Decomposition Of Space Research Articles

Modelling and vector control of dual three‐phase PMSM with one‐phase open

This study proposes a generic mathematical modelling and decoupling fault-tolerant vector control for dual three-phase permanent magnet synchronous machine (PMSM) with one phase open based on the conventional dual three-phase voltage source inverters, accounting for the mutual coupling between two sets of three-phase windings and the second harmonic inductance. When the dual three-phase PMSM has one phase open, the permanent flux-linkages are asymmetric and there are second harmonic components in the conventional synchronous reference frame (dq-frame). Based on the proposed mathematical modelling, both permanent magnet flux-linkages and currents become DC values in the dq-frame, and therefore, the conventional proportional integral (PI) controller can be used to regulate the dq-axis currents. Then, a decoupling fault-tolerant vector control with/without a dedicated feed-forward compensation is proposed to validate the correctness of the proposed mathematical modelling. Experimental results on a prototype dual three-phase PMSM with one phase open show that the second harmonic dq-axis currents can be well suppressed simply by the conventional PI controller and dedicated feed-forward compensation. It also shows that the decoupling fault-tolerant control based on the proposed modelling and control method has excellent dynamic performance, which is equivalent to the vector space decomposition control for the healthy machine.

Investigating teachers' enactment of engineering design practices in a CAD simulation‐enhanced learning environment

AbstractEngineering design problems are ill‐structured, and as a result, learners find it challenging to engage productively in relevant practices of analysis, synthesis, and evaluation for solving problems in the domain. Teachers find it particularly difficult to effectively support such engagement. Thus, there is a need to understand how teachers orchestrate their classrooms for maximizing opportunities for students to engage in these practices. In this paper, we use the case study methodology to investigate how teachers materialize and enact engineering design practices in a CAD simulation‐enhanced learning environment. Three teachers (cases) provide evidence for the following orchestration techniques—scaffolding development of students' expertise via teacher‐guided decomposition of problem space, apriori teacher‐led parameter determination, and student‐generated contrasting cases. These techniques scaffolded students' engagement in engineering design practices in all three cases. Common themes across the three cases—problem decomposition, modeling of expert practices, and facilitating students' active involvement—revealed a combination of pedagogical strategies that were interconnected and made evident through the cognitive apprenticeship model. The strategies suggest the integration of types of knowledge and engineering practices required for effective apprenticeships in similar contexts.

P-Schatten commutators of projections

Let $${\mathcal {H}}={\mathcal {H}}_+\oplus {\mathcal {H}}_-$$ be a fixed orthogonal decomposition of the complex separable Hilbert space $${\mathcal {H}}$$ in two infinite-dimensional subspaces. We study the geometry of the set $${\mathcal {P}}^p$$ of selfadjoint projections in the Banach algebra $${\mathcal {A}}^p=\{A\in {\mathcal {B}}({\mathcal {H}}): [A,E_+]\in {\mathcal {B}}_p({\mathcal {H}})\},$$ where $$E_+$$ is the projection onto $${\mathcal {H}}_+$$ and $${\mathcal {B}}_p({\mathcal {H}})$$ is the Schatten ideal of p-summable operators ( $$1\le p <\infty$$ ). The norm in $${\mathcal {A}}^p$$ is defined in terms of the norms of the matrix entries of the operators given by the above decomposition. The space $${\mathcal {P}}^p$$ is shown to be a differentiable $$C^\infty$$ submanifold of $${\mathcal {A}}^p$$ , and a homogeneous space of the group of unitary operators in $${\mathcal {A}}^p$$ . The connected components of $${\mathcal {P}}^p$$ are characterized, by means of a partition of $${\mathcal {P}}^p$$ in nine classes, four discrete classes, and five essential classes: (1) the first two corresponding to finite rank or co-rank, with the connected components parametrized by these ranks; (2) the next two discrete classes carrying a Fredholm index, which parametrizes their components; (3) the remaining essential classes, which are connected.

