Performance assessment of controller designed for electrical systems with second order dynamics

An assessment technique that analyzes the servo and regulatory characteristics of the proportional integral derivative controller is designed for time-delayed second-order stable processes.

The minimum theoretical error expression for integral of the absolute errors (IAE_o) is obtained from the preferred servo and regulatory transfer functions dependent on the step changes in reference and load variables.

The error-based index is outlined to estimate the controller that is derived using internal model-based control or direct synthesis method. The ratio between derived IAE_o and the IAE_actual gained from the loop response that experiences step input variations gives rise to a dimensionless error index. This error index measures the behaviour of the controller by considering the index value. If the error index value is larger than 0.8, then the effort taken by the controller is good or else retuning is expected.

The efficacy of the index to validate the controller is verified by applying on a few second-order electrical processes. The results are simulated for both reference tracking and load rejection tasks to demonstrate the rationality of the presented index.