A zero compensation approach to singular H2 and H∞ problems

In this work we analyse singular H² and H^∞ problems for which the usual Riccati equations become ill-posed owing to the existence of plant zeros at infinity. We adopt a two-step approach to the analysis. First we replace the usual Riccati equations with two generalized eigenproblems; these problems are always well-posed. Next we extract those structural elements which pertain to the troublesome plant zeros. We do this by introducing pre-compensators which cancel the offending zeros. In so doing, we temporarily relax the controller properness constraint that is traditionally imposed in H² and H^∞ problems by allowing pole-zero cancellations between the plant and controller at infinity. Since no significant added complexity of analysis results, we also treat the case of singularity due to finite jω-axis plant zeros by relaxing the internal stability requirement and allowing finite jω-axis pole-zero cancellations. The resultant theory allows us to specify necessary and sufficient conditions for the existence of solutions to singular H² and H^∞ problems. The existence conditions and the resultant control laws are expressed directly in terms of the eigenvalues and eigenvectors of two Hamiltonian matrices associated with the problem. The theory also gives some insight into the character of the subset of all proper, internally stabilizing solutions, including whether this set is nonempty. An example is included.     

Heat resistance of metal-intermetallic compositions based on NiAl

Heat resistance of the intermetallic compound NiAl, its alloys with Hf and Nb, and composition materials with a microhoneycomb structure (tungsten honeycombs with a wall thickness of 0.3–3 μm and a core of NiAl or the NiAl-4 at% Nb alloy) are investigated. The oxidation rate (w ⁺) is calculated by the weight increment from oxidation in air at t = 1000–1300°C for τ ≤ 21 h, and the rate of burning loss (w ^?) is calculated by the weight loss during removal of the scale. NiAl and its alloy have the minimal oxidation rate: 4.4 wt % Hf (w ⁺ = 4.5–20 g/(m² h) at 1200°C). Resistance to scaling of NiAl composites of (13–44) at% W(Mo) is much lower than that of the NiAl intermetallic compound. The higher the content of refractory metal, the lower the resistance to scaling. It depends weakly on the method of compositing of the material (honeycomb structure NiAl-W or mixture of the grains of NiAl and W with sizes of 10–20 μm); however, short-term heating of a composite with a honeycomb structure (13% W, layer 0.5 μm) to 1200–1300°C (above the test temperature) can reduce the rate of subsequent oxidation at t = 1000°C by a factor of 200, and at t = 1100°C by a factor of 30.