Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Dynamic insulation wikipedia , lookup
Water heating wikipedia , lookup
R-value (insulation) wikipedia , lookup
Solar water heating wikipedia , lookup
Thermoregulation wikipedia , lookup
Solar air conditioning wikipedia , lookup
Cogeneration wikipedia , lookup
Heat equation wikipedia , lookup
Thermal conduction wikipedia , lookup
Dynamic processes Causes of delay in process systems Whenever material or energy flows into or out of certain system, it takes time. Thus, the level of a liquid, the temperature of the vessel or the position of the solid mass cannot change suddenly. They are subjects to delays which are dependent on the magnitude of the capacity and the resistance to the inflow of material or energy. Heater process: Electric hot water boiler has electric power Pin (w). We assume that the metal parts of the systems (resistor and casing) are Picture 1 small compared to mass of water. Thermal power Q = c * m * ΔT c = heat capacity of water m = mass ΔT = Twater - Tambient = temperature difference (1) ΔT Tambient Twater Pin First let's assume that insulation of the boiler is very good. There are no heat transfer from boiler. Heater resistor is switched on with constant power. Next block diagram describes the case Pin WATER ΔTout Temperature difference Power/w STEP Picture 2 Equation (1) gives ΔT = Q/(c * m) (2) Energy of vessel = Q = W = ∫Pdt (3) Equations (2) and (3) gives: ΔT = ∫Pdt/(c * m) (4) We have got temperature difference to the process, if input power is step function. With constant power equation (4) gives: ΔT = P * t/(c * m) Time-domain plot is growing strait line. Laplace transform: Laplace transforms are used to solve dynamic systems. Time-domain signals are transferred to s-domain signals. s = jω, ω = angular velocity Computer based transient analyses are using L-transform. Integral change to multiplication and gives easy handling for equations. Matlab simulink can utilize L-transforms. Time-domain Time-domain Time-domain Pin s-domain ∫Pdt = W 1/S 1/c*m STEP integrator ΔT GAIN Picture 3 P ΔT Transient Analyse ΔT P Time Pout Pout Let´s assume that isolation of the boiler is not perfect. ΔT Heat is transferred through the walls of vessel. Q = U * A * ΔT Twater Tambient (5) Q = Transferred heat w. U = Conductance w/m2K ΔT = Tout - Tin = Temperature difference A = Area of casing m2 Pin Pin + STEP s-domain ∫Pdt = W 1/S - GAIN integrator U * A * ΔT 1/c*m ΔT U * A = 0.2 GAIN Picture 4 ΔT Temperature difference of the boiler is not any more strait line. It is exponential and it reaches certain maximum level after a long time. In this example power loses are huge and temperature inside of the vessel doesn't get over 100 degrees. ΔT Pin Transient analyse ΔT Time We can edit the block diagram and substitute the feedback: Block diagram in picture 4 can be more simple. Feed-back block diagram with integrator is substituted to one transfer function. Step response will remain the same figure and magnitude. Pin STEP 5/(5s+1) ΔT Transfer function Picture 5 Transfer function formula can be written: A/(τs + 1) A = Gain of the transfer function = ΔT/Pin , K/w τ = Time constant , second Next graph describes common step response. Any process with one "energy store" is indentical. The process has 1st order delay. Step function 0...100 A Output = A * (1 - e-t/τ) Exponent function of 1 st order delay 63,2 τ = Time constant Time/s Next processes have similar responses: in R + out C RC-circuit, τ = R * C +Force ΔT =Tmass - Tambient out mass in Heat power Velocity out in - Force, example wind force SECOND ORDER DELAYS Always we cannot describe the process with one delay. Example of heat process: water Cattle Electric heater plate Heat resistor Power/w τ1 Resistor Tresist Tplate τ2 Heater plate τ3 Cattle Tcattle τ4 Water Twater Step response 1...4 delays, τ1 = τ2 = τ3 = τ4 = 1 s out in input step = 100 time TRANSPORT DELAY Delays are also caused by the time taken for material to travel along pipes or conveyors from one place to another. This type delay, shown in next figure. Temperature mixed water Hot water velocity = v Distance to measuring point = L Time delay = L/v Could water Step response of the prosess Transport delay = 2 s, Capacitive delay = 3s RELATIVE DIFFICULTY OF THE PROCESS Step response of the process is run to the open-loop system: Step B Relative change in output signal Step response Tt A Controllability S = Tr/Tt S < 4 difficult to control S > 4 easy to control Tr Sketch deepest tangent to the response and mark the points A and B. A = minimum level of response. B = maximum level of response (after a long period) Dynamic Process Simulation Information What is the difference between mathematical models and simulations? On this site we will use the term "mathematical models" to represent sets of equations that mathematically describe the process. The term "simulator" refers to a computer program or a digital system running a computer program that implements the mathematical model. The simulator may be connected to the control system or may be embedded within the control system. What types of simulations used in process engineering? Static Static simulations, typically used in process design, simulate the process at steady state conditions, usually at the design operating conditions. Time is not a variable. Dynamic Dynamic models consider time as a variable and simulate the process over a period of time. A dynamic simulation can be used to estimate or illustrate the response, over time, to a change in the process. This primary concern of this site is dynamic models.