Search results for: grid stability

Authors: G. Petruzzelli, F. Pedron, M. Grifoni, A. Pera, I. Rosellini, B. Pezzarossa

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The addition of lime as Ca(OH)2 to sewage sludge to destroy pathogens (Escherichia coli), was evaluated also in relation to heavy metal bioavailability. The obtained results show that the use of calcium hydroxide at the dose of 3% effectively destroyed pathogens ensuring the stability at high pH values over long period and the duration of the sewage sludge stabilization. In general, lime addition decreased the total extractability of heavy metals indicating a reduced bioavailability of these elements. This is particularly important for a safe utilization in agricultural soils to reduce the possible transfer of heavy metals to the food chain.

Keywords: Biological sludge, Ca(OH)2, copper, pathogens, sanitation, zinc.

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Authors: M. Vijaya Kini, R. S. Pai, D. Srikanth Rao, Satish Shenoy B, R. Pai

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The stability characteristics of water lubricated journal bearings having three axial grooves are obtained theoretically. In this lubricant (water) is fed under pressure from one end of the bearing, through the 3-axial grooves (groove angles may vary). These bearings can use the process fluid as the lubricant, as in the case of feed water pumps. The Reynolds equation is solved numerically by the finite difference method satisfying the boundary conditions. The stiffness and damping coefficient for various bearing number and eccentricity ratios, assuming linear pressure drop along the groove, shows that smaller groove angles better results.

Keywords: 3-axial groove, dynamic characteristics, groovelocation, water lubricated bearings.

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Authors: C. Nallusamy, A. Sabari, K. Suganya

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Geographical routing protocol requires node physical location information to make forwarding decision. Geographical routing uses location service or position service to obtain the position of a node. The geographical information is a geographic coordinates or can be obtained through reference points on some fixed coordinate system. Link can be formed between two nodes. Link lifetime plays a crucial role in MANET. Link lifetime represent how long the link is stable without any failure between the nodes. Link failure may occur due to mobility and because of link failure energy of nodes can be drained. Thus this paper proposes survey about link lifetime prediction using geographical information.

Keywords: MANET, Geographical routing, Link lifetime, Link stability.

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Authors: Jyh-Yang Wu, Sheng-Gwo Chen

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In this paper, we present a simple effective numerical geometric method to estimate the divergence of a vector field over a curved surface. The conservation law is an important principle in physics and mathematics. However, many well-known numerical methods for solving diffusion equations do not obey conservation laws. Our presented method in this paper combines the divergence theorem with a generalized finite difference method and obeys the conservation law on discrete closed surfaces. We use the similar method to solve the Cahn-Hilliard equations on evolving spherical surfaces and observe stability results in our numerical simulations.

Keywords: Conservation laws, diffusion equations, Cahn-Hilliard Equations, evolving surfaces.

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Authors: Asad Islam, Khalid Parvez

Abstract:

Compressor fans in modern aircraft engines are of considerate importance, as they provide majority of thrust required by the aircraft. Their challenging environment is frequently subjected to non-uniform inflow conditions. These conditions could be either due to the flight operating requirements such as take-off and landing, wake interference from aircraft fuselage or cross-flow wind conditions. So, in highly maneuverable flights regimes of fighter aircrafts affects the overall performance of an engine. Since the flow in compressor of an aircraft application is highly sensitive because of adverse pressure gradient due to different flow orientations of the aircraft. Therefore, it is prone to unstable operations. This paper presents the study that focuses on axial compressor response to inlet flow orientations for the range of angles as 0 to 15 degrees. For this purpose, NASA Rotor-37 was taken and CFD mesh was developed. The compressor characteristics map was generated for the design conditions of pressure ratio of 2.106 with the rotor operating at rotational velocity of 17188.7 rpm using CFD simulating environment of ANSYS-CFX®. The grid study was done to see the effects of mesh upon computational solution. Then, the mesh giving the best results, (when validated with the available experimental NASA’s results); was used for further distortion analysis. The flow in the inlet nozzle was given angle orientations ranging from 0 to 15 degrees. The CFD results are analyzed and discussed with respect to stall margin and flow separations due to induced distortions.

Keywords: Angle, ANSYS-CFX®, axial compressor, Bladegen®, CFD, distortions.

