Robust design of sliding mode control for airship trajectory tracking with uncertainty and disturbance estimation

The robotic airship can provide a promising aerostatic platform for many potential applications.These applications require a precise autonomous trajectory tracking control for airship.Airship has a nonlinear and uncertain dynamics.It is prone to wind disturbances that offer a challenge for a trajectory tracking control design.This paper addresses the airship trajectory tracking problem having time varying reference path.A lumped parameter estimation approach under model uncertainties and wind disturbances is opted against distributed parameters.It uses extended Kalman filter(EKF)for uncertainty and disturbance estimation.The estimated parameters are used by sliding mode controller(SMC)for ultimate control of airship trajectory tracking.This comprehensive algorithm,EKF based SMC(ESMC),is used as a robust solution to track airship trajectory.The proposed estimator provides the estimates of wind disturbances as well as model uncertainty due to the mass matrix variations and aerodynamic model inaccuracies.The stability and convergence of the proposed method are investigated using the Lyapunov stability analysis.The simulation results show that the proposed method efficiently tracks the desired trajectory.The method solves the stability,convergence,and chattering problem of SMC under model uncertainties and wind disturbances.

Intermodal Competition: Cargo Airships versus Long-Haul Trucking for Perishable Commodities

Intermodal competition changes with changes in technology, economics, and environmental concerns. Trucks and airships are generally considered not to be competitors, but this depends on the distance of haul. The tonne-kilometer cost of trucking rises much more quickly with distance than it does the cost of a cargo airship. At some distance, the two modes are direct substitutes. The costs of the Mexico-Canada refrigerated truck supply chain are compared with the costs of a 100t-lift, electrically-powered airship. The flight characteristics of the Hindenburg Zeppelin are used as a model for a modern cargo airship. The supply chain cost of trucking tomatoes is used to test the theorical proposition. The cost difference works out to about US10￠/kg (5￠/lb) advantage for trucking Mexican tomatoes to Canada. However, this cost disadvantage of the airship could be made up by their vibrationless ride, better air circulation and one-day service versus four days by truck. This alternative form of transportation could have a positive impact on worldwide north-south distribution of food. Airships can overcome trade barriers and distance to open new markets for perishable food exports. In addition, they would reduce the carbon emissions of transport. Canada imports 160,000 refrigerated truckloads of fruits and vegetables by from the southern US and Mexico. With an average driving distance of 3,000 km, these trucks emit 606,000 MT of CO2 annually. Airships powered by hydrogen fuel cells would have zero-carbon emissions. Markets are not yet incorporating the environmental advantage of airships in any freight comparison, but inevitably this will be important.

Biaxial tensile properties and elastic constants evaluation of envelope material for airship

This paper presents an experimental study to determine the tensile properties of the envelope fabric Uretek3216L under biaxial cyclic loading.First the biaxial cyclic tests were carefully carried out on the envelope material to obtain the stress-strain data and the corresponding nonlinearity and orthotropy of the material were analyzed. Then for some determination options with different stress ratios the least squares method minimizing the strain terms was used to calculate the elastic constants from the experimental data.Finally the influences of the determination options with different stress ratios and the reciprocal relationship on the elastic constants were discussed.Results show that the orthotropy of the envelope material can be attributed to the unbalanced crimp of their constitutive yarns in warp and weft directions and the elastic constants vary noticeably with the determination options as well as the normalized stress ratios.In real design practice it is more reasonable to use constants determined for specific stress states in particular stress ratios depending on the project＆#39;s needs.Also calculating the structures with two limitative sets of elastic constants instead of using only one set is recommendable in light of the great variety of the constant＆#39;s values.

SINGULAR PERTURBATION APPROACH TO MOVING MASS CONTROL OF BUOYANCY-DRIVEN AIRSHIP IN 3-D SPACE

The attitude control problem and the guidance problem are solved in 3-D for a buoyancy-driven airship actuated by the combined effects of an internal air bladder which modulates the airshiprs net weight and of two moving masses which modulate its center of mass. A simple and clear modeling is introduced to derive the 8 degree of freedom （DOF） mathematical model. Nonlinear control loops are derived through maximal feedback linearization with internal stability for both dynamics in the longitudinal plane and in the lateral plane. Based on a singular perturbation approach, the superposition of these two control actions in the longitudinal plane and in the lateral plane is shown to achieve the control of the dynamics in 3-D space. The simulations of the airship tracking specified attitude, moving direction and speed in 3-D space are presented.

