This article explores the architectural and engineering significance of surfaces of the second order, with a particular focus on the one-sheet hyperboloid of revolution. The study begins with a historical overview of architectural forms, highlighting the evolution from primitive shelters to complex spatial structures. Mathematical foundations are introduced through quadratic equations, illustrating the formation of second-order surfaces such as the elliptic paraboloid and hyperboloid. Special attention is given to the structural properties of the one-sheet hyperboloid, a doubly ruled surface that enables construction using straight beams, despite its curved geometry. Its advantages—strength, wind resistance, and material efficiency—are discussed, along with typical assembly methods such as segment welding and overlapping connections. The article further examines the iconic Shukhov Tower in Moscow, a pioneering example of hyperboloid design. It outlines the construction methodology, including the telescopic assembly process and challenges such as structural fatigue and support failure. The analysis demonstrates how Vladimir Shukhov’s innovations contributed to global architectural and engineering practices. Finally, the article emphasizes the hyperboloid’s relevance in modern construction and research, illustrating its blend of geometric rationality, aesthetic expressiveness, and structural efficiency. This synthesis of art and science continues to inspire both professionals and the public, highlighting the enduring value of advanced geometric principles in architecture.

Keywords: hyperboloid, quadratic surface, hyperboloid of revolution, engineering structure, architectural form, Shukhov Tower, steel structure, spatial lattice, structural technology, lattice shell

This paper presents the application of the model predictive control (MPC) technique for direct vector control  of induction motor drive. Three MPC controllers have been employed; one for adjusting the motor speed, the second for rotor flux control and the last one is specialized for controlling the motor currents. A simple models of induction motor is employed in the MPC structure so as to minimize the computational load. a cassced  The effectiveness of the proposed scheme has been successfully verified through simulations.  The performance of the system including the MPC controller is compared with the corresponding one using the traditional PI controller. The results proved that the induction motor with the MPC controller has superior transient response, and good robustness in face of uncertainties including load disturbance. Moreover, accurate tracking performance has been achieved. 

Keywords: Ac drives, Induction Motor, Model Predictive Control, vector control, field oriented control.