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Authors: G. Khamooshian

Abstract:

One of the main points of application of the mechanisms of the series and parallel is the subject of managing them. The control of this mechanism and similar mechanisms is one that has always been the intention of the scholars. On the other hand, modeling the behavior of the system is difficult due to the large number of its parameters, and it leads to complex equations that are difficult to solve and eventually difficult to control. In this paper, a six-linkage robot has been presented that could be used in different areas such as medical robots. Using these robots needs a robust control. In this paper, the system equations are first found, and then the system conversion function is written. A new controller has been designed for this robot which could be used in other parallel robots and could be very useful. Parallel robots are so important in robotics because of their stability, so methods for control of them are important and the robust controller, especially in parallel robots, makes a sense.

Keywords: 3-RRS, 6 linkage, parallel robot, control.

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Authors: Sung Ho Ahn, Jintae Hong, Chang Young Joung, Tae Ho Yang, Sung Ho Heo, Seo Yun Jang

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The performances of nuclear fuels and materials are qualified at an irradiation system in research reactors operating under the commercial nuclear power plant conditions. Fuel centerline temperature, coolant temperature, neutron flux, deformations of fuel stack and swelling are important parameters needed to analyze the nuclear fuel performances. The dimensional stability of nuclear fuels is a key parameter measuring the fuel densification and swelling. In this study, the fuel stack elongation is measured using a LVDT. A mockup LVDT instrumented fuel rod is developed. The performances of mockup LVDT instrumented fuel rod is evaluated by experiments.

Keywords: Axial deformation, elongation measurement, in-pile instrumentation, LVDT.

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Authors: Norsinnira Zainul Azlan, Hiroshi Yamaura

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This paper presents a new adaptive impedance control strategy, based on Function Approximation Technique (FAT) to compensate for unknown non-flat environment shape or time-varying environment location. The target impedance in the force controllable direction is modified by incorporating adaptive compensators and the uncertainties are represented by FAT, allowing the update law to be derived easily. The force error feedback is utilized in the estimation and the accurate knowledge of the environment parameters are not required by the algorithm. It is shown mathematically that the stability of the controller is guaranteed based on Lyapunov theory. Simulation results presented to demonstrate the validity of the proposed controller.

Keywords: Adaptive impedance control, Function Approximation Technique (FAT), impedance control, unknown environment position.

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Authors: Hanaa T. El-Madany, Faten H. Fahmy, Ninet M. A. El-Rahman, Hassen T. Dorrah

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Renewable energy resources are inexhaustible, clean as compared with conventional resources. Also, it is used to supply regions with no grid, no telephone lines, and often with difficult accessibility by common transport. Satellite earth stations which located in remote areas are the most important application of renewable energy. Neural control is a branch of the general field of intelligent control, which is based on the concept of artificial intelligence. This paper presents the mathematical modeling of satellite earth station power system which is required for simulating the system.Aswan is selected to be the site under consideration because it is a rich region with solar energy. The complete power system is simulated using MATLAB–SIMULINK.An artificial neural network (ANN) based model has been developed for the optimum operation of earth station power system. An ANN is trained using a back propagation with Levenberg–Marquardt algorithm. The best validation performance is obtained for minimum mean square error. The regression between the network output and the corresponding target is equal to 96% which means a high accuracy. Neural network controller architecture gives satisfactory results with small number of neurons, hence better in terms of memory and time are required for NNC implementation. The results indicate that the proposed control unit using ANN can be successfully used for controlling the satellite earth station power system.

Keywords: Satellite, neural network, MATLAB, power system.

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Authors: B. Chetti, W. A. Crosby

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The work described in this paper is an investigation of the static and dynamic characteristics of two-lobe journal bearings taking into consideration the thermal effects. A thermo-hydrodynamic solution of a finite two-lobe journal bearing is performed by solving the generalized form Reynolds equation with the energy equation, taking into consideration viscosity variation across the film thickness. The static and dynamic characteristics were numerically obtained. The results are evaluated for different values of viscosity-temperature coefficient and Peclet number. The results show that considering the thermal effects in the solution of the two-lobe journal bearing has a marked on the study of its stability.

Keywords: Two-lobe bearing, thermal effect, static and dynamic characteristics.

