Illustration 5.3: Response of a level system with PI control to a set-point change. We will now look at the above system to a change in the set-point from 1 m to 1.1 m i.e. A m). The inlet flow will be constant at 0.001 m3/s. The controller constants are as before. The closed loop transfer function is
Note that this equation is in radians (not degrees!). The student should do the inverse transform i order to check the above result. The response is plotted in Figure 5.8.
Eigure 5.8: Response of the level system with PI control to a change in the set-point.
It is helpful to look at the differences between the two types of control looked at so far(P and PD. The proportional control was not oscillatory, but did not bring the response back to the set-point. The PI control was oscillatory, but did bring the level in the tank back to the set-point. Which type of control is better? The answer will depend on the process that we are controlling: normally it is best if the response of the process is returned to the set-point. However in the case of liquid levels in ta there is no reason to insist that the level return to the set-point, as long as the liquid level does not reach the top or bottom of the tank. In fact tight process control of liquid level can be bad control, as we can see if we look at the manipulated variable(the flow out of the t in Example 5.2(the response of the PI process to a load disturbance). This variable is plotted in Figure 5.9