Series-parallel six-element synthesis of biquadratic impedances

The object of this paper is to give a complete treatment of the realizability of positive-real biquadratic impedance functions by six-element series-parallel networks comprising resistors, capacitors, and inductors. This question was studied but not fully resolved in the classical electrical circuit literature. Renewed interest in this question arises in the synthesis of passive mechanical impedances. Recent work by the authors has introduced the concept of a regular positive-real functions. It was shown that five-element networks are capable of realizing all regular and some (but not all) nonregular biquadratic positive-real functions. Accordingly, the focus of this paper is on the realizability of nonregular biquadratics. It will be shown that the only six-element series-parallel networks which are capable of realizing nonregular biquadratic impedances are those with three reactive elements or four reactive elements. We identify a set of networks that can realize all the nonregular biquadratic functions for each of the two cases. The realizability conditions for the networks are expressed in terms of a canonical form for biquadratics. The nonregular realizable region for each of the networks is explicitly characterized. © 2004-2012 IEEE.

Parallel coordinates in computational engineering design

Modern Engineering Design involves the deployment of many computational tools. Re- search on challenging real-world design problems is focused on developing improvements for the engineering design process through the integration and application of advanced com- putational search/optimization and analysis tools. Successful application of these methods generates vast quantities of data on potential optimum designs. To gain maximum value from the optimization process, designers need to visualise and interpret this information leading to better understanding of the complex and multimodal relations between param- eters, objectives and decision-making of multiple and strongly conflicting criteria. Initial work by the authors has identified that the Parallel Coordinates interactive visualisation method has considerable potential in this regard. This methodology involves significant levels of user-interaction, making the engineering designer central to the process, rather than the passive recipient of a deluge of pre-formatted information. In the present work we have applied and demonstrated this methodology in two differ- ent aerodynamic turbomachinery design cases; a detailed 3D shape design for compressor blades, and a preliminary mean-line design for the whole compressor core. The first case comprises 26 design parameters for the parameterisation of the blade geometry, and we analysed the data produced from a three-objective optimization study, thus describing a design space with 29 dimensions. The latter case comprises 45 design parameters and two objective functions, hence developing a design space with 47 dimensions. In both cases the dimensionality can be managed quite easily in Parallel Coordinates space, and most importantly, we are able to identify interesting and crucial aspects of the relationships between the design parameters and optimum level of the objective functions under con- sideration. These findings guide the human designer to find answers to questions that could not even be addressed before. In this way, understanding the design leads to more intelligent decision-making and design space exploration. © 2012 AIAA.

Output disturbance rejection using parallel model predictive control

The solution time of the online optimization problems inherent to Model Predictive Control (MPC) can become a critical limitation when working in embedded systems. One proposed approach to reduce the solution time is to split the optimization problem into a number of reduced order problems, solve such reduced order problems in parallel and selecting the solution which minimises a global cost function. This approach is known as Parallel MPC. The potential capabilities of disturbance rejection are introduced using a simulation example. The algorithm is implemented in a linearised model of a Boeing 747-200 under nominal flight conditions and with an induced wind disturbance. Under significant output disturbances Parallel MPC provides a significant improvement in performance when compared to Multiplexed MPC (MMPC) and Linear Quadratic Synchronous MPC (SMPC). © 2013 IEEE.