Initial Angular Position Research Articles

Послідовне встановлення двох двигунів внутрішнього згоряння на автомобілі як метод зниження нерівномірності крутного моменту

An analysis of studies on the possibility of reducing fuel consumption of cars by replacing their power plants with two internal combustion engines installed in series is carried out. It has been determined that it is possible to reduce fuel consumption by reducing the unevenness of torque at the transmission input shaft, which in turn depends on the relative angular orientation of the crankshafts of the installed internal combustion engines. The study has determined that when installing two consecutive internal combustion engines, each of which generates an indicator torque that obeys the harmonic law, it makes it possible to shift the curves of the indicator torque and the crankshaft angle so that both engines operate in opposite phases. It is proposed to use a method of increasing the energy efficiency of cars by using two consecutive internal combustion engines, the crankshafts of which are installed relative to their initial angular position with the difference in the angular coordinates (angles of rotation) of the crankshafts of both engines relative to the initial position, which allows to reduce unproductive energy losses. Approximating the actual curves of change of the indicator torque by the harmonic law, taking into account the angle of rotation of the crankshaft, graphs of dependence of the indicator torque on the angle of rotation of the crankshaft of four-stroke internal combustion engines with different numbers of cylinders are constructed. It has been determined that with an increase in the number of cylinders of an internal combustion engine and the coefficient of the share of torque on the drive wheels, there is a decrease in the coefficient of unproductive energy consumption, which takes into account the influence of the unevenness of the indicator torque. The problem of ensuring the operation of the second engine in the counterphase of the first engine is solved, which should be fulfilled by the ratio of the angles of rotation of the crankshafts of the first and second engines relative to the initial (zero) position with the difference in the angular coordinates (angles of rotation) of the crankshafts of both engines relative to the initial position. The results of calculating the angle of the crankshafts' relative position when two internal combustion engines are installed sequentially in the opposite phase indicate a decrease in this angle with an increase in the number of cylinders.

On the dynamics and wakes of a freely settling Platonic polyhedron in a quiescent Newtonian fluid

We investigate systematically the free settling of a single Platonic polyhedron in an unbounded domain filled with an otherwise quiescent Newtonian fluid. We consider a particle–fluid density mimicking a rock in water. Five Platonic polyhedrons of increasing sphericity are studied for a range of Galileo numbers $10 \leqslant \mathcal {G}a \leqslant 300$ . We construct a regime map in the parameter space of Galileo number and particle volume fraction ( $\mathcal {G}a, \phi$ ), highlighting how the angularity of the Platonic polyhedron impacts its settling path and the onset of instabilities. We find that the initial angular position solely affects the transient settling process. All the Platonic polyhedrons maintain a stable settling angular position at low $\mathcal {G}a$ . Higher angularity leads to path unsteadiness at lower $\mathcal {G}a$ . Path instability progresses from steady vertical to unsteady vertical, followed by oblique settling observed for highly spherical particles, but helical settling (HS) for more angular particles. The particle autorotation is found to be the pivotal factor influencing path instability and the regime transition of angular particles. Beginning in the unsteady oblique and helical regimes, particle autorotation becomes more prevalent, escalating further in the chaotic regime as $\mathcal {G}a$ increases. The particle angular velocity vector is shown to be predominantly situated in the horizontal plane. A thorough force balance in the horizontal plane reveals that the Magnus force is the primary driving force of the HS regime. Additionally, we establish two new empirical correlations to predict the particle settling velocity and the disturbed wake length that solely require the physical properties of the system ( $\mathcal {G}a$ and $\phi$ ). Our numerical results suggest that an increase of the density ratio from $2$ to $3$ exerts only a marginal impact on the path instability of the most angular particle, the settling tetrahedron.

