Adaptive boundary control for unstable parabolic PDEs—Part II: Estimation-based designs

The certainty equivalence approach to adaptive control is commonly used with two types of identifiers: passivity-based identifiers and swapping identifiers. The “passive” (also known as “observer-based”) approach is the prevalent identification technique in existing results on adaptive control for PDEs but has so far not been used in boundary control problems. The swapping approach, prevalent in finite-dimensional adaptive control is employed here for the first time in adaptive control of PDEs. For a class of unstable parabolic PDEs we prove a separation principle result for both the passive and swapping identifiers combined with the backstepping boundary controllers. The result is applicable in any dimension. For physical reasons we restrict our attention to dimensions no higher than three. The results of the paper are illustrated by simulations.     

Effects of molybdenum additions on the structure, depth, and austenite grain size of the case of carburized 0.13% carbon steels

Carbon (0.13%) steel samples containing about 0.48% molybdenum (Mo) singly and in combination with nickel (Ni) were carburized in a natural Titas gas atmosphere at a temperature of 1223 K (950 °C) and at a pressure of about 0.10 MPa (15 psia) for time periods ranging from 1–4 h followed by slow cooling in the furnace. Their microstructure was studied by optical microscopy. The austenite grain size of the case and the case depths were determined. It was found that Mo and Ni alone and in combination decrease the thickness of the cementite network near the surface of the carburized case of the steels. However, Ni is found to be more effective than Mo in decreasing the thickness of cementite network. Both Mo and Ni enhance the formation of Widmanstätten cementite plates at the grain boundary and within the grains near the surface of the carburized steels. However, Ni alone is more effective than Mo in the formation of Widmanstätten cementite plates. In the presence of Ni, Mo is much more effective in the formation of Widmanstätten cementite plates than Mo in absence of Ni. It was also revealed that both Mo and Ni increased the case depth. Ni is more effective than Mo in increasing the case depth. The combined effect of Mo and Ni is much greater than that of either Mo or Ni alone in increasing case depth. Mo as Mo carbide (Mo₂C) particles refined the austenite grain size of the carburized case. Ni in solution was not found to have any effect in restricting grain growth of austenite, but the presence of Ni enhances the austenite grain size refining effect of Mo in the carburized case.     

Capacity planning in job-shop environment

Presented here is a computerized capacity planning system for the IBM Microcomputer family. The system maintains the profile of the job shop in a data base along with data pertinent to various products that can be manufactured in the shop. Projected orders for the planning period are input to the system with their associated quantities and delivery dates. The system uses the forward and backward loading rules in generating capacity loading scenarios. User selects the best course of action which may satisfy delivery dates subject to the limitations of the work centers. Efficiency figures are provided to aid the user in his/her decision.     

Interaction bounds in multivariable control systems

Time-domain limitations due to right half-plane zeros and poles in linear multivariable control systems are studied. Lower bounds on the interaction are derived. They show not only how the location of zeros and poles are critical in multivariable systems, but also how the zero and pole directions influence the performance. The results are illustrated on the quadruple-tank process, which is a new multivariable laboratory process.     

Hardware and software architecture for power quality analysis

This paper presents a novel concept for power quality hardware and software architecture. Software tools related to detection, classification and characterization of power quality events can be integrated into a Distribution Control Center in which the interconnection between different subsystems is being carried out through the Internet allowing flexibility to the system. This system is implemented using wavelet analysis applied in all proposed algorithms. Different power quality events are taken as examples to illustrate the capabilities of the proposed method. The obtained results reveal that the proposed architecture is feasible to be implemented as an integral part of a control center system.The proposed system has the property of fast and accurate detection and classification of any power quality disturbance event and introduces a new PQ index determination that allows characterizing any type of disturbance including the non-periodic signals.     

Extensions of LDA by PCA mixture model and class-wise features

Linear discriminant analysis (LDA) is a data discrimination technique that seeks transformation to maximize the ratio of the between-class scatter and the within-class scatter. While it has been successfully applied to several applications, it has two limitations, both concerning the underfitting problem. First, it fails to discriminate data with complex distributions since all data in each class are assumed to be distributed in the Gaussian manner. Second, it can lose class-wise information, since it produces only one transformation over the entire range of classes. We propose three extensions of LDA to overcome the above problems. The first extension overcomes the first problem by modelling the within-class scatter using a PCA mixture model that can represent more complex distribution. The second extension overcomes the second problem by taking different transformation for each class in order to provide class-wise features. The third extension combines these two modifications by representing each class in terms of the PCA mixture model and taking different transformation for each mixture component. It is shown that all our proposed extensions of LDA outperform LDA concerning classification errors for synthetic data classification, hand-written digit recognition, and alphabet recognition.     

A tolerant approach to reconstruct topology from unorganized trimmed surfaces

Presented in this paper is a topology reconstruction algorithm from a set of unorganized trimmed surfaces. Error-prone small geometric elements are handled to give proper topological information. It gives complete topology to topologically complete models, and it is also tolerant to incomplete models. The proposed algorithm is vertex-based in that clues for topological information are searched from the set of vertices first, not from that of edges.