Search results for: hysteresis current control

Authors: Rooholah Hasanizadeh, Saadan Zokaei

Abstract:

Energy efficient protocol design is the aim of current researches in the area of sensor networks where limited power resources impose energy conservation considerations. In this paper we care for Medium Access Control (MAC) protocols and after an extensive literature review, two adaptive schemes are discussed. Of them, adaptive-rate MACs which were introduced for throughput enhancement show the potency to save energy, even more than adaptive-power schemes. Then we propose an allocation algorithm for getting accurate and reliable results. Through a simulation study we validated our claim and showed the power saving of adaptive-rate protocols.

Keywords: Adaptive-rate, adaptive-power, MAC protocol, energy efficiency, sensor networks.

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Authors: Marwan Abukhaled, Ibrahim Sadek

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This paper presents the vibrations suppression of a thermoelastic beam subject to sudden heat input by a distributed piezoelectric actuators. An optimization problem is formulated as the minimization of a quadratic functional in terms of displacement and velocity at a given time and with the least control effort. The solution method is based on a combination of modal expansion and variational approaches. The modal expansion approach is used to convert the optimal control of distributed parameter system into the optimal control of lumped parameter system. By utilizing the variational approach, an explicit optimal control law is derived and the determination of the corresponding displacement and velocity is reduced to solving a set of ordinary differential equations.

Keywords: Optimal control, Thermoelastic beam, variational approach, modal expansion approach

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Authors: Malinwo Estone Ayikpa

Abstract:

Electric power systems are likely to operate with minimum losses and voltage meeting international standards. This is made possible generally by control actions provide by automatic voltage regulators, capacitors and transformers with on-load tap changer (OLTC). With the development of photovoltaic (PV) systems technology, their integration on distribution networks has increased over the last years to the extent of replacing the above mentioned techniques. The conventional analysis and simulation tools used for electrical networks are no longer able to take into account control actions necessary for studying distributed PV generation impact. This paper presents an unbalanced optimal power flow (OPF) model that minimizes losses with association of active power generation and reactive power control of single-phase and three-phase PV systems. Reactive power can be generated or absorbed using the available capacity and the adjustable power factor of the inverter. The unbalance OPF is formulated by current balance equations and solved by primal-dual interior point method. Several simulation cases have been carried out varying the size and location of PV systems and the results show a detailed view of the impact of PV distributed generation on distribution systems.

Keywords: Distribution system, losses, photovoltaic generation, primal-dual interior point method, reactive power control.

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Authors: Ei Ei Moe, Zaw Min Aung, Kyawt Khin

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This paper puts forward one kind of air-fuel ratio control method with PI controller. With the help of MATLAB/SIMULINK software, the mathematical model of air-fuel ratio control system for distributorless CNG engine is constructed. The objective is to maintain cylinder-to-cylinder air-fuel ratio at a prescribed set point, determined primarily by the state of the Three- Way-Catalyst (TWC), so that the pollutants in the exhaust are removed with the highest efficiency. The concurrent control of airfuel under transient conditions could be implemented by Proportional and Integral (PI) controller. The simulation result indicates that the control methods can easily eliminate the air/fuel maldistribution and maintain the air/fuel ratio at the stochiometry within minimum engine events.

Keywords: Distributorless CNG Engine, Mathematical Modelof Air-fuel control, MATLAB/SIMULINK, PI controller

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Authors: Jung-Chuan Chou, Wei-Lun Hsia

Abstract:

A measurement system for pH array sensors is introduced to increase accuracy, and decrease non-ideal effects successfully. An array readout circuit reads eight potentiometric signals at the same time, and obtains an average value. The deviation value or the extreme value is counteracted and the output voltage is a relatively stable value. The errors of measuring pH buffer solutions are decreased obviously with this measurement system, and the non-ideal effects, drift and hysteresis, are lowered to 1.638mV/hr and 1.118mV, respectively. The efficiency and stability are better than single sensor. The whole sensing characteristics are improved.

Keywords: Array sensors, measurement system, non-ideal effects, pH sensor, readout circuit.

