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
a vaccume guage connected to chamber 40kpa at location where atmospheri pressure is100kpa .determine absolute pressure
theories for the origin of petroleum, methods for detection of petroleum deposits, fractional distillation
Feasibility study: In order to take wise investments in a market-place experiencing rising stages of risk, companies are turning to feasibility studies to find out if they must propose new products, services or commence a new business endeavor. The ma
Explain the importance to remember about the radial bearings?
What is meant by the term LILO?
Explain difference between the Rated Speed and Economic Speed?
Difference between projectile motion and rocket motion:A projectile has no motor or rocket on it, therefore all of its momentum is provided to it as it is launched. An illustration of a projectile would be pen which you throw across a room.
Steam turbine diaphragm: Steam turbine includes of phases, number and size of the phases depends on the break horse-power of the turbine. The phase has set of moving and fixed blades. Moving blades are joined to th
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
18,76,764
1949647 Asked
3,689
Active Tutors
1444860
Questions Answered
Start Excelling in your courses, Ask an Expert and get answers for your homework and assignments!!