Optimal H2 order-one reduction by solving eigenproblems for polynomial equations

A method is given for solving an optimal H2 approximation problem for SISO linear time-invariant stable systems. The method, based on constructive algebra, guarantees that the global optimum is found; it does not involve any gradient-based search, and hence avoids the usual problems of local minima. We examine mostly the case when the model order is reduced by one, and when the original system has distinct poles. This case exhibits special structure which allows us to provide a complete solution. The problem is converted into linear algebra by exhibiting a finite-dimensional basis for a certain space, and can then be solved by eigenvalue calculations, following the methods developed by Stetter and Moeller. The use of Buchberger's algorithm is avoided by writing the first-order optimality conditions in a special form, from which a Groebner basis is immediately available. Compared with our previous work the method presented here has much smaller time and memory requirements, and can therefore be applied to systems of significantly higher McMillan degree. In addition, some hypotheses which were required in the previous work have been removed. Some examples are included.

Designing MPC controllers by reverse-engineering existing LTI controllers

This technical report presents a method for designing a constrained output-feedback model predictive controller (MPC) that behaves in the same way as an existing baseline stabilising linear time invariant output-feedback controller when constraints are inactive. The baseline controller is cast into an observer-compensator form and an inverse-optimal cost function is used as the basis of the MPC controller. The available degrees of design freedom are explored, and some guidelines provided for the selection of an appropriate observer-compensator realisation that will best allow exploitation of the constraint-handling and redundancy management capabilities of MPC. Consideration is given to output setpoint tracking, and the method is demonstrated with three different multivariable plants of varying complexity.

Bias-dependent recovery time of all-optical resonant nonlinearity in InGaAsP/InGaAsP MQW waveguide

We have investigated a resonant refractive nonlinearity in a semiconductor waveguide by measuring intensity dependent phase shifts and bias-dependent recovery times. The measurements were performed on an optimized 750-μm-long AR coated buried heterostructure MQW p-i-n waveguide with a bandedge at 1.48 μm. Figure 1 shows the experimental arrangement. The mode-locked color center laser was tuned to 50 meV beyond the bandedge and 8 ps pulses with peak incident power up to 57 W were coupled into the waveguide. Some residual bandtail absorption remains at this wavelength and this is sufficient to cause carriers to be photogenerated and these give rise to a refractive nonlinearity, predominantly by plasma and bandfilling effects. A Fabry-Perot interferometer is used to measure the spectrum of the light which exits the waveguide. The nonlinearity within the guide causes self phase modulation (SPM) of the light and a study of the spectrum allows information to be recovered on the magnitude and recovery time of the nonlinear phase shift with a reasonable degree of accuracy. SPM spectra were recorded for a variety of pulse energies coupled into he unbiased waveguide. Figure 2 shows the resultant phase shift measured from the SPM spectra as a function of pulse energy. The relationship is a linear one, indicating that no saturation of the nonlinearity occurs for coupled pulse energies up to 230 pJ. A π phase shift, the minimum necessary for an all-optical switch, is obtained for a coupled pulse energy of 57 pJ while the maximum phase shift, 4 π, was measured for 230 pJ. The SPM spectra were highly asymmetric with pulse energy shifted to higher frequencies. Such spectra are characteristic of a slow, negative nonlinearity. This relatively slow speed is expected for the unbiased guide as the recovery time will be of the order of the recombination time of the photogenerated electrons, about 1 ns for InGaAsP material. In order to reduce the recovery time of the nonlinearity, it is necessary to remove the photogenerated carriers from the waveguide by a process other than recombination. One such technique is to apply a reverse bias to the waveguide in order to sweep the carriers out. Figure 3 shows the effect on the recovery time of the nonlinearity of applying reverse bias to the waveguide for 230 pJ coupled power. The recovery time was reduced from one much longer than the length of the pulse, estimated to be about 1 ns, at zero bias to 18 ± 3 ps for a bias voltage greater than -4 V. This compares with a value of 24 ps obtained in a bulk waveguide.

Simulating intertwined design processes that have similar structures: A case study of a small company that creates made-to-order fashion products

The authors use simulation to analyse the resource-driven dependencies between concurrent processes used to create customised products in a company. Such processes are uncertain and unique according to the design changes required. However, they have similar structures. For simulation, a level of abstraction is chosen such that all possible processes are represented by the same activity network. Differences between processes are determined by the customisations that they implement. The approach is illustrated through application to a small business that creates customised fashion products. We suggest that similar techniques could be applied to study intertwined design processes in more complex domains. Copyright © 2011 Inderscience Enterprises Ltd.