Chapter 6 Applied Instructions Example 2: Tuning the parameters used with the PID instruction Suppose that the transfer function of the plant is the first-order function ( ) a + s b = s G , the SV is 1, the sampling time Ts is 10 milliseconds. It is suggested that you follow these steps when tuning the parameters. Step 1: First, set the K I and the K D to 0. Next, set the K P to 5, 10, 20 and 40 successively, and record the target values and the process values. The results are shown in the following diagram. 1.5 K =40 P K =20 P K =10 P SV=1 1 K =5 P 0.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Time (sec) Step 2 : When the K P is 40, there is overreaction.
When the K P is 20, the reaction curve of PV is close to SV, and there is no overreaction. However, due to the fast start-up, the transient output value (MV) is big. Neither 40 nor 20 is a suitable value. When the K P is 10, the reaction curve of PV approaches SV smoothly. When K P is 5, the reaction is 6_ too slow. Therefore, K P = 10 is the best choice. Step 3 : After setting K P to 10, increase K I . For example, K I is successively set to 1, 2, 4, and 8. K I should not be larger than K P . Then, increase K D . For example, successively set K D to 0.01, 0.05, 0.1, and 0.2. K D should not be larger than ten percent of K P .
Finally, the relation between PV and SV is shown in the following diagram. 1.5 PV=SV 1 0.5 K =10,K =8,K =0.2 P I D 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Time (sec) Note: This example is only for reference. You must tune the parameters properly according to the actual condition of the control system. 6-211