A contribution to the investigation of acoustic interferences in aircraft distributed propulsion

The objective of this work is to better understand the acoustic interferences created by distributed propulsion engines based on an approach that combines RANS simulation results for the aerodynamic prediction and analytical models to calculate acoustics. A multi-propeller configuration without wing is considered for this investigation. The propeller geometry and the operating conditions are realistic for a regional transport airplane. In the first part of the paper, the results obtained by two different and independent prediction methods are compared. One method is well-established and serves as validation for the second, low-order method, which is better suited for design-to-noise applications since it requires less details as input and is computationally faster by several orders of magnitude. The good agreement between both methods, obtained for a single propeller as well as for the distributed propeller configuration, is exploited in the second part of the paper to investigate the role of acoustic interferences. Taking acoustic interferences into account drastically affects the directivity of the tonal emission. Compared to the results obtained by considering the propellers as if they were uncorrelated, the far-field sound pressure levels can be significantly lower at the radiation nodes or amplified up to the theoretical limit of 9 dB calculated for eight propellers. The directivity patterns depend on the relative initial angular positions of the propellers. When these positions are randomly varied according to the uniform probability density distribution model, the mean result (expectation) is the same as if the propellers were considered as uncorrelated. Finally, the results show that the probability that the acoustic level is lower than the mean value is higher than 50% because of the positive skewness of the probability distribution of the resulting pressure amplitude. Even though the propeller–propeller and propeller–wing interactions were not considered, the essence of the findings is expected to remain valid for more complex configurations because those interactions are rotor phase-locked.

MATHEMATICAL MODEL OF THE DEPENDENCE OF THE STARTING TORQUE OF AN ASYNCHRONOUS ELECTRICAL MOTOR ON THE INITIAL ANGULAR POSITION OF THE ROTOR

The current trend of recent decades is the growing role of the automated electric drive built on the basis of asynchronous electric motors. This is connected both with the development of theoretical approaches that allow to model the behavior of the latter with high accuracy, and with a significant increase in reliability and a decrease in the cost of power semiconductor technology, which in turn made it possible to improve operational characteristics and reduce the cost of such systems as a whole. The consequence of this trend is that asynchronous motors are increasingly used not only in classic electric drive systems with easy starting conditions, but also increasingly used in traction electric drives and electric drives with large starting moments, which were traditionally implemented on the basis of direct current motors. This circumstance leads to the appearance of additional technical difficulties in the design and operation of asynchronous electric motors, which is associated with the peculiarities of their natural mechanical characteristics, which have a slightly underestimated value of the starting torque. And although this shortcoming can be eliminated by increasing the power reserve of the engine when designing the electric drive, such a compromise solution will have significant disadvantages associated with a decrease in efficiency and an increase in the cost of the electric drive as a whole. It is obvious that this circumstance determines the need for further theoretical research aimed at improving the starting characteristics of asynchronous motors. Considering what has been said, today the induction motor remains the most common electric machine used in various fields of activity. Moreover, the share of asynchronous motors used in industry is growing rapidly, and the scope of their use is constantly expanding. A. therefore, the development of a mathematical model of the dependence of the starting torque on the angular position of the rotor, which in the future would allow improving the starting characteristics of asynchronous motors, is an urgent scientific and applied problem that has significant practical value. In the article, the equation of the dependence of the starting torque of an asynchronous motor on the initial position of its rotor is obtained, which makes it possible, taking into account the design features of the AD, to uniquely calculate the value of the mechanical torque that occurs on the motor shaft when it is started with the nominal supply voltage. The mathematical dependence of the deviation of the AD starting moment on the initial rotation angle of the rotor was obtained, which can be used as a corrective mathematical model of the AD control system. The simulation of the dependence of the torque of an asynchronous motor on the initial position of its rotor was carried out, which made it possible to confirm the adequacy of the obtained mathematical dependence. It is shown that the change of the starting torque during rotation of the AD rotor occurs according to the sinusoidal law. It is theoretically proven that deviations of the starting torque at different initial angular positions of the rotor can reach ± 6.5% of the nominal value.

