Abstract
Today, most manufacturing control systems are complex and expensive, so they are limited to employ a small number of function evaluations for optimal design. Yet, looking for optimization methods with the less-computational cost is an open issue in engineering control systems. This paper aims to propose an effective adaptive optimization approach by integrating Kriging surrogate and Particle Swarm Optimization (PSO). In this method, a novel iterative adaptive approach is utilized using two sets of training samples including initial training and adaptive sample points. The initial training points are designed by space-filling design, while the adaptive points are generated using a new jackknife resampling approach. The proposed approach can effectively convergence towards the global optimal point using a small number of function evaluations. The efficiency and applicability of the proposed algorithm are evaluated using the optimal design of the fractional-order PID (FOPID) controller for some benchmark transfer functions. Then, the introduced approach is applied for tuning the parameters and the sensitivity analysis of the FOPID controller for a dynamic production-inventory control system. The results are in good agreement with the results reported in the literature, while the proposed approach is executed with a lower computational burden.
Highlights
The main motivation of the current study is to develop a new method for tuning fractional-order PID (FOPID) controllers when the proposed method is specified in two main specifications including i) a black-box method that does need applying dynamic mathematical expressions of a control system, and ii) a less-expensive method with the lower number of function evaluations
The Particle Swarm Optimization (PSO) used in the proposed algorithm has the same parameter adjustment as the PSO that individually is used for direct FOPID tuning
The FOPID controller tuned by the proposed algorithm produces a smooth and fast output comparing to the controllers tuned by the PSO, Grey Wolf Optimizer (GWO), Ant Lion Optimizer (ALO), Ant-Colony Optimization (ACO), and GA methods
Summary
Control engineering refers to the use of automatic control to make systems or processes reach the desired behavior while operating under certain constraints. This discipline has been being intensively enlarged over the past decades due to the advancement of modern technologies and the development of new systems, in particular intelligent systems [1]. Proportional-Integral-Derivative (PID) controllers with feedback control structures are widely used for industrial process control. While more powerful control techniques are readily available, the PID controller is still popular due to its relative simplicity and applicability to a wide range of industrial control problems, see [2]–[5]. The output of a PID controller equal to the control input of the plant in the time-domain is:
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