Autonomous Underwater Gliders Research Articles

Evaluation of the ocean component on different coupled hurricane forecasting models using upper-ocean metrics relevant to air-sea heat fluxes during Hurricane Dorian (2019)

In August 2019 Hurricane Dorian traveled through the Caribbean Sea and Tropical Atlantic before devastating the Bahamas. The operational hurricane forecasting models under-predicted the intensity evolution of Dorian prior to the storm reaching its maximum strength. Research studies have shown that a more realistic upper-ocean characterization in coupled atmosphere-ocean models used to forecast hurricanes has the potential to lead to more accurate hurricane intensity forecasts. In this work, we evaluated four ocean products: the ocean component from one NOAA operational hurricane forecasting model that used ocean initial conditions from climatology, the ocean components from two NOAA experimental models using ocean initial conditions from a data-assimilative operational ocean model, and one US Navy data-assimilative operational ocean model for reference. The upper-ocean metrics used to evaluate the models include mixed layer temperature, mixed layer salinity, ocean heat content and depth-averaged temperature in the top 100 m. The observations used are temperature and salinity profiles from an array of six autonomous underwater gliders deployed in the Caribbean region during the 2019 hurricane season. We found that, even though the four models have good skill in predicting temperature and salinity over the whole observed water column, skill significantly deteriorates for the upper-ocean metrics. In particular, the models failed to capture the barrier layer that was present during the passage of Hurricane Dorian through the glider array. We also found that even small differences in the mixed layer temperature along the storm track on the hurricane models evaluated, led to noticeable differences in the total enthalpy fluxes delivered from the ocean to the atmosphere throughout the storm’s synoptic history. These findings highlight the need to improve the upper-ocean initial conditions and representation in coupled atmosphere-ocean models as part of the larger efforts to improve the various modeling aspects that control the hurricane intensity forecast.

A multi-platform Guidance, Navigation and Control system for the autosub family of Autonomous Underwater Vehicles

Over the last decade, there has been a proliferation of marine robots such as Unmanned Surface Vehicles (USVs), Autonomous Underwater Vehicles (AUVs) and underwater gliders. The variety of vehicles’ capabilities and styles has led to numerous strategies to address the Guidance, Navigation and Control (GNC) tasks. In particular, a recent trend in the advancements of GNC systems is to develop modular, multi-platform solutions. This paper illustrates the approach followed in the development of the GNC system for the different types of AUV of the Autosub family. The presented system is decomposed into several interconnected components, each implemented as a standalone software module. Each component is highly-reconfigurable and easily extensible, and the interactions between the modules rely on generic-purpose interfaces. Such a design enables the execution of a broad range of autonomous missions, as well as the integration and deployment of the system on marine platforms with very diverse characteristics, not limited to the vehicles of the Autosub class. Experimental results obtained in real-time during in water campaigns are provided to demonstrate the effectiveness of the proposed system and its versatility on a wide range of platforms and missions.

Behavior-Based Formation Control Digital Twin for Multi-AUG in Edge Computing

The new generation of artificial intelligence technology has improved the autonomous monitoring capabilities of marine equipment. The ocean monitoring platform based on edge computing realizes the autonomous collaboration of multi-agent equipment groups. Autonomous Underwater Glider (AUG) is a new type of energy-saving marine equipment that can realize long-range ocean exploration. However, the non-negligible power constraints, time delays, communication failures and other unfavorable factors in the special underwater working environment have brought great challenges to the underwater monitoring operations of multi-AUG systems. This research establishes an improved artificial potential field method scheme based on the Maritime Internet of Things, which is based on the AUG leader's edge device to control multi-AUGs. In this process, an improved artificial potential field method is designed to solve the local optimal problem through behavior-based path optimization. Then, multi-AUGs are controlled to adapt to the task team plan based on the edge computing of the AUG leader. From the experimental results, it effectively realizes the AUG group cooperative control in the leader mode. Meanwhile, we established a marine communication model and AUG physics engine control model to complete a digital twin of multi-AUG monitoring tasks.