Nonlinear, Rate-Dependent Evaluation of Flight Damping Derivatives of the Orion Crew Module

In the continued development of the Orion crew module, NASA is challenged with characterizing and predicting static and dynamic stability during the atmospheric reentry of the capsule. A thorough understanding of the aerodynamic behavior of the crew module in the subsonic regime is essential for safe return, as this flight regime presents the largest dynamic instability recently demonstrated by the Ascent Abort-2 (AA2) flight test. Forced oscillation wind-tunnel tests were conducted with varying frequency, amplitude, and offset angles to determine the rate-dependent static and dynamic derivatives. A novel data reduction technique was employed to obtain a nonlinear representation of the damping derivatives of the capsule as a function of both its angular position and rate from the aerodynamic force/moment measurements. Finally, a nonlinear, second-order model, two-degree-of-freedom ordinary differential equation was formulated to predict the response of the crew module based on initial angular positions, and , and angular rates, and . The accuracy of the model was assessed through direct comparisons with the NASA Ascent Abort-2 flight test. Through benchmark comparisons against the AA2 flight-test data and rate-invariant models, the utility of the second-order model was proven, establishing a low-cost, computationally efficient manner of predicting crew module motion and stability that could be leveraged in flight to improve guidance and navigation control algorithms.

Mechanisms kinematic analysis by geometric and computational approach

The kinematics of a four-bar mechanism and others extern elements using one developed method is investigated. The basic four bar mechanism is coupled with a sliding element in a straight line and another sliding element guided by a straight line coupled to a rotating connection. The positions, speeds and accelerations are investigated in the full possible cycle. The PC and the Excel spreadsheet are used for the kinematic solution and simulation of the mechanical system. The kinematic analysis is performed considering specified the initial and end angular positions of the input bar, with an established angular increment. The method used allowed to verify the kinematic of the mechanism with precision and also the working simulation and the visualization, making it a viable alternative and allowing the information of the results.

Deep reinforcement learning for active control of flow over a circular cylinder with rotational oscillations

An active control strategy for flow over a circular cylinder with rotational oscillations is automatically learned based on a deep reinforcement learning algorithm. Specifically, the proximal policy optimization is used to minimize the averaged drag coefficient of cylinder by properly selecting the rotational angular velocity. The data for training is sampled by direct numerical simulation of flow past a rotational circular cylinder, which is recognized by the immersed boundary method and the active control is applied to the flow in real time. The flow configurations are observed by the detecting probes located inside them and modified by the agent of deep reinforcement learning through changing the angular velocity with time. After several episodes of training, the reinforcement learning agent is shown to discover a robust and convergent control strategy, by which the cylinder is able to choose an appropriate rotational angular velocity to modify the wake based on its observation of the instantaneous flow field, resulting in a substantial drag reduction. The network architecture is tested at different Reynolds numbers, i.e. 100, 200 and 300, and drag reduction rates of 10%, 19% and 21% are obtained, respectively. Effects of initial flow field and angular velocity, position and number of detecting probes and hyper-parameters of the deep reinforcement learning architecture are also examined.

Dynamic Problem of Optimal Control of Spacecraft Attitude under Restriction on Phase Variables