Switching-Table-Based Direct Torque Control of Dual Three-Phase PMSMs With Closed-Loop Current Harmonics Compensation

In this article, the new closed-loop current harmonics compensation strategy is introduced in the switching-table-based direct torque control (ST-DTC) of dual three-phase permanent magnet synchronous machines. The harmonic current distortion is the major problem of ST-DTC of multiphase machines and is typically caused by the lack of control in the auxiliary x-y subspace under the vector space decomposition model. The synthetic vectors to obtain average zero voltage in the x-y subspace can be a solution. However, this cannot compensate for current harmonics; for example, due to dead-time and back-electromotive force distortion, which is also mapped into the x-y subspace. Therefore, in this article, the x-y voltage references are obtained by the closed control loop that controls x-y currents to zero. To modulate the nonzero x-y voltage reference, the new modulation approach employing voltage vector groups in the x-y subspace together with the new switching table is developed and incorporated into ST-DTC. Meanwhile, the analysis of the two available sets of 12 voltage vector groups illustrates a tradeoff between linear range in the x-y subspace and the dc-link voltage utilization rate. Finally, the effectiveness of the proposed ST-DTC strategy is verified through experiments and simulation.

Study on Collision Detection and Force Feedback Algorithm in Virtual Surgery.

The development of virtual reality technology is expected to solve traditional surgical training. The lack of methods has brought revolutionary advances in technology. The virtual surgery system based on collision detection and force feedback can enable the operator to have stronger interaction, which is an exploration of the feature of touch in virtual reality technology. Reality is an important indicator of the virtual surgical system. This article improves the realism of the system from the visual and tactile senses and uses the surrounding ball collision detection and force feedback algorithms to build a realistic surgical platform. In the virtual surgery training system, the introduction of force feedback greatly improves the sense of presence during virtual surgery interaction. The operator can feel the softness and hardness of different tissues and organs through the force feedback device. Virtual reality is an interdisciplinary comprehensive technology that has been widely used in military, film, medical, and gaming fields. Virtual reality can simulate the objective world and display it visually, making people feel immersive. Virtual surgery provides surgeons with a recyclable surgical practice platform and can help doctors perform preoperative rehearsals and predict the results of surgery. The design of collision detection and force feedback algorithms is a prerequisite to ensure the immersion and transparency of the virtual surgical training system. This article mainly introduces the collision detection and force feedback algorithm research in virtual surgery, with the intention of providing some ideas and directions for the development of virtual surgery. This paper proposes two collision detection algorithms, space decomposition method and hierarchical bounding box method, and three force feedback algorithms including spring mass point algorithm, Runge–Kutta method, and Euler method to construct virtual surgery collision detection and force feedback. Experiment with the Overall System Architecture. This paper proves through experimental results that the average collision detection time after the application of the improved collision detection and force feedback algorithm in the virtual surgery system is more than 80.7% less than the traditional method, which greatly improves the detection speed.

Yuri Manin on Biomolecules as Quantum Computers

In 1980, Russian mathematician Yuri Manin published Computable and Uncomputable. On pages 14 and 15 of his introduction, Manin suggests that “Molecular biology furnishes examples of the behavior of natural (not engineered by humans) systems which we have to describe in terms initially devised for discrete automata.” Manin then describes the remarkable energy efficiency of naturally occurring biomolecular processes such as DNA replication. He proposes modeling such behaviors in terms of unitary rotations in a finite-dimensional Hilbert space. The decomposition of such systems then corresponds to the tensor product decomposition of the state space, that is, to quantum entanglement. Manin’s initial focus on biological molecules as examples of highly energy-efficient quantum automata is unique among quantum computing’s founding figures since both he and other early leaders quickly moved to the then-new and exciting concept of von Neumann automata. The von Neumann formalism reinterpreted molecular quantum computing in terms of qubits, which made it possible to imagine the power of quantum computing as not much more than a superposition of virtual binary computers. This paper provides the original excerpt of Manin’s molecular computing argument. A useful analytical feature of Manin’s pre-von-Neumann model of quantum computation is its openness to new formalisms that avoid accidentally making classical physics dominant over the quantum world by expressing quantum states only in terms of concepts such as automata that assume extreme classical precision and complexity.

Parallel Dynamic Domain Decomposition in Space - Time for Data Assimilation problems

In the present work we employ a load balancing scheme involving an adaptive and dynamic workload redistribution both along Space and Time directions for solving Data Assimilation problems where the observations are non-uniformly distributed, general sparse and its distribution changes during the time. We will consider the Constrained Least Square model (CLS) as prototype of Data Assimilation problems and we will validate the proposed approach on different configurations. Validation is performed using Parallel Computing Toolbox of MATLABR2013a on high performance hybrid computing architecture.