Ocean mixing during Hurricane Ida (2021): the impact of a freshwater barrier layer

Tropical cyclones are +ne of the costliest and deadliest natural disasters globally, and impacts are currently expected to worsen with a changing climate. Hurricane Ida (2021) made landfall as a category 4 storm on the US Gulf coast after intensifying over a Loop Current eddy and a freshwater barrier layer. This freshwater layer extended from the coast to the open ocean waters south of the shelf-break of the northern Gulf of Mexico (GoM). An autonomous underwater glider sampled this ocean feature ahead of Hurricane Ida operated through a partnership between NOAA, Navy, and academic institutions. In this study we evaluate hurricane upper ocean metrics ahead of and during the storm as well as carry out 1-D shear driven mixed layer model simulations to investigate the sensitivity of the upper ocean mixing to a barrier layer during Ida’s intensification period. In our simulations we find that the freshwater barrier layer inhibited cooling by as much as 57% and resulted in enhanced enthalpy flux to the atmosphere by as much as 11% and an increase in dynamic potential intensity (DPI) of 5 m s-1 (~9.72 knots) in the 16 hours leading up to landfall. This highlights the utility of new ocean observing systems in identifying localized ocean features that may impact storm intensity ahead of landfall. It also emphasizes the northern Gulf of Mexico and the associated Mississippi River plume as a region and feature where the details of upper ocean metrics need to be carefully considered ahead of landfalling storms.

Cessation of Labrador Sea Convection Triggered by Distinct Fresh and Warm (Sub)Mesoscale Flows

Abstract By ventilating the deep ocean, deep convection in the Labrador Sea plays a crucial role in the climate system. Unfortunately, the mechanisms leading to the cessation of convection and, hence, the mechanisms by which a changing climate might affect deep convection remain unclear. In winter 2020, three autonomous underwater gliders sampled the convective region and both its spatial and temporal boundaries. Both boundaries are characterized by higher subdaily mixed layer depth variability sampled by the gliders than the convective region. At the convection boundaries, buoyant intrusions—including eddies and filaments—instead of atmospheric warming primarily trigger restratification by bringing buoyancy with a comparable contribution from either fresh or warm intrusions. At the edges of these intrusions, submesoscale instabilities, such as symmetric instabilities and mixed layer baroclinic instabilities, seem to contribute to the decay of the intrusions. In winter, enhanced lateral buoyancy gradients are correlated with strong destabilizing surface heat fluxes and alongfront winds. Consequently, winter atmospheric conditions and buoyant intrusions participate in halting convection by triggering restratification while surface fluxes are still destratifying. This study reveals freshwater anomalies in a narrow area offshore of the Labrador Current and near the convective region; this area has received less attention than the more eddy-rich West Greenland Current, but is a potential source of freshwater in closer proximity to the region of deep convection. Freshwater fluxes from the Arctic and Greenland are expected to increase under a changing climate, and our findings suggest that they may play an active role in the restratification of deep convection.

An autonomous underwater glider serving large spatiotemporal monitoring in hadal zones

Hadal zones are immensely difficult to explore due to their incredibly harsh environments. In this study, an autonomous underwater glider called Petrel-XPLUS was developed for monitoring hadal zones at large spatiotemporal scales. This glider is equipped with a bionic gradient functional housing, the multi-material pressure housing, to cope with the coupled effects of extremely high pressure and density variations, endowing it with light weight, near-neutral buoyancy, and sufficient onboard energy. Furthermore, an innovative dual-eccentric attitude-regulating mechanism is proposed to increase the pitch angle range from [−45°, 45°] to [−90°, 90°] and enrich four types of glider motion modes. This mechanism and a depth-averaged flow-based path planning method enable the glider to handle the superimposed effects of unknown currents and complex topography for effective access to the hadal zone floor. The developed glider has an operating range of 5000 km or 80 dives to a depth of 11,000 m in a single mission lasting 200 d. Petrel-XPLUS successfully completed three dives exceeding 10,000 m with a maximum depth of 10,619 m and an average station-keeping accuracy of 2.018 km during a sea trial in the Mariana Trench. Our study provides a novel technical reference for facilitating hadal exploration.