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Authors: Mohammad Reza Askari, Mohsen Kazemi, Ali Asghar Baziar

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In this treatise we will study the capability of static compensator for reactive power to stabilize sheen voltage with motor loading on power networks system. We also explain the structure and main function of STATCOM and the method to control it using STATCOM transformer current to simultaneously predict after telling about the necessity of FACTS tools to compensate in power networks. Then we study topology and controlling system to stabilize voltage during start of inductive motor. The outcome of stimulat by MATLAB software supports presented controlling idea and system in the treatise.

Keywords: Power network, inductive motor, reactive power, stability of voltage, STATCOM, FACTS

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Authors: L.C. Kgomari, R.K.K.Mbaya

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This research was conducted to develop a correlation between microstructure of HSLA steel and the mechanical properties that occur as a result of both laser and mechanical forming processes of the metal. The technique of forming flat metals by applying laser beams is a relatively new concept in the manufacturing industry. However, the effects of laser energy on the stability of metal alloy phases have not yet been elucidated in terms of phase transformations and microhardness. In this work, CO2 laser source was used to irradiate the surface of a flat metal then the microstructure and microhardness of the metal were studied on the formed specimen. The extent to which the microstructure changed depended on the heat inputs of up to 1000 J/cm2 with cooling rates of about 4.8E+02 K/s. Experimental results revealed that the irradiated surface of a HSLA steel had transformed to austenitic structure during the heating process.

Keywords: Laser, Forming, Microstructure

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Authors: H. Abderrezek, M. N. Harmas

Abstract:

DC-DC converters are widely used as reliable power source for many industrial and military applications, computers and electronic devices. Several control methods were developed for DC-DC converters control mostly with asymptotic convergence. Synergetic control (SC) is a proven robust control approach and will be used here in a so called terminal scheme to achieve finite time convergence. Lyapounov synthesis is adopted to assure controlled system stability. Furthermore particle swarm optimization (PSO) algorithm, based on an integral time absolute of error (ITAE) criterion will be used to optimize controller parameters. Simulation of terminal synergetic control of a DC-DC converter is carried out for different operating conditions and results are compared to classic synergetic control performance, that which demonstrate the effectiveness and feasibility of the proposed control method.

Keywords: DC-DC converter, PSO, finite time, terminal, synergetic control.

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Authors: Carla E. O. de Moraes, Gladson O. Antunes, Mauro A. Rincon

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The aim of this paper is to study the internal stabilization of the Bernoulli-Euler equation numerically. For this, we consider a square plate subjected to a feedback/damping force distributed only in a subdomain. An algorithm for obtaining an approximate solution to this problem was proposed and implemented. The numerical method used was the Finite Difference Method. Numerical simulations were performed and showed the behavior of the solution, confirming the theoretical results that have already been proved in the literature. In addition, we studied the validation of the numerical scheme proposed, followed by an analysis of the numerical error; and we conducted a study on the decay of the energy associated.

Keywords: Bernoulli-Euler Plate Equation, Numerical Simulations, Stability, Energy Decay, Finite Difference Method.

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Authors: B. G. Sampath, K. C. R. Perera, W. A. S. I. Wijesuriya, V. P. C. Dassanayake

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In this paper the design, development and testing of a stabilizer control system for a Quad-rotor is presented which is focused on the maneuverability. The mechanical design is performed along with the design of the controlling algorithm which is devised using fuzzy logic controller. The inputs for the system are the angular positions and angular rates of the Quad-rotor relative to three axes. Then the output data is filtered from an accelerometer and a gyroscope through a Kalman filter. In the development of the stability controlling system Mandani fuzzy model is incorporated. The results prove that the fuzzy based stabilizer control system is superior in high dynamic disturbances compared to the traditional systems which use PID integrated stabilizer control systems.

Keywords: Fuzzy stabilizer, maneuverability, PID, Quad-rotor.

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Authors: Lukumba Phiri, Simon Tembo, Kumbuso Joshua Nyoni

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In Zambia, recent initiatives by various power operators like ZESCO, CEC, and consumers like the mines, to upgrade power systems into smart grids, target an even tighter integration with information technologies to enable the integration of renewable energy sources, local and bulk generation, and demand response. Thus, for the reliable operation of smart grids, its information infrastructure must be secure and reliable in the face of both failures and cyberattacks. Due to the nature of the systems, ICS/SCADA cybersecurity and governance face additional challenges compared to the corporate networks, and critical systems may be left exposed. There exist control frameworks internationally such as the NIST framework, however, they are generic and do not meet the domain-specific needs of the SCADA systems. Zambia is also lagging in cybersecurity awareness and adoption, and therefore there is a concern about securing ICS controlling key infrastructure critical to the Zambian economy as there are few known facts about the true posture. In this paper, we present a stochastic Edged-based Anomaly Detection for SCADA systems (SEADS) framework for threat modeling and risk assessment. SEADS enables the calculation of steady-steady probabilities that are further applied to establish metrics like system availability, maintainability, and reliability.