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Authors: S. Leghmizi, S. Liu, F. Naeim

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This paper presents a fuzzy control system for a three degree of freedom (3-DOF) stabilized platform with explicit decoupling scheme. The system under consideration is a system with strong interactions between three channels. By using the concept of decentralized control, a control structure is developed that is composed of three control loops, each of which is associated with a single-variable fuzzy controller and a decoupling unit. Takagi-Sugeno (TS) fuzzy control algorithm is used to implement the fuzzy controller. The decoupling units design is based on the adaptive theory reasoning. Simulation tests were established using Simulink of Matlab. The obtained results have demonstrated the feasibility and effectiveness of the proposed approach. Simulation results are represented in this paper.

Keywords: 3-DOF platform of a ship carried antenna, the concept of decentralized control, Takagi-Sugeno (TS) fuzzy control algorithm, Simulink.

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Authors: B. Moaveni, S. Morovati

Abstract:

In recent years, increasing the usage of railway transportations especially in developing countries caused more attention to control systems railway vehicles. Consequently, designing and implementing the modern control systems to improve the operating performance of trains and locomotives become one of the main concerns of researches. Dynamic braking systems is an important safety system which controls the amount of braking torque generated by traction motors, to keep the adhesion coefficient between the wheel-sets and rail road in optimum bound. Adhesion force has an important role to control the braking distance and prevent the wheels from slipping during the braking process. Cascade control structure is one of the best control methods for the wide range of industrial plants in the presence of disturbances and errors. This paper presents cascade control structure based on two forward simple controllers with two feedback loops to control the slip ratio and braking torque. In this structure, the inner loop controls the angular velocity and the outer loop control the longitudinal velocity of the locomotive that its dynamic is slower than the dynamic of angular velocity. This control structure by controlling the torque of DC traction motors, tries to track the desired velocity profile to access the predefined braking distance and to control the slip ratio. Simulation results are employed to show the effectiveness of the introduced methodology in dynamic braking system.

Keywords: Cascade control, dynamic braking system, DC traction motors, slip control.

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Authors: Markus Reichhartinger, Martin Horn

Abstract:

In this paper, the application of sliding-mode control to a permanent-magnet synchronous motor (PMSM) is presented. The control design is based on a generic mathematical model of the motor. Some dynamics of the motor and of the power amplification stage remain unmodelled. This model uncertainty is estimated in realtime. The estimation is based on the differentiation of measured signals using the ideas of robust exact differentiator (RED). The control law is implemented on an industrial servo drive. Simulations and experimental results are presented and compared to the same control strategy without uncertainty estimation. It turns out that the proposed concept is superior to the same control strategy without uncertainty estimation especially in the case of non-smooth reference signals.

Keywords: sliding-mode control, Permanent-magnet synchronous motor, uncertainty estimation, robust exact differentiator.

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Authors: Jan Erik Stellet

Abstract:

This article presents a detailed analysis and comparative performance evaluation of model reference adaptive control systems. In contrast to classical control theory, adaptive control methods allow to deal with time-variant processes. Inspired by the works [1] and [2], two methods based on the MIT rule and Lyapunov rule are applied to a linear first order system. The system is simulated and it is investigated how changes to the adaptation gain affect the system performance. Furthermore, variations in the reference model parameters, that is changing the desired closed-loop behaviour are examinded.

Keywords: Adaptive control systems, Adaptation gain, MIT rule, Lyapunov rule, Model reference adaptive control.

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Authors: H. Troudi, M. Ghiss, Z. Tourki, M. Ellejmi

Abstract:

Packed columns of liquefied petroleum gas (LPG) consists of separating the liquid mixture of propane and butane to pure gas components by the distillation phenomenon. The flow of the gas and liquid inside the columns is operated by two ways: The co-current and the counter current operation. Heat, mass and species transfer between phases represent the most important factors that influence the choice between those two operations. In this paper, both processes are discussed using computational CFD simulation through ANSYS-Fluent software. Only 3D half section of the packed column was considered with one packed bed. The packed bed was characterized in our case as a porous media. The simulations were carried out at transient state conditions. A multi-component gas and liquid mixture were used out in the two processes. We utilized the Euler-Lagrange approach in which the gas was treated as a continuum phase and the liquid as a group of dispersed particles. The heat and the mass transfer process was modeled using multi-component droplet evaporation approach. The results show that the counter-current process performs better than the co-current, although such limitations of our approach are noted. This comparison gives accurate results for computations times higher than 2 s, at different gas velocity and at packed bed porosity of 0.9.

Keywords: Co-current, counter current, Euler Lagrange model, heat transfer, mass transfer.