An analytical solution to the optimal control problem of spacecraft reorientation from an arbitrary initial angular position into a required final angular position under the restrictions on control functions and phase variables is presented (the controlling moment and angular velocity are restricted). Time of slew maneuver is minimized. The specific case was considered when maximum admissible kinetic energy of rotation is significant restriction. Constructing the optimal control of reorientation is based on Pontryagin’s maximum principle and the quaternionic variables and models. It is shown that optimal mode is piecewise-continuous control when a direction of spacecraft’s angular momentum is constant relative to the inertial coordinate system during rotation of a spacecraft; for a per forming an optimal turn, the moment of forces is parallel to a straight line fixed in inertial space. Two types of optimal control are possible depending on the given initial and final positions and spacecraft’s moments of inertia — relay control with one switching point when the controlling moment is maximal over the entire time interval of control (segments of acceleration and braking), and relay control with two switching point consisting of intensive acceleration, motion by inertia with the absented moment and an exit onto restriction of rotation energy, and then final braking with the maximum controlling moment. The analytical equations and relations for a finding the optimal control program are written down. The calculation formulas for determining the time characteristics of maneuver and computing a duration of acceleration and braking are given. The proposed algorithm of control provides maximally fast implementation of spacecraft reorientation under the limited kinetic energy of rotation. For an axially symmetric solid body (spacecraft), the optimal control problem, in dynamical statement, was solved completely — we obtained the dependences as explicit functions of time for the control variables, and relations for calculating the key parameters of the law of control are derived. The numerical example and results of mathematical simulation of spacecraft motion under the optimal control are presented, demonstrating the practical feasibility of the developed method for control of spacecraft attitude.

Design of an Adaptive Super-Twisting Control for the Cart-Pole Inverted Pendulum System

A cart-pole inverted pendulum system is one of the underactuated systems that has been used in many applications. This research aims to study the design and the effectiveness of the Adaptive Super-Twisting controller to stabilize the system by comparing it with other previous control methods. A stabilization control of the pendulum upright using the Adaptive Super-Twisting algorithm (ASTA), was investigated. The proposed controller was designed based on the decoupling algorithm method to solve the coupled control input in the system model. We then compared the proposed stabilizing controller with first-order sliding mode control (FOSMC) and Super-Twisting algorithm (STA) in Matlab/Simulink simulation and realistic computer simulation. We developed the computer simulation using anyKode Marilou software, which adopted Open-Dynamic Engine (ODE) as a physics engine. In Matlab/Simulink simulation, we considered three different scenarios: a nominal system, a system with uncertainty, and a disturbed system. Meanwhile, in a computer simulation, we only presented the comparison of different controllers' performances for the realized system. Both results showed that the three controllers could stabilize the pendulum upright with a 0.1 rad initial angular position around the vertical axis. Under the same conditions, the ASTA and STA controllers had similar performances; they both have less chattering and faster convergence than the FOSMC approach. However, the FOSMC approach had the least energy delivered and smallest errors than the other two approaches.

Razlike između konvencionalne i sumo varijante tehnike mrtvog dizanja - kinematička, kinetička i elektromiografska studija

Deadlift is a measure of the overall strength of the whole body and it is one of the three exercises in the powerlifting competition. There are conventional and sumo variant of deadlift. The aim of this study was to determine the differences between the two lifting techniques from the aspect of kinematics, kinetics and electromyography. Nine physically active men, average age 29.1 ± 3.3 years, body height 181.0 ± 1.0 cm, body weight 82.3 ± 13.3 kg and body massindex 25.0 ± 3.8 kg/m2 were recruited forthisstudy. Each subject lifted weight close to his own body weight with three repetitions, in three series, for each of the techniques. The speed of one lift was 3 seconds for each of the phases (concentric and eccentric). The angles and amplitudes for the following figurative points were monitored: trunk in relation to the horizontal plane (angle), center of the hip joint and center of the knee joint in the "liftoff" (LO - position in which the weight separates from the ground) and "knee passing" (KP - position in which the weight passes in front of the knee position), i.e. in the liftoff-knee passing (LO-KP), knee passing-lift completion (KP-LC; LC - final, i.e. completely upright body position) and liftoff-lift completion (LOLC) phase. The mechanical work was monitored as a one of the kinetic variables. Electromyographic activity was monitored for the following muscles: m. vastus medialis, m. vastus lateralis, m. rectus femoris, m. gluteus Maximus, m. erector spinae (L3-L4), m. semimembranosus and m. biceps femoris caput longum. The monitored electromyographic variablewasthe average normalized amount of muscle activation in relation to maximal voluntary contraction, for all 18 individual deadlift repetitions (3 series × 3 repetitions × 2 techniques). One-way analysis of variance with repeated measurements (for the amount of muscle activation and performed mechanical work) and two-way analysis of variance with repeated measurements (for angles and amplitudes) were used for statistical data processing. Significant differences were found between techniques in the initial angular positions in all monitored joints (p<0.05), except for the angle in the knee joint where the trend was observed (p=0.0996), as well as in the transit position for the trunk angle relative to the horizontal plane and angle at the hip joint (p<0.05). There was a statistically significant difference between techniques in amplitudes in the hip joint during KP-LC phase (p<0.05) and total amplitude (p<0.05), as well as in the knee joint during LO-KP phase (p<0.05) and total amplitude in the form of a trend (p=0.0996). The performed mechanical work is significantly higher when lifting the load with the conventional deadlift technique (DLcon) (p<0.05). Activation of medial and lateral heads of m. quadriceps femoris is significantly higher (p<0.05) when lifting with sumo deadlift technique (DLsu). It was noticed that activation of postural muscle groups (m. erector spinae, m. gluteus maximum, m. semitendinosus and m. biceps femoris caput longum) is higher when lifting the load with DLcon, but not significantly (p>0.05).

