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A novel approach to fuel–air ratio (FAR) control for spark ignition (SI) engines is presented in this study. The FAR dynamics are modelled as a first-order plus time-varying delay system. Time delay in the control plant is not approximated using the Pade formula. For controller design purposes, it is described as a time-varying delay in the measurement output. A gain-scheduled delay-dependent controller, regarding the time delay as a time-varying parameter, is then designed to track FAR reference and minimise the effects of disturbances on FAR regulation. The proposed controller guarantees the stability of closed-loop system and induced *L* _{2} norm performance using Lyapunov–Krasovskii functional. The design method is then formulated in terms of linear matrix inequalities that leads to a convex optimisation problem and can be solved by parameter gridding technique. Simulation results validate the FAR regulation of proposed controller over the large range of time delay, which covers most engine operating conditions in practice.

Hierarchical scalar bases and hierarchical vector bases that span the Nédélec mixed-order spaces have been proposed for the most common two- and three-dimensional cells. These bases maintain appropriate continuity in a mesh containing multiple cell shapes. In particular, the vector bases maintain the tangential or normal continuity in the curl- or divergence-conforming case, respectively. The use of orthogonal scalar polynomials to systematically construct the basis functions is believed to offer a simpler approach for enhancing their linear independence as their polynomial order increases than the partial orthogonalization of the final vector functions. The process by which the basis functions were obtained is described in detail. Numerical results for the matrix condition numbers suggest that these hierarchical bases exhibit reasonable linear independence for large orders.

In this chapter, we consider the representation of vector functions (often referred to as “vector fields”) with low-order (constant and linear) polynomial basis functions on simple cells, such as triangles or quadrilateral cells in two dimensions or tetrahedrons and bricks in three dimensions. As will soon be apparent, there are multiple ways of defining vector basis functions, and therefore the approach requires some consideration. The proper representation of a function depends on what will be done with it-do we need to compute the curl of the function, for instance? If so, the representation might be different than if we need to compute the divergence of the function. We use the term curl conforming to denote the space of vector functions that maintain first-order tangential-vector continuity throughout the domain and can be differentiated via the curl operation, without producing unbounded or generalized functions (Dirac delta functions) in the process. The term divergence conforming is used to denote the complementary space of vector functions that maintain first-order normal-vector continuity throughout the domain and can therefore be differentiated via the divergence operation. (First order or C_{0} continuity is continuity of the function itself, but not necessarily continuity of its first derivatives.) The simple low-order polynomial vector basis functions in widespread use are either curl conforming or divergence conforming; seldom we will use functions that maintain complete continuity and belong to both the curl-conforming and divergence-conforming spaces, although it is possible to define such functions.

In this study, a new statistical monitoring technique based on efficient projection to latent structures (EPLS) is proposed for quality-relevant fault detection in multivariate processes that exhibit collinear measurements. The algorithm decomposes process variables into three subspaces according to singular value decomposition (SVD) and principal component analysis. This method effectively solves the problems of real-time and effectiveness in the quality-relevant fault diagnosis of industrial processes. EPLS takes full advantage of good nature of SVD. As a result, the calculation of the projection process is greatly reduced. It is reasonable that the process data space was projected to three subspaces, a quality-relevant subspace, a quality-irrelevant subspace and a residual subspace. EPLS algorithm not only effectively avoids the tedious iterative calculation, but also makes more explicit spatial resolution. The framework of quality-relevant fault monitoring based on EPLS algorithm was proposed as well in this study. A challenging problem, real industrial hot strip mill process, is used to illustrate the effectiveness of the proposed method.

Owing to their complexity, accurate and detailed models of anaerobic digestion cannot be used for online monitoring and control. To this aim reduced order models have to be considered. In this chapter, a modification of the well-known AMOCO model is first proposed in order to widen its field of applicability. Then, to perform parameter identification, a linear fractional transformation (LFT) formulation is derived, thanks to the use of a symbolic manipulation tool applied to an object-oriented model formulation. The approach has been applied to two case tests: in the first test, the data used for identification have been generated by a simulation of the fully detailed Anaerobic Digestion Model no. 1 (ADM1) model, assuming waste activated sludge as influent substrate, and in the second, the data have been collected on a real plant, used for anaerobic digestion of agricultural wastes.

This paper describes an efficient implementation of a form of linear semi-infinite programming (LSIP). We look at maximizing (minimizing) a linear function over a set of constraints formed by positive trigonometric polynomials. Previous studies about LSIP are formulated using semi-definite programming (SDP), this is typically done by using the Kalman Yakubovich Popov (KYP) lemma or using a trace operation involving a Grammian matrix, which can be computationally expensive. The proposed algorithm is based on simplex method that directly solves the LSIP without any parameterization. Numerical results show that the proposed LISP algorithm is significantly more efficient than existing SDP solvers using KYP lemma and Grammian matrix, in both execution time and memory.

Given a graph G = (V, E) with a set W ⊆ V of vertices, we enumerate colorings to W such that for every two enumerated colorings c and c' the corresponding colored graphs (G, c) and (G, c') are not isomorphic. This problem has an important application in the study of isomers of chemical graphs such as generation of benzen isomers from a tree-like chemical graph structure. The number of such colorings can be computed efficiently based on Polya's theorem. However, enumerating each from the set of these colorings without using a large space is a challenging problem in general. In this paper, we propose a method for enumerating these colorings when the automorphisms of G are determined by two axial symmetries, and show that our algorithm can be implemented to run in polynomial delay and polynomial space.

Word search is a classical puzzle to search for all given words on a given assignment of letters to a rectangular grid (matrix). This problem is clearly in P. The inverse of this problem is more difficult, which asks to assign letters in a given alphabet to a matrix of given size so that every word in a given wordset can be found horizontally, vertically, or diagonally. This problem is in NP; it admits a trivial polynomial-size certificate. We prove its NP-hardness. It turns out to be so even under the following restrictions: 1) the alphabet size is 2 (binary) and 2) all the words to be found are of length at most 2. These results are optimal in the sense that decreasing these bounds 2 to 1 makes the problem be trivially in P.

Polynomial parahermitian matrices can accurately and elegantly capture the space-time covariance in broadband array problems. To factorise such matrices, a number of polynomial EVD (PEVD) algorithms have been suggested. At every step, these algorithms move various amounts of off-diagonal energy onto the diagonal, to eventually reach an approximate diagonalisation. In practical experiments, we have found that the relative performance of these algorithms depends quite significantly on the type of parahermitian matrix that is to be factorised. This paper aims to explore this performance space, and to provide some insight into the characteristics of PEVD algorithms.

This paper presents a flexure pressure sensor fabricated by means of 3D printing. This sensor combined with a biosimulant artifact from the National Institute of Standards and Technology (NIST) is used to measure the severity of injuries caused in the case of a robot impact with a human. The stiffness matrix is derived for the structure by means of screw theory. A Finite Element (FE) model is constructed to verify the analytical model and obtain the allowable pressure with regard to the yield stress.

According to the characteristics of a new type of complex joint in the space steel structure, one model of automatic assembly system with 6-DOF was designed. Base on Denavit-Hartenberg method and matrix inverse operation principle, the positive and forward kinematics algorithm of an assembly machine is proposed and the main parameters of pose algorithm are calculated. The automatic assembly machine was designed, and its structure and principle of operation strategy was elaborated.By the control method of point to point, experimental data are obtained and then are compared with the theoretical data. The results show that this pose algorithm and its assembly control strategy is available. The maximum deviation of the rotating joint is 0.11 degrees and the maximum deviation of transfer joint is 0.1mm, which can meet the assembly demand in practice.