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Authors: A. Leelasantitham, B. Srisuchinwong

Abstract:

A high-frequency low-power sinusoidal quadrature oscillator is presented through the use of two 2nd-order low-pass current-mirror (CM)-based filters, a 1st-order CM low-pass filter and a CM bilinear transfer function. The technique is relatively simple based on (i) inherent time constants of current mirrors, i.e. the internal capacitances and the transconductance of a diode-connected NMOS, (ii) a simple negative resistance RN formed by a resistor load RL of a current mirror. Neither external capacitances nor inductances are required. As a particular example, a 1.9-GHz, 0.45-mW, 2-V CMOS low-pass-filter-based all-current-mirror sinusoidal quadrature oscillator is demonstrated. The oscillation frequency (f0) is 1.9 GHz and is current-tunable over a range of 370 MHz or 21.6 %. The power consumption is at approximately 0.45 mW. The amplitude matching and the quadrature phase matching are better than 0.05 dB and 0.15°, respectively. Total harmonic distortions (THD) are less than 0.3 %. At 2 MHz offset from the 1.9 GHz, the carrier to noise ratio (CNR) is 90.01 dBc/Hz whilst the figure of merit called a normalized carrier-to-noise ratio (CNRnorm) is 153.03 dBc/Hz. The ratio of the oscillation frequency (f0) to the unity-gain frequency (fT) of a transistor is 0.25. Comparisons to other approaches are also included.

Keywords: Sinusoidal quadrature oscillator, low-pass-filterbased, current-mirror bilinear transfer function, all-current-mirror, negative resistance, low power, high frequency, low distortion.

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Authors: Archana S. Nanoty, A. R. Chudasama

Abstract:

Three-phase induction machines are today a standard for industrial electrical drives. Cost, reliability, robustness and maintenance free operation are among the reasons these machines are replacing dc drive systems. The development of power electronics and signal processing systems has eliminated one of the greatest disadvantages of such ac systems, which is the issue of control. With modern techniques of field oriented vector control, the task of variable speed control of induction machines is no longer a disadvantage. The need to increase system performance, particularly when facing limits on the power ratings of power supplies and semiconductors, motivates the use of phase number other than three, In this paper a novel scheme of connecting two, three phase induction motors in parallel fed by two inverters; viz. VSI and CSI and their vector control is presented.

Keywords: Field oriented control, multiphase induction motor, power electronics converter.

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Authors: N.H. Mvungi

Abstract:

This paper addresses control of commutation of switched reluctance (SR) motor without the use of a physical position detector. Rotor position detection schemes for SR motor based on magnetisation characteristics of the motor use normal excitation or applied current /voltage pulses. The resulting schemes are referred to as passive or active methods respectively. The research effort is in realizing an economical sensorless SR rotor position detector that is accurate, reliable and robust to suit a particular application. An effective and reliable means of generating commutation signals of an SR motor based on inductance profile of its stator windings determined using active probing technique is presented. The scheme has been validated online using a 4-phase 8/6 SR motor and an 8-bit processor.

Keywords: Position detection, rotor position, sensorless, switched reluctance, SR.

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Authors: Nur Aisyah Jalalludin, Arwindra Rizqiawan, Goro Fujita

Abstract:

In this study, we aim to demonstrate a microgrid system experimental simulation for an easy understanding of a large-scale microgrid system. This model is required for industrial training and learning environments. However, in order to create an exact representation of a microgrid system, the laboratory-scale system must fulfill the requirements of a grid-connected inverter, in which power values are assigned to the system to cope with the intermittent output from renewable energy sources. Aside from that, during fluctuations in load capacity, the grid-connected system must be able to supply power from the utility grid side and microgrid side in a balanced manner. Therefore, droop control is installed in the inverter’s control board to maintain a balanced power sharing in both sides. This power control in a stand-alone condition and droop control in a grid-connected condition must be implemented in order to maintain a stabilized system. Based on the experimental results, power control and droop control can both be applied in the system by comparing the experimental and reference values.

Keywords: Droop control, droop characteristic, grid-connected inverter, microgrid, power control.

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Authors: B. Farhadinia

Abstract:

In this article, it is considered a class of optimal control problems constrained by differential and integral constraints are called canonical form. A modified measure theoretical approach is introduced to solve this class of optimal control problems.

Keywords: control problem, Canonical form, Measure theory.

