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.
The value engineering method focuses on functional values, and aims to increase the difference between the cost and value of a product: by lowering cost and/or adding value. In many cases, the emphasis is simply on reducing costs, and the design effor
In the below system, d = 6 in., D = 12 in., Δz1 = 6 ft, and Δz2 = 12 ft. The discharge of water in the given system is 10 cfs. Is the machine a turbine or a pump ? Determine the pressures at points A and B? Neglect head losses. Suppos
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
Water flows via a pipe of about 300 mm diameter at the rate of 66 L/s. Evaluate the value of the manometer reading, ‘h’. The Specific gravity of manometer liquid is taken as 0.8.
Quantity: The total quantity of the product predicted and, more importantly, the production rates and batch sizes needed, should be specified. This will have implications for the types of manufacturing equipment and work organization necessary. It wil
What is meant by the term LILO?
a vaccume guage connected to chamber 40kpa at location where atmospheri pressure is100kpa .determine absolute pressure
Pneumatic system is a system which employs air to power something. For illustration, have you seen the tube systems at the bank drive-up tellers? Air is employed to push the tubes back and forth from the teller to customer. Q : Lubricating oil in turbines Except the Except the lubrication, explain the other two functions of the lubricating oil in some of the turbines?
Except the lubrication, explain the other two functions of the lubricating oil in some of the turbines?
Why Centrifugal Pump is known as the High Discharge pump?
18,76,764
1936651 Asked
3,689
Active Tutors
1435624
Questions Answered
Start Excelling in your courses, Ask an Expert and get answers for your homework and assignments!!