Feedforward Control of Liquid LevelSnapshot of the front panel of the simulator:
Description of the simulated systemThe system being simulated is a level control system based on feedback PI control from level measurement and with the possibility of including feedforward control from outflow (disturbance) and from level setpoint. The simulator is implemented in LabVIEW Simulation Module. The PID controller is the LabVIEW PID Advanced function. The mathematical model of the process to be controlled is based on mass balance of the contents, which is water, of the tank. The mass balance is as follows: rho*A*dh(t)/dt = F_{in}(t) - F_{out}(t) Here the inflow F_{in}(t) is assumed to be the same as the pump control signal u(t), hence both are in unit of kg/s. Solving for the time-derivative gives dh(t)/dt = [1/(rho*A)]*[u(t) - F_{out}(t)] which constitutes the process model written as a state-space model. This model will be the basis of the development of the feedforward control action, cf. the tasks below. VideoHere is an instructional video where the present simulator is used as an example: Feedforward control. AimsThe aim of this simulator is to demonstrate the benefit for the level control by using feedforward control in addition to the (compulsory) feedback control. MotivationFeedforward control can improve the control substantially, i.e. the control error may become substantially smaller compared to not using feedforward. However, feedforward control may be difficult to implement because a process model is required (in the present example, however, the process model is quite simple), and disturbances have to be measured, implying extra expenses. TasksIn all the task below always use feedback control (with PI controller), i.e. set the PI controller in automatic mode. The PI parameter settings can be as shown in the figure above. 1. Deriving the feedforward control function: Assume that the level control setpoint is h_{SP} [m].From the process model given above, show that the feedforward control function is u_{f}(t) = A*rho*dh_{SP}(t)/dt + F_{out}(t) Explain the physical meaning of this feedforward control! Does this control function "make sense"? You should never implement a pure time-differentiation because the time-derivative is very sensitive to noise and abrupt changes of the signal to be differentiated. In stead, you should implement a smoothed derivative by letting the signal pass through a lowpass filter before the differentiation. According to this we modify the feedforward from setpoint part of our feedforward controller as shown below: u_{f}(t) = A*rho*dh_{SP,filt}(t)/dt + F_{out}(t) where h_{SP,filt} is a lowpass filtered level setpoint. The filter may be a time-constant filter: h_{SP,filt}(s) = ]1/(T_{f}s+1)] h_{SP}(s) where T_{f} is the filter time-constant. In the simulator the time constant is set to 5 sec. 2. Not using feedforward control:
3. Using feedforward control:
Updated 5. March 2009. Developed by Finn Haugen. E-mail: finn@techteach.no. |