Temperature Control of Liquid TankSnapshot of the front panel of the simulator:
Description of the simulated systemA temperature control system for a water tank with continuous inflow and outflow is simulated. The water is heated by a heating element which controlled by the controller. The temperature is measured by a temperature sensor which in practice may be a Pt100 element or a thermocouple. The process model on which the simulator is based is a 1. order model based on energy balance under the assumption of homogenous conditions in the liquid in the tank. The processs model also contains a time delay which represents the time delay which in practice exists between an exitation of the heating element and the response in the temperature sensor. In addition the simulator contains a 1. order transfer function representing a time constant in the heating element. VideoHere are some instructional videos where the present simulator is used as an example:
Process modelKnowledge about the process model is not necessary for doing the tasks below. The parameter values are shown on the front panel of the simulator. The process model used in the simulator is based on energy balance: (1) d(crVT_{1})/dt = K_{e}u + cw(T_{inn} - T_{1}) + U(T_{env} - T_{1}) where K_{e}u = P is the power delivered by the heating element. T_{1} is the temperature in the tank assuming homogenous conditions. In practice there is a time delay between an excitation in the heating element and the response in the temperature sensor: (2) T(t) = T_{1}(t-t) We assume that this time delay is inversely proportional to the mass flow w: (3) t = K_{t}/w By taking the Laplsce transform of the model above we can get the following transfer function from the control signal to the temperature T: (4) T(s)/u(s) = H(s) = [Ku/(Ts+1)]e^{-ts} Thus a first order model with time delay. The parameters of H(s) are: (5) Gain Ku = K_{e}/(cw+U) (6) Time constant T_{k} = rV/(w+U/c) (7) Time delay t = K_{t}/w In addition the simulator contains a 1. order transfer function representing a time constant in the heating element. (This submodel is not shown in the model above.) Aims
In other words: You will get knowledge about the basics of control! MotivationControl systems are essential in industrial processes since it is important and useful to control process variables so that they are kept on or close to specifies values (setpoints). The PID controller is the most frequently used control function in industrial systems. In the industry temperature control is used on e.g. reactors and heat exchangers. TasksThe nominal operating point of the process is defined as follows:
The default process parameter values are as shown on the this snapshot of the front panel of the simulator. Unless otherwise stated it is assumed that the tasks below are executed while the simulator runs.
Updated 4. March 2009. Developed by Finn Haugen. E-mail: finn@techteach.no. |