Virtual-Vector-Based FCS Model Predictive Current Control with Duty Cycle Optimization for Dual Three-Phase Motors

This paper presents an improved finite control set model predictive current control (FCS-MPCC) based on virtual vectors with duty cycle control for dual three-phase permanent magnet synchronous motor (DTP PMSM) drives. Virtual vectors synthesized by two basic voltage vectors of the inverter are introduced to suppress the harmonic current by the vector space decomposition (VSD) model. And the virtual vectors with the optimal duty cycle can be obtained by duty cycle control using zero vectors to generate a fixed switching frequency. Moreover, a simple scheme of centrosymmetric switching patterns is presented for the realtime implementation. In this way, the performance of current tracking is improved while the computational burden is reduced. Finally, results of simulation analysis and DSP test for the three different strategies are given to verify the validity of the proposed strategy.

An improved bounding algorithm for approximating multistate network reliability based on state-space decomposition method

The evaluation of two-terminal multistate network reliability precisely is a NP-hard problem. Approximating the reliability bounds with state space decomposition is an effective method to tradeoff the computational effort and the acceptable reliability approximate value when the scale of the network is relatively large. This decomposition process cannot avoid the shortage of a large amount of computational effort consumed by sets of unspecified states with little contributions to reliability bounds. Thus, preset critical values are used to filter out sets of unspecified states with less probability. However, managers cannot predict the preset critical value that satisfies their demand. Therefore, we first proposed a serial bounding algorithm based on the breadth-first mechanism, wherein sets of unspecified states on the same generation are all decomposed before moving to the next generation. The mechanism of combining serial computing with parallel computing is further developed to fully utilize computer capability. In addition, the preset critical values are not required before running the algorithm. The results of efficiency comparison demonstrate that the proposed algorithm can significantly improve the efficiency for approximating multistate network reliability. Stability investigations show that the computational efficiency of the proposed algorithm is more stable and effective under various component state distributions.

An Enhanced SVPWM Strategy Based on Vector Space Decomposition for Dual Three-Phase Machines Fed by Two DC-Source VSIs

This article presents an enhanced space vector pulse width modulation (SVPWM) strategy based on vector space decomposition (VSD) for the dual three-phase machines fed by two dc-source voltage source inverters (VSIs). Compared with existing methods that only account for balanced dc-link voltages, the proposed method considers unbalanced dc-link voltages in both the α-β and z <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -z <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> planes. Two categories of medium voltage vectors are first defined in this article. An enhanced 12-sector SVPWM strategy that toggles two categories of medium voltage vectors in each fixed 30° sector is proposed. Moreover, the performance of the proposed method, including the modulation depth, the range of the dc-link voltage ratio, and the toggling point of the medium vector is analyzed. The proposed method can reduce the computational burden of the complicated sector classifications and it easily chooses suitable vectors to track the reference voltage with changes in the dc-link voltage ratio. The experimental results of the proposed SVPWM techniques are verified in a dual three-phase permanent magnet synchronous machine (PMSM) fed by two dc-source VSIs.

Decomposition in decision and objective space for multi-modal multi-objective optimization

Multi-modal multi-objective optimization problems (MMMOPs) have multiple subsets within the Pareto-optimal Set, each independently mapping to the same Pareto-Front. Prevalent multi-objective evolutionary algorithms are not purely designed to search for multiple solution subsets, whereas, algorithms designed for MMMOPs demonstrate degraded performance in the objective space. This motivates the design of better algorithms for addressing MMMOPs. The present work identifies the crowding illusion problem originating from using crowding distance globally over the entire decision space. Subsequently, an evolutionary framework, called graph Laplacian based Optimization using Reference vector assisted Decomposition (LORD), is proposed, which uses decomposition in both objective and decision space for dealing with MMMOPs. Its filtering step is further extended to present LORD-II algorithm, which demonstrates its dynamics on multi-modal many-objective problems. The efficacies of the frameworks are established by comparing their performance on test instances from the CEC 2019 multi-modal multi-objective test suite and polygon problems with the state-of-the-art algorithms for MMMOPs and other multi- and many-objective evolutionary algorithms. The manuscript is concluded by mentioning the limitations of the proposed frameworks and future directions to design still better algorithms for MMMOPs. The source code is available at https://worksupplements.droppages.com/lord.

Decompositions of Dynamical Systems Induced by the Koopman Operator

For a topological dynamical system we characterize the decomposition of the state space induced by the fixed space of the corresponding Koopman operator. For this purpose, we introduce a hierarchy of generalized orbits and obtain the finest decomposition of the state space into absolutely Lyapunov stable sets. Analogously to the measure-preserving case, this yields that the system is topologically ergodic if and only if the fixed space of its Koopman operator is one-dimensional.