Stabilization and trajectory tracking of autonomous airship's planar motion

The stabilization and trajectory tracking problems of autonomous airship＇s planar motion are studied. By defining novel configuration error and velocity error, the dynamics of error systems are derived. By applying Lyapunov stability method, the state feedback control laws are designed and the close-loop error systems are proved to be uniformly asymptotically stable by Matrosov theorem. In particular, the controller does not need knowledge on system parameters in the case of set-point stabilization, which makes the controller robust with respect to parameter uncertainty. Numerical simulations illustrate the effectiveness of the controller designed.

DYNAMIC MODELING FOR AIRSHIP EQUIPPED WITH BALLONETS AND BALLAST

Total dynamics of an airship is modeled. The body of an airship is taken as a submerged rigid body with neutral buoyancy, i. e. , buoyancy with value equal to that of gravity, and the coupled dynamics between the body with ballonets and ballast is considered. The total dynamics of the airship is firstly derived by Newton-Euler laws and Kirchhoff＇ s equations. Furthermore, by using Hamiltonian and Lagrangian semidirect product reduction theories, the dynamics is formulated as a Lie-Poisson system, or also an Euler-Poincare system. These two formulations can be exploited for the control design using energy-based methods for Hamiltonian or Lagrangian system.

Adaptive fuzzy sliding mode control for robotic airship with model uncertainty and external disturbance

An adaptive fuzzy sliding mode control （AFSMC） ap- proach is proposed for a robotic airship. First, the mathematical model of an airship is derived in the form of a nonlinear control system. Second, an AFSMC approach is proposed to design the attitude control system of airship, and the global stability of the closed-loop system is proved by using the Lyapunov stability theorem. Finally, simulation results verify the effectiveness and robustness of the proposed control approach in the presence of model uncertainties and external disturbances.

Structural Performance Evaluation Procedure for Large Flexible Airship of HALE Stratospheric Platform Conception

Basic loads applied on the airship envelope were analyzed.The resultant forces,the static bending moment and the dynamic bending moment were formulated.Based on classic linear elastic membrane theory,the procedures to calculate the minimum pressure were proposed for sufficient rigidity evaluation.The limit load capacity was further investigated,and the related formula were developed.Finally,the stress and internal forces analysis was carried out for cylindrical and non-cylindrical approximations of envelope hull of airship.The present research is very valuable to the overall preliminary design of airship and further research.

Airship aerodynamic model estimation using unscented Kalman filter

An airship model is made-up of aerostatic,aerodynamic,dynamic,and propulsive forces and torques.Besides others,the computation of aerodynamic forces and torques is difficult.Usually,wind tunnel experimentation and potential flow theory are used for their calculations.However,the limitations of these methods pose difficulties in their accurate calculation.In this work,an online estimation scheme based on unscented Kalman filter(UKF)is proposed for their calculation.The proposed method introduces six auxiliary states for the complete aerodynamic model.UKF uses an extended model and provides an estimate of a complete state vector along with auxiliary states.The proposed method uses the minimum auxiliary state variables for the approximation of the complete aerodynamic model that makes it computationally less intensive.UKF estimation performance is evaluated by developing a nonlinear simulation environment for University of Engineering and Technology,Taxila(UETT)airship.Estimator performance is validated by performing the error analysis based on estimation error and 2-σ uncertainty bound.For the same problem,the extended Kalman filter(EKF)is also implemented and its results are compared with UKF.The simulation results show that UKF successfully estimates the forces and torques due to the aerodynamic model with small estimation error and the comparative analysis with EKF shows that UKF improves the estimation results and also it is more suitable for the under-consideration problem.

AIRSHIP ATTITUDE TRACKING SYSTEM

The attitude tracking control problem for an airship with parameter uncertainties and external disturbances was considered in this paper. The mathematical model of the airship attitude is a multi-input/multi-output uncertain nonlinear system. Based on the characteristics of this system, a design method of robust output tracking controllers was adopted based on the upper-bounds of the uncertainties. Using the input/output feedback linearization approach and Liapunov method, a control law was designed, which guarantees that the system output exponentially tracks the given desired output. The controller is easy to compute and complement. Simulation results show that, in the closed-loop system, precise attitude control is accomplished in spite of the uncertainties and external disturbances in the system.

