Torque Vector Research Articles

A Hölder-continuous Extended State Observer for Rigid Body Attitude Dynamics

Estimating rigid body attitude dynamics in the presence of unknown or uncertain torques, has applications to unmanned aerial, ground, (under)water and space vehicles. This work provides a new approach to estimating the attitude states and unknown, time-varying, (disturbance) torque vector acting on a rigid body, using an extended state observer. The observer design uses the concept of geometric homogeneity to obtain its stability. A Lyapunov stability analysis is carried out to prove its stability properties. The resulting observer for the attitude states and disturbance torque is smooth, Hölder-continuous, and exhibits almost globally finite-time stable (AG-FTS) with a constant disturbance torque in body frame. These properties are theoretically shown, and a numerical simulation is carried out to demonstrate how the observer works in a realistic attitude estimation scenario.

On the equations of warped disc dynamics

ABSTRACT The 1D evolution equations for warped discs come in two flavours: For very viscous discs, the internal torque vector $\boldsymbol {G}$ is uniquely determined by the local conditions in the disc, and warps tend to damp out rapidly if they are not continuously driven. For very inviscid discs, on the other hand, $\boldsymbol {G}$ becomes a dynamic quantity, and a warp will propagate through the disc as a wave. The equations governing both regimes are usually treated separately. A unified set of equations was postulated recently by Martin et al., but not yet derived from the underlying physics. The standard method for deriving these equations is based on a perturbation series expansion, which is a powerful, but somewhat abstract technique. A more straightforward method is to employ the warped shearing box framework of Ogilvie & Latter, which so far has not yet been used to derive the equations for the wave-like regime. The goal of this paper is to analyse the warped disc equations in both regimes using the warped shearing box framework, to derive a unified set of equations, valid for small warps, and to discuss how our results can be interpreted in terms of the affine tilted-slab approach of Ogilvie.

Optimal heliocentric transfers of a Sun-facing heliogyro

A heliogyro is a rotating solar sail with the reflecting surface divided into a number of long and slender blades, which are stiffened by a spin-induced centrifugal force. Each blade can rotate around its own longitudinal axis so as to change the pitch angle and allow the thrust vector to be effectively controlled. The aim of this paper is to analyze the optimal heliocentric transfers of a Sun-facing heliogyro, that is, a heliogyro whose fundamental plane is always perpendicular to the Sun-spacecraft line. A simplified analytical model of the thrust and torque vectors provided by a Sun-facing heliogyro is illustrated, using the characteristic acceleration as a performance parameter. The proposed thrust vector model is then exploited to calculate the minimum flight times in a set of two-dimensional heliocentric transfers. Using an indirect method and a semi-analytical approach for trajectory optimization, some exemplary cases are discussed, such as circle-to-circle Earth-Mars and Earth-Venus transfers or a simplified mission to the asteroid 25143 Itokawa.

Optimization problem of attitude control of a spacecraft with bounded rotary energy using quaternions

The original control problem of optimal reorientation from a state of rest to a state of rest is considered and solved. The control function is torque vector. Problem of optimal control is investigated in detail for statement when control is restricted and the used functional of optimality includes kinematical rotary energy and time of maneuver. For solving and synthesis of the optimal control program, the quaternion method and the Pontryagin’s maximum principle are applied. Analytic solution of the proposed problem is presented basing on the differential equation connecting the angular velocity vector and quaternion of spacecraft attitude. It is shown that a chosen criterion of optimality provides a turn of a spacecraft with rotation energy which does not exceed the required value. This property of proposed control increases safety of flight. The time-optimal problem was solved also. The control law is formulated in the form of an explicit dependence of the control variables on the phase coordinates. All key expressions and equations are written in quaternion form which is convenient for onboard realization and implementation. The analysis of the special control regime of the spacecraft was made. Analytical formulas were written for duration of acceleration and braking. For specific cases of spacecraft configurations (dynamically symmetric spacecraft and spheric-symmetrical spacecraft as particular cases), complete solution of optimal control problem in closed form is given. Numerical example and the results of mathematical simulation for spacecraft motion under optimal control are demonstrated. This data supplements the made theoretical descriptions, and illustrates the practical feasibility of the designed algorithm for controlling the spatial orientation of the spacecraft showing reorientation process in visual form.