Invariant generalized complex geometry on maximal flag manifolds and their moduli

We describe moduli spaces of invariant generalized complex structures and moduli spaces of invariant generalized Kähler structures on maximal flag manifolds under B-transformations. We give an alternative description of the moduli space of generalized complex structures using pure spinors, and describe a cell decomposition of these moduli spaces induced by the action of the Weyl group.

Modelling driver decision-making at railway level crossings using the abstraction decomposition space

The objective of this paper is to cast users of railway level crossings as flexible and adaptive decision-makers, and to apply a cognitive systems engineering approach to discover new behaviour-based insights for improving safety. Collisions between trains and road vehicles at railway level crossings/grade crossings remain a global issue. It is still far from apparent why drivers undertake some of the behaviours that lead to collisions, and there remains considerable justification for continuing to explore this issue with novel methods and approaches. In this study, 220 level crossing encounters by 22 car drivers were subject to analysis. Concurrent verbal protocols provided by drivers as they drove an instrumented vehicle around a pre-defined route were subject to content analysis and mapped onto Rasmussen’s Abstraction Decomposition Space. Three key results emerged. First, when they realise they are in a crossing environment, drivers’ natural tendencies are to look for trains (even if not required), slow down (again, even if not required), and for their behaviour to be shaped by a wide variety of constraints and affordances (some, but not all, put there for that purpose by railway authorities). The second result is that expert decision-making in these situations does not describe a trajectory from high-level system purposes to low-level physical objects. Instead, drivers remain at intermediate and lower levels of system abstraction, with many loops and iterations. The final finding is that current level crossing systems are inadvertently constraining some desirable behaviours, affording undesirable ones, and that unexpected system elements are driving behaviour in ways not previously considered. Railway level crossings need to be designed to reveal their functional purpose much more effectively than at present.

Demagnetization fault reconstruction for six-phase permanent magnet synchronous motor by improved super-twisting algorithm-based sliding-mode observer

Demagnetization fault causes the performance degradation of a permanent magnet synchronous motor (PMSM) drive system. Therefore, it is of great importance to reconstruct demagnetization fault in real-time. This paper firstly presents a demagnetization fault reconstruction method for a six-phase permanent magnet synchronous motor (SP-PMSM). A super-twisting algorithm-based sliding-mode Luenberger observer (STA-SMLO) is designed. It can eliminate the chattering of the sliding mode observer (SMO) and effectively isolate the influence of motor speed on the observer. The mathematical model of the demagnetized SP-PMSM is constructed by the vector space decomposition (VSD). Then, an STA-SMLO, which combines a super-twisting algorithm-based sliding-mode observer (STA-SMO) with a Luenberger-observer (LO), is designed to reconstruct the demagnetization fault of the SP-PMSM precisely. Moreover, a strong Lyapunov function is designed to ensure the stability of STA-SMLO. Experiment results of hardware-in-the-loop simulation (HILS) demonstrate the feasibility and advantages of the method.

Modeling the trajectory of motion of a linear dynamic system with multi-point conditions.

The motion of the linear dynamic system with given properties is modeled; conditions for system state at various arbitrarily points in time are given. Simulated movement carried out due to the calculated input vector function. The method of undefined coefficients is used to construct the input vector function and the corresponding trajectory. The proposed method consists in the formation of the state vector function, the trajectory of motion and the input vector function in exponential-polynomial form, that is, in the form of linear combinations of the powers of the time parameter with vector coefficients. This linear combination is complemented by a scalar exponential function with an additional parameter in the exponent to change the type of trajectory. To find the introduced coefficients, formulas and a linear algebraic system are formed. To find the introduced coefficients, the formed linear combinations are substituted directly into the equations describing the dynamic system and into the given multipoint conditions for finding the entered coefficients. All this leads to obtaining algebraic formulas and linear algebraic systems. Only the matrices included in the system that describe the dynamics of the model (and similar matrices with higher exponents) are the coefficients for the unknown parameters of the resulting algebraic system. It is proved that the fulfillment of the condition Kalman is sufficient for the solvability of the resulting system. To substantiate the solvability of the system, the properties of finite-dimensional mappings are used: decomposition of spaces into subspaces, projectors on subspaces, semi-inverse operators. But for the practical use of the proposed method, it is sufficient to solve the obtained linear algebraic system and use the obtained linear formulas. The correctness of the obtained model is investigated. Due to the non-uniqueness of the solution to the problem posed, the trajectory of motion can be unstable. It is revealed which components of the desired coefficients are arbitrary. It is showed which ones to choose, to make the movement steady, that is, so that small changes in the given multi-point values, as well as a small change parameters of the dynamic system corresponded to a small change in the trajectory of motion. An example is given of constructing trajectories of a material point in a vertical plane under the action of a reactive force in order to hit a given point with a given speed.