Keywords: Anomaly detection, SmartGrid, edge, maintainability, reliability, stochastic process.

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Authors: Alpha Bolinao, Francine Rose De Castro, Jessie Kate Lumba, Raztine Mae Paeste, Hannah Grace Tosio

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The present study aimed to know the role of verbal bullying in the lives of obese teenagers exposed to it. The study employed a qualitative design specifically the phenomenological approach that focuses on the obese teenagers’ verbal bullying experiences. The study also used the social constructivism approach wherein it described the obese teenagers’ verbal bullying experiences as they interact with the social world. Through purposive and referral sampling technique, the researchers were able to choose twelve (12) respondents from different schools around the City of Manila, enrolled in the School Year 2015-2016, ages 16-21 years old, has experienced verbal bullying for the last ten (10) years and with the Body Mass Index (BMI) of equal to or greater than 30. Upon the consent of the respondents, ethical considerations were ensured. In-depth one (1) hour interviews were guided by the researchers’ aide memoir. The recorded interviews were transcribed into a field text and the responses were thoroughly analyzed through Thematic Analysis and Kelly’s Repertory Grid. It was found that the role of verbal bullying in the lives of obese teenagers exposed to it is a process and is best described through a syringe, or the 5S Responses of Obese Teenagers in Bullying, with five conceptual themes which also signify the experiences and the process that obese teenagers have gone through after experiencing verbal bullying. The themes conceptualized were: Suffering, self-doubt, suppression, self-acceptance and sanguineness. This paper may serve as a basis for a counseling program to help the obese teenagers cope with their bullying experiences.

Keywords: Obesity, obese teenagers, bullying, experiences.

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Authors: Ramli Nazir, Hossein Moayedi

Abstract:

Soil confinement systems serve as effective solutions to any erosion control project. Various confinements systems, namely triangular, circular and rectangular with the size of 50, 100, and 150 mm, and with a depth of 10 mm, were embedded in soil samples at slope angle of 60°. The observed soil mass losses for the confined soil systems were much smaller than those from unconfined system. As a result, the size of confinement and rainfall intensity have a direct effect on the soil mass loss. The triangular and rectangular confinement systems showed the lowest and highest soil loss masses, respectively. The slopes also failed much faster in the unconfined system than in the confined slope.

Keywords: Erosion control, Soil confinement, Soil erosion, Slope stability.

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Authors: Manisha Dubey, Pankaj Gupta

Abstract:

This paper presents a systematic approach for the design of power system stabilizer using genetic algorithm and investigates the robustness of the GA based PSS. The proposed approach employs GA search for optimal setting of PSS parameters. The performance of the proposed GPSS under small and large disturbances, loading conditions and system parameters is tested. The eigenvalue analysis and nonlinear simulation results show the effectiveness of the GPSS to damp out the system oscillations. It is found tat the dynamic performance with the GPSS shows improved results, over conventionally tuned PSS over a wide range of operating conditions.

Keywords: Genetic Algorithm, Genetic power system stabilizer, Power system stabilizer, Small signal stability

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Authors: Birs Isabela, Muresan Cristina, Folea Silviu, Prodan Ovidiu

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The wing is one of the most important parts of an airplane because it ensures stability, sustenance and maneuverability of the airplane. Because of its shape, the airplane wing can be simplified to a smart beam. Active vibration suppression is realized using piezoelectric actuators that are mounted on the surface of the beam. This work presents a tuning procedure of fractional order controllers based on a graphical approach of the frequency domain representation. The efficacy of the method is proven by practically testing the controller on a laboratory scale experimental stand.

Keywords: Fractional order controller, piezoelectric actuators, smart beam, vibration suppression.