A developed combined control method for induction machine drives based on PWM

PurposeThe purpose of this paper is to develop a combined control (CC) technique based on the direct torque control (DTC) strategy and vector control (VC) method, to improve the overall performance of a three-phase induction machine (TPIM) drives.Design/methodology/approachThe proposed control scheme includes a table-based DTC strategy in connection with a proportional-integral-sliding mode controller and pulse width modulation switching strategy. The control system has merits of DTC technique such as simple structure, less dependent on machine parameters, fast dynamic response and merits of VC technique such as high accuracy and constant switching frequency.FindingsTo validate the effectiveness of the proposed control system, simulation and experimental studies are carried out for a 0.75 kW TPIM in different operating conditions. The achieved results show the superiority of the proposed method in terms of fast dynamics and simple structure compared to the VC strategy and low speed and torque ripples and constant switching frequency compared to the DTC method.Originality/valueCompared to the conventional CC strategies, the control law of the proposed method is based on DTC theory and modulation is established based on VC. In other words, the variable switching frequency which is one of the main disadvantages of the conventional CC strategies is rectified using the proposed CC scheme.

Coordinated control of distributed drive electric vehicle by TVC and ESC based on function allocation

Safe and comfortable driving experience includes the improvement of handling performance and stability control. This paper proposed a coordinated controller based on the function allocation for the handling performance and stability of distributed drive electric vehicles. The proposed controller has three layers. The upper control layer designs a dynamic stability envelope boundary suitable for various driving conditions through the phase plane method, and on this basis, the function allocation rules of torque vector control (TVC) strategy and electronic stability control (ESC) strategy were formulated. The medium control layer used the robust [Formula: see text] dynamic output feedback control method and the improved particle swarm optimization (PSO) parameter self-adjusting method to calculate the additional yaw moment required by the TVC strategy and the ESC strategy, respectively. The two types of additional yaw moment are implemented by the in-wheel motor and the hydraulic brake mechanism respectively. The lower control layer optimized the four-wheel torque and braking force based on the optimal tire load rate using the quadratic programming method. The proposed coordinated controller was performed in the CarSim/Simulink co-simulation platform and tested in a real vehicle platform. The results show that the proposed controller can improve the vehicle dynamic response according to the driver’s intention, thus bringing the better handling performance and stability.

Effect of synergetic control in hybrid PV‐Wind system response

This paper presents a non-linear controller based in synergetic controller (SC) that used for Wind and PV systems to reduce the chattering phenomenon, tracks rapidly and maintain the Maximum Power Point (MPP) under different environmental and load conditions. To approve the effectiveness of the proposed approach, comparative analysis of MPPT controller built using Perturb and observation for PV system and torque vector for Wind power system, with MPPT controller implemented using synergetic control in the both renewable sources in the hybrid system. The results show that SC MPPT is robust and maintain the power balancing with meeting multiple objectives of standalone hybrid systems such as rapidity of response, robustness under the external variations and no chattering problem as compared with the other controllers.

The influence of engine gyroscopic moments on vehicle transient handling

This study presents the dynamics of a 15-DOF model of the vehicle by performing simulations to investigate the vehicle handling dynamics in J-turn maneuver. Using Newton’s equations of motion, the equations of motion for the sprung and unsprung masses are all written in the vehicle coordinate system and the tire is modeled with the Pacejka 89 model. Since the engine crankshaft has a rotation relative to the vehicle coordinate system, in order to investigate the effect of the engine gyroscopic moments on the vehicle handling dynamics, the effect of the crankshaft rotation on the torque vector of external forces is considered. The direction of crankshaft rotation can change the direction of engine rotation in the direction of the wheels rotation or in the opposite direction of their rotation, which causes some changes in the gyroscopic torque vector of the engine. Due to the rotation speed of the crankshaft and its moment of inertia, the gyroscopic moments which resulted from the angular momentum of the engine crankshaft are considerable. These gyroscopic moments are added to the torque equation of external forces in the vehicle coordinate system and affect the vehicle handling dynamics. By using the numerical method of Newmark, vehicle’s dynamic behavior is investigated and the validation of its dynamic behavior is done by ADAMS/Car software. This study shows that in transverse engine, if the direction of engine rotation is in the opposite direction of the wheels, the vehicle handling dynamics is improved.