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Authors: Amir Badkoubeh, Guchuan Zhu

Abstract:

This paper addresses the problem of asymptotic tracking control of a linear parabolic partial differential equation with indomain point actuation. As the considered model is a non-standard partial differential equation, we firstly developed a map that allows transforming this problem into a standard boundary control problem to which existing infinite-dimensional system control methods can be applied. Then, a combination of energy multiplier and differential flatness methods is used to design an asymptotic tracking controller. This control scheme consists of stabilizing state-feedback derived from the energy multiplier method and feed-forward control based on the flatness property of the system. This approach represents a systematic procedure to design tracking control laws for a class of partial differential equations with in-domain point actuation. The applicability and system performance are assessed by simulation studies.

Keywords: Tracking Control, In-domain point actuation, PartialDifferential Equations.

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Authors: Cherdvong Saengsupavanich

Abstract:

The impact of a proposed pier on tidal current alteration was evaluated. The proposed pier location was in Salad Bay on Koa Kood Island, Trat province, Thailand, and was designed to accommodate passenger ships with a draft of less than 2 m. The study began with collecting necessary data, including bathymetric, water elevation and tidal current characteristics. The impact was assessed using a software package (MIKE21). Although the results showed that the pier would affect the existing current pattern, the change was determined to be insignificant, as the design of the piles for the pier provided sufficient spacing to let the current flow as freely as possible. Consequences of the altered current, such as seabed erosion, water stagnation, sediment deposition and navigational risk were assessed. Environmental mitigation measures might be necessary if the impacts were considered unacceptable.

Keywords: Environmental impact assessment, pier, tidal currentchange, coastal engineering and management

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Authors: A. N. K. Nasir, R. M. T. Raja Ismail, M. A. Ahmad

Abstract:

The objective of this paper is to compare the time specification performance between conventional controller PID and modern controller SMC for an inverted pendulum system. The goal is to determine which control strategy delivers better performance with respect to pendulum-s angle and cart-s position. The inverted pendulum represents a challenging control problem, which continually moves toward an uncontrolled state. Two controllers are presented such as Sliding Mode Control (SMC) and Proportional- Integral-Derivatives (PID) controllers for controlling the highly nonlinear system of inverted pendulum model. Simulation study has been done in Matlab Mfile and simulink environment shows that both controllers are capable to control multi output inverted pendulum system successfully. The result shows that Sliding Mode Control (SMC) produced better response compared to PID control strategies and the responses are presented in time domain with the details analysis.

Keywords: SMC, PID, Inverted Pendulum System.

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Authors: S. Sukparungsee

Abstract:

In reality, the process observations are away from the assumption that are normal distributed. The observations could be skew distributions which should use an asymmetric chart rather than symmetric chart. Consequently, this research aim to study the robustness of the asymmetric Tukey’s control chart for skew and non-skew distributions as Lognormal and Laplace distributions. Furthermore, the performances in detecting of a change in parameter of asymmetric and symmetric Tukey’s control charts are compared by Average ARL (AARL). The results found that the asymmetric performs better than symmetric Tukey’s control chart for both cases of skew and non-skew process observation.

Keywords: Asymmetric control limit, average of average run length, Tukey’s control chart and skew distributions.

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Authors: A. Bellar, M.K. Fellah, A.M. Si Mohammed, M. Bensaada, L. Boukhris

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This paper presents the use of the predictive fuzzy logic controller (PFLC) applied to attitude control system for agile micro-satellite. In order to reduce the effect of unpredictable time delays and large uncertainties, the algorithm employs predictive control to predict the attitude of the satellite. Comparison of the PFLC and conventional fuzzy logic controller (FLC) is presented to evaluate the performance of the control system during attitude maneuver. The two proposed models have been analyzed with the same level of noise and external disturbances. Simulation results demonstrated the feasibility and advantages of the PFLC on the attitude determination and control system (ADCS) of agile satellite.

