Rapid estimation of PID minimum variance

PID controllers are the most common type of controllers used in industry. However, to find the best PID performance is a challenging task. Assessment of the best PID performance leads to the minimization of the deviation from set point as indicated by closed loop transfer function. This is a non-convex optimization problem and there is no direct solution for finding this benchmark. Solving this problem iteratively as proposed in literature requires long calculation times. Furthermore, iterative methods are not guaranteed to find the minimum value. Using as many as possible infinite impulse response coefficients, or increasing the number of finite impulse coefficients gradually, causes undesirably large calculation times. We propose a fast method to evaluate the minimum variance by a fixed number of finite impulse response coefficients. This finite impulse model is double the size of the stable system impulse response (it contains the transient response and the same duration of steady state). Thus it avoids undesired iteration, and consequently, the PID minimum variance is quickly evaluated. Time is a critical factor as the purpose to assess this index is for use in online monitoring. The proposed method is tested on benchmark simulation examples from literature.