On the Stability and Control of the Bicycle

2008 ◽  
Vol 61 (6) ◽  
Author(s):  
Robin S. Sharp
Keyword(s):  
Control Theory ◽  
Equations Of Motion ◽  
Gain Control ◽  
High Gain ◽  
Torque Control ◽  
Complex Case ◽  
Steering Control ◽  
Stability And Control ◽  
The Stability ◽  
And Control

After some brief history, a mathematical model of a bicycle that has become a benchmark is described. The symbolic equations of motion of the bicycle are given in two forms and the equations are interpreted, with special reference to stability. The mechanics of autostabilization are discussed in detail. The relationship between design and behavior is shown to be heavily speed-dependent and complex. Using optimal linear preview control theory, rider control of the bicycle is studied. It is shown that steering control by an optimal rider, especially at low speeds, is powerful in comparison with a bicycle’s self-steering. This observation leads to the expectation that riders will be insensitive to variations in design, as has been observed in practice. Optimal preview speed control is also demonstrated. Extensions to the basic treatment of bicycle dynamics in the benchmark case are considered so that the modeling includes more realistic representations of tires, frames, and riders. The implications for stability predictions are discussed and it is shown that the moderate-speed behavior is altered little by the elaborations. Rider control theory is applied to the most realistic of the models considered and the results indicate a strong similarity between the benchmark case and the complex one, where they are directly comparable. In the complex case, steering control by rider-lean-torque is feasible and the results indicate that, when this is combined with steer-torque control, it is completely secondary. When only rider-lean-torque control is possible, extended preview is necessary, high-gain control is required, and the controls are relatively complex. Much that is known about the stability and control of bicycles is collected and explained, together with new material relating to modeling accuracy, bicycle design, and rider control.

Stability and Control of a Parametrically Excited Rotating Beam

1998 ◽  
Vol 120 (4) ◽  
pp. 462-470 ◽  
Author(s):  
S. C. Sinha ◽  
Dan B. Marghitu ◽  
Dan Boghiu
Keyword(s):  
Equations Of Motion ◽  
System Stability ◽  
Flexible Beam ◽  
Parametrically Excited ◽  
Stability And Control ◽  
Rotation Parameters ◽  
The Stability ◽  
And Control ◽  
Time Invariant ◽  
Time Periodic

In this paper the stability and control of a parametrically excited, rotating flexible beam is considered. The equations of motion for such a system contain time periodic coefficients. Floquet theory and a numerical integration are used to evaluate the stability of the linearized system. Stability charts for various sets of damping, parametric excitation, and rotation parameters are obtained. Several resonance conditions are found and it is shown that the system stability can be significantly changed due to the rotation. Such systems can be used as preliminary models for studying the flap dynamics and control of helicopter rotor blades and flexible mechanisms among other systems. To control the motion of the system, an observer based controller is designed via Lyapunov-Floquet transformation. In this approach the time periodic equations are transformed into a time invariant form, which are suitable for the application of standard time invariant controller design techniques. Simulations for several combinations of excitation and rotation parameters are shown.

Flight control and flight experiments of a tilt-propeller VTOL UAV

2018 ◽  
Vol 40 (8) ◽  
pp. 2454-2465 ◽  
Author(s):  
Zafer Öznalbant ◽  
Mehmet Ş. Kavsaoğlu
Keyword(s):  
Flight Control ◽  
Equations Of Motion ◽  
Control Methods ◽  
Stability And Control ◽  
Flight Mode ◽  
Aerial Vehicle ◽  
The Stability ◽  
And Control ◽  
Pitch Tilt ◽  
Fixed Pitch

The purpose of this work is to present a study on the stability and control of an unmanned, fixed wing, vertical take-off and landing aerial vehicle. This airplane is driven by a fixed-pitch tilt-propeller system with the capability of vertical take-off and landing as well as conventional flight. The novelty of the vehicle is the use of a fixed-pitch propeller system instead of variable-pitch tilt-rotors. There are three flight modes: vertical, transitional and conventional flight modes. Each flight mode has different dynamic characteristics. Therefore, these modes each need dedicated flight control methods. In this paper, the equations of motion are generated by modelling the aerodynamic and propulsion forces and moments. After performing trim condition calculations, longitudinal stability characteristics are investigated for each flight mode. The control methods are described for vertical, transitional and conventional flight modes. Stability augmentation systems, which consist of proportional and proportional/integral controller, are applied. A number of flight tests, including vertical, transitional and conventional flights, have been successfully performed with a prototype aircraft.

