Optimal Backstepping Control of a VR Spherical Motor

2000 ◽  
Author(s):  
Kok-Meng Lee ◽  
Raye Sosseh
Keyword(s):  
Degrees Of Freedom ◽  
Control Design ◽  
Design Tool ◽  
Spherical Motor ◽  
Lyapunov Techniques ◽  
Variable Reluctance ◽  
Output Torque ◽  
Minimum Total Energy ◽  
Overall Stability ◽  
Three Degrees Of Freedom

Abstract This paper considers the control of a variable reluctance (VR) spherical motor that offers some unique features by combining the roll, pitch and yaw motion in a single joint. The 3-DOF VR motor has multiple independent inputs, and the output torque is direction varying and orientation-dependent and as a result, the control for such a motor is significantly more challenging than the single-axis motor. We formulate a new three-degrees-of-freedom (3-DOF) VR motor control design tool using backstepping, where the inputs are optimized to achieve minimum total energy consumed. The torque has been derived as a linear combination of the square of the input currents, a form computationally friendlier than its quadratic counterpart for real-time implementation. The overall stability of the system is shown using Lyapunov techniques. Simulation results are illustrated to show the performance of the controller.

Design Optimization of a Three Degrees-of-Freedom Variable-Reluctance Spherical Wrist Motor

1995 ◽  
Vol 117 (3) ◽  
pp. 378-388 ◽  
Author(s):  
R. B. Roth ◽  
Kok-Meng Lee
Keyword(s):  
Prediction Model ◽  
Degrees Of Freedom ◽  
Spherical Motor ◽  
Constraint Equations ◽  
Variable Reluctance ◽  
Potential Applications ◽  
Spherical Wrist ◽  
Optimization Methodology ◽  
Improved Performance ◽  
Three Degrees Of Freedom

This paper presents the basis for optimizing the design of a three degrees-of-freedom (DOF) variable reluctance (VR) spherical motor which offers some attractive features by combining pitch, roll, and yaw motion in a single joint. The spherical wrist motor offers a major performance advantage in trajectory planning and control as compared to the popular three-consecutive-rotational joint wrist. Since an improved performance estimate is required, a method for optimizing the VR spherical motor’s magnetics was developed. This paper begins with a presentation of the geometrical independent and dependent variables which fully described the design of a VR spherical motor. These variables are derived from examination of the torque prediction model. Next, a complete set of constraint equations governing geometry, thermal limitations, amplifier specifications, iron saturation, and leakage flux are derived. Finally, an example problem is presented where the motor’s geometry is determined by maximizing the output torque at one rotor position. The concept of developing a spherical motor with uniform torque characteristics is discussed with respect to the optimization methodology. It is expected that the resulting analysis will improve the analytical torque prediction model by the inclusion of constraint equations, aid in developing future VR spherical motor designs, improve estimates of performance, and therefore will offer better insight into potential applications.

A Spherical DC Servo Motor With Three Degrees of Freedom

1989 ◽  
Vol 111 (3) ◽  
pp. 398-402 ◽  
Author(s):  
K. Kaneko ◽  
I. Yamada ◽  
K. Itao
Keyword(s):  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Matrix Elements ◽  
Servo Motor ◽  
Constant Matrix ◽  
Spherical Motor ◽  
The Matrix ◽  
Three Degrees Of Freedom

A spherical DC servo motor with three degrees of freedom is proposed. First, the process of generating three-dimensional torque is analyzed to obtain the torque constant matrix. The matrix elements are shown to vary with rotor inclination, and winding currents are shown to interfere with each other. Then, the dynamics of the spherical motor are investigated theoretically and experimentally, considering torque interference, gyro moment and gravity. Finally, the trajectory of the prototype motor is shown in order to clarify its abilities. This new spherical motor is expected to produce a smaller, a lighter mechanism, since no gears or linkages are needed.

scholarly journals Chaotic Assessment of the Heave and Pitch Dynamics Motions of Air Cushion Vehicles

2021 ◽  
Vol 26 (2) ◽  
pp. 219-234
Author(s):  
A.S. Sowayan
Keyword(s):  
Degrees Of Freedom ◽  
Control Design ◽  
Design Parameters ◽  
Bernoulli’S Equation ◽  
Proposed Model ◽  
Frequency Domains ◽  
Air Cushion ◽  
Base Radius ◽  
Air Cushion Vehicles ◽  
Three Degrees Of Freedom

Abstract In this study, a three degrees of freedom nonlinear air cushion vehicle (ACV) model is introduced to examine the dynamic behavior of the heave and pitch responses in addition to the cushion pressure of the ACV in both time and frequency domains. The model is based on the compressible flow Bernoulli’s equation and the thermodynamics nonlinear isentropic relations along with the Newton second law of translation and rotation. In this study, the dynamical investigation was based on a numerical simulation using the stiff ODE solvers of the Matlab software. The chaotic investigations of the proposed model are provided using the Fast Fourier Transform (FFT), the Poincaré maps, and the regression analysis. Three control design parameters are investigated for the chaotic studies. These parameters are: ACV mass (M), the mass flow rate entering the cushion volume (ṁin ), and the ACV base radius (r). Chaos behavior was observed for heave, and pitch responses as well as the cushion pressure.

Design of a Spherical Motor with Three Degrees of Freedom

CIRP Annals ◽  
2000 ◽  
Vol 49 (1) ◽  
pp. 289-294 ◽  
Author(s):  
E.h.M. Week ◽  
T. Reinartz ◽  
G. Henneberger ◽  
R.W. De Doncker
Keyword(s):  
Degrees Of Freedom ◽  
Spherical Motor ◽  
Three Degrees Of Freedom

Linear coupled model for floating wind turbine control

2018 ◽  
Vol 42 (2) ◽  
pp. 115-127 ◽  
Author(s):  
Alessandro Fontanella ◽  
Ilmas Bayati ◽  
Marco Belloli
Keyword(s):  
Degrees Of Freedom ◽  
Coupled Model ◽  
Control Design ◽  
Offshore Wind ◽  
Order Model ◽  
Reduced Order ◽  
Offshore Wind Turbines ◽  
Wind Turbine Control ◽  
Floating Offshore Wind Turbines ◽  
Three Degrees Of Freedom

This work deals with an analytical linear coupled model describing the integrated aero-hydrodynamics of floating offshore wind turbines. Three degrees of freedom (platform surge, platform pitch and rotor azimuth) were considered with the goal of building a reduced-order model suitable for being integrated in control design algorithms as well as to be used for a straightforward evaluation and comprehension of the global system dynamics.

On Model Feedback Control for Robot Manipulators

1991 ◽  
Vol 113 (3) ◽  
pp. 371-378 ◽  
Author(s):  
T. Narikiyo ◽  
T. Izumi
Keyword(s):  
Control Systems ◽  
Degrees Of Freedom ◽  
Robot Manipulators ◽  
Control Design ◽  
Parameter Uncertainties ◽  
Uncertain Dynamics ◽  
Classical Control ◽  
Multivariate Control ◽  
Control Methodology ◽  
Three Degrees Of Freedom

Robot manipulators are highly coupled nonlinear systems and their motions are influenced by uncertain dynamics such as coulomb friction. These nonlinearities and uncertainties disturb the performance of control systems. In this paper, a control design methodolgy is proposed for the purpose of reducing the adverse effects of parameter uncertainties and disturbances. This control structure is similar to that of classical control. Unlike classical control, this control methodology accommodates multivariate control systems with uncertain dynamics and disturbances. The control design methodology is applied to a three-degrees-of-freedom directly driven robot. Simulation and experimental results demonstrate excellent robustness.

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