why iam getting negative settling time for load frequency of two area system by using pid controller

for both the areas response iam getting negative settling time

[Mathieu NOE]

how are you getting negative settling time ?

[deekshith]

once please check this image the waveforms are settling in negative graph can you please tell me the reasons for that and iam using pid controller in the model

[Sam Chak]

Hi @deekshith,

The reason for obtaining negative steady-state responses is due to the presence of equilibria with negative values in the closed-loop system.

It would be advisable to modify the title to prevent any confusion with the concept of negative settling time, as the time dimension progresses forward even when moving at relatively low speeds, as inferred from the Special Theory of Relativity.

If you are interested in exploring the root cause, kindly provide the mathematical model of the Two-Area Power System (TAPS), preferably in transfer function or state-space form, along with the designed gains in the PID controllers. This information will greatly aid in investigating the issue further.

[deekshith]

please check this is my simulink model can help me by informing me the mistakes

[Sam Chak]

Hi @deekshith,

Unfortunately, I am unable to check the Simulink model as there is no mathematical model, such as a transfer function, available to establish the mapping between the system's input and output. However, the key to understanding the steady-state response lies in the design of the controllers.

Answer 1

[Yash]

Hi Deekshith!

Based on the output response graph you've shared, it appears that the waveforms exhibit a positive settling time. The primary concern, however, seems to be the negative peak overshoot or the negative steady-state response you are encountering.

Since you have not shared any mathematical model depicting the simulink model, it is very not possible for us to determine the exact reason causing this issue. The problem could arise from various factors, such as a missing negative sign in a gain block or incorrect equations in one or more transfer functions.

To troubleshoot this issue, consider the following steps:

• Examine all the gain blocks to ensure they are configured correctly.
• Review the equations in all transfer functions for accuracy.
• Divide the complete model into smaller submodels and analyze the steady-state response of each to isolate the problem (this approach is akin to unit testing).
• Check for nonlinearity in the system. Nonlinear characteristics of the system components can lead to complex responses, including negative overshoot.

These steps should help you identify and rectify the issue, leading to improved model performance.