In this paper, we introduce and study a new class of sets called hexa regular closed (Rh -closed for short), hexa regular open (Rh -open for short), hexa regular semi-closed (RS)h -closed for short), hexa regular semi- open ((RS)h -open for short), hexa regular weakly closed sets ((RW)h -closed for short), hexa regular weakly open sets ((RW)h - open for short) in hexa topological space. Some interesting propositions based on this set are introduced and established with suitable examples and their properties are also discussed.

PID controller plays very important role in many process control industries. In this paper ZieglerNichols controller, Tyreus and Luyben controller, Cohen Coon controller are used to control the level of the conical tank. The controller is designed based on the mathematical model of the system. Non-linear variation is exigent in conical tank because of some of the awkwardness compared to linear system based on analysis, non-linear system is preferred by number of industries. For disposal of solid material non-linear is the system will be best supporter for controller used for conical tank. In this work, a non linear tank process is identified as first order plus dead time model and identified model is used for controller implementation. The closed loop response of process system is obtained using MATLAB simulink. Based upon obtained results and time domain specifications best tuning PID controller parameter is highlighted.