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.

An exponential stability criterion for certain nonlinear systems

Improved sufficient conditions are derived for the exponential stability of a nonlinear time varying feedback system having a time invariant blockG in the forward path and a nonlinear time varying gain ϕ(.)k(t) in the feedback path. φ(.) being an odd monotone nondecreasing function. The resulting bound on $$\left( {{{\frac{{dk}}{{dt}}} \mathord{\left/ {\vphantom {{\frac{{dk}}{{dt}}} k}} \right. \kern-\nulldelimiterspace} k}} \right)$$ is less restrictive than earlier criteria.

A Nonlinear Approach for Re-entry Guidance of Reusable Launch Vehicles Using Model Predictive Static Programming

A nonlinear suboptimal guidance scheme is developed for the reentry phase of the reusable launch vehicles. A recently developed methodology, named as model predictive static programming (MPSP), is implemented which combines the philosophies of nonlinear model predictive control theory and approximate dynamic programming. This technique provides a finite time nonlinear suboptimal guidance law which leads to a rapid solution of the guidance history update. It does not have to suffer from computational difficulties and can be implemented online. The system dynamics is propagated through the flight corridor to the end of the reentry phase considering energy as independent variable and angle of attack as the active control variable. All the terminal constraints are satisfied. Among the path constraints, the normal load is found to be very constrictive. Hence, an extra effort has been made to keep the normal load within a specified limit and monitoring its sensitivity to the perturbation.

Optimal Nonlinear Control and Estimation for a Reusable Launch Vehicle During Reentry Phase

In this paper a nonlinear optimal controller has been designed for aerodynamic control during the reentry phase of the Reusable Launch Vehicle (RLV). The controller has been designed based on a recently developed technique Optimal Dynamic Inversion (ODI). For full state feedback the controller has required full information about the system states. In this work an Extended Kalman filter (EKF) is developed to estimate the states. The vehicle (RLV) has been has been consider as a nonlinear Six-Degree-Of-Freedom (6-DOF) model. The simulation results shows that EKF gives a very good estimation of the states and it is working well with ODI. The resultant trajectories are very similar to those obtained by perfect state feedback using ODI only.

Nonlinear ensemble prediction of chaotic daily rainfall

The significance of treating rainfall as a chaotic system instead of a stochastic system for a better understanding of the underlying dynamics has been taken up by various studies recently. However, an important limitation of all these approaches is the dependence on a single method for identifying the chaotic nature and the parameters involved. Many of these approaches aim at only analyzing the chaotic nature and not its prediction. In the present study, an attempt is made to identify chaos using various techniques and prediction is also done by generating ensembles in order to quantify the uncertainty involved. Daily rainfall data of three regions with contrasting characteristics (mainly in the spatial area covered), Malaprabha, Mahanadi and All-India for the period 1955-2000 are used for the study. Auto-correlation and mutual information methods are used to determine the delay time for the phase space reconstruction. Optimum embedding dimension is determined using correlation dimension, false nearest neighbour algorithm and also nonlinear prediction methods. The low embedding dimensions obtained from these methods indicate the existence of low dimensional chaos in the three rainfall series. Correlation dimension method is done on th phase randomized and first derivative of the data series to check whether the saturation of the dimension is due to the inherent linear correlation structure or due to low dimensional dynamics. Positive Lyapunov exponents obtained prove the exponential divergence of the trajectories and hence the unpredictability. Surrogate data test is also done to further confirm the nonlinear structure of the rainfall series. A range of plausible parameters is used for generating an ensemble of predictions of rainfall for each year separately for the period 1996-2000 using the data till the preceding year. For analyzing the sensitiveness to initial conditions, predictions are done from two different months in a year viz., from the beginning of January and June. The reasonably good predictions obtained indicate the efficiency of the nonlinear prediction method for predicting the rainfall series. Also, the rank probability skill score and the rank histograms show that the ensembles generated are reliable with a good spread and skill. A comparison of results of the three regions indicates that although they are chaotic in nature, the spatial averaging over a large area can increase the dimension and improve the predictability, thus destroying the chaotic nature. (C) 2010 Elsevier Ltd. All rights reserved.

On an asymptotic method of Krylov-Bogoliubov for overdamped nonlinear systems

A general asymptotic method based on the work of Krylov-Bogoliubov is developed to obtain the response of nonlinear over damped systems. A second-order system with both roots real is treated first and the method is then extended to higher-order systems. Two illustrative examples show good agreement with results obtained by numerical integration.

