Dynamic model for the paper machine headbox
Explain and derive the Dynamic model for the paper machine headbox?
Expert
We'll first develop a dynamic model for the paper machine headbox.A stock balance around the headbox. A suffix hb refers to the head box. Accumulation = Input – Outputdmhb/dt = ρqin – ρqoutNow ρ, is the stock density, but since the consistancy is 0.5% only, ρ = ρw = Water densityd(ρVhb)/dt = ρqin – ρqoutdVhb/dt = qin – qoutAhbdh/dt = qin – qoutwhere, Ahb, is the c/s area of header and assumed to be constant. qout, is the flow out of the header, and is only through slice, and can be written as, CAs(2gh)1/2, where As, is the cross sectional area of slice perpendicular to the flow, and C is characteristic constant coefficient for the slice.Hence, Ahbdh/dt = qin – CAs(2gh)1/2,To find, we can write Bernoulli's equation between Vacuum Degasser and Headbox. Suffix vd refers to vacuum degasser. Pvd/ρ + W = (Phb + ρgh)/ρ + V2/2 V = {2[Pvd - (Phb + ρgh)]/ρ + 2W}1/2 qin = AinV = Ain{2[Pvd - (Phb + ρgh)]/ρ + 2W}1/2Hence the dynamic model is, Ahbdh/dt = Ain{2[Pvd - (Phb + ρgh)]/ρ + 2W}1/2 – CAs(2gh)1/2,where the rate of stock height change in head box is related to the pressure in vacuum degasser and height. We have to linearize the non linear dynamic model. So that the effective model will be,τdh'/dt = KpP'hb + Khh',So as we see the the response of the height of stock to variations in vacuum degasser pressure is first order lag. We don't know the dynamics of level sensor or transmitter, but we'll assume it's also first order lag. Hence the effective system will be a second order. And hence it'll be oscillatory, and we propose the PID controller for level control by manipulating the speed of fan pump. Using MATLAB control toobox and given values of the parameters in the problem, we approximately find the following controller parameter settings. Kc = 9.6, τI = 2.3 min, τD = 3.5 min.Similarly, a propotional integral controller is proposed for pressure control in head box.The pressure in the head box is related to in flow of air, which is controlled by PI controller. The air is available at pressure of 300 kPa. dPhb/dt = f(Qin), where is the inlet flow rate of air. This will be pure capacitive system, hence we propose PI controller. We find the controller parameters for this, Kc = 14.5, τI = 4.5 min.
Life expectancy: This part of the specification will state how long the product should remain in working order provided the customer gives reasonable care and maintenance. Also take into account technological advances and ongoing improvements that wou
Size and weight: If the product is particularly small the cost may be increased if more precise manufacturing methods are demanded. Weight restriction will as well influence materials to be utilized: this in turn will influence the manufacturing proce
How pressure of oil is managed when starting or stopping the medium-sized turbine?
Mechanism: The mechanism is a system of moving parts which changes an input motion and force into the desired output force and motion.
The water level in a tank is about 20 m above the ground. A hose is joined to the bottom of the tank, and the nozzle in the end of the hose is pointed to straight up. The tank is at sea level, and the water surface is open to the environment. In the line leading from
Differentiate the term Brazing and Welding?
What is critical speed?
From Bernoulli's equation we know that presure head + velocity head at inlet and outlet header is same. If so what is ' W' then in the equation ?
(a) The response for an undamped single degree of freedom system under free vibration is given as where ωn is the natural frequency and A and B are unknown that can be determined from the initial conditions. The response 
You are working in a company that has developed a process to produce DNA vaccines from E.coli. After the fermentation step a lysis step is used to release the DNA from the cells resulting in a sticky mixture. You find that an aggressive cleaning solution heated to 80°C is required to
18,76,764
1950891 Asked
3,689
Active Tutors
1457601
Questions Answered
Start Excelling in your courses, Ask an Expert and get answers for your homework and assignments!!