Proporcjonalne - Integral- Derivative (PID) controllers are widely used in level control systems to maintain desired liquid levels. Proper tuning of PID parameters is essential for optimal performance. Thii s article provides numerical examples of PID parameter calculations for level control applications.

Parametry systemu Basic

Consider a level control system with the following parameters:

  • Process gain (K, 1;, 1; FLT: 0, 3;, 3; p, 1; FLT:, 3;) = 2
  • Process time constant (τ Δ1; Δ1; FLT: 0 XXX3; EDX3; p XXX1; EDX1; FLT: 1 EFY3; EDX3;) = 50 sekund
  • Dead time (L) = 10 seconds

Parametr PID Kalkulacja

Using the Ziegler- Nichols tuning methode, the ultimate gain (K presendi1; FLT: 0 presendi3; British 3; u presendi1; FLT: 1 presendi3; British 3;) and ultimate period (T presendi1; British 1; FLT: 2 presenti3; u Presendition 1; British 1; FLT: 3 presential 3; Determinad experimentally. Assume:

  • K Xi1; Xi1; FLT: 0 Xi3; Xi3; u Xi1; Xi1; FLT: 1 Xi3; Xi3; = 6
  • T = 1; 1; FLT: 0 = 3; FLT: 0 = 3; FLT: 1 = 3; FLT: 1 = 3; FLT: 1 = 4 sekundy

Parametry PID are calculated as follows:

Proporcjonal Gain (K 'vir1; Gior1; FLT: 0' vir3; Gior3; p 'vir1; Gior1; Gulf: 1' vir3; Gior3;)

K = 1; Xi1; FLT: 0 Xi3; Xi3; p = 1; Xi1; FLT: 1 Xi3; Xi3; = 0,6 × K = 1; FLT: 2 Xi3; Xi3; u Xi1; Xi1; FLT: 3 XI3; Xi3; Xi3; = 0,6 × 6 = 3,6

Integral Time (T Xi1; Xi1; FLT: 0 Xi3; Xi3; I Xi1; Xi1; FLT: 1 Xi3; Xi3;)

T = 1; Xi1; FLT: 0 Xi3; Xi3; I = 1; Xi1; FLT: 1 Xi3; Xi3; = 0,5 × T = 1; Xi1; FLT: 2 Xi3; Xi3; Xi1; FLT: 3 XI3; Xi3; Xi3; = 0,5 × 40 = 20 sekund

Derivative Time (T is 1; T is 1; FLT: 0 is 3; ED3; D is 1; ED1; FLT: 1 is 3; EDT 3;)

T = 1; Xi1; FLT: 0 Xi3; Xi3; D Xi1; Xi1; FLT: 1 Xi3; Xi3; = 0,125 × T = 1; Xi1; FLT: 2 Xi3; Xi3; Xi1; FLT: 3 XI3; Xi3; Xi3; = 0,125 × 40 = 5 sekund

Ustawienie PID final

Te tuned PID controller parameters are:

  • K, 1, 1, FLT: 0, 0, 3, p, 1, 1, 1, 3, 6
  • T = 1; 1; FLT: 0 = 3; I = 1; FLT: 1 = 3; FLT = 2
  • T = 1; 1; FLT: 0 = 3; D = 1; FLT: 1 = 3; FLT: = 5 sekund