Numerical Examples of Pid Parameter Calculations for Level Control Applications

Proportional-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. This article provides numerical examples of PID parameter calculations for level control applications.

Basic System Parameters

Consider a level control system with the following parameters:

• Process gain (K_p) = 2
• Process time constant (τ_p) = 50 seconds
• Dead time (L) = 10 seconds

PID Parameter Calculation

Using the Ziegler-Nichols tuning method, the ultimate gain (K_u) and ultimate period (T_u) are determined experimentally. Assume:

• K_u = 6
• T_u = 40 seconds

PID parameters are calculated as follows:

Proportional Gain (K_p)

K_p = 0.6 × K_u = 0.6 × 6 = 3.6

Integral Time (T_I)

T_I = 0.5 × T_u = 0.5 × 40 = 20 seconds

Derivative Time (T_D)

T_D = 0.125 × T_u = 0.125 × 40 = 5 seconds

Final PID Settings

The tuned PID controller parameters are:

• K_p = 3.6
• T_I = 20 seconds
• T_D = 5 seconds