Kinetic Analysis of Vectored Electric Propulsion System for Stratosphere Airship

To enhance the controllability of stratosphere airship,a vectored electric propulsion system is used.By using the Lagrangian method,a kinetic model of the vectored electric propulsion system is established and validated through ground tests.The fake gyroscopic torque is first proposed,which the vector mechanism should overcome besides the inertial torque and the gravitational torque.The fake gyroscopic torque is caused by the difference between inertial moments about two principal inertial axes of the propeller in the rotating plane,appears only when the propeller is rotating and is proportional with the rotation speed.It is a sinusoidal pulse,with a frequency that is twice of the rotation speed.Considering the fake gyroscope torque pulse and aerodynamic efficiency,three blade propeller is recommended for the vectored propulsion system used for stratosphere airship.

Attitude control allocation strategy of high altitude airship based on synthetic performance optimization

This paper presents a method for solving the attitude control problem of high altitude airship (HAA) with aerodynamic fin and vectored thruster control. The algorithm is based on the synthetic optimization of dynamic performance and energy consumption of airship. Firstly, according to the system overall configuration, the dynamic model of HAA was established and the HAA linearized model of longitudinal plane motion was obtained. Secondly, using the classic PID control theory, the HAA attitude control system was designed. Thirdly, through analyzing the dynamic performance of airship with fin or vectored thruster control, the synthetic performance index function with different weighting functions was determined. By means of optimizing the obtained performance index function, the attitude control of high altitude airship with good dynamic performance and low energy consumption was achieved. Finally, attitude control allocation strategy was designed for the airship station keeping at an altitude of 22 km. The simulation experiment proved the validity of the proposed algorithm.

Cargo Airships: International Competition

The advance of transportation technology depends on science and economics. During the 1930s, airships and airplanes competed head-to-head for the Atlantic passenger market. When World War 2 broke out, everything changed. Over the next five years, the combined combatants built over half of a million military airplanes. By the end of the war, four-engine, high-altitude bombers and jet engines were developed. Further investment in airplane technology was stimulated by the Cold War. All this public investment was adapted to civilian passenger jet airplanes. By 1980, dedicated jet airplanes were in use as cargo carriers. Despite the growth of the cargojet market over the past three decades, rising fuel costs and environmental concerns are changing the economics of airships and airplanes again. Investment in large cargo airships is returning. Much of the technology developed for fixed-wing aircraft can be applied to cargo airships. New materials, better engines, control systems and engineering eliminate the need for large ground crews and improve airship reliability and safety. However, two fundamental design issues have yet to be resolved: structural integrity and buoyancy control. A worldwide competition is underway on three continents to develop the dominant design for a cargo airship. This paper examines the alternative design approaches and presents the status of the international competition.

Modeling and analysis of moving-mass actuated stratospheric airship

A moving-mass control method is introduced to stratospheric airship for its special working condition of low atmospheric density and low speed.The dynamic equation of airship is derived by using the Newton-Euler method and the mechanism of attitude control by moving masses is studied.Then the passive gliding of airship by the moving masses is given based on the theory of glider,and attitude control capability between moving mass and elevator is compared at different airspeed.Analysis results show that the motion of masses changes the gravity center of the airship system,which makes the inertia tensor and the gravity moment vary.Meanwhile,the aerodynamic angles are generated,which results in the change of aerodynamic moment.Control efficiency of moving masses is independent of airspeed.Thus the moving-mass control has the advantage over the aerodynamic surfaces at low airspeed.

