A FRAMEWORK FOR THE ERROR ANALYSIS OF DISCONTINUOUS FINITE ELEMENT METHODS FOR ELLIPTIC OPTIMAL CONTROL PROBLEMS AND APPLICATIONS TO C-0 IP METHODS

In this article, an abstract framework for the error analysis of discontinuous Galerkin methods for control constrained optimal control problems is developed. The analysis establishes the best approximation result from a priori analysis point of view and delivers a reliable and efficient a posteriori error estimator. The results are applicable to a variety of problems just under the minimal regularity possessed by the well-posedness of the problem. Subsequently, the applications of C-0 interior penalty methods for a boundary control problem as well as a distributed control problem governed by the biharmonic equation subject to simply supported boundary conditions are discussed through the abstract analysis. Numerical experiments illustrate the theoretical findings.

Optimal control problem for the time-dependent Kirchhoff-Love plate in a domain with rough boundary

In this paper, we study the asymptotic behavior of an optimal control problem for the time-dependent Kirchhoff-Love plate whose middle surface has a very rough boundary. We identify the limit problem which is an optimal control problem for the limit equation with a different cost functional.

STOKES' SYSTEM IN A DOMAIN WITH OSCILLATING BOUNDARY: HOMOGENIZATION AND ERROR ANALYSIS OF AN INTERIOR OPTIMAL CONTROL PROBLEM

Homogenization and error analysis of an optimal interior control problem in the framework of Stokes' system, on a domain with rapidly oscillating boundary, are the subject matters of this article. We consider a three dimensional domain constituted of a parallelepiped with a large number of rectangular cylinders at the top of it. An interior control is applied in a proper subdomain of the parallelepiped, away from the oscillating volume. We consider two types of functionals, namely a functional involving the L-2-norm of the state variable and another one involving its H-1-norm. The asymptotic analysis of optimality systems for both cases, when the cross sectional area of the rectangular cylinders tends to zero, is done here. Our major contribution is to derive error estimates for the state, the co-state and the associated pressures, in appropriate functional spaces.

Shock tunnel experiments on control of shock induced large separation bubble using boundary layer bleed

Shock-Boundary Layer Interaction (SBLI) often occurs in supersonic/hypersonic flow fields. Especially when accompanied by separation (termed strong interaction), the SBLI phenomena largely affect the performance of the systems where they occur, such as scramjet intakes, thus often demanding the control of the interaction. Experiments on the strong interaction between impinging shock wave and boundary layer on a flat plate at Mach 5.96 are carried out in IISc hypersonic shock tunnel HST-2. The experiments are performed at moderate flow total enthalpy of 1.3 MJ/kg and freestream Reynolds number of 4 million/m. The strong shock generated by a wedge (or shock generator) of large angle 30.96 degrees to the freestream is made to impinge on the flat plate at 95 mm (inviscid estimate) from the leading edge, due to which a large separation bubble of length (75 mm) comparable to the distance of shock impingement from the leading edge is generated. The experimental simulation of such large separation bubble with separation occurring close to the leading edge, and its control using boundary layer bleed (suction and tangential blowing) at the location of separation, are demonstrated within the short test time of the shock tunnel (similar to 600 mu s) from time resolved schlieren flow visualizations and surface pressure measurements. By means of suction - with mass flow rate one order less than the mass flow defect in boundary layer - a reduction in separation length by 13.33% was observed. By the injection of an array of (nearly) tangential jets in the direction of mainstream (from the bottom of the plate) at the location of separation - with momentum flow rate one order less than the boundary layer momentum flow defect - 20% reduction in separation length was observed, although the flow field was apparently unsteady. (C) 2014 Elsevier Masson SAS. All rights reserved.

Improved switching frequency variation control of hysteresis controlled voltage source inverter-fed IM drives using current error space vector

A constant switching frequency current error space vector-based hysteresis controller for two-level voltage source inverter-fed induction motor (IM) drives is proposed in this study. The proposed controller is capable of driving the IM in the entire speed range extending to the six-step mode. The proposed controller uses the parabolic boundary, reported earlier, for vector selection in a sector, but uses simple, fast and self-adaptive sector identification logic for sector change detection in the entire modulation range. This new scheme detects the sector change using the change in direction of current error along the axes jA, jB and jC. Most of the previous schemes use an outer boundary for sector change detection. So the current error goes outside the boundary six times during sector change, in one cycle,, introducing additional fifth and seventh harmonic components in phase current. This may cause sixth harmonic torque pulsations in the motor and spread in the harmonic spectrum of phase voltage. The proposed new scheme detects the sector change fast and accurately eliminating the chance of introducing additional fifth and seventh harmonic components in phase current and provides harmonic spectrum of phase voltage, which exactly matches with that of constant switching frequency voltage-controlled space vector pulse width modulation (VC-SVPWM)-based two-level inverter-fed drives.