On Improving the Maneuverability of a Space Vehicle Managed by Inertial Executive Bodies

The problem of increasing the maneuverability of a spacecraft (SC) by minimizing the duration of rotations around the center of mass is solved. The case is studied when the orientation is controlled using inertial actuators (power gyroscopes, gyrodynamics). The problem of the fastest possible turn of an SC using gyrodynes from an arbitrary initial angular position to the desired final angular position is considered in detail. Using the maximum principle of L.S. Pontryagin, as well as quaternion models and methods for solving the problems of controlling the motion of an SC, a solution to the problem is obtained. The conditions of the optimality of the reorientation mode without unloading the gyrosystem are written in an analytical form and the properties of the optimal motion are studied. Formalized equations and calculation expressions are presented for constructing an optimal control program taking into account the possible perturbations. The key relationships that determine the optimal values of the parameters of the rotation control law are given. The results of mathematical modeling of the motion of an SC with the optimal control are presented, demonstrating the practical feasibility of the developed algorithm for controlling the spatial orientation of an SC. A condition is formulated for determining the moment of the start of braking from measurements of the current motion parameters, which significantly increases the accuracy of bringing an SC into a predetermined resting position in the presence of restrictions on the control moment.

Effects of Attitude Parameterization Methods on Attitude Controller Performance

This paper intends to compare the effect of the attitude parameterization method on the performance of the attitude controller designed with the direct feedback of corresponding attitude states. To achieve this, the proportional-derivative controllers using the finite rotation angles and the modified Rodrigues parameters are designed with the same structure and equivalent performance of the direct quaternion-feedback control. It has been demonstrated through a series of comparative analyses that three different parameterization methods can be commonly used in designing their direct feedbacks for the spacecraft’s attitude control. Next, the effects of the nonlinear transform relations among three parameterizations are thoroughly investigated through the controller-response analyses for an eigen-axis rest-to-rest maneuver with varying the initial angular position. The controller designed with the finite rotation angles shows a consistent performance regardless of the initial angular position. Whereas, those using other two methods show large variations in their response characteristics. From the results, it can be concluded that the direct feedback controller designed with the finite rotation angles outperforms those using the modified Rodrigues parameters or the quaternion, especially when the spacecraft experiences an aggressive maneuver or has a wide operating range of the attitude.