Energy-Efficient Space–Air–Ground–Ocean-Integrated Network Based on Intelligent Autonomous Underwater Glider

Internet of Things (IoT) has extended its coverage to various spatial domains and has established interconnection to serve widespread applications of a larger spatial scale. Such IoT is called SAGOI-Net, which consists of multiple battery-powered heterogeneous devices. Hence, energy efficiency is the key point of SAGOI-Net to be stably operated for a long time without manual maintenance. This paper proposes a novel scheme of energy efficient autonomous and decentralized SAGOI-Net establishment using intelligent Autonomous Underwater Glider (AUG) to serve marine applications. The proposed SAGOI-Net is energy efficient because the energy consumption is minimized by: 1) Employing non-propeller-driven AUG; 2) Navigating AUG under water without acoustic sensor or extra energy-consuming vision sensors; 3) Equipping the self-navigation (SN) system based on lightweight neural network model to save the energy consumption of onboard computing resource. Moreover, assuming the AUG navigation problem as time series regression, the proposed scheme designs SAGOI-Net to be autonomous and decentralized with the aid of lightweight Long Short-Term Memory (LSTM) network-based self-navigation (SN-LSTM) system of AUG. The lightweight SN-LSTM model is trained end-to-end on dynamically modeled AUG motion information along with numerically modeled ocean environment data to quantitively analyze the impact of the ocean environment on AUG. The simulation results demonstrate superior performance of the AUG self-navigation along with energy efficiency of the proposed SAGOI-Net.

Spatial Variability of Turbulent Mixing From an Underwater Glider in a Large, Deep, Stratified Lake

AbstractRecent efforts using microstructure turbulence measurements have contributed to our understanding of the overall energy budget in lakes and linkages to vertical fluxes. A paucity of lake‐wide turbulence measurements hinders our ability to assess how representative such budgets are at the basin scale. Using an autonomous underwater glider equipped with a microstructure payload, we explored the spatial variability of turbulence in pelagic and near‐shore regions of Lake Geneva. Dissipation rates of kinetic energy and thermal variance were estimated by fitting temperature gradient fluctuations spectra to the Batchelor spectrum. In deep waters, turbulent dissipation rates in the surface and thermocline were mild (∼10−8 W kg−1) and weakened toward the hypolimnion (∼10−11 to 10−10 W kg−1). The seasonal thermocline exhibited inhibited interior mixing, with extremely low values of mixing efficiency (Rif ≪ 0.1). In contrast, in the slope zone, a band of significantly enhanced energy dissipation (∼5 × 10−8 W kg−1) extended well above the bottom boundary layer and was associated with strong, efficient mixing (Rif > 0.17). The resulting contribution of the slope region to basin‐scale mixing was large, with 90% of the basin‐wide mixing—and only 30% energy dissipation—occurring within 4 km of the shoreline. This boundary mixing will modify overturning circulation and the transport pathways of dissolved compounds exchanged with the sediments. The dynamics responsible for the shift in the mixing regime, which appears crucial for the mixing budget of lakes, could not be fully unraveled with the collected observations. Additional model data analyses hint at the role of submesoscale instabilities.

A copula-based method of risk prediction for autonomous underwater gliders in dynamic environments.

Autonomous underwater gliders (AUGs) are effective platforms for oceanic research and environmental monitoring. However, complex underwater environments with uncertainties could pose the risk of vehicle loss during their missions. It is therefore essential to conduct risk prediction to assist decision making for safer operations. The main limitation of current studies for AUGs is the lack of a tailored method for risk analysis considering both dynamic environments and potential functional failures of the vehicle. Hence, this study proposed a copula-based approach for evaluating the risk of AUG loss in dynamic underwater environments. The developed copula Bayesian network (CBN) integrated copula functions into a traditional Bayesian belief network (BBN), aiming to handle nonlinear dependencies among environmental variables and inherent technical failures. Specifically, potential risk factors with causal effects were captured using the BBN. A Gaussian copula was then employed to measure correlated dependencies among identified risk factors. Furthermore, the dependence analysis and CBN inference were performed to assess the risk level of vehicle loss given various environmental observations. The effectiveness of the proposed method was demonstrated in a case study, which considered deploying a Slocum G1 Glider in a real water region. Risk mitigation measures were provided based on key findings. This study potentially contributes a tailored tool of risk prediction for AUGs in dynamic environments, which can enhance the safety performance of AUGs and assist in risk mitigation for decision makers.