Switching frequency variation control in hysteresis PWM controller for IM drives using variable parabolic bands for current error space phasor

Variation of switching frequency over the entire operating speed range of an induction motor (M drive is the major problem associated with conventional two-level three-phase hysteresis controller as well as the space phasor based PWM hysteresis controller. This paper describes a simple hysteresis current controller for controlling the switching frequency variation in the two-level PWM inverter fed IM drives for various operating speeds. A novel concept of continuously variable hysteresis boundary of current error space phasor with the varying speed of the IM drive is proposed in the present work. The variable parabolic boundary for the current error space phasor is suggested for the first time in this paper for getting the switching frequency pattern with the hysteresis controller, similar to that of the constant switching frequency voltage-controlled space vector PWM (VC-SVPWM) based inverter fed IM drive. A generalized algorithm is also developed to determine parabolic boundary for controlling the switching frequency variation, for any IM load. Only the adjacent inverter voltage vectors forming a triangular sector, in which tip of the machine voltage vector ties, are switched to keep current error space vector within the parabolic boundary. The controller uses a self-adaptive sector identification logic, which provides smooth transition between the sectors and is capable of taldng the inverter up to six-step mode of operation, if demanded by drive system. The proposed scheme is simulated and experimentally verified on a 3.7 kW IM drive.

Analysis of performance of a hot gas injection thrust vector control system

The complex three-dimensional flowfield produced by secondary injection of hot gases in a rocket nozzle for thrust vector control is analyzed by solving unsteady three-dimensional Euler equations with appropriate boundary conditions. Various system performance parameters like secondary jet amplification factor and axial thrust augmentation are deduced by integrating the nozzle wall pressure distributions obtained as part of the flowfield solution and compared with measurements taken in actual static tests. The agreement is good within the practical range of secondary injectant flow rates for thrust vector control applications.

A New Liquid Level Sensor for Process-Control Applications

Many process-control systems are air-operated. In such an environment, it would be desirable and economical to use pneumatic sensors. Bubble-back pressure sensors perform quite satisfactorily, but in case of viscous inflammable and slurry-like liquids with a tendency to froth, this level sensor is inadequate. The method suggested in this paper utilizes a pneumatic capacitor, one boundary of which is formed by the liquid level, to modulate a fluid amplifier feedback oscillator. The absence of moving parts and economy obtained makes this method attractive for process-control applications. The system has been mathematically modeled and simulated on an IBM 360/44 digital computer. Experimental values compare fairly well with the theoretical results. For the range tested, the sensor is found to have a linear frequency variation with the liquid level Extended running in the laboratory shows that the system is very reliable. This system has been found insensitive to temperature variations of up to 15ðC.

A Novel Method for the Uniform Incorporation of Grain-Boundary Layer Modifiers in Positive Temperature Coefficient of Resistivity Barium Titanate

The presently developed two-stage process involves diping the prefired porous disks of n-BaTiO3 in nonaqueous solutions containing Al-buty rate, Ti-isopropoxide, and tetraethyl silicate and subsequent sintering. This leads to uniform distribution of the grain-boundary layer (GBL) modifiers (Al2O3+ TiO2+ SiO2) and better control of the grain size as well as the positive temperature coefficient of resistivity characteristics. The technique is particularly suited for GBL modifiers in low concentrations (< 1%).

A Rotor Flux Estimation During Zero and Active Vector Periods Using Current Error Space Vector From a Hysteresis Controller for a Sensorless Vector Control of IM Drive

This paper proposes a sensorless vector control scheme for general-purpose induction motor drives using the current error space phasor-based hysteresis controller. In this paper, a new technique for sensorless operation is developed to estimate rotor voltage and hence rotor flux position using the stator current error during zero-voltage space vectors. It gives a comparable performance with the vector control drive using sensors especially at a very low speed of operation (less than 1 Hz). Since no voltage sensing is made, the dead-time effect and loss of accuracy in voltage sensing at low speed are avoided here, with the inherent advantages of the current error space phasor-based hysteresis controller. However, appropriate device on-state drops are compensated to achieve a steady-state operation up to less than 1 Hz. Moreover, using a parabolic boundary for current error, the switching frequency of the inverter can be maintained constant for the entire operating speed range. Simple sigma L-s estimation is proposed, and the parameter sensitivity of the control scheme to changes in stator resistance, R-s is also investigated in this paper. Extensive experimental results are shown at speeds less than 1 Hz to verify the proposed concept. The same control scheme is further extended from less than 1 Hz to rated 50 Hz six-step operation of the inverter. Here, the magnetic saturation is ignored in the control scheme.

