Proportional- Integral- Derivative (PID) controllers are widely used in level control systems to maintain desired liquid levels. Proper tuning of PID commerters is essential for optimal performance. This article provides numical examples of PID parameteter calculations for level control applications.

Basic System Parameters

Konsider a level control system with the following parameters:

  • Process gain (K 'I1; CLANE1; FLT: 0' I3; CLANE3; p 'I1; CLANE1; CLANE1; CLANE3;) = 2
  • Process time constant (τ times1; times1; FL1; FLT: 0 times3; times1; times1; FLT: 1 times3; time3;) = 50 seconds
  • Dead time (L) = 10 seconds

PID Parameter Calculation

Using te Ziegler- Nichols tuning method, thee ultimate gain (K 'I1; FLT: 0' I3; FL3; u 'I1; FLT: 1' I3; 'I3;) and ultimate periody (T' I1; 'I1; FLT: 2' I3; u 'I1;' I1; FLT: 3 'I1;' I3; 'I3;) are determinad experimentally. Assume:

  • K 'I1; IH1; IH33; IH33; U' I1; IH1; IH33; IH33; IH33; = 6
  • T-CLAS1; CLAS1; CLAS3; CLAS3; U-CLAS1; CLAS1; CLAS3; CLAS3; = 40 seconds

Patrony PID are calculated a následující:

Proportional Gain (K 'I1;' I1; 'FLT: 0' I3; 'I3;' P 'I1;' I1; 'FLT: 1' I3; 'I3;)

K 'I1;' I1; 'FLT: 0' I3; 'I3; p' I1; 'I1;' FLT: 1 'I3;' II3; 'II1;' II1; 'FLT: 2' II3; 'II1;' IIII1; 'IIIII3;' III3; 'III3;' III0 '= 0, 6 × 6 = 3.6

Integrál Time (T 'I1;' I1; 'FLT: 0' I3; 'II3;' II1; 'II1;' III1; 'FLT: 1' II3; 'II3;)

T 'I1;' I1; 'III1;' IIIIII1; 'III1;' IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII@@

Deriváty Time (T 'I1;' I1; 'FLT: 0' 3; 'I3;' D 'I1;' I1; 'FLT: 1' I3; 'I3;)

T 'I1;' I1; 'FLT: 0' I3; 'I3;' II1; 'II1;' IIIIII; 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII@@

Final PID Settings

Te tuned PID controller parameters are:

  • K-CY1; CY1; CY11; CY13; CY11; CY11; CY11; CY13; CY13; = 3.6
  • T-CLAS1; CLAS1; CLAS3; CLAS3; I-CLAS1; CLAS1; CLAS3; CLAS3; = 20 seconds
  • T-CLAS1; CLAS1; CLAS3; CLAS3; CLAS1; CLAS1; CLAS1; CLAS3; CLAS3; = 5 seconds