Hydrodynamic Shape Design and Self-Propulsion Analysis of a Hybrid-Driven AUG

Due to the lack of a powerful propulsion device in conventional autonomous underwater gliders (AUGs), their mobility and flexibility are insufficient, thus not being capable of also ensuring the stability of the motion route. Thus, it is necessary to further develop hybrid-driven AUGs. This paper applied CFD simulation and experimental analysis methods to study and design a hybrid-driven AUG with a propeller optimized from a type of AUG with swept-forward and swept-back wings. Through parameter adjustment, the hydrodynamic configuration was optimized, and the optimal hull design and hydrofoil type selection were proposed. The lift–drag ratio could be improved by up to 22.5% at an angle of attack of 8 degrees. The optimized AUG was combined with a single propeller for self-propulsion simulation. Aiming at the problem caused by the propeller torque on the AUG, the strategy of a contra-rotating propeller (CRP) was conducted to self-eliminate the propeller torque. The simulation results show that in the self-propulsion state, the torque of the contra-rotating propeller could be reduced by more than 92% compared with that of a single propeller, greatly reducing the impact on the hybrid-driven AUG and raising the navigation stability.

Design, Hydrodynamic Analysis, and Testing of a Bio-inspired Movable Bow Mechanism for the Hybrid-driven Underwater Glider

Hybrid-driven Underwater Glider (HUG) is a new type of underwater vehicle which integrates the functions of an Autonomous Underwater Glider (AUG) and an Autonomous Unmanned Vehicle (AUV). Although HUG has the characteristics of long endurance distance, its maneuverability still has room to be improved. This work introduces a new movement form of the neck of the underwater creature into HUG and proposes a parallel mechanism to adjust the attitude angle and displacement of the HUG’s bow, which can improve the steering maneuverability. Firstly, the influence of bow movement and rotation on the hydrodynamic force and flow field of the whole machine is analyzed by using the Computational Fluid Dynamics (CFD) method. The degree of freedom, attitude control range and movement amount of the Movable Bow Mechanism (MBM) are obtained, and then the design of MBM is completed based on these constraints. Secondly, the kinematic and dynamic models of MBM are established based on the closed vector method and the Lagrange equation, respectively, which are fully verified by comparing the results of simulation in Matlab and Adams software, then a Radial Basis Function (RBF) neural network adaptive sliding mode controller is designed to improve the dynamic response effect of the output parameters of MBM. Finally, a prototype of MBM is manufactured and assembled. The kinematic, dynamics model and controller are verified by experiments, which provides a basis for applying MBM in HUGs.

Multi-AUG three-dimensional path planning and secure cooperative path following under DoS attacks

This article is concerned with the design of a three-dimensional path planning and secure event-triggered cooperative path following for multiple disk-type autonomous underwater gliders (AUGs) in the presence of underwater obstacles and denial-of service (DoS) attacks. A three-dimensional collision-free path planning method is firstly proposed by using a quantum-behaved adaptive particle swarm optimization method in the global path planning layer and an artificial potential field method in the local path planning layer. Secondly, a path variable update law is devised based on a three-dimensional line-of-sight guidance mechanism, which can achieve the cooperative control for networked AUGs, in addition, AUGs can stop at the target points automatically. Finally, an event-triggered mechanism is presented to achieve secure cooperative control for AUGs under the unreliable network environment in the presence of DoS attacks. The stability is validated based on the input-to-state stability theory. Simulation results and numerical analysis demonstrate the effectiveness of the proposed integrated three-dimensional collision-free path planning and secure event-triggered cooperative path following method.

Water Mass Variations in the Maluku Channel of the Indonesian Seas During the Winter of 2018–2019

AbstractAn autonomous underwater glider was deployed in the Maluku Channel during 1 December 2018 through 21 February 2019 to measure temperature and salinity profiles of the upper ∼1,000 m continuously. The measurements suggest intraseasonal variations of the Pacific water mass intrusions into the Maluku Channel, which has not been reported before. The North Pacific Tropical and Intermediate Waters are found to intrude episodically into the eastern Maluku Channel at the depths of 130–180 m and 250–300 m, respectively, during January through February of 2019, each lasting for a few days to a week. The Antarctic Intermediate Water was present in the middle and western Maluku Channel between 600 and 800 m with intraseasonal variability. The South Pacific Subsurface Water was only found to intrude into the eastern Maluku Channel between 250 and 300 m during the first two transections in early December of 2018. Concurrent meter data from three moorings in the Maluku and Talaud‐Halmahera Channels are used to verify the water mass movement. The subsurface and intermediate water mass variations here are found to be closely related to the swing of the Mindanao Current near the Maluku Channel. These intraseasonal water mass intrusions are important aspects of water exchange between the western Pacific Ocean and the Indonesian seas.