Keywords: Agile micro-satellite, Attitude control, fuzzy logic, predictive control

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Authors: Pingping Zhang, Yanpeng Cai, Jianlong Wang

Abstract:

Stormwater storage tank (SST) is a popular low impact development technology for reducing stormwater runoff in the construction of sponge city. At present, it is difficult to perform the automatic control of SST for reducing peak flow. In this paper, fuzzy control was introduced into the peak control of SST to improve the efficiency of reducing stormwater runoff. Firstly, the design of SST was investigated. A catchment area and a return period were assumed, a SST model was manufactured, and then the storage capacity of the SST was verified. Secondly, the control parameters of the SST based on reducing stormwater runoff were analyzed, and a schematic diagram of real-time control (RTC) system based on peak control SST was established. Finally, fuzzy control system of a double input (flow and water level) and double output (inlet and outlet valve) was designed. The results showed that 1) under the different return periods (one year, three years, five years), the SST had the effect of delayed peak control and storage by increasing the detention time, 2) rainfall, pipeline flow, the influent time and the water level in the SST could be used as RTC parameters, and 3) the response curves of flow velocity and water level fluctuated very little and reached equilibrium in a short time. The combination of online monitoring and fuzzy control was feasible to control the SST automatically. This paper provides a theoretical reference for reducing stormwater runoff and improving the operation efficiency of SST.

Keywords: Stormwater runoff, stormwater storage tank, real-time control, fuzzy control.

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Authors: Ahmed Abbas, M.R. M Rizk, Mohamed El-Sayed

Abstract:

This paper presents a new adaptive DMC controller that improves the controller performance in case of plant-model mismatch. The new controller monitors the plant measured output, compares it with the model output and calculates weights applied to the controller move. Simulations show that the new controller can help improve control performance and avoid instability in case of severe model mismatches.

Keywords: Adaptive control, dynamic matrix control, DMC, model predictive control

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Authors: Amirhossein Asadabadi, Amir Anvar

Abstract:

Small satellites have become increasingly popular recently as a means of providing educational institutes with the chance to design, construct, and test their spacecraft from beginning to the possible launch due to the low launching cost. This approach is remarkably cost saving because of the weight and size reduction of such satellites. Weight reduction could be realised by utilising electromagnetic coils solely, instead of different types of actuators. This paper describes the restrictions of using only “Electromagnetic" actuation for 3D stabilisation and how to make the magnetorquer based attitude control feasible using Fuzzy Logic Control (FLC). The design is developed to stabilize the spacecraft against gravity gradient disturbances with a three-axis stabilizing capability.

Keywords: Fuzzy, Attitude Control, Small Satellite, Fuzzy Logic Control, Electromagnetic, Magnetic Control.

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Authors: Ian A. Grout

Abstract:

In this paper, the design and development of a system to provide hand motion and gesture control of laboratory test equipment is considered and discussed. The Leap Motion controller is used to provide an input to control a laboratory power supply as part of an electronic circuit experiment. By suitable hand motions and gestures, control of the power supply is provided remotely and without the need to physically touch the equipment used. As such, it provides an alternative manner in which to control electronic equipment via a PC and is considered here within the field of human computer interaction (HCI).

Keywords: Control, hand gesture, human computer interaction, test equipment.

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Authors: M. Nayeemuddin, T. Bramhananda Reddy, M. Vijaya Kumar

Abstract:

Acoustic noise becoming ever more obnoxious radiated by voltage source inverter fed induction motor drive in modern and industrial applications. The drive utilized for industrial and modern applications should use “spread spectrum” innovation known as Random pulse width modulation (PWM) algorithms where acoustic noise emanates through the machine should be critically concerned. This paper illustrates three types of random PWM control algorithms with fixed switching frequency namely 1) Random modulating PWM 2) Random carrier PWM and 3) Random modulating-carrier PWM. The spectrum plots of the motor stator current demonstrate the strength and robustness of the proposed PWM algorithms. To affirm the proposed algorithms, experimental tests have been conducted using dSPACE rt1104 control board on a v/f control three phase induction motor drive fed by DC link cascaded multilevel inverter.

Keywords: Multilevel inverter, acoustic noise, CSVPWM, total harmonic distortion, random PWM algorithm.

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Authors: Abdul Rashid Husain, Mohamad Noh Ahmad, Abdul Halim Mohd. Yatim

Abstract:

In this paper, stabilization of an Active Magnetic Bearing (AMB) system with varying rotor speed using Sliding Mode Control (SMC) technique is considered. The gyroscopic effect inherited in the system is proportional to rotor speed in which this nonlinearity effect causes high system instability as the rotor speed increases. Also, transformation of the AMB dynamic model into a new class of uncertain system shows that this gyroscopic effect lies in the mismatched part of the system matrix. Moreover, the current gain parameter is allowed to be varied in a known bound as an uncertainty in the input matrix. SMC design method is proposed in which the sufficient condition that guarantees the global exponential stability of the reduced-order system is represented in Linear Matrix Inequality (LMI). Then, a new chattering-free control law is established such that the system states are driven to reach the switching surface and stay on it thereafter. The performance of the controller applied to the AMB model is demonstrated through simulation works under various system conditions.

