Active vibration suppression of beams with discrete actuators using optimal dynamic inversion

Most of the structural elements like beams, cables etc. are flexible and should be modeled as distributed parameter systems (DPS) to represent the reality better. For large structures, the usual approach of 'modal representation' is not an accurate representation. Moreover, for excessive vibrations (possibly due to strong wind, earthquake etc.), external power source (controller) is needed to suppress it, as the natural damping of these structures is usually small. In this paper, we propose to use a recently developed optimal dynamic inversion technique to design a set of discrete controllers for this purpose. We assume that the control force to the structure is applied through finite number of actuators, which are located at predefined locations in the spatial domain. The method used in this paper determines control forces directly from the partial differential equation (PDE) model of the system. The formulation has better practical significance, both because it leads to a closed form solution of the controller (hence avoids computational issues) as well as because a set of discrete actuators along the spatial domain can be implemented with relative ease (as compared to a continuous actuator)

An optimal dynamic inversion approach for controlling a class of one-dimensional nonlinear distributed parameter systems

Combining the principles of dynamic inversion and optimization theory, a new approach is presented for stable control of a class of one-dimensional nonlinear distributed parameter systems, assuming the availability a continuous actuator in the spatial domain. Unlike the existing approximate-then-design and design-then-approximate techniques, here there is no need of any approximation either of the system dynamics or of the resulting controller. Rather, the control synthesis approach is fairly straight-forward and simple. The controller formulation has more elegance because we can prove the convergence of the controller to its steady state value. To demonstrate the potential of the proposed technique, a real-life temperature control problem for a heat transfer application is solved. It has been demonstrated that a desired temperature profile can be achieved starting from any arbitrary initial temperature profile.

Through ring umbrella inversion of a molecular rattle

We report theoretical investigations on some [Ring]Li--(+) compounds, which can exhibit a through ring umbrella like inversion. Our studies predict cyclononatetraenyllithium to be molecular rattle, in which such inversions can occur. The potential energy for the motion is a double well, with an activation barrier of 11.50 kcal/mol. We find that the lithium should go through the ring easily by an excitation to nu = 17 vibrational level. (C) 2002 Elsevier Science B.V. All rights reserved.

Robustness Study of a Dynamic Inversion Control Law for a High Performance Aircraft

In the design of °ight control system modeling uncertainties in the form of param-eter variations is one of the major problems. It is even more critical for high performance aircrafts,since such aircrafts are purposefully designed unstable to enhance their performance (especially ma-neuverability). Hence the °ight control system needs to be quite e®ective in both assuring accurate tracking of pilot commands, while simultaneously assuring overall stability of the aircraft. In addi-tion, the control system must also be su±ciently robust to cater for possible parameter variations and inaccuracies . The primary aim of this paper is to carry out a robustness study of a dynamic inversion based nonlinear control design for a high performance aircraft, which has been developed recently [1].

Energy-insensitive Guidance of Solid Motor Propelled Long Range Flight Vehicles Using MPSP and Dynamic Inversion

A energy-insensitive explicit guidance design is proposed in this paper by appending newlydeveloped nonlinear model predictive static programming technique with dynamic inversion, which render a closed form solution of the necessary guidance command update. The closed form nature of the proposed optimal guidance scheme suppressed the computational difficulties, and facilitate realtime solution. The guidance law is successfully verified in a solid motor propelled long range flight vehicle, for which developing an effective guidance law is more difficult as compared to a liquid engine propelled vehicle, mainly because of the absence of thrust cutoff facility. The scheme guides the vehicle appropriately so that it completes the mission within a tight error bound assuming that the starting point of the second stage to be a deterministic point beyond the atmosphere. The simulation results demonstrate its ability to intercept the target, even with an uncertainty of greater than 10% in the burnout time

Command Tracking in High Performance Aircrafts: A New Dynamic Inversion Design

This paper proposes a new straight forward technique based on dynamic inversion, which is applied for tracking the pilot commands in high performance aircrafts.Pilot commands assumed in longitudinal mode are normal acceleration and total velocity(while roll angle and lateral acceleration are maintained at zero). In lateral mode, roll rate and total velocity are used as pilot commands (while climb rate and lateral acceleration are maintained at zero). Ensuring zero lateral acceleration leads to a better turn co-ordination. A six degree-of-freedom model of F-16 aircraft is used for both control design as well as simulation studies. Promising results are obtained which are found to be superior as compared to an existing approach (which is also based on dynamic inversion). The new approach has two potential benefits, namely reduced oscillatory response and reduced control magnitude. Another advantage of this approach is that it leads to a significant reduction of tuning parameters in the control design process.

