datasets because they are too small. This study includes a very accurate DL model as well as a novel system that integrates cloud services and allows users to directly enhance an existing data set, which can increase the accuracy of DL techniques. Therefore, the Long Short-Term Memory (LSTM) model with controller is chosen for efficient type-1 diabetes prediction. Experimental validation of the proposed Nonlinear Model Predictive Control (NMPC)_LSTM algorithm method is compared with other conventional DL algorithms. The proposed controller method achieves excellent blood glucose set point tracking and the proposed algorithms achieves 98.95% accuracy for the obtained data. It outperforms other existing methods with an increase in percentage accuracy compared to the Benchmark Pima Indian Diabetes Datasets (PIDD).

Improved Adaptive CCS-MPCC for Distorted Model Parameters Mitigation of IPMSM Drives

In this study, a robust adaptive model continuous-control-set model predictive current control (CCS-MPCC) method is proposed for interior permanent magnet synchronous motors (IPMSMs) considering the existing disturbances, unmodeled dynamics, and parameter variations. The novel aspect of this research is that it merges the improved dynamic, useful properties of model predictive control (MPC), which includes easy implementation and fast dynamic response, together with the most effective criterion of an adaptive controller (i.e., robustness to model uncertainties), that result in enhanced dynamic and steady-state control performance despite unknown and changing disturbances. Unlike the conventional CCS-MPCC approach that heavily depends on the accurate knowledge of the system model to attain improved control performance, the proposed method achieves satisfactory control performance (e.g., fast dynamic response, smaller steady-state error, and low stator current THD) by stabilizing the state errors to approach zero and compensating for variations in the model parameters using the designed feedback control terms and adaptive control terms, respectively. The stability of the proposed control method is ensured by the state errors asymptotically decaying to zero. The proposed approach was simulated and then implemented on a PSIM simulation tool and a prototype IPMSM test bench using TI TMS320F28335 DSP, respectively, to confirm its feasibility.

Direct Control Method for Linear-Rotary Switched Reluctance Motor With Two Radial Windings

For Linear-Rotary Switched Reluctance Motors (LRSRMs) with two radial windings, the coupling between torque and axial force increases the complexity of control. Due to the calculation of current in existing control method for LRSRMs, the complicated derivation of current expression was necessary, and some constraints were also introduced which meant the difficulties on designing the current control algorithm were greatly increased. In order to solve these problems, a direct torque and direct axial force (DTC&DAFC) control method is proposed in this paper. By the way of selecting appropriate space voltage vectors, the proposed method can directly regulate torque and axial force at the same time to achieve rotation and linear motion and significantly reduce the ripple of the torque. Moreover, the mechanism of two-DOF motion and the principle of the proposed method are demonstrated in detail based on a 6/4 LRSRM with two radial windings. Based on MATLAB/Simulink and the experimental prototype, the feasibility of the proposed control method has been verified according to the simulation and experimental results.

Self-Stabilizing Control Strategy of Stabilized Platform for Rotary Steerable Drilling System Based on Adaptive Backstepping Control

To enhance the robustness of the toolface angle control in a fully rotary steerable drilling tool, a backstepping control law and a drilling fluid flow adaptive law are devised based on the dynamic model of the stable platform. The Lyapunov function is constructed, and it is proven that the adaptive backstepping control system of the stabilized platform is stable. Furthermore, in order to address problems such as the friction dead zone and excessive rotational kinetic energy in the stabilized platform system, which could cause toolface angle oscillations and the rapid rotation of the stabilized platform, we additionally propose an online estimation method for the balancing torque and velocity-angle control switching strategy. By combining the backstepping control law, drilling fluid flow adaptive law, and velocity-angle control switching strategy, a self-stabilizing control strategy for the stabilized platform is established. In comparison with the PID control method, the simulation results show the superiority of the proposed scheme under complex disturbances from a downhole environment. And the drilling simulation experiment results indicate that the proposed control method has a good anti-interference capability under various conditions, including drilling fluid flow rate, inclination angle, and drill collar rotational speed. Therefore, the proposed control method can improve the robustness of the stabilized platform control system.

Nonlinear Controller-Based Mitigation of Adverse Effects of Cyber-Attacks on the DC Microgrid System

Cyber-attacks have adverse impacts on DC microgrid systems. Existing literature shows plenty of attack detection methods but lacks appropriate mitigation and prevention approaches for cyber-attacks in DC microgrids. To overcome this limitation, this paper proposes a novel solution based on a nonlinear controller to mitigate the adverse effects of various cyber-attacks, such as distributed denial of service attacks and false data injection attacks, on various components of a DC microgrid system consisting of a photovoltaic power source, a permanent magnet synchronous generator-based variable speed wind generator, a fuel cell, battery energy storage, and loads. To demonstrate the effectiveness of the proposed solution, single and repetitive cyber-attacks on specific components of the microgrid have been considered. An index-based quantitative improvement analysis for the proposed control method has been made. Extensive simulations have been performed by the MATLAB/Simulink V9 software. Simulation results demonstrate the effectiveness of the proposed nonlinear controller-based method in mitigating the adverse effects of cyber-attacks. Moreover, the performance of the proposed method is better than that of the proportional-integral controller. Due to the simplicity of the proposed solution, it can easily be implemented in real practice.

RBFNN-Based Adaptive Integral Sliding Mode Feedback and Feedforward Control for a Lower Limb Exoskeleton Robot

In this paper, an adaptive trajectory tracking control method combining proportional–integral–derivative (PID) control, Radial Basis Function neural network (RBFNN)-based integral sliding mode control (ISMC), and feedforward control, i.e., the PIDFF-ISMC method, is proposed. The PIDFF-ISMC method aims to deal with the dynamic uncertainties, disturbances, and slow response in lower limb exoskeleton robot systems. Firstly, the Lagrange function is utilized to establish dynamic models that include frictional force and unmodeled dynamics. Secondly, the feedback controller is composed of PID and RBFNN-based ISMC to improve tracking performance and decrease the chattering phenomenon. The feedforward controller is adopted to reduce the response time by employing inverse dynamic models. Finally, the Lyapunov function proves the stability of the proposed control method. The experimental results show that the proposed control method can effectively reduce the trajectory tracking error and response time at two different speeds while alleviating control input chattering.

Research on Adaptive Cycle Engine Mode Transition Control Method

Mode transition is an important dynamic process of an adaptive cycle engine (ACE). In order to obtain a smooth mode transition process, the closed-loop controller is designed based on the strong robust augmented linear quadric regulator (ALQR) method, and with the objective of minimizing the thrust fluctuation in the process of mode transition, an open-loop geometrical mechanism control schedules optimization method based on Bézier curves is proposed, so that the closed-loop control and the open-loop control can work in coordination. The simulation results at the subsonic cruise operating point and supersonic cruise operating point show that based on the optimized open-loop geometrical mechanism control schedules and the designed closed-loop ALQR control system, the ACE achieves fast and smooth geometrical mechanisms and engine output transition during the mode transition process with a maximum thrust fluctuation of 2.58%, which is much smaller than that of the traditional linear variation geometric mechanisms with a maximum 4.64% thrust fluctuation, which verifies the effectiveness of the proposed control method.