Active vibration suppression of non-linear beams using optimal dynamic inversion

Euler–Bernoulli beams are distributed parameter systems that are governed by a non-linear partial differential equation (PDE) of motion. This paper presents a vibration control approach for such beams that directly utilizes the non-linear PDE of motion, and hence, it is free from approximation errors (such as model reduction, linearization etc.). Two state feedback controllers are presented based on a newly developed optimal dynamic inversion technique which leads to closed-form solutions for the control variable. In one formulation a continuous controller structure is assumed in the spatial domain, whereas in the other approach it is assumed that the control force is applied through a finite number of discrete actuators located at predefined discrete locations in the spatial domain. An implicit finite difference technique with unconditional stability has been used to solve the PDE with control actions. Numerical simulation studies show that the beam vibration can effectively be decreased using either of the two formulations.

Halosulfuron-methyl: A selective herbicide option for the control of the invasive 'Cyperus aromaticus' (Ridley) Mattf. and Kukenth (Navua sedge)

There are currently limited options for the control of the invasive tropical perennial sedge 'Cyperus aromaticus' (Ridley) Mattf. and Kukenth (Navua sedge). The potential for halosulfuron-methyl as a selective herbicide for Navua sedge control in tropical pastures was investigated by undertaking successive field and shade house experiments in North Queensland, Australia. Halosulfuron-methyl and adjuvant rates, and combinations with other herbicides, were examined to identify a herbicide regime that most effectively reduced Navua sedge. Our research indicated that combining halosulfuron- methyl with other herbicides did not improve efficacy for Navua sedge control. We also identified that low rates of halosulfuron-methyl (25 g ha-1 a.i.) were just as effective as higher rates (73 g ha-1 a.i.) at controlling the sedge, and that this control relied on the addition of the adjuvant Bonza at the recommended concentration (1% of the spray volume). Pot trials in the controlled environment of the shade house achieved total mortality under these regimes. Field trials demonstrated more variable results with reductions in Navua sedge ranging between 40-95% at 8-10 weeks after treatment. After this period (16-24 weeks after treatment), regrowth of sedge, either from newly germinated seed, or of small plants protected from initial treatment, indicated sedge populations can rapidly increase to levels similar to pre-application, depending on the location and climatic conditions. Such variable results highlight the need for concerted monitoring of pastures to identify optimal treatment times. Ideally, initial treatment should be done when the sedge is healthy and actively growing, with follow up-treatments applied when new seed heads are produced from regrowth.

Nonlinear Control Design for an Air-breathing Engine with State Estimation

A nonlinear control design approach is presented in this paper for a challenging application problem of ensuring robust performance of an air-breathing engine operating at supersonic speed. The primary objective of control design is to ensure that the engine produces the required thrust that tracks the commanded thrust as closely as possible by appropriate regulation of the fuel flow rate. However, since the engine operates in the supersonic range, an important secondary objective is to ensure an optimal location of the shock in the intake for maximum pressure recovery with a sufficient margin. This is manipulated by varying the throat area of the nozzle. The nonlinear dynamic inversion technique has been successfully used to achieve both of the above objectives. In this problem, since the process is faster than the actuators, independent control designs have also been carried out for the actuators as well to assure the satisfactory performance of the system. Moreover, an extended Kalman Filter based state estimation design has been carried out both to filter out the process and sensor noises as well as to make the control design operate based on output feedback. Promising simulation results indicate that the proposed control design approach is quite successful in obtaining robust performance of the air-breathing system.

A Modified Dubins Method for Optimal Path Planning of a Miniature Air Vehicle Converging to a Straight Line Path

This paper presents a Dubins model based strategy to determine the optimal path of a Miniature Air Vehicle (MAV), constrained by a bounded turning rate, that would enable it to fly along a given straight line, starting from an arbitrary initial position and orientation. The method is then extended to meet the same objective in the presence of wind which has a magnitude comparable to the speed of the MAV. We use a modification of the Dubins' path method to obtain the complete optimal solution to this problem in all its generality.

