An Improved Nonlinear Dynamic Inversion Method for Altitude and Attitude Control of Nano Quad-Rotors under Persistent Uncertainties

Nonlinear dynamic inversion(NDI)has been applied to the control law design of quad-rotors mainly thanks to its good robustness and simplicity of parameter tuning.However,the weakness of relying on accurate model greatly restrains its application on quad-rotors,especially nano quad-rotors(NQRs).NQRs are easy to be influenced by uncertainties such as model uncertainties(mainly from complicated aerodynamic interferences,strong coupling in roll-pitch-yaw channels and inaccurate aerodynamic prediction of rotors)and external uncertainties(mainly from winds or gusts),particularly persistent ones.Therefore,developing accurate model for altitude and attitude control of NQRs is difficult.To solve this problem,in this paper,an improved nonlinear dynamic inversion(INDI)method is developed,which can reject the above-mentioned uncertainties by estimating them and then counteracting in real time using linear extended state observer(LESO).Comparison with the traditional NDI(TNDI)method was carried out numerically,and the results show that,in coping with persistent uncertainties,the INDI-based method presents significant superiority.

Dynamic Stability Analysis of Linear Time-varying Systems via an Extended Modal Identification Approach

The problem of linear time-varying（LTV） system modal analysis is considered based on time-dependent state space representations, as classical modal analysis of linear time-invariant systems and current LTV system modal analysis under the ＂frozen-time＂ assumption are not able to determine the dynamic stability of LTV systems. Time-dependent state space representations of LTV systems are first introduced, and the corresponding modal analysis theories are subsequently presented via a stabilitypreserving state transformation. The time-varying modes of LTV systems are extended in terms of uniqueness, and are further interpreted to determine the system＇s stability. An extended modal identification is proposed to estimate the time-varying modes, consisting of the estimation of the state transition matrix via a subspace-based method and the extraction of the time-varying modes by the QR decomposition. The proposed approach is numerically validated by three numerical cases, and is experimentally validated by a coupled moving-mass simply supported beam exper- imental case. The proposed approach is capable of accurately estimating the time-varying modes, and provides anew way to determine the dynamic stability of LTV systems by using the estimated time-varying modes.

Global bifurcations and multi-pulse chaotic dynamics of rectangular thin plate with one-to-one internal resonance

Global bifurcations and multi-pulse chaotic dynamics for a simply supported rectangular thin plate are studied by the extended Melnikov method. The rectangular thin plate is subject to transversal and in-plane excitation. A two-degree-of-freedom nonlinear nonautonomous system governing equations of motion for the rectangular thin plate is derived by the von Karman type equation and the Galerkin approach. A one-to- one internal resonance is considered. An averaged equation is obtained with a multi-scale method. After transforming the averaged equation into a standard form, the extended Melnikov method is used to show the existence of multi-pulse chaotic dynamics, which can be used to explain the mechanism of modal interactions of thin plates. A method for calculating the Melnikov function is given without an explicit analytical expression of homoclinic orbits. Furthermore, restrictions on the damping, excitation, and detuning parameters are obtained, under which the multi-pulse chaotic dynamics is expected. The results of numerical simulations are also given to indicate the existence of small amplitude multi-pulse chaotic responses for the rectangular thin plate.

BTT autopilot design for agile missiles with aerodynamic uncertainty

The approach to the synthesis of autopilot with aerody- namic uncertainty is investigated in order to achieve large maneu- verability of agile missiles. The dynamics of the agile missile with reaction-jet control system （RCS） are presented. Subsequently, the cascade control scheme based on the bank-to-turn （B-I-T） steering technique is described. To address the aerodynamic un- certainties encountered by the control system, the active distur- bance rejection control （ADRC） method is introduced in the autopi- lot design. Furthermore, a compound controller, using extended state observer （ESO） to online estimate system uncertainties and calculate derivative of command signals, is designed based on dynamic surface control （DSC）. Nonlinear simulation results show the feasibility of the proposed approach and validate the robust- ness of the controller with severe unmodeled dynamics.

DOWNSCALING FORECAST OF MONTHLY PRECIPITATION OVER GUANGXI BASED ON BP NEURAL NETWORK MODEL

Variables fields such as enstrophy, meridional-wind and zonal-wind variables are derived from monthly 500 hPa geopotential height anomalous fields. In this work, we select original predictors from monthly 500-hPa geopotential height anomalous fields and their variables in June of 1958 - 2001, and determine comprehensive predictors by conducting empirical orthogonal function (EOF) respectively with the original predictors. A downscaling forecast model based on the back propagation (BP) neural network is built by use of the comprehensive predictors to predict the monthly precipitation in June over Guangxi with the monthly dynamic extended range forecast products. For comparison, we also build another BP neural network model with the same predictands by using the former comprehensive predictors selected from 500-hPa geopotential height anomalous fields in May to December of 1957 - 2000 and January to April of 1958 - 2001. The two models are tested and results show that the precision of superposition of the downscaling model is better than that of the one based on former comprehensive predictors, but the prediction accuracy of the downscaling model depends on the output of monthly dynamic extended range forecast.