Methods of configuration test and deformation analysis for large airship

In recent years, high-altitude aerostats have been increasingly developed in the direction of multi-functionality and large size. Due to the large size and the high flexibility, new challenges for large aerostats have appeared in the configuration test and the deformation analysis. The methods of the configuration test and the deformation analysis for large airship have been researched and discussed. A tested method of the configuration,named internal scanning, is established to quickly obtain the spatial information of all surfaces for the large airship by the three-dimensional(3D) laser scanning technology. By using the surface wrap method, the configuration parameters of the large airship are calculated. According to the test data of the configuration, the structural dimensions such as the distances between the characteristic sections are measured. The method of the deformation analysis for the airship contains the algorithm of nonuniform rational B-splines(NURBS) and the finite element(FE)method. The algorithm of NURBS is used to obtain the reconfiguration model of the large airship. The seams are considered and the seam areas are divided. The FE model of the middle part of the large airship is established. The distributions of the stress and the strain for the large airship are obtained by the FE method. The position of the larger deformation for the airship is found.

Robust H_∞ directional control for a sampled-data autonomous airship

A robust H∞ directional controller for a sampled-data autonomous airship with polytopic parameter uncertainties was proposed. By input delay approach, the linearized airship model was transformed into a continuous-time system with time-varying delay. Sufficient conditions were then established based on the constructed Lyapunov-Krasovskii functional, which guarantee that the system is mean-square exponentially stable with H∞ performance. The desired controller can be obtained by solving the obtained conditions. Simulation results show that guaranteed minimum H∞ performance γ=1.4037 and fast response of attitude for sampled-data autonomous airship are achieved in spite of the existence of parameter uncertainties.

Experiment and numerical simulation on the characteristics of fluid–structure interactions of non-rigid airships

Fluid-structure interaction is an important issue for non-rigid airships with inflated envelopes. In this study, a wind tunnel test is conducted, and a loosely coupled procedure is correspondingly established for numerical simulation based on computational fluid dynamics and nonlinear finite element analysis methods. The typical results of the numerical simulation and wind tunnel experiment, including the overall lift and deformation, are in good agreement with each other. The results obtained indicate that the effect of fluid-structure interaction is noticeable and should be considered for non-rigid airships. Flow- induced deformation can further intensify the upward lift force and pitching moment, which can lead to a large deformation. Under a wind speed of 15 m/s, the lift force of the non-rigid model is increased to approximatelv 60% compared with that of the rigid model under a high angle of attack.

Study on Pressure Coefficient Distribution of the Airship Zhiyuan-1

A wind tunnel tests with different configurations,pitch and yaw angles were performed to study the wind load characteristics of the rigid model of the airship Zhiyuan-1. The rigid model was aimed to simulate a technical demonstrating stratospheric airship named Zhiyuan-1 according to the similarity principle of geometric and Reynolds number. Based on the results of wind tunnel test,the features of pressure coefficient distributions on the surface of the airship were described. It was indicated that the fins and the gondola of airship hardly have the effect on the pressure distribution on the surface of airship,but have obviously effect on the local areas near the fins and the gondola.

The Constitutive Relation of a Fabric Membrane Composite for a Stratospheric Airship Envelope Based on Invariant Theory

The study of stratospheric airships has become the focus in many countries in recent years,because of its potential applications in many fields.Lightweight and high strength envelopes are the keys to the design of stratospheric airships,as it directly determines the endurance flight performance and loading deformation characteristics of the airship.A typical envelope of any stratospheric airship is a coated-fabric material which is composed of a fiber layer and several functional membrane layers.According to composite structure,nonlinearity and viscoelasticity are the two main characteristics of such envelope.Based on the analysis on the interaction between the different components in the micro-mechanical model of the coated-fabric,several invariant values reflecting the characteristics of the envelope material are obtained according to invariant theory.Furthermore,the constitutive equation that describes the viscoelasticity of the envelope material is derived.The constitutive equation can represent both the individual roles of the warp and weft fibers,and their further coupled interactions.The theoretical computation results were verified by off-axial tension tests.The results can help gain a deeper understanding of the mechanical mechanism and provide a reference for structural design of envelope material.

Design of robust stability augmentation system for an airship using genetic algorithm

This paper presents the design of stability augmentation system (SAS) for the airship, which is robust with respect to parametric plant uncertainties. A robust pole placement approach is adopted in the design, which uses genetic algorithm (GA) as the optimization tool to derive the most robust solution of the state-feedback gain matrix K. The method can guarantee the resulting closed-loop poles to remain in a specified allocation region despite plant parameter uncertainty. Thus, the longitudinal stability of the airship is augmented by robustly assigning the closed-loop poles in a prescribed region of the left half s-plane.