Determination of optimal trajectory under design constraints for a satellite launch vehicle

An optimal pitch steering programme of a solid-fuel satellite launch vehicle to maximize either (1) the injection velocity at a given altitude, or (2) the size of circular orbit, for a given payload is presented. The two-dimensional model includes the rotation of atmosphere with the Earth, the vehicle's lift and drag, variation of thrust with time and altitude, inverse-square gravitational field, and the specified initial vertical take-off. The inequality constraints on the aerodynamic load, control force, and turning rates are also imposed. Using the properties of the central force motion the terminal constraint conditions at coast apogee are transferred to the penultimate stage burnout. Such a transformation converts a time-free problem into a time-fixed one, reduces the number of terminal constraints, improves accuracy, besides demanding less computer memory and time. The adjoint equations are developed in a compact matrix form. The problem is solved on an IBM 360/44 computer using a steepest ascent algorithm. An illustrative analysis of a typical launch vehicle establishes the speed of convergence, and accuracy and applicability of the algorithm.

Trajectory sensitivity modification in optimal linear systems

A new procedure for reducing trajectory sensitivity for the optimal linear regulator is described. The design is achieved without increase in the order of optimization and without the feedback of trajectory sensitivity. The procedure is also used in the input signal design problem for linear system identification by interpreting it as increasing trajectory sensitivity with respect to parameters to be estimated.

A closed-form optimal tuning of mass dampers for one degree-of-freedom systems under rotating unbalance forcing

This paper is focused on the study of a vibrating system forced by a rotating unbalance and coupled to a tuned mass damper (TMD). The analysis of the dynamic response of the entire system is used to define the parameters of such device in order to achieve optimal damping properties. The inertial forcing due to the rotating unbalance depends quadratically on the forcing frequency and it leads to optimal tuning parameters that differ from classical values obtained for pure harmonic forcing. Analytical results demonstrate that frequency and damping ratios, as a function of the mass parameter, should be higher than classical optimal parameters. The analytical study is carried out for the undamped primary system, and numerically investigated for the damped primary system. We show that, for practical applications, proper TMD tuning allows to achieve a reduction in the steady-state response of about 20% with respect to the response achieved with a classically tuned damper. Copyright © 2015 by ASME.

An optimal dynamic inversion-based neuro-adaptive approach for treatment of chronic myelogenous leukemia

Combining the advanced techniques of optimal dynamic inversion and model-following neuro-adaptive control design, an innovative technique is presented to design an automatic drug administration strategy for effective treatment of chronic myelogenous leukemia (CML). A recently developed nonlinear mathematical model for cell dynamics is used to design the controller (medication dosage). First, a nominal controller is designed based on the principle of optimal dynamic inversion. This controller can treat the nominal model patients (patients who can be described by the mathematical model used here with the nominal parameter values) effectively. However, since the system parameters for a realistic model patient can be different from that of the nominal model patients, simulation studies for such patients indicate that the nominal controller is either inefficient or, worse, ineffective; i.e. the trajectory of the number of cancer cells either shows non-satisfactory transient behavior or it grows in an unstable manner. Hence, to make the drug dosage history more realistic and patient-specific, a model-following neuro-adaptive controller is augmented to the nominal controller. In this adaptive approach, a neural network trained online facilitates a new adaptive controller. The training process of the neural network is based on Lyapunov stability theory, which guarantees both stability of the cancer cell dynamics as well as boundedness of the network weights. From simulation studies, this adaptive control design approach is found to be very effective to treat the CML disease for realistic patients. Sufficient generality is retained in the mathematical developments so that the technique can be applied to other similar nonlinear control design problems as well.