Some new concepts in nonlinear systems

Some new concepts characterizing the response of nonlinear systems are developed. These new concepts are denoted by the terms, the transient system equivalent, the response vector, and the space-phase components. This third concept is analyzed in comparison with the well-known technique of symmetrical components. The performance of a multiplicative feedback control system is represented by a nonlinear integro-differential equation; its solution is obtained by the principle of variation of parameters. The system response is treated as a vector and is resolved into its space-phase components. The individual effects of these components on the performance of the system are discussed. The suitability of the technique for the transient analysis of higher order nonlinear control systems is discussed.

Characterisation of antibiotic-resistant psychrotrophic bacteria in raw milk

Dynamics of raw milk associated bacteria during cold storage of raw milk and their antibiotic resistance was reviewed, with focus on psychrotrophic bacteria. This study aimed to investigate the significance of cold storage of raw milk on antibiotic-resistant bacterial population and analyse the antibiotic resistance of the Gram-negative antibiotic-resistant psychrotrophic bacteria isolated from the cold-stored raw milk samples. Twenty-four raw milk samples, six at a time, were obtained from lorries that collected milk from Finnish farms and were stored at 4°C/4 d, 6°C/3 d and 6°C/4 d. Antibiotics representing four classes of antibiotics (gentamicin, ceftazidime, levofloxacin and trimethoprim-sulfamethoxazole) were used to determine the antibiotic resistance of mesophilic and psychrotrophic bacteria during the storage period. A representative number of antibiotic-resistant Gram-negative isolates retrieved from the cold-stored raw milk samples were identified by the phenotypic API 20 NE system and a few isolates by the 16S rDNA gene sequencing. Some of the isolates were further evaluated for their antibiotic resistance by the ATB PSE 5 and HiComb system. The initial average mesophilic counts were found below 105 CFU/mL, suggesting that the raw milk samples were of good quality. However, the mesophilic and psychrotrophic population increased when stored at 4°C/4 d, 6°C/3 d and 6°C/4 d. Gentamicin- and levofloxacin-resistant bacteria increased moderately (P < 0.05) while there was a considerable rise (P < 0.05) of ceftazidime- and trimethoprim-sulfamethoxazole-resistant population during the cold storage. Of the 50.9 % (28) of resistant isolates (total 55) identified by API 20 NE, the majority were Sphingomonas paucimobilis (8), Pseudomonas putida (5), Sphingobacterium spiritivorum (3) and Acinetobacter baumanii (2). The analysis by ATB PSE 5 system suggested that 57.1% of the isolates (total 49) were multiresistant. This study showed that the dairy environment harbours multidrug-resistant Gramnegative psychrotrophic bacteria and the cold chain of raw milk storage amplifies the antibioticresistant psychrotrophic bacterial population.

Effective treatment of infectious diseases: A nonlinear adaptive control theoretic approach

A nonlinear adaptive system theoretic approach is presented in this paper for effective treatment of infectious diseases that affect various organs of the human body. The generic model used does not represent any specific disease. However, it mimics the generic immunological dynamics of the human body under pathological attack, including the response to external drugs. From a system theoretic point of view, drugs can be interpreted as control inputs. Assuming a set of nominal parameters in the mathematical model, first a nonlinear controller is designed based on the principle of dynamic inversion. This treatment strategy was found to be effective in completely curing "nominal patients". However, in some cases it is ineffective in curing "realistic patients". This leads to serious (sometimes fatal) damage to the affected organ. To make the drug dosage design more effective, a model-following neuro-adaptive control design is carried out using neural networks, which are trained (adapted) online. From simulation studies, this adaptive controller is found to be effective in killing the invading microbes and healing the damaged organ even in the presence of parameter uncertainties and continuing pathogen attack.