Bringing spacecraft into solar-oriented attitude by the measurements of a single-axis angular-rate sensor and an optical solar sensor

The algorithm of the turn of the spacecraft from an initial arbitrary angular position at an arbitrary angular rate to a solar-oriented attitude is investigated. Minimum essential equipment of the motion control system required for the purpose of ensuring maintenance of solar orientation is defined: a solar sensor, a single-axis angular-rate sensor, low-thrust liquid rocket engines. A solution of the problem of defining the spacecraft angular rate vector by the measurements of the deviation of the optical axis of the solar sensor from the sun vector and the single-axis angular-rate sensor is presented. The conditions under which control action on the rocket engines for the purpose of changing the value of the angular-rate vector for the Sun to get into the field of viewing of the solar sensor or for the spacecraft stabilization are defined. Mathematical modeling of the spacecraft attitude control system with the unknown initial state vector of motion is carried out. The results of mathematical modeling confirmed the efficiency of the proposed algorithm in terms of reducing propellant fuel consumption and high-speed performance. In comparison with the known methods of solving the problem of reducing angular speed (a lengthy process with the use of a magnetic system or a fast process with the use of a three-axis angular-rate sensor and rocket engines) the duration of the process of reducing angular speeds is the same as in normal operation, however, at the same time the problem of bringing spacecraft into the solar oriented attitude is solved.

An Embedded Strategy for Online Identification of PMSM Parameters and Sensorless Control

A sensorless speed tracking control for permanent magnet synchronous motors has been considered in this paper. In particular, a set of polynomial equations is derived from the output of the electrical subsystem in order to compute online the motor parameters and the initial angular position of the rotor. Then, a sliding mode-based control strategy, coupled with an observer using only electrical signals, guarantees the robust asymptotical tracking of a reference speed without measuring rotor velocity and position. The proposed approach has been experimentally tested on an embedded board.

Synthesis of the Optimal Control of the Spacecraft Orientation Using Combined Criteria of Quality

The dynamic problem of a spacecraft’s (SC) rotation from an arbitrary initial angular position to a given final angular position is considered and solved. The case is investigated when the control is limited, and the minimized functional combines, in a given, proportion, the time of the maneuver and the integral of the energy of rotation. The construction of the optimal control is based on the quaternionic differential equation relating the vector of the angular momentum of the SC with the quaternion of the orientation of the body-related coordinate system. The control law is formulated in the form of an explicit dependence of the control variables on the phase coordinates. The analysis of the special control regime of the SC is carried out. Based on the conditions of transversality, as the necessary conditions for optimality, the optimal value of the kinetic energy of rotation when moving in a special control regime is determined. The created control algorithms allow turning of an SC with a kinetic rotation energy, which does exceed a predetermined level. For a dynamically symmetric SC, the problem of spatial reorientation is solved completely. The results of the mathematical modeling of the motion of an SC under the optimal control are presented, demonstrating the practical feasibility of the developed algorithm for controlling the spatial orientation of the SC.

Effects of Elastic Hinges on Input Torque Requirements for a Motorized Indirect-Driven Flapping-Wing Compliant Transmission Mechanism

This paper presents compliant transmission mechanisms for a flapping-wing micro air vehicle. The purpose of this mechanism is to reduce power consumption, a critical issue in this kind of vehicles, as well as to minimize the peak input torque required by the driving motor, which helps to maintain flight stability and reduces mechanical shocks of the structure. We first describe the development of pseudo-rigid-body model of the mechanism and the analysis of the corresponding kinematics. Second, we compute the required input torque for driving stable flapping motions, from the perspectives of work and energy. For this computation, two methods are applied, one based on the principle of virtual work and another one based on rigid-body dynamics. Our mathematical analysis demonstrates that both methods are consistent with each other in terms of the resulting input torque from the motor. Finally, according to the results from the input torque analysis, the main parameters characterizing the compliant joints, the torsional stiffness of virtual spring and initial neutral angular position, are optimized. The experimental results carried out with two different mechanical setups, one with rigid components, and another one with flexible components, demonstrate the relationship between the input voltage (that is directly related to flapping frequency) and power saving of the compliant mechanism. The average power consumption is reduced of up to 4%, and peak power consumption is reduced up to 25% using the compliant transmission mechanisms compared to the rigid mechanism. The experiments also show a clear relationship between flapping frequency and power savings.