Open GL–Open CL Solar Radiation Pressure Modeling with Time-Varying Spacecraft Geometries

A method for the fast computation of spacecraft force and torque due to solar radiation pressure (SRP) is presented. A faceted model is employed that tracks which elements of a time-varying geometry are exposed to the sunlight, but sunlight reflections are not modeled. The method uses the highly parallel execution capabilities of commodity graphics processing unit (GPU) and the Open Graphics Library (OpenGL) and Open Compute Language (OpenCL) to render a spacecraft mesh on the GPU. A custom-developed OpenGL render pipeline computes the per-model facet SRP forces and torques that are summed on the GPU before the resultant spacecraft force and torque vectors are copied back to the CPU bound process. The process is validated on spherical and cubic test shapes. The evaluation accommodates spacecraft self-shadowing and is capable of accounting for arbitrary spacecraft articulation. Material properties are encoded with the model to provide realistic specular, diffuse, and absorption surface light interactions. Numerical simulations illustrate the impact of geometric fidelity and articulated surfaces. The faceted OpenGL-OpenCL method is up to an order of magnitude faster on integrated GPU hardware than high-end graphics card as the process is not demanding on the GPU and benefits from the fast memory transfer of on-chip processors.

A New Solving Procedure for the Kelvin–Kirchhoff Equations in Case of a Falling Rotating Torus

We present a new solving procedure in this paper for Kelvin–Kirchhoff equations, considering the dynamics of a falling rigid rotating torus in an ideal incompressible fluid, assuming additionally the dynamical symmetry of rotation for the rotating body, [Formula: see text]. The fundamental law of angular momentum conservation is used for the aforementioned solving procedure. The system of Euler equations for the dynamics of torus rotation is explored for an analytic way of presentation of the approximated solution (where we consider the case of laminar flow at slow regime of torus rotation). The second finding is that the Stokes boundary layer phenomenon on the boundaries of the torus also assumed additionally at the formulation of basic Kelvin–Kirchhoff equations (for which the analytical expressions for the components of fluid’s torque vector [Formula: see text] were obtained earlier). The results for calculating the components of angular velocity [Formula: see text] should then be used for full solving the momentum equation of Kelvin–Kirchhoff system. The trajectories of motion can be divided into, preferably, three classes: zigzagging, helical spiral motion, and the chaotic regime of oscillations.

Simultaneous three-axis torque measurements of micromagnetism

Measurements of magnetic torque are most commonly preformed about a single axis or component of torque. Such measurements are very useful for hysteresis measurements of thin film structures in particular, where high shape anisotropy yields a near-proportionality of in-plane magnetic moment and the magnetic torque along the perpendicular in-plane axis. A technique to measure the full magnetic torque vector (three orthogonal torque components) on micro- and nano-scale magnetic materials is introduced. The method is demonstrated using a modified, single-paddle silicon-on-insulator resonant torque sensor. The mechanical compliances to all three orthogonal torque components are maximized by clamping the sensor at a single point. Mechanically-resonant AC torques are driven by an RF field containing a frequency component for each fundamental torsional mode of the device, and the resulting displacements read out through optical position-sensitive detection. Measurements are compared against micromagnetic simulations of mechanical torque to augment the interpretation of the signals. As an application example, simultaneous observations of hysteresis in the net magnetization along with the field-dependent in-plane anisotropy is highly beneficial for studies of exchange bias.

Sliding Mode Observer for Speed Sensorless Linear Induction Motor Drives

In this paper, a sliding mode observer (SMO) for the speed-sensorless direct torque vector control of linear induction motor(LIM) is proposed, considering the influence of dynamic end effects. The proposed SMO estimate the motor speed, the rotor flux, the angular position of the rotor flux, and the speed dependent parameter w, only by using the measured stator voltages and stator currents. The nonlinear sliding mode technique guarantees very good performance for different situations of motor speed. The proposed SMO does not use complicated observer gains and robust to the parameter variation over the full-speed range. Moreover, the convergence of SMO is proven by using the Lyapunov theory. Furthermore, LIM Drive state observability is presented with detailed analysis. The performance of the proposed SMO is verified by hardware-in-the-loop test (HIL) system. Furthermore, a comparative study with and Luenberger observer(LO) and model reference adaptive system(MRAS) is presented.

