Optimal design of fractional-order PID controller for five bar linkage robot using a new particle swarm optimization algorithm

Abstract

This paper introduces a new version of the particle swarm optimization (PSO) method. Two basic modifications for the conventional PSO algorithm are proposed to improve the performance of the algorithm. The first modification inserts adaptive accelerator parameters into the original velocity update formula of the PSO which speeds up the convergence rate of the algorithm. The ability of the algorithm in escaping from local optima is improved using the second modification. In this case, some particles of the swarm, which are named the superseding particles, are selected to be mutated with some probability. The proposed modified PSO (MPSO) is simple to be implemented, fast and reliable. To validate the efficiency and applicability of the MPSO, it is applied for designing optimal fractional-order PID (FOPID) controllers for some benchmark transfer functions. Then, the introduced MPSO is applied for tuning the parameters of FOPID controllers for a five bar linkage robot. Sensitivity analysis over the fractional order of the PID controller is also provided. Numerical simulations reveal that the MPSO can optimally tune the parameters of FOPID controllers.

Review of fractional PID controller

“…If the closed loop system becomes unstable, then the cost function is penalized by a significant value. The fractional PID controller was also tested for robustness against uncertainties of the model parameters and the same method was used for designing the fractional controller for a five bar linkage robot [95] .…”

A New Simulation-based Robust Optimal Design of FOPID Controller for Five Bar Linkage Robot in a Cyber-physical System

“…In addition, the exploitation occurs when these two values are both small. PSO has attracted wide attention in control engineering design problems due to its algorithmic simplicity and powerful search performance [62], [63]. However, PSO algorithm that requires a large number of fitness evaluations before locating the global optimum is often prevented from being applied to computationally expensive real-world problems [64].…”

“…Numeric values of the parameters of the five-bar manipulator dynamics are taken from [62], [90] as shown in Table 1. From the data driven in Table 1, it is revealed that The search procedure for the robust optimal result is done in the ranges as [62]: Moreover, according to an updated set of training samples, a new GP surrogate is constructed after each sequential EI iteration.…”

“…Numeric values of the parameters of the five-bar manipulator dynamics are taken from [62], [90] as shown in Table 1. From the data driven in Table 1, it is revealed that The search procedure for the robust optimal result is done in the ranges as [62]: Moreover, according to an updated set of training samples, a new GP surrogate is constructed after each sequential EI iteration. It is important to note that we avoid extrapolation of GP surrogate in each sequential iteration by setting two different rules, i) we consider a death penalty for any point that is investigated by PSO and is located out of bounds of training points, ii) in order to estimate GP prediction error using jackknife leave-one-out approach, we only remove input combination's rows that don't locate on the margin of design space (see Section 3.1.5).…”

Optimization of ANFIS controllers using improved ant colony to control an UAV trajectory tracking task

“…In [56] authors presented the optimal trajectory tracking control of robotic manipulator using an ACO algorithm based PID controller. An optimal design of PID using particle swarm optimization algorithm (PSO) for the control of five bar linkage robot has been introduced in [57]. A PSO algorithm for fuzzy predictive control has been developed and applied for quadrupletank process in [58].…”