Analytical study of starting current of the induction motor stator

In a three-phase coordinate system, the induction motor is described by a system of nonlinear differential equations of the eighth order, which in a general case does not have an analytical solution. The system of IM equations can be considerably simplified for the starting mode with a stationary rotor. When analyzing the specified operating mode, periodic coefficients in the IM equations that depend on the angular position of the rotor are transformed into constant magnitudes. Further simplification of the system of IM equations implies the exclusion of motion equations, which is also associated with the accepted assumption about the immobility of the rotor. We assume that the stator of IM is connected to a power line according to the circuit without a zero wire. This makes it possible to exclude from the common system two equations of electrical equilibrium of the windings, for one stator and one rotor winding, by applying the Kirchhoff's first law. As a result of the performed transformations, we obtained a simplified system of IM equations with a stationary rotor, which, in contrast to the complete system, is a system of linear differential equations of the fourth order and is presented in the Cauchy form, which can be solved analytically. Using the methods of analysis of dynamic objects in a state space, we obtained expressions for the coefficients of IM characteristic equation and its roots, as well as for the matrix of IM transfer functions when the rotor is stationary. An analysis of expressions for the roots of the characteristic equation shows that the character of roots of the IM characteristic equation depends on the initial angular position of the IM rotor. This is explained by the fact that a change in the initial angular position of the rotor changes the magnitude of mutual inductance between separate windings of IM, which affects the processes of energy transfer between stator and rotor windings.

Quadratic Optimal Control in Reorienting a Spacecraft in a Fixed Time Period in a Dynamic Problem Statement

A dynamic problem of a spacecraft (SC) turning from an arbitrary initial angular position to the required final angular position is considered and solved. The termination time of the maneuver is known. To optimize the turn control program, the quadratic criterion of quality is used; the minimized functional characterizes the energy consumption. The construction of the optimal control of the turn is based on quaternion variables and Pontryagin’s maximum principle. It is shown that during the optimal turn, the moment of forces is parallel to a straight line immobile in space and the angular momentum direction in the rotation process of the SC is constant relative to the inertial coordinate system. The formalized equations and calculation expressions to determine the optimal turn program are obtained. For a dynamically symmetric SC, a complete solution to the reorientation problem in the closed form is given. An example and results of the mathematical simulation of the dynamics of the SC’s motion under the optimal control are presented, which demonstrate the practical feasibility of the developed method to control the SC’s attitude.

Theory of Kinematic Motion Control of a Rigid Body

The authors present a review of the works on the theory of kinematic control of the rotational (angular) motion of a rigid body and spatial motion of a free rigid body, which is a composition of the rotational and translational (trajectory) movements of a rigid body. The theory is based on the use of the quaternion and biquaternion kinematic models of the rigid body motion. They also provide a review of the papers devoted to the problems of construction of the optimal laws of change of the angular momentum of a dynamically symmetric rigid body and rigid body with an arbitrary mass distribution, which ensures its optimal translation from an arbitrary initial angular position to the desired final angular position. These tasks occupy an intermediate position between the kinematic and dynamic problems of control of the rotational rigid body motion and play an important role in the theory of control of orientation of the spacecraft using the rotating flywheels. The theory of kinematic motion control has various topical applications in the space flight mechanics, inertial navigation, and mechanics of robotics.

Nonlinear parameter estimation using polynomials and resultants – Application to electrical drives

This paper proposes the use of algebraic geometry tools, i.e. resultants, for the estimation of uncertainties in a nonlinear system. With the focus on the case-study of electrical drives, an algorithm based on the solution of polynomial equalities obtained by processing the system outputs is shown to be capable to accurately reconstruct the motor resistance and initial angular position in finite time using only the measurement of the currents. Moreover, the procedure to extend the method for handling more challenging scenarios or dealing with other types of systems is provided.