An optimal weighted-average congestion based pricing scheme for enhanced QoS

Pricing is an effective tool to control congestion and achieve quality of service (QoS) provisioning for multiple differentiated levels of service. In this paper, we consider the problem of pricing for congestion control in the case of a network of nodes under a single service class and multiple queues, and present a multi-layered pricing scheme. We propose an algorithm for finding the optimal state dependent price levels for individual queues, at each node. The pricing policy used depends on a weighted average queue length at each node. This helps in reducing frequent price variations and is in the spirit of the random early detection (RED) mechanism used in TCP/IP networks. We observe in our numerical results a considerable improvement in performance using our scheme over that of a recently proposed related scheme in terms of both throughput and delay performance. In particular, our approach exhibits a throughput improvement in the range of 34 to 69 percent in all cases studied (over all routes) over the above scheme.

Glycemic Control in Diabetic Pregnancies: Effects on Fetal and Maternal Outcome

Background: Both maternal and fetal complications are increased in diabetic pregnancies. Although hypertensive complications are increased in pregnant women with pregestational diabetes, reports on hypertensive complications in women with gestational diabetes mellitus (GDM) have been contradictory. Congenital malformations and macrosomia are the main fetal complications in Type 1 diabetic pregnancies, whereas fetal macrosomia and birth trauma but not congenital malformations are increased in GDM pregnancies. Aims: To study the frequency of hypertensive disorders in gestational diabetes mellitus. To evaluate the risk of macrosomia and brachial plexus injury (Erb’s palsy) and the ability of the 2-hour glucose tolerance test (OGTT) combined with the 24-hour glucose profile to distinguish between low and high risks of fetal macrosomia among women with GDM. To evaluate the relationship between glycemic control and the risk of fetal malformations in pregnancies complicated by Type 1 diabetes mellitus. To assess the effect of glycemic control on the occurrence of preeclampsia and pregnancy-induced hypertension in Type 1 diabetic pregnancies. Subjects: A total of 986 women with GDM and 203 women with borderline glucose intolerance (one abnormal value in the OGTT) with a singleton pregancy, 488 pregnant women with Type 1 diabetes (691 pregnancies and 709 offspring), and 1154 pregnant non-diabetic women (1181 pregnancies and 1187 offspring) were investigated. Results: In a prospective study on 81 GDM patients the combined frequency of preeclampsia and PIH was higher than in 327 non-diabetic controls (19.8% vs 6.1%, p<0.001). On the other hand, in 203 women with only one abnormal value in the OGTT, the rate of hypertensive complications did not differ from that of the controls. Both GDM women and those with only one abnormal value in the OGTT had higher pre-pregnancy weights and BMIs than the controls. In a retrospective study involving 385 insulin-treated and 520 diet-treated GDM patients, and 805 non-diabetic control pregnant women, fetal macrosomia occurred more often in the insulin-treated GDM pregnancies (18.2%, p<0.001) than in the diet-treated GDM pregnancies (4.4%), or the control pregnancies (2.2%). The rate of Erb’s palsy in vaginally delivered infants was 2.7% in the insulin-treated group of women and 2.4% in the diet-treated women compared with 0.3% in the controls (p<0.001). The cesarean section rate was more than twice as high (42.3% vs 18.6%) in the insulin-treated GDM patients as in the controls. A major fetal malformation was observed in 30 (4.2%) of the 709 newborn infants in Type 1 diabetic pregnancies and in 10 (1.4%) of the 735 controls (RR 3.1, 95% CI 1.6–6.2). Even women whose levels of HbA1c (normal values less than 5.6%) were only slightly increased in early pregnancy (between 5.6 and 6.8%) had a relative risk of fetal malformation of 3.0 (95% CI 1.2–7.5). Only diabetic patients with a normal HbA1c level (<5.6%) in early pregnancy had the same low risk of fetal malformations as the controls. Preeclampsia was diagnosed in 12.8% and PIH in 11.4% of the 616 Type 1 diabetic women without diabetic nephropathy. The corresponding frequencies among the 854 control women were 2.7% (OR 5.2; 95% CI 3.3–8.4) for preeclampsia and 5.6% (OR 2.2, 95% CI 1.5–3.1) for PIH. Multiple logistic regression analysis indicated that glycemic control, nulliparity, diabetic retinopathy and duration of diabetes were statistically significant independent predictors of preeclampsia. The adjusted odds ratios for preeclampsia were 1.6 (95% CI 1.3–2.0) for each 1%-unit increment in the HbA1c value during the first trimester and 0.6 (95% CI 0.5–0.8) for each 1%-unit decrement during the first half of pregnancy. In contrast, changes in glycemic control during the second half of pregnancy did not alter the risk of preeclampsia. Conclusions: In type 1 diabetic pregnancies it is extremely important to achieve optimal glycemic control before pregnancy and maintain it throughout pregnancy in order to decrease the complication rates both in the mother and in her offspring. The rate of fetal macrosomia and birth trauma in GDM pregnancies, especially in the group of insulin-treated women, is still relatively high. New strategies for screening, diagnosing, and treatment of GDM must be developed in order to decrease fetal and neonatal complications.

