Tuning Optimal Proportional–Integral–Derivative Controllers for Desired Closed-Loop Response Using the Method of Moments

In the direct synthesis method of controller design, the optimality of the controller parameters are strongly affected by the approximations involved in developing the process models and the choice of desired closed-loop response characteristics. This work (i) captures the process dynamic characteristics through the method of moments; (ii) proposes a tuning parameter λ in the direct synthesis method, which is optimized through the minimization of integrated absolute error (IAE) subject to the constraint on peak sensitivity; and (iii) provides correlations for optimal λ values as a function of process parameters. First-order plus delay time (FOPDT), second-order plus delay time (SOPDT), and second-order with inverse response (SOIR) models are used to characterize the process dynamics and as desired closed-loop transfer functions. The efficacy of the proposed method is illustrated with the help of several types of processes. The proposed controller tuning method performs equally well as compared to other methods for plants approximated with FOPDT models and has been shown to be very effective for SOPDT and SOIR models.