Proportional- Integral- Derivative (PID) controlers are widely used id in leul control systems to maintain desired liquid levels. Proper tuning of PID parameters is essential for optimal performance. Tiss article provides numericál examples of PID parameteur calculations for leak control applications.

Basic System Parameters

A leoll control system with the following parameters:

  • Processzek gain (K) (1; 1; FLT: 0) 3; WHN3; PHN1; FLT: 1) 3N3; WHN3;) = 2
  • Processzes time constant (Σ1;) = 50 seconds
  • Dead time (L) = 10 másodperc

PID Parameter Calculation

Usinggh the Ziegler- Nichols tuning metod, the ultimate gain (K '1;) FLT: 0' 3; W.3; u '1; FLT: 1' 3; W.1;) and ultimate 'd (T' 1; 1d 's FLT: 2' 3; u '1d; FLT: 3' 3d; W.3d; ') are determinedally. Asmäge:

  • K '1;' 1; FLT: 0 '3;' 3; u '1;' 1c '; FLT: 1' 3d '; = 6
  • T '1; -1; FLT: 0' 3; U '1; -1c'; FLT: 1 '3d; = 40 mbs

PID parameters are calculated ad as follow:

Proportionál Gain (K) 1; 1; FLT: 0 '3; FLT: 0' 3; p '1; 1c'; FLT: 1 '3d;' 3d; ')

K '1; 1; FLT: 0' 3; p '1; FLT: 1' 3; '3d'; = 0.6 × K '-1d' 1d; FLT: 2 '3d'; u '1d; FLT: 3' 3d; = 0.6 × 6 = 3,6

Intreprel Time (T) 1; 1; FLT: 0) 3; WH3; I) 1d; FLT: 1) 3d; WH3d;)

T '1; 1; FLT: 0' 3; I '1; FLT: 1' 3; '3d'; = 0.5 × T '1d' 1d; FLT: 2 '3d'; u '1d' 1d; FLT: 3 '3d; = 0.5 × 40 = 20

Származtatott ügyletek (T) Time (T) (1d; 1d; FLT: 0) 3d; D) 1d; FLT: 1 d.m.m.m.m.m.m.m.)

T '1; 1; FLT: 0' 3; D '1; FLT: 1' 3; '3d'; = 0,125 × T '1d' 1d; FLT: 2 '3d'; u '1d' 1d; FLT: 3 '3d; = 0,125 × 40 = 5 messs

Final PID Settings

A PID-k irányítják a parameters are:

  • K '1;' 1; FLT: 0 '3;' 3; p '1c'; FLT: 1 '3d'; = 3,6
  • T '1; -1; FLT: 0' 3; I '1c'; FLT: 1 '3d'; = 20 mfs
  • T '1; I'; T '1; FLT: 0' 3; D '1d'; FLT: 1 '3d; = 5 messs