Interface-induced field-like optical spin torque in a ferromagnet/heavy metal heterostructure

Abstract The manipulation of magnetization in a metallic ferromagnet by using optical helicity has been much attracted attention for future opto-spintronic devices. The optical helicity–induced torques on the magnetization, optical spin torque, have been observed in ferromagnetic thin films recently. However, the interfacial effect of the optical spin torque in ferromagnet/nonmagnetic heavy metal heterostructures have not been addressed so far, which are widely utilized to efficiently control magnetization via electrical means. Here, we studied optical spin torque vectors in the ferromagnet/nonmagnetic heavy metal heterostructures and observed that in-plane field-like optical spin torque was significantly increased with decreasing ferromagnetic layer thicknesses. The interfacial field-like optical spin torque was explained by the optical Rashba–Edelstein effect caused by the structural inversion symmetry breaking. This work will aid in the efficient optical manipulation of thin film nanomagnets using optical helicity.

Satellite attitude control using a novel Constrained Magnetic Linear Quadratic Regulator

This paper addresses a novel Constrained Magnetic Linear Quadratic Regulator (CM-LQR) scheme that generates a control torque vector on a plane approximately perpendicular to the local geomagnetic field. This control torque nearly precisely guarantees the production of an equivalent mechanical torque. The main ideas in the proposed method are (1) excluding the actuator dynamics from the system dynamics, and (2) incorporating the designed dynamics in the problem formulation using an algebraic mathematical constraint. In this way, a common time-variant system is transformed into a time-invariant system. The proposed CM-LQR generates the control torque via adjusting a time-variant control weighting matrix according to the geomagnetic field feedback. Unlike previous methods, our proposed control torque has a negligible parallel projection to the local geomagnetic field, and thus, it can be utilized fully by the magnetorquers. The hybrid Genetic Algorithm (GA) and Sequential Quadratic Programming (SQP) methods are applied to find an optimum state weighting matrix. Moreover, numerical simulation is performed to evaluate the performance and agility of the closed-loop control system. In addition, the obtained results are compared with a conventional magnetic LQR attitude controller to confirm that the presented scheme results in more agility and lower steady-state error in the attitude maneuver of the magnetically actuated satellites.

Minimally Model-Based Trajectory Tracking and Variable Impedance Control of Flexible-Joint Robots

This article presents a novel control scheme that primarily provides a solution to the problem of simultaneously performing stable trajectory tracking and variable impedance control (VIC) of flexible-joint robots. The existing asymptotically stabilizing tracking controllers for compliant robots rely upon several model-based terms and their derivatives. Contrarily, the proposed minimally model-based trajectory tracking control scheme requires knowledge of only the gravitational torque vector model. Although interaction and tracking performance enhancements are achievable through VIC, its operation introduces energy injections, thereby impacting closed-loop stability/passivity. Existing VIC passivity preservation techniques deal exclusively with rigid-joint robots. To this end, the proposed method introduces the minimally model-based trajectory tracking variable impedance control scheme, which ensures passivity/stability when applying VIC to flexible-joint robots. Numerical and experimental results corroborate the controllers' efficacy in terms of realizing VIC interaction and tracking tasks, thus enabling flexible-joint robots to stably replicate biologically inspired behaviors.

Effect of the magnus force and torque on the projectile flight range

The paper considers the origin of the Magnus force and torque in the course of the projectile flight; analytical dependencies for their determination are given and justified. The mutual orientation of the Magnus force and angular torque vectors with respect to those of the drag and lift forces, as well as with respect to the stalling, polar quenching and equatorial damping torques acting on the projectile in flight is discussed. The effect of the Magnus force and torque on the firing characteristics of artillery systems is assessed. A mathematical model of the projectile flight is presented, as well as constraints that are imposed on it and that do not considerably affect the accuracy of the description of the spatial motion of the projectile. The mathematical model is implemented programmatically on the basis of a standard subroutine for numerical integration of differential equations written in the Maple software and contains the motion equations for the projectile mass center, the motion equations with respect to the projectile mass center and equations that allow one to determine the coordinates of the projectile fall points in the base reference system. To assess the effect of Magnus force and torque on the projectile flight range, the difference method is employed, which consists in solving the system of differential equations of the spatial motion of the projectile such that changing the magnitude of the Magnus force and torque (at the assumption of the constancy of the aerodynamic forces and torques), one obtains the variation in the projectile flight range. A protocol and a scheme for assessing the effect of deviation of the projectile range on the accuracy of determination of the Magnus force strength and torque, as well as the results of numerical simulation of the deviation of the flight range for the ОФ-462Ж projectile of the 122-mm howitzer Д-30 depending on the accuracy of determination of aerodynamic force coefficients and Magnus torque are presented. It is shown that the largest deviations in the projectile flight range are observed when shooting at large launching angles and full charge (projectile speed 690 m / s); the smallest corresponding values are observed for the fourth charge (projectile speed 276 m / s) at small launching angles.