Keywords: Active Magnetic Bearing (AMB), Sliding ModeControl (SMC), Linear Matrix Inequality (LMI), mismatcheduncertainty.

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Authors: Chuan-Kun Liu, Chi-Wang Li

Abstract:

Simultaneous recovery of copper and DCA from simulated MEUF concentrated stream was investigated. Effects of surfactant (DCA) and metal (copper) concentrations, surfactant to metal molar ratio (S/M ratio), electroplating voltage, EDTA concentration, solution pH, and salt concentration on metal recovery and current efficiency were studied. Electric voltage of -0.5 V was shown to be optimum operation condition in terms of Cu recovery, current efficiency, and surfactant recovery. Increasing Cu recovery and current efficiency were observed with increases of Cu concentration while keeping concentration of DCA constant. However, increasing both Cu and DCA concentration while keeping S/M ratio constant at 2.5 showed detrimental effect on Cu recovery at DCA concentration higher than 15 mM. Cu recovery decreases with increasing pH while current efficiency showed an opposite trend. It is believed that conductivity is the main cause for discrepancy of Cu recovery and current efficiency observed at different pH. Finally, it was shown that EDTA had adverse effect on both Cu recovery and current efficiency while addition of NaCl salt had negative impact on current efficiency at concentration higher than 8000 mg/L.

Keywords: metal recovery, MEUF waste, surfactant, electroplating.

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Authors: Jong-Bae Lee, Seongsoo Lee

Abstract:

This paper proposes an adaptive discharge time control method to balance cell voltages in alternating battery cell discharging method. In the alternating battery cell discharging method, battery cells are periodically discharged in turn. Recovery effect increases battery output voltage while the given battery cell rests without discharging, thus battery operation time of target system increases. However, voltage mismatch between cells leads two problems. First, voltage difference between cells induces inter-cell current with wasted power. Second, it degrades battery operation time, since system stops when any cell reaches to the minimum system operation voltage. To solve this problem, the proposed method adaptively controls cell discharge time to equalize both cell voltages. In the proposed method, battery operation time increases about 19%, while alternating battery cell discharging method shows about 7% improvement.

Keywords: Battery, Recovery Effect, Low-Power, Alternating Battery Cell Discharging, Adaptive Discharge Time Control.

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Authors: Jie Jin

Abstract:

In this paper, a new CMOS current-mode single input and multi-outputs (SIMO) universal filter and quadrature oscillator with a similar circuit are proposed. The circuits only consist of three Current differencing transconductance amplifiers (CDTA) and two grounded capacitors, which are resistorless, and they are suitable for monolithic integration. The universal filter uses minimum CDTAs and passive elements to realize SIMO type low-pass (LP), high-pass (HP), band-pass (BP) band-stop (BS) and all-pass (AP) filter functions simultaneously without any component matching conditions. The angular frequency (ω0) and the quality factor (Q) of the proposed filter can be electronically controlled and tuned orthogonal. By some modifications of the filter, a new current-mode four-phase quadrature oscillator (QO) can be obtained easily. The condition of oscillation (CO) and frequency of oscillation (FO) of the QO can be controlled electronically and independently through the bias current of the CDTAs, and it is suitable for variable frequency oscillator. Moreover, all the passive and active sensitivities of the circuits are low. SPICE simulation results are included to confirm the theory.

Keywords: Universal Filter, Quadrature Oscillator, Current mode, Current differencing transconductance amplifiers.

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Authors: Krishna S. Raghuwaiya, Shonal Singh, Jito Vanualailai

Abstract:

In this paper, we study the formation control problem for car-like mobile robots. A team of nonholonomic mobile robots navigate in a terrain with obstacles, while maintaining a desired formation, using a leader-following strategy. A set of artificial potential field functions is proposed using the direct Lyapunov method for the avoidance of obstacles and attraction to their designated targets. The effectiveness of the proposed control laws to verify the feasibility of the model is demonstrated through computer simulations

Keywords: Control, Formation, Lyapunov, Nonholonomic

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