Some Stability and Control Aspects of Airframe/Propulsion System Interactions on the YF-12 Airplane

1974 ◽  
Vol 96 (3) ◽  
pp. 820-826 ◽  
Author(s):  
D. T. Berry ◽  
G. B. Gilyard
Keyword(s):  
Static Stability ◽  
Propulsion System ◽  
Jet Propulsion ◽  
Stability And Control ◽  
The Stability ◽  
And Control ◽  
Large Aircraft

Airframe/propulsion system interactions can strongly affect the stability and control of supersonic cruise aircraft. These interactions generate forces and moments similar in magnitude to those produced by the aerodynamic controls, and can cause significant changes in vehicle damping and static stability. This in turn can lead to large aircraft excursions or high pilot workload, or both. For optimum integration of an airframe and its jet propulsion system, these phenomena may have to be taken into account.

scholarly journals Advanced Modelling of KF Implemented Flying Wing

2019 ◽  
Vol 11 (4) ◽  
Author(s):  
Widanalage Dakshina ◽  
Thiwanka Fernando
Keyword(s):  
Extreme Condition ◽  
Flow Conditions ◽  
Ongoing Research ◽  
Stability And Control ◽  
Advanced Phase ◽  
Landing Gears ◽  
Two Phases ◽  
The Stability ◽  
And Control ◽  
Base Design

This research carries out the advanced phase in correlation with the previous published design of KF Implemented Flying Wing. At the primary stage the basic design was considered under omission of non-static components and turbulent conditions. At this stage the simulations have taken a step ahead with improved flow conditions and advanced modeling of the design. As per the design aspects the engines, pylons, landing gears and shape improvements were done with solid modeling. Due to the computational limitations this was divided in to two phases as cruising conditions with non-static components and further studies to be carried out in Takeoff and Landing conditions with extended landing gears. Under the stability and control conditions a separate research is being carried out in achieving the optimum capability. Propfan engine selected for extreme condition evaluations. The implementations were made without disrupting the base design which was presented in phase one basic simulation carried out prior to this. The simulation results deemed to be promising for the first stage as well as the effect of new components. The secondary target areas are to be carried out in further ongoing research as well

scholarly journals Study On Setting Method of Flatness Target Curve of SUNDWIG 20-High Mill Considering Target Crown

2021 ◽  
Author(s):  
Jianliang Sun ◽  
Mingze Yan ◽  
Mingyuan Li ◽  
Tongtong Hao
Keyword(s):  
Control Theory ◽  
Cold Rolling ◽  
Hot Rolling ◽  
New Method ◽  
Discrimination Model ◽  
Flatness Control ◽  
Simulation Results ◽  
The Stability ◽  
And Control

Abstract The flatness target curve is important in the flatness control theory. The accuracy of flatness target curve is an important factor to determine the load of flatness control means and flatness quality. Aiming at the defect that crown of each pass after rolling cannot be controlled quantitatively in the traditional target curve formulation of cold rolling, a new method considering the target crown was proposed. Specifically, the target crown of each pass can be set by combining the total proportional crown change in hot rolling field to each pass and the instability discrimination model in cold rolling field. the total proportional crown change of incoming material and finished product is allocated to each pass, and the instability discrimination model is applied to ensure the stability of the plate. The purpose of new method is to control of the crown of each pass quantitatively, so that the flatness and thickness of plate can meet the production requirements. Taking SUNDWIG 20-high mill and typical rolling products as an example, the simulation results show that, on the basis of ensuring the flatness and obtaining the minimum available crown after rolling, the model can make the flatness and crown meet the production requirements at the same time and control the crown of each pass after rolling quantitatively by setting the target crown of each pass.