Active Vibration Suppression of One-dimensional Nonlinear Structures Using Optimal Dynamic Inversion

A flexible robot arm can be modeled as an Euler-Bernoulli beam which are infinite degrees of freedom (DOF) system. Proper control is needed to track the desired motion of a robotic arm. The infinite number of DOF of beams are reduced to finite number for controller implementation, which brings in error (due to their distributed nature). Therefore, to represent reality better distributed parameter systems (DPS) should be controlled using the systems partial differential equation (PDE) directly. In this paper, we propose to use a recently developed optimal dynamic inversion technique to design a controller to suppress nonlinear vibration of a beam. The method used in this paper determines control forces directly from the PDE model of the system. The formulation has better practical significance, because it leads to a closed form solution of the controller (hence avoids computational issues).

On the two dimensional effective electron mass in quantum wells, inversion layers and NIPI superlattices of Kane type semiconductors in the presence of strong light waves: Simplified theory and relative comparison

An attempt is made to study the two dimensional (2D) effective electron mass (EEM) in quantum wells (Qws), inversion layers (ILs) and NIPI superlattices of Kane type semiconductors in the presence of strong external photoexcitation on the basis of a newly formulated electron dispersion laws within the framework of k.p. formalism. It has been found, taking InAs and InSb as examples, that the EEM in Qws, ILs and superlattices increases with increasing concentration, light intensity and wavelength of the incident light waves, respectively and the numerical magnitudes in each case is band structure dependent. The EEM in ILs is quantum number dependent exhibiting quantum jumps for specified values of the surface electric field and in NIPI superlattices; the same is the function of Fermi energy and the subband index characterizing such 2D structures. The appearance of the humps of the respective curves is due to the redistribution of the electrons among the quantized energy levels when the quantum numbers corresponding to the highest occupied level changes from one fixed value to the others. Although the EEM varies in various manners with all the variables as evident from all the curves, the rates of variations totally depend on the specific dispersion relation of the particular 2D structure. Under certain limiting conditions, all the results as derived in this paper get transformed into well known formulas of the EEM and the electron statistics in the absence of external photo-excitation and thus confirming the compatibility test. The results of this paper find three applications in the field of microstructures. (C) 2011 Elsevier Ltd. All rights reserved.

Phase inversion in agitated liquid-liquid dispersions: Anomalous effect of electrolyte

An imbalance between breakup and coalescence of drops in turbulent liquid-liquid dispersions leads to inversion of phases the dispersed phase becomes continuous and vice versa. An increase in the rate of coalescence of drops is expected to decrease the dispersed phase fraction at which inversion occurs. In the present work, we increased the rate of coalescence of drops by adding electrolyte to pure liquid-liquid dispersions. The experiments carried out for three representative liquid-liquid systems show that contrary to the expectation the addition of an electrolyte increases the dispersed phase fraction at which inversion occurs for both, oil-in-water and water-in-oil dispersions. The step-down experiments confirm that the addition of the electrolyte increases the rate of coalescence of drops in lean dispersions under the same conditions, thereby confirming an anomalous effect of the presence of an electrolyte on the stability of dispersions. (C) 2012 Elsevier Ltd. All rights reserved.

Noniterative inversion strategy for photoacoustic tomography: recovery of absorbed energy map from boundary pressure measurements

The inverse problem in photoacoustic tomography (PAT) seeks to obtain the absorbed energy map from the boundary pressure measurements for which computationally intensive iterative algorithms exist. The computational challenge is heightened when the reconstruction is done using boundary data split into its frequency spectrum to improve source localization and conditioning of the inverse problem. The key idea of this work is to modify the update equation wherein the Jacobian and the perturbation in data are summed over all wave numbers, k, and inverted only once to recover the absorbed energy map. This leads to a considerable reduction in the overall computation time. The results obtained using simulated data, demonstrates the efficiency of the proposed scheme without compromising the accuracy of reconstruction.