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Authors: Ion Smeureanu, Marian Dardala, Adriana Reveiu

Abstract:

The new programming technologies allow for the creation of components which can be automatically or manually assembled to reach a new experience in knowledge understanding and mastering or in getting skills for a specific knowledge area. The project proposes an interactive framework that permits the creation, combination and utilization of components that are specific to mathematical training in high schools. The main framework-s objectives are: • authoring lessons by the teacher or the students; all they need are simple operating skills for Equation Editor (or something similar, or Latex); the rest are just drag & drop operations, inserting data into a grid, or navigating through menus • allowing sonorous presentations of mathematical texts and solving hints (easier understood by the students) • offering graphical representations of a mathematical function edited in Equation • storing of learning objects in a database • storing of predefined lessons (efficient for expressions and commands, the rest being calculations; allows a high compression) • viewing and/or modifying predefined lessons, according to the curricula The whole thing is focused on a mathematical expressions minicompiler, storing the code that will be later used for different purposes (tables, graphics, and optimisations). Programming technologies used. A Visual C# .NET implementation is proposed. New and innovative digital learning objects for mathematics will be developed; they are capable to interpret, contextualize and react depending on the architecture where they are assembled.

Keywords: Adaptor, automatic assembly learning component and user control.

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Authors: A. A. Hussen, I. N. Jleta

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Micro-electromechanical system (MEMS) accelerometers and gyroscopes are suitable for the inertial navigation system (INS) of many applications due to low price, small dimensions and light weight. The main disadvantage in a comparison with classic sensors is a worse long term stability. The estimation accuracy is mostly affected by the time-dependent growth of inertial sensor errors, especially the stochastic errors. In order to eliminate negative effects of these random errors, they must be accurately modeled. In this paper, the Allan variance technique will be used in modeling the stochastic errors of the inertial sensors. By performing a simple operation on the entire length of data, a characteristic curve is obtained whose inspection provides a systematic characterization of various random errors contained in the inertial-sensor output data.

Keywords: Allan variance, accelerometer, gyroscope, stochastic errors.

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Authors: Shonal Singh, Bibhya Sharma, Jito Vanualailai, Avinesh Prasad

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This paper considers the autonomous navigation problem of multiple n-link nonholonomic mobile manipulators within an obstacle-ridden environment. We present a set of nonlinear acceleration controllers, derived from the Lyapunov-based control scheme, which generates collision-free trajectories of the mobile manipulators from initial configurations to final configurations in a constrained environment cluttered with stationary solid objects of different shapes and sizes. We demonstrate the efficiency of the control scheme and the resulting acceleration controllers of the mobile manipulators with results through computer simulations of an interesting scenario.

Keywords: Artificial potential fields, kinodynamic constraints, Lyapunov-based control scheme, Lyapunov stability, minimum distance technique, nonholonomic manipulator.

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Authors: Marco Raciti Castelli, Alberto Castelli, Ernesto Benini

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The construction of a civil structure inside a urban area inevitably modifies the outdoor microclimate at the building site. Wind speed, wind direction, air pollution, driving rain, radiation and daylight are some of the main physical aspects that are subjected to the major changes. The quantitative amount of these modifications depends on the shape, size and orientation of the building and on its interaction with the surrounding environment.The flow field over a flat roof model building has been numerically investigated in order to determine two-dimensional CFD guidelines for the calculation of the turbulent flow over a structure immersed in an atmospheric boundary layer. To this purpose, a complete validation campaign has been performed through a systematic comparison of numerical simulations with wind tunnel experimental data.Several turbulence models and spatial node distributions have been tested for five different vertical positions, respectively from the upstream leading edge to the downstream bottom edge of the analyzed model. Flow field characteristics in the neighborhood of the building model have been numerically investigated, allowing a quantification of the capabilities of the CFD code to predict the flow separation and the extension of the recirculation regions.The proposed calculations have allowed the development of a preliminary procedure to be used as a guidance in selecting the appropriate grid configuration and corresponding turbulence model for the prediction of the flow field over a twodimensional roof architecture dominated by flow separation.

Keywords: CFD, roof, building, wind.

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Authors: T. Hussein

Abstract:

The use of power system stabilizers (PSSs) to damp power system swing mode of oscillations is practical important. Our purpose is to retune the power system stabilizer (PSS1A) parameters in Unitrol D produced by ABB– was installed in 1995in Benghazi North Power Plants (BNPPs) at General Electricity Company of Libya (GECOL). The optimal values of the power system stabilizer (PSS1A) parameters are determined off-line by a particle swarm optimization technique (PSO). The objective is to damp the local and inter-area modes of oscillations that occur following power system disturbances. The retuned power system stabilizer (PSS1A) can cope with large disturbance at different operating points and has enhanced power system stability.

