On the general solution of the state deadbeat control problem

In this note, the state deadbeat control problem is considered. It is shown that, after appropriate change of basis of input and state spaces, the general solution of the state deadbeat control problem can be expressed completely by the rows of the powers of system matrix. This result yields a very simple procedure for the calculation of a state feedback deadbeat control gain. It also provides the number of free parameters which could be used for further design purposes. The results are illustrated by an example at the end of the note     

Phase equilibria in the system ZnO-B2O3-SiO2 at 950° C

Phase equilibria in the system ZnO-B₂O₃-SiO₂ investigated at 950°C using quenching and X-ray powder diffraction techniques. The binary phases reported reviously were confirmed but no ternary phases were found. Solid-solution effects were investigated for the primary and binary phases by comparison of patterns; no solid solutions were detected. There is a large Quid area in the high-B₂O₃ corner of the phase diagram. h is found that zinc orthosilicate,-2ZnO · SiO₂, dissolves in this to form a zinc-oxide-rich borosilicate liquid but 4ZnO · 3B₂O₃ does not. Them is also a liquid eutectic at approximate composition 65ZnO-25B₂O₃-10-SiO₂ (wt%). The rate of volatilization and loss of B₂O₃ was also investigated for 4ZnO · 3B₂O₃ and it was concluded that although volatilization occurs, the loss was insufficient at the firing times and temperature used to invalidate the major features of the diagram.