Robust tuning and sensitivity analysis of stochastic integer andfractional‐order PIDcontrol systems: application ofsurrogate‐basedrobustsimulation‐optimization

Abstract

This paper aims to make a trade‐off between performance and robustness in stochastic control systems with probabilistic uncertainties. For this purpose, we develop a surrogate‐based robust simulation‐optimization approach for robust tuning and analyzing the sensitivity of stochastic controllers. Kriging surrogate is combined with robust design optimization to construct a robust simulation‐optimization model in the class of dual response surfaces. Randomness in simulation experiments due to uncertainty is analyzed through bootstrapping technique by computing confidence regions for the estimation of Pareto frontier. Results confirmed a proper trade‐off between the model's performance with the measure of expected Integral Squared Error (ISE) and robustness against uncertainty in the plant's physical parameters. Finally, the proposed method is evaluated in terms of accuracy, computational cost, and simplicity particularly in comparison with some common existed techniques in the tuning of the Proportional‐Integral‐Derivative (PID) and Fractional‐Order PID (FOPID) controllers.

New Adaptive Surrogate-Based Approach Combined Swarm Optimizer Assisted Less Tuning Cost of Dynamic Production-Inventory Control System

“…However, there is still a challenging research problem since most of the integer and fractional-order PID controllers are suffering from badly-tuned parameters, being the reason why they operate improperly in nonoptimal regions [15], [16]. The optimization-based tuning methods for the complex control systems are classified into mathematical methods, simulation-based methods, and surrogates [17], [18]. Investigating less computationally expensive (i.e., a smaller number of iterations or function evaluations) methods for achieving optimal design controller has also become a main challenging topic in the control engineering practice.…”

Robust Optimal Placement and Sensitivity Analysis of Multiple Transmitting Antennas Under Uncertainty: A New Surrogate-Based Evolutionary Algorithm

“…Most of the standardized residuals should be within the interval −3 ≤ 𝐷 𝑠 ≤ 3, and any observation outside of this interval (outlier) is potentially unacceptable with respect to its observed simulation output [36], [37].…”

“…The surrogate model constructed in Step 5 has to be validated to ensure that its predictive power is sufficient for design optimization purposes. Here, validation is executed using the leave-one-out cross validation (𝑘 = 1) [36], [37], which works as follows. First delete the 𝑠 𝑡ℎ input combination and the relevant output from the complete set of the 𝑙th combination (𝑠 = 1,2, … , 𝑙), i.e., to avoid the extrapolation by Kriging, we avoid dropping the sample points in the margin.…”

Robust design of fractional order IMC controller for fractional order processes with time delay

“…6 However, in recent years, FO controller has been drawn attention in academia and industry for a wide range of applications. 7,8 This controller is a generalization of the IO controller. It was initially introduced by Oustaloup into the control system field.…”

“…Since then, a wide range of control techniques has been proposed for the PID controller 6 . However, in recent years, FO controller has been drawn attention in academia and industry for a wide range of applications 7,8 . This controller is a generalization of the IO controller.…”