Keywords: Static excitation system, particle swarm optimization (PSO), power system stabilizer (PSS).

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Authors: Ahmad Forouzantabar, Babak Gholami, Mohammad Azadi

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An adaptive neural network controller for autonomous underwater vehicles (AUVs) is presented in this paper. The AUV model is highly nonlinear because of many factors, such as hydrodynamic drag, damping, and lift forces, Coriolis and centripetal forces, gravity and buoyancy forces, as well as forces from thruster. In this regards, a nonlinear neural network is used to approximate the nonlinear uncertainties of AUV dynamics, thus overcoming some limitations of conventional controllers and ensure good performance. The uniform ultimate boundedness of AUV tracking errors and the stability of the proposed control system are guaranteed based on Lyapunov theory. Numerical simulation studies for motion control of an AUV are performed to demonstrate the effectiveness of the proposed controller.

Keywords: Autonomous Underwater Vehicle (AUV), Neural Network Controller, Composite Adaptation.

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Authors: Dag A.H. Samuelsen, Olaf H. Graven

Abstract:

Introducing Electromagnetic Interference and Electromagnetic Compatibility, or “The Art of Black Magic", for engineering students might be a terrifying experience both for students and tutors. Removing the obstacle of large, expensive facilities like a fully fitted EMC laboratory and hours of complex theory, this paper demonstrates a design of a laboratory setup for student exercises, giving students experience in the basics of EMC/EMI problems that may challenge the functionality and stability of embedded system designs. This is done using a simple laboratory installation and basic measurement equipment such as a medium cost digital storage oscilloscope, at the cost of not knowing the exact magnitude of the noise components, but rather if the noise is significant or not, as well as the source of the noise. A group of students have performed a trial exercise with good results and feedback.

Keywords: EMC, EMI, engineering project, student laboratory.

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Authors: Salem Belhaj, Moncef Tagina

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This paper is aimed at describing a delay-based endto- end (e2e) congestion control algorithm, called Very FAST TCP (VFAST), which is an enhanced version of FAST TCP. The main idea behind this enhancement is to smoothly estimate the Round-Trip Time (RTT) based on a nonlinear filter, which eliminates throughput and queue oscillation when RTT fluctuates. In this context, an evaluation of the suggested scheme through simulation is introduced, by comparing our VFAST prototype with FAST in terms of throughput, queue behavior, fairness, stability, RTT and adaptivity to changes in network. The achieved simulation results indicate that the suggested protocol offer better performance than FAST TCP in terms of RTT estimation and throughput.

Keywords: Fast tcp, RTT, delay estimation, delay-based congestion control, high speed TCP, large bandwidth delay product.

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Authors: Jay Singh, C. B. Vishwakarma, Kalyan Chatterjee

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A mixed method by combining modified pole clustering technique and modified cauer continued fraction is proposed for reducing the order of the large-scale dynamic systems. The denominator polynomial of the reduced order model is obtained by using modified pole clustering technique while the coefficients of the numerator are obtained by modified cauer continued fraction. This method generated 'k' number of reduced order models for kth order reduction. The superiority of the proposed method has been elaborated through numerical example taken from the literature and compared with few existing order reduction methods.

Keywords: Modified Pole Clustering, Modified Cauer Continued Fraction, Order Reduction, Stability, Transfer Function.

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Authors: Tlotlollo Sidwell Hlalele, Shengzhi Du

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High-voltage power transmission lines are the back bone of electrical power utilities. The stability and continuous monitoring of this critical infrastructure is pivotal. Nine-Sigma representing Eskom Holding SOC limited, South Africa has a major problem on proactive detection of fallen power lines and real time sagging measurement together with slipping of such conductors. The main objective of this research is to innovate RFID technology to solve this challenge. Various options and technologies such as GPS, PLC, image processing, MR sensors and etc., have been reviewed and draw backs were made. The potential of RFID to give precision measurement will be observed and presented. The future research will look at magnetic and electrical interference as well as corona effect on the technology.

Keywords: Precision Measurement, RFID and Sag.

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