Inversion of moments to retrieve joint probabilities in quantum sequential measurements

A sequence of moments obtained from statistical trials encodes a classical probability distribution. However, it is well known that an incompatible set of moments arises in the quantum scenario, when correlation outcomes associated with measurements on spatially separated entangled states are considered. This feature, viz., the incompatibility of moments with a joint probability distribution, is reflected in the violation of Bell inequalities. Here, we focus on sequential measurements on a single quantum system and investigate if moments and joint probabilities are compatible with each other. By considering sequential measurement of a dichotomic dynamical observable at three different time intervals, we explicitly demonstrate that the moments and the probabilities are inconsistent with each other. Experimental results using a nuclear magnetic resonance system are reported here to corroborate these theoretical observations, viz., the incompatibility of the three-time joint probabilities with those extracted from the moment sequence when sequential measurements on a single-qubit system are considered.

Simultaneous attitude control and trajectory tracking of a micro quadrotor: a SNAC aided nonlinear dynamic inversion approach

This paper presents an advanced single network adaptive critic (SNAC) aided nonlinear dynamic inversion (NDI) approach for simultaneous attitude control and trajectory tracking of a micro-quadrotor. Control of micro-quadrotors is a challenging problem due to its small size, strong coupling in pitch-yaw-roll and aerodynamic effects that often need to be ignored in the control design process to avoid mathematical complexities. In the proposed SNAC aided NDI approach, the gains of the dynamic inversion design are selected in such a way that the resulting controller behaves closely to a pre-synthesized SNAC controller for the output regulation problem. However, since SNAC is based on optimal control theory, it makes the dynamic inversion controller to operate near optimal and enhances its robustness property as well. More important, it retains two major benefits of dynamic inversion: (i) closed form expression of the controller and (ii) easy scalability to command tracking application even without any apriori knowledge of the reference command. Effectiveness of the proposed controller is demonstrated from six degree-of-freedom simulation studies of a micro-quadrotor. It has also been observed that the proposed SNAC aided NDI approach is more robust to modeling inaccuracies, as compared to the NDI controller designed independently from time domain specifications.

Effect of choice of basis functions in neural network for capturing unknown function for dynamic inversion control

The basic requirement for an autopilot is fast response and minimum steady state error for better guidance performance. The highly nonlinear nature of the missile dynamics due to the severe kinematic and inertial coupling of the missile airframe as well as the aerodynamics has been a challenge for an autopilot that is required to have satisfactory performance for all flight conditions in probable engagements. Dynamic inversion is very popular nonlinear controller for this kind of scenario. But the drawback of this controller is that it is sensitive to parameter perturbation. To overcome this problem, neural network has been used to capture the parameter uncertainty on line. The choice of basis function plays the major role in capturing the unknown dynamics. Here in this paper, many basis function has been studied for approximation of unknown dynamics. Cosine basis function has yield the best response compared to any other basis function for capturing the unknown dynamics. Neural network with Cosine basis function has improved the autopilot performance as well as robustness compared to Dynamic inversion without Neural network.

Modeling Equitable Distribution of Water: Dynamic Inversion-Based Controller Approach

It is a well-known fact that most of the developing countries have intermittent water supply and the quantity of water supplied from the source is also not distributed equitably among the consumers. Aged pipelines, pump failures, and improper management of water resources are some of the main reasons for it. This study presents the application of a nonlinear control technique to overcome this problem in different zones in the city of Bangalore. The water is pumped to the city from a large distance of approximately 100km over a very high elevation of approximately 400m. The city has large undulating terrain among different zones, which leads to unequal distribution of water. The Bangalore, inflow water-distribution system (WDS) has been modeled. A dynamic inversion (DI) nonlinear controller with proportional integral derivative (PID) features (DI-PID) is used for valve throttling to achieve the target flows to different zones of the city. This novel approach of equitable water distribution using DI-PID controllers that can be used as a decision support system is discussed in this paper.