Experimental Demonstration of H{infty} Control based Active Vibration Suppression in Composite Fin-tip of Aircraft using Optimally Placed Piezoelectric Patch Actuators

The goal of this study is the multi-mode structural vibration control in the composite fin-tip of an aircraft. Structural model of the composite fin-tip with surface bonded piezoelectric actuators is developed using the finite element method. The finite element model is updated experimentally to reflect the natural frequencies and mode shapes accurately. A model order reduction technique is employed for reducing the finite element structural matrices before developing the controller. Particle swarm based evolutionary optimization technique is used for optimal placement of piezoelectric patch actuators and accelerometer sensors to suppress vibration. H{infty} based active vibration controllers are designed directly in the discrete domain and implemented using dSpace® (DS-1005) electronic signal processing boards. Significant vibration suppression in the multiple bending modes of interest is experimentally demonstrated for sinusoidal and band limited white noise forcing functions.

Optimal resource allocation in conflicts with the Lanchester linear law (2,1) model

This paper presents a detailed analysis of a model for military conflicts where the defending forces have to determine an optimal partitioning of available resources to counter attacks from an adversary in two different fronts in an area fire situation. Lanchester linear law attrition model is used to develop the dynamical equations governing the variation in force strength. Here we address a static resource allocation problem namely, Time-Zero-Allocation (TZA) where the resource allocation is done only at the initial time. Numerical examples are given to support the analytical results.

Uplink Power Control and Base Station Association in Multichannel Cellular Networks

A combined base station association and power control problem is studied for the uplink of multichannel multicell cellular networks, in which each channel is used by exactly one cell (i.e., base station). A distributed association and power update algorithm is proposed and shown to converge to a Nash equilibrium of a noncooperative game. We consider network models with discrete mobiles (yielding an atomic congestion game), as well as a continuum of mobiles (yielding a population game). We find that the equilibria need not be Pareto efficient, nor need they be system optimal. To address the lack of system optimality, we propose pricing mechanisms. It is shown that these mechanisms can be implemented in a distributed fashion.

Optimal configurations of active fiber composites based on asymptotic torsional analysis - art. no. 641413

Active Fiber Composites (AFC) possess desirable characteristics over a wide range of smart structure applications, such as vibration, shape and flow control as well as structural health monitoring. This type of material, capable of collocated actuation and sensing, call be used in smart structures with self-sensing circuits. This paper proposes four novel applications of AFC structures undergoing torsion: sensors and actuators shaped as strips and tubes; and concludes with a preliminary failure analysis. To enable this, a powerful mathematical technique, the Variational Asymptotic Method (VAM) was used to perform cross-sectional analyses of thin generally anisotropic AFC beams. The resulting closed form expressions have been utilized in the applications presented herein.

Optimal Resource Partitioning in a Military Conflict based on Lanchester Attrition Models

This paper develops a model for military conflicts where the defending forces have to determine an optimal partitioning of available resources to counter attacks from an adversary in two different fronts. The Lanchester attrition model is used to develop the dynamical equations governing the variation in force strength. Three different allocation schemes - Time-Zero-Allocation (TZA), Allocate-Assess-Reallocate (AAR), and Continuous Constant Allocation (CCA) - are considered and the optimal solutions are obtained in each case. Numerical examples are given to support the analytical results.