Adaptive control of vibration transmission in a strut system

In this article, theoretical and the experimental studies are reported on the adaptive control of vibration transmission in a strut system subjected to a longitudinal pulse train excitation. In the control scheme, a magneto-strictive actuator is employed at the downstream transmission point in the secondary path. The actuator dynamics is taken into account. The system boundary parameters are first estimated off-line, and later employed to simulate the system dynamics. A Delayed-X Filtered-E spectral algorithm is proposed and implemented in real time. The underlying mechanics based filter construction allows for the time varying system dynamics to be taken into account. This work should be of interest for active control of vibration and noise transmission in helicopter gearbox support struts and other systems.

Estimating the Hausdorff-Besicovitch dimension of boundary of basin of attraction in helicopter trim

Helicopter trim involves solution of nonlinear force equilibrium equations. As in many nonlinear dynamic systems, helicopter trim problem can show chaotic behavior. This chaotic behavior is found in the basin of attraction of the nonlinear trim equations which have to be solved to determine the main rotor control inputs given by the pilot. This study focuses on the boundary of the basin of attraction obtained for a set of control inputs. We analyze the boundary by considering it at different magnification levels. The magnified views reveal intricate geometries. It is also found that the basin boundary exhibits the characteristic of statistical self-similarity, which is an essential property of fractal geometries. These results led the authors to investigate the fractal dimension of the basin boundary. It is found that this dimension is indeed greater than the topological dimension. From all the observations, it is evident that the boundary of the basin of attraction for helicopter trim problem is fractal in nature. (C) 2012 Elsevier Inc. All rights reserved.

Design of corona control rings for EHV/UHV line hardwares and substations

The components of EHV/UHV lines and substations can produce significant corona. To limit the consequent Radio Interference and Audible Noise on these systems, suitable corona control rings are employed. The shapes of these rings could vary from circular to rectangular with smooth bends. Many manufacturers seem to adopt trial and error method for arriving at the final design. As such neither the present testing standard nor the final design adopted consider the practical scenario like corona produced by deposition of dirt, bird droppings, etc. The present work aims to make a first step in addressing this practically important problem. This requires an accurate evaluation of the electric field and a reliable method for the evaluation of corona inception. Based on a thorough survey of pertinent literature, the critical avalanche criteria as applicable to large electrodes, has been adopted. Taking the rain drop on the surface as the biggest protrusion, conducting protrusions modeled as semi-ellipsoid is considered as representative for deposition of dust or the boundary of bird droppings etc. Through examples of 4 00 kV and 765 kV class toroidal corona rings, the proposed method is demonstrated. This work is believed to be useful to corona ring manufacturers for EHV/UHV systems.

A Space-Vector-Based Hysteresis Current Controller for a General n-Level Inverter-Fed Drive With Nearly Constant Switching Frequency Control

A current-error space-vector-based hysteresis current controller for a general n-level voltage-source inverter (VSI)-fed three-phase induction motor (IM) drive is proposed here, with control of the switching frequency variation for the full linear modulation range. The proposed current controller monitors the space-vector-based current error of an n-level VSI-fed IM to keep the current error within a parabolic boundary, using the information of the current triangular sector in which the tip of the reference vector lies. Information of the reference voltage vector is estimated using the measured current-error space vectors, along the alpha- and beta-axes. Appropriate dimension and orientation of this parabolic boundary ensure a switching frequency spectrum similar to that of a constant-switching-frequency voltage-controlled space vector pulsewidth modulation (PWM) (SVPWM)-based IM drive. Like SVPWM for multilevel inverters, the proposed controller selects inverter switching vectors, forming a triangular sector in which the tip of the reference vector stays, for the hysteresis PWM control. The sector in the n-level inverter space vector diagram, in which the tip of the fundamental stator voltage stays, is precisely detected, using the sampled reference space vector estimated from the instantaneous current-error space vectors. The proposed controller retains all the advantages of a conventional hysteresis controller such as fast current control, with smooth transition to the overmodulation region. The proposed controller is implemented on a five-level VSI-fed 7.5-kW IM drive.

Simultaneous source localization and boundary mapping for contaminants

This paper addresses the problem of localizing the sources of contaminants spread in the environment, and mapping the boundary of the affected region using an innovative swarm intelligence based technique. Unlike most work in this area the algorithm is capable of localizing multiple sources simultaneously while also mapping the boundary of the contaminant spread. At the same time the algorithm is suitable for implementation using a mobile robotic sensor network. Two types of agents, called the source localization agents (or S-agents) and boundary mapping agents (or B-agents) are used for this purpose. The paper uses the basic glowworm swarm optimization (GSO) algorithm, which has been used only for multiple signal source localization, and modifies it considerably to make it suitable for both these tasks. This requires the definition of new behaviour patterns for the agents based on their terminal performance as well as interactions between them that helps the swarm to split into subgroups easily and identify contaminant sources as well as spread along the boundary to map its full length. Simulations results are given to demonstrate the efficacy of the algorithm.