Modelling the flight dynamics of the hang glider

2005 ◽  
Vol 109 (1102) ◽  
pp. I-XX ◽  
Author(s):  
M. V. Cook ◽  
M. Spottiswoode
Keyword(s):  
Complex Geometry ◽  
Equations Of Motion ◽  
Linear Equations ◽  
Flight Dynamics ◽  
Control Analysis ◽  
Stability Margins ◽  
Stability And Control ◽  
Centre Of Gravity ◽  
Weight Shift ◽  
And Control

AbstractThe development of the non-linear equations of motion for the hang glider from first principles is described, including the complex geometry of control by pilot ‘weight shift’. By making appropriate assumptions the linearised small perturbation equations are derived for the purposes of stability and control analysis. The mathematical development shows that control is effected not by pilot weight shift, but by centre of gravity shift and that lateral-directional control by this means is weak, and is accompanied by significant instantaneous adverse response.The development of a comprehensive semi-empirical mathematical model of the flexible wing aerodynamics is described. In particular, the modelling attempts to quantify camber and twist dependencies. The performance of the model is shown to compare satisfactorily with measured hang glider wing data obtained in earlier full scale experiments. The mathematical aerodynamic model is then used to estimate the hang glider stability and control derivatives over the speed envelope for substitution into the linearised equations of motion.Solution of the equations of motion is illustrated and the flight dynamics of the typical hang glider are described. In particular, the dynamic stability properties are very similar to those of a conventional aeroplane, but the predicted lateral directional stability margins are significantly larger. The depth of mathematical modelling employed enables the differences to be explained satisfactorily. The unique control properties of the hang glider are described in some detail. Pitch and roll control of the hang glider is an aerodynamic phenomenon and results from the pilot adjusting his position relative to the wing in order to generate out of trim aerodynamic control moments about the centre of gravity. Maximum control moments are limited by hang glider geometry which is dependent on the length of the pilot‘s arm. The pilot does not generate control moments directly by shifting his weight relative to the wing. The modelling thus described would seem to give a plausible description of the flight dynamics of the hang glider.

scholarly journals Stability and control of planar compass gait walking with series-elastic ankle actuation

2016 ◽  
Vol 39 (3) ◽  
pp. 312-323 ◽  
Author(s):  
Deniz Kerimoğlu ◽  
Ömer Morgül ◽  
Uluç Saranli
Keyword(s):  
Equations Of Motion ◽  
Period Doubling ◽  
Basic Structure ◽  
System Stability ◽  
Gravitational Potential Energy ◽  
Extended Model ◽  
Stability And Control ◽  
Inclined Surfaces ◽  
And Control ◽  
Series Elastic

Passive dynamic walking models are capable of capturing basic properties of walking behaviours and can generate stable human-like walking without any actuation on inclined surfaces. The passive compass gait model is among the simplest of such models, consisting of a planar point mass and two stick legs. A number of different actuation methods have been proposed both for this model and its more complex extensions to eliminate the need for a sloped ground, balancing collision losses using gravitational potential energy. In this study, we introduce and investigate an extended model with series-elastic actuation at the ankle towards a similar goal, realizing stable walking on level ground. Our model seeks to capture the basic structure of how humans utilize toe push-off prior to leg liftoff, and is intended to eventually be used for controlling the ankle joint in a lower-body robotic orthosis. We derive hybrid equations of motion for this model, and show numerically through Poincaré analysis that it can achieve asymptotically stable walking on level ground for certain choices of system parameters. We then study the bifurcation regimes of period doubling with this model, leading up to chaotic walking patterns. Finally, we show that feedback control on the initial extension of the series ankle spring can be used to improve and extend system stability.

Paper 5. Directional Stability and Control of a Vessel in Restricted Waters

1972 ◽  
Vol 14 (7) ◽  
pp. 29-33 ◽  
Author(s):  
M. Fujino
Keyword(s):  
Hydrodynamic Force ◽  
Equations Of Motion ◽  
Narrow Channel ◽  
Order Theory ◽  
Stability Criteria ◽  
First Order ◽  
Stability And Control ◽  
First Order Theory ◽  
And Control ◽  
Improve Stability

By way of introduction the paper discusses conflicting observations of stability behaviour of ships in restricted waters. The equations of motion of a ship in a narrow channel are given, leading to stability criteria; differences from the deep water case are highlighted. More qualitatively, the theory also illustrates the asymmetric hydrodynamic force. Criteria are outlined for an automatic control system to improve stability. However, the first-order theory is shown to provide an inadequate description of all experimental results.

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