Hybrid Localized Spectral Decomposition for Multiscale Problems

We consider a finite element method for elliptic equations with heterogeneous and possibly high-contrast coefficients based on primal hybrid formulation. We assume minimal regularity of the solutions. A space decomposition as in FETI and BDCC induces an embarrassingly parallel preprocessing and leads to a final system of size independent of the coefficients. The resulting solution is in equilibrium, and all PDEs involved are elliptic. One of the problems in the pre-processing step is nonlocal but with exponentially decaying solutions, enabling a practical scheme where the basis functions have an extended, but still local, support. To make the method robust with respect to high-contrast coefficients, we enrich the space solution via local eigenvalue problems, obtaining an optimal a priori error estimate that mitigates the effect of having coefficients with different magnitudes. The technique developed is dimensional independent and easy to extend to other elliptic problems such as elasticity.

ПИРАМИДАЛЬНАЯ СХЕМА ПОСТРОЕНИЯ БИОРТОГОНАЛЬНЫХ ВЕЙВЛЕТ-КОДОВ НАД КОНЕЧНЫМИ ПОЛЯМИ

The existence of a biorthogonal decomposition of the space V of dimension n over the field GF(q) is constructively proved, namely, two representations of it are obtained as direct sums of subspaces V = W0⊕W1⊕. . .⊕WJ⊕VJ and V = W˜0⊕W˜1⊕. . .⊕W˜J⊕V˜J ,such that at the j-th level of the decomposition, for 0 &lt; j 6 J, Vj−1 = Vj⊕Wj , V˜j−1 == V˜j ⊕ W˜j , the subspace Vj is orthogonal to W˜j , and the subspace Wj is orthogonal to V˜j . The partition of the space at the j-th level is made with the help of pairs of level filters (hj, gj) and (h˜j, g˜j), for the construction of which the corresponding algorithms have been developed and theoretically proved. A new family of biorthogonal wavelet codes is built on the basis of the multilevel wavelet decomposition scheme with coding rate 2−L, where L is the number of used decomposition levels, and examples of such codes are given.

Electromagnetic Steklov eigenvalues: approximation analysis

We continue the work of Camano et al. [SIAM J. Math. Anal. 49 (2017) 4376–4401] on electromagnetic Steklov eigenvalues. The authors recognized that in general the eigenvalues do not correspond to the spectrum of a compact operator and hence proposed a modified eigenvalue problem with the desired properties. The present article considers the original and the modified electromagnetic Steklov eigenvalue problem. We cast the problems as eigenvalue problem for a holomorphic operator function A(⋅). We construct a “test function operator function” T(⋅) so that A(λ) is weakly T(λ)-coercive for all suitable λ, i.e. T(λ)*A(λ) is a compact perturbation of a coercive operator. The construction of T(⋅) relies on a suitable decomposition of the function space into subspaces and an apt sign change on each subspace. For the approximation analysis, we apply the framework of T-compatible Galerkin approximations. For the modified problem, we prove that convenient commuting projection operators imply T-compatibility and hence convergence. For the original problem, we require the projection operators to satisfy an additional commutator property which concerns the tangential trace. The existence and construction of such projection operators remain open questions.

Systems of Polynomial Equations, Higher-Order Tensor Decompositions, and Multidimensional Harmonic Retrieval: A Unifying Framework. Part II: The Block Term Decomposition

In Part I we proposed a multilinear algebra framework to solve 0-dimensional systems of polynomial equations with simple roots. We extend this framework to incorporate multiple roots: a block term decomposition (BTD) of the null space of the Macaulay matrix reveals the dual (sub)space of a disjoint root in each term. The BTD is the joint triangularization of multiplication tables and a three-way generalization of the Jordan canonical form in the matrix case, intimately related to the border rank of a tensor. We hint at and illustrate flexible numerical optimization-based algorithms.