Monthly Extended Predicting Experiments with Nonlinear Regional Prediction.PartⅠ:Prediction of Zonal Mean Flow

Systematic errors have recently been founded to be distinct in the zonal mean component forecasts, which account for a large portion of the total monthly-mean forecast errors. To overcome the difficulty of numerical model, the monthly pentad-mean nonlinear dynamic regional prediction models of the zonal mean geopotential height at 200, 300, 500, and 700 hPa based on a large number of historical data （NCEP/NCAR reanalysis data） were constituted by employing the local approximation of the phase space reconstruction theory and nonlinear spatio-temporal series prediction method. The 12-month forecast experiments of 1996 indicated that the results of the nonlinear model are better than those of the persistent, climatic prediction, and T42L9 model either over the high- and mid-latitude areas of the Northern and Southern Hemispheres or the tropical area. The root-mean-square of the monthly-mean height of T42L9 model was considerably decreased with a change of 30.4%, 26.6%, 82.6%, and 39.4%, respectively, over the high- and mid-latitudes of the Northern Hemisphere, over the high- and mid-latitudes of the Southern Hemisphere, over the tropics and over the globe, and also the corresponding anomaly correlation coefficients over the four areas were respectively increased by 0.306-0.312, 0.304-0.429, 0.739-0.746, and 0.360-0.400 （averagely a relative change of 11.0% over the globe） by nonlinear correction after integration, implying that the forecasts given by nonlinear model include more useful information than those of T42L9 model.

Monthly Extended Predicting Experiments with Nonlinear Regional Prediction.PartⅡ:Improvement of Wave Component Prediction

Based on Chen et al. （2006）, the scheme of the combination of the pentad-mean zonal height departure nonlinear prediction with the T42L9 model prediction was designed, in which the pentad zonal heights at all the 12-initial-value-input isobar levels from 50 hPa to 1000 hPa except 200, 300, 500, and 700 hPa were derived from nonlinear forecasts of the four levels by means of a good correlation between neighboring levels. Then the above pentad zonal heights at 12 isobar-levels were transformed to the spectrum coefficients of the temperature at each integration step of T42L9 model. At last, the nudging was made. On account of a variety of error accumulation, the pentad zonal components of the monthly height at isobar levels output by T42L9 model were replaced by the corresponding nonlinear results once more when integration was over. Multiple case experiments showed that such combination of two kinds of prediction made an improvement in the wave component as a result of wave-flow nonlinear interaction while reducing the systematical forecast errors. Namely the monthly-mean height anomaly correlation coefficients over the high- and mid-latitudes of the Northern Hemisphere, over the Southern Hemisphere and over the globe increased respectively from 0.249 to 0.347, from 0.286 to 0.387, and from 0.343 to 0.414 （relative changes of 31.5%, 41.0%, and 18.3%）. The monthly-mean root-mean-square error （RMSE） of T42L9 model over the three areas was considerably decreased, the relative change over the globe reached 44.2%. The monthly-mean anomaly correlation coeffi- cients of wave 4-9 over the areas were up to 0.392, 0.200, and 0.295, with the relative change of 53.8%, 94.1%, and 61.2%, and correspondingly their RMSEs were decreased respectively with the rate of 8.5%, 6.3%, and 8.1%. At the same time the monthly-mean pattern of parts of cases were presented better.

Splicing Signals in the Human Hemoglobin Genes at the Sequence and Folding Levels

Identification of the splice sites is a critical and tough issue in eukaryotic genome annotation. Here, a statistical study is introduced for detecting the splicing signals in the human hemoglobin （Hb） pre-mRNAs by using the approaches of regional pairwise alignment, splicing weight matrix scoring, and dynamic extended folding. First, the regional pairwise alignment results show that the coding regions of the human Hb genes are at a high level for both conservation and fluctuation. Second, the weighted matrix scoring results indicate that, although the authentic splicing motifs are always scored the highest in a sequence, the sequence motif alone is inadequate to precisely define the splice sites. Finally, we deduce the RNA frame structures by applying an extended folding approach to analyze the stable folding elements. We find out that the splice sequences tend to take stretching and partially paired conformations, which benefit recognition and competitive binding of the splicing factors. These results indicate that precise splicing is an integrated effect of multiple mechanisms of signal recognition at the level of sequence and structure.