A new variant of the B-dot control for spacecraft magnetic detumbling

With using the B-dot control law for magnetic detumbling, there will be no need for angular velocity measurements. The B-dot control law is a torque projection-based controller, however, it is not guaranteed to have the dipole moment orthogonal to the magnetic field, especially as the angular velocity gets smaller during detumbling, resulting in a suboptimal torque vector. This paper presents a new variant of the B-dot control. By computing an equivalent angular velocity, based on the magnetic field data, it is possible to develop a control law that guarantees the magnetic dipole moment to remain in the plane orthogonal to the ambient magnetic field. Using Monte Carlo simulations, the proposed B-dot control is compared to two other variants of B-dot control laws: a simple B-dot control and a recent variable gain B-dot control. The results show that the proposed B-dot control outperforms the other B-dot control laws in terms of the speed of detumbling and the power consumption.

Solving procedure for the Kelvin–Kirchhoff equations in case of buoyant (or the falling) ellipsoid of rotation

We have presented in this communication a new solving procedure for Kelvin–Kirchhoff equations, considering the dynamics of rising the quasi-rigid ellipsoid of rotation in an ideal incompressible fluid (up to the surface), assuming additionally the dynamical symmetry of rotation for the rising body, I1=I2. Fundamental law of angular momentum conservation has been used for the aforementioned solving procedure. The system of Euler equations for dynamics of non-rigid ellipsoid rotation has been explored in regard to the existence of an analytic way of presentation for the approximated solution (where we suppose that components of fluid’s torque vector {Ti} are approximately proportional to the appropriate components of angular velocity {Ωi}). The results of calculations for the components of angular velocity {Ωi} should then be used for solving momentum equation of Kelvin–Kirchhoff system. Thus, the full system of equations of Kelvin–Kirchhoff problem has been explored with respect to the existence of an analytic way of presentation of the general solution. The last but not least, we have pointed out the 1-st integral of Kelvin–Kirchhoff system under the aforesaid additional assumption for fluid’s torque vector {Ti} when {Ii} = const (but without the additional restriction of dynamical symmetry onto the form of the rising body, I1=I2).

Optimal Reference Frame Angle Approach for Air-Gap Flux Minimization in Dual Stator Winding Induction Machines

Dual stator winding induction machines (DSWIMs), which have two sets of three-phase windings with unequal pole pairs in their stator and a standard squirrel cage rotor, have overcame the narrow speed operation region and circulating current problems exists in other types of dual winding machines. These advantages are resulted from the independent operation of their winding sets. The independent operation of winding sets will be guaranteed if the flux saturation is avoided. This letter proposes a novel reference frame angle determination technique that not only guarantees the flux saturation avoidance but also results in flux optimization in DSWIMs. Despite pervious methods, the proposed method does not require position or speed sensor and it is easily applicable in various control schemes and in different reference frames. This method is implemented in a flux and torque vector control system for driving a 3.3 kW DSWIM. The experimental results confirm the effectiveness of the proposed method. Moreover, by implementing the proposed method, the torque sharing between the two winding sets is properly done according to the power rating of each of them.

A Simplified Method for Dynamic Equation of Robot in Generalized Coordinate System

This paper presents a simplified method of dynamic equations in a generalized coordinate system, which decouples the relative motion of the front and back links of the robot joint, and maps generalized angular variables to the same angular datum. Because of the decoupling between absolute angle variables, the complexity of the coefficient matrix of the dynamic equation of the system is reduced, which facilitates the application of the actual series robot system. The simplified process is derived in detail, and the equivalent relation between the generalized relative coordinates and the generalized absolute coordinate dynamics is demonstrated. The relation can be extended to the dynamic equations of different generalized coordinate variables. Aimed at the problem that the quasi-input moment vectors obtained in generalized absolute coordinates cannot be directly used without considering the dynamic coupling of the whole system, the linear relationship between the input moment vectors in absolute and relative coordinates is found. In the end, a simplified example of the Euler-Lagrange dynamic equation for multi-degree-of-freedom manipulator is given. The relationship between the two input torque vectors is simulated by MATLAB and verifies that the input torque can be indirectly calculated by finding the quasi input torque under the absolute coordinates.