Position tracking of an autonomous underwater glider based on adaptive filtered backstepping control

This paper considers the problem of position tracking control of the autonomous underwater gliders, which operates under the environment of model uncertainties and external disturbances. The motion of the glider is controlled by ballast mass and moving mass, which have limited dynamic range. An adaptive control system for position tracking based on filtered backstepping is proposed, and neural networks and sliding mode control are used to improve robustness. Next, using Lyapunov stability theory, it is proved that all the signals are bounded and tracking errors eventually converge to a neighborhood of zero. The presented controller can be easily put into practice without the requirement to know the parameters of the glider and the value of external environmental disturbances. Finally, the effectiveness and good robustness of the proposed control system are verified by simulation results.

Heuristic Surface Path Planning Method for AMV-Assisted Internet of Underwater Things

Ocean exploration is one of the fundamental issues for the sustainable development of human society, which is also the basis for realizing the concept of the Internet of Underwater Things (IoUT) applications, such as the smart ocean city. The collaboration of heterogeneous autonomous marine vehicles (AMVs) based on underwater wireless communication is known as a practical approach to ocean exploration, typically with the autonomous surface vehicle (ASV) and the autonomous underwater glider (AUG). However, the difference in their specifications and movements makes the following problems for collaborative work. First, when an AUG floats to a certain depth, and an ASV interacts via underwater wireless communication, the interaction has a certain time limit and their movements to an interaction position have to be synchronized; secondly, in the case where multiple AUGs are exploring underwater, the ASV needs to plan the sequence of surface interactions to ensure timely and efficient data collection. Accordingly, this paper proposes a heuristic surface path planning method for data collection with heterogeneous AMVs (HSPP-HA). The HSPP-HA optimizes the interaction schedule between ASV and multiple AUGs through a modified shuffled frog-leaping algorithm (SFLA). It applies a spatial-temporal k-means clustering in initializing the memeplex group of SFLA to adapt time-sensitive interactions by weighting their spatial and temporal proximities and adopts an adaptive convergence factor which varies by algorithm iterations to balance the local and global searches and to minimize the potential local optimum problem in each local search. Through simulations, the proposed HSPP-HA shows advantages in terms of access rate, path length and data collection rate compared to recent and classic path planning methods.

Detection efficiency of an autonomous underwater glider carrying an integrated acoustic receiver for acoustically tagged Pacific herring

AbstractAutonomous underwater vehicles (AUVs) or gliders are increasingly being used with acoustic telemetry to elucidate fish movements while collecting simultaneous environmental data. We assessed the utility of an AUV equipped with an integrated acoustic receiver to detect Pacific herring (Clupea pallasii) in Prince William Sound, AK, USA. A range test evaluated the effect of glider flight characteristics and environmental conditions on the detection efficiency of transmitters at varying depths. While distance from transmitters was the strongest predictor of detections, glider depth had a variable effect on detection efficiency which depended on transmitter depth and dive orientation. The detection efficiency of the glider-mounted acoustic receiver was less affected by wind speed and water level than that of stationary acoustic receivers deployed within the study area. The AUV also performed repeated, adaptive transects in an area of ∼630 km2 area and detected 30 Pacific herring transmitters without a priori knowledge of their locations. Of these herring transmitters, 14 were presumed shed after repeated detections within the same area, and 2 were detected at multiple locations. This study is the first to demonstrate that glider-mounted acoustic receivers have high detection efficiency for transmitters at varying depths and can detect movements of migratory forage fish in large search areas.

Design and Construction of Hybrid Autonomous Underwater Glider for Underwater Research

The main goal of this paper was to design and construct a hybrid autonomous underwater glider (HAUG) with a torpedo shape, a size of 230 cm in length and 24 cm in diameter. The control, navigation, and guidance system were executed simultaneously using a Udoo X86 minicomputer as the main server and three BeagleBone Black single-board computers as the clients. The simulations showed a controlled horizontal speed of 0.5 m/s in AUV mode and 0.39 to 0.51 m/s in glide mode with a pitch angle between 14.13∘ and 26.89∘. In addition, the field experiments under limited space showed the proposed HAUG had comparable results with the simulation, with a horizontal speed in AUV mode of 1 m/s and in glide mode of around 0.2 m/s. Moreover, the energy consumption with an assumption of three cycles of gliding motion per hour was 51.63 watts/h, which enabled the HAUG to perform a mission for 44.74 h. The proposed HAUG was designed to hold pressure up to 200 m under water and to perform underwater applications such as search and rescue, mapping, surveillance, monitoring, and maintenance.