A neural network based CBIR system using STI features and relevance feedback

Multimedia mining primarily involves, information analysis and retrieval based on implicit knowledge. The ever increasing digital image databases on the Internet has created a need for using multimedia mining on these databases for effective and efficient retrieval of images. Contents of an image can be expressed in different features such as Shape, Texture and Intensity-distribution(STI). Content Based Image Retrieval(CBIR) is an efficient retrieval of relevant images from large databases based on features extracted from the image. Most of the existing systems either concentrate on a single representation of all features or linear combination of these features. The paper proposes a CBIR System named STIRF (Shape, Texture, Intensity-distribution with Relevance Feedback) that uses a neural network for nonlinear combination of the heterogenous STI features. Further the system is self-adaptable to different applications and users based upon relevance feedback. Prior to retrieval of relevant images, each feature is first clustered independent of the other in its own space and this helps in matching of similar images. Testing the system on a database of images with varied contents and intensive backgrounds showed good results with most relevant images being retrieved for a image query. The system showed better and more robust performance compared to existing CBIR systems

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

A modern system theory based nonlinear control design is discussed in this paper for successful operation of an air-breathing engine operating at supersonic speed. The primary objective of the control design of such an air-breathing engine is to ensure that the engine dynamically produces the thrust that tracks a commanded value of thrust as closely as possible by regulating the fuel flow to the combustion system. However, since the engine operates in the supersonic range, an important secondary objective is to manage the shock wave configuration in the intake section of the engine which is manipulated by varying the throat area of the nozzle. A nonlinear sliding mode control 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 are also carried out for the actuators as well to assure the satisfactory performance of the system. Moreover, to filter out the sensor and process noises and to estimate the states for making the control design operate based on output feedback, an Extended Kalman Filter based state estimation design is also carried out. The promising simulation results suggest that the proposed control design approach is quite successful in obtaining robust performance of the air-breathing engine.

Nonlinear measures of heart rate time series: influence of posture and controlled breathing

In this study, we investigated measures of nonlinear dynamics and chaos theory in regards to heart rate variability in 27 normal control subjects in supine and standing postures, and 14 subjects in spontaneous and controlled breathing conditions. We examined minimum embedding dimension (MED), largest Lyapunov exponent (LLE) and measures of nonlinearity (NL) of heart rate time series. MED quantifies the system's complexity, LLE predictability and NL, a measure of deviation from linear processes. There was a significant decrease in complexity (P<0.00001), a decrease in predictability (P<0.00001) and an increase in nonlinearity (P=0.00001) during the change from supine to standing posture. Decrease in MED, and increases in NL score and LLE in standing posture appear to be partly due to an increase in sympathetic activity of the autonomous nervous system in standing posture. An improvement in predictability during controlled breathing appears to be due to the introduction of a periodic component. (C) 2000 published by Elsevier Science B.V.

Study of the random vibration of nonlinear systems by the Gaussian closure technique

A technique is developed to study random vibration of nonlinear systems. The method is based on the assumption that the joint probability density function of the response variables and input variables is Gaussian. It is shown that this method is more general than the statistical linearization technique in that it can handle non-Gaussian excitations and amplitude-limited responses. As an example a bilinear hysteretic system under white noise excitation is analyzed. The prediction of various response statistics by this technique is in good agreement with other available results.

Eigenvalues of kinematical conservation laws (KCL) based 3-D weakly nonlinear ray theory (WNLRT)

System of kinematical conservation laws (KCL) govern evolution of a curve in a plane or a surface in space, even if the curve or the surface has singularities on it. In our recent publication K. R. Arun, P. Prasad, 3-D kinematical conservation laws (KCL): evolution of a surface in R-3-in particular propagation of a nonlinear wavefront, Wave Motion 46 (2009) 293-311] we have developed a mathematical theory to study the successive positions and geometry of a 3-D weakly nonlinear wavefront by adding an energy transport equation to KCL. The 7 x 7 system of equations of this KCL based 3-D weakly nonlinear ray theory (WNLRT) is quite complex and explicit expressions for its two nonzero eigenvalues could not be obtained before. In this short note, we use two different methods: (i) the equivalence of KCL and ray equations and (ii) the transformation of surface coordinates, to derive the same exact expressions for these eigenvalues. The explicit expressions for nonzero eigenvalues are important also for checking stability of any numerical scheme to solve 3-D WNLRT. (C) 2010 Elsevier Inc. All rights reserved.

Invariant norm quantifying nonlinear content of Hamiltonian systems

Given a Hamiltonian system, one can represent it using a symplectic map. This symplectic map is specified by a set of homogeneous polynomials which are uniquely determined by the Hamiltonian. In this paper, we construct an invariant norm in the space of homogeneous polynomials of a given degree. This norm is a function of parameters characterizing the original Hamiltonian system. Such a norm has several potential applications. (C) 2010 Elsevier Inc. All rights reserved.