Acoustic sampling of Antarctic krill with simulated underwater buoyancy gliders: Does the sawtooth dive pattern work?

Autonomous underwater gliders may be viable adjuncts to or in some cases replacements for ship-based oceanographic sampling. Gliders and ships acoustically sample the water column differently, with ships sampling all depths simultaneously in a single vertical pulse and gliders sampling shorter vertical segments of the water column in an up and down, sawtooth pattern. We simulated gliders following this flight pattern to sample the densities at depth of Antarctic krill (Euphausia superba), a patchily-distributed crustacean that is targeted by an international fishery. Krill densities from ship-based surveys conducted between 2001 to 2011 were treated as the “true” population densities sampled by the simulated gliders. Depth-integrated densities estimated from the glider sampling were compared to the population densities for each year. Coverage probabilities (the proportion of population means within a standard deviation of the glider sample means) for gliders diving to 150 m were near 100% in most years, better than the nominal 68%. Gliders diving to a maximum depth of 150 m estimated the annual population means better than gliders diving deeper because shallow dives provided more samples for a given length of trackline. Modeling the zero and non-zero data as separate distributions (the delta approach), an alternative to the lognormal CV approach used in this study, resulted in less accurate estimates of krill population densities. These results suggest that the sawtooth flight pattern of gliders can produce density estimates of krill comparable to the annual time series of density estimates from ship-based surveys. Gliders may also be useful to survey other patchily-distributed pelagic organisms.

Canyon Downwelling and Water Mass Influences on Winter Zooplankton Distributions in the Coastal Northeast Pacific

AbstractSubmarine canyons are considered biological hotspots due to enhanced mixing, upwelling, and other dynamic processes. There have been few observational surveys of canyon processes or zooplankton‐watermass relations during stormy downwelling seasons. In winter 2017, three autonomous underwater gliders provided highly‐resolved hydrographic and zooplankton backscatter observations in and around a canyon in the Northeast Pacific. While a glider's slow speed typically confounds spatial and temporal signals, the concurrent use of multiple gliders, sampling a canyon transect repeatedly, allowed us to explore the canyon system both spatially (i.e., canyon influence) and temporally (i.e., changing water type fractions). Canyon downwelling displaced the pycnocline by about 30 m depth over the scale of the canyon, which is ∼30% of the total pycnocline depth deviation observed over the course of the study. Diel vertically migrating (DVM) zooplankton generally stayed above the pycnocline and mean zooplankton volume scattering strength (Sv) in the upper water column (above the pycnocline) was higher when the pycnocline was deeper. At mid‐depths (150–200 m depth), zooplankton backscatter and DVM behavior were correlated with water type fractions, with higher Sv being associated with higher proportions of Pacific Equatorial Water and stronger DVM being associated with higher proportions of Pacific Subarctic Upper Water. Winter zooplankton distributions appear to be influenced by multiple, interacting drivers including canyon dynamics and water mass composition. In our study, the latter was found to have the stronger influence on zooplankton distribution.

Fast fixed-time vertical plane motion control of autonomous underwater gliders in shallow water

In this paper, a fast fixed-time vertical plane motion controller is proposed for autonomous underwater gliders (AUGs) gliding in shallow water. The influence of speed-sensorless conditions, model uncertainties, unknown time-varying external disturbances, input saturations, and state delay are taken into account. To improve control performance, a fast fixed-time stable system is first presented. Based on the system, an adaptive extended state observer (ESO) is developed for estimating speed, model uncertainties, and external disturbances. A fast fixed-time controller is designed for improving the gliding efficiency and reducing the risk of hitting the ocean floor. Moreover, an input saturation auxiliary system and an advance compensation method are presented to cope with input saturations and state delay. According to Lyapunov theory, it is proved that the AUG states can converge into a small neighborhood within a fixed time. Finally, simulation results demonstrate the rapidity and effectiveness of the designed control method.