Optimal design of non‐fragile PID controller

Abstract

This paper solves the controller gains uncertainty problem, which may lead to undesirable responses and an unstable system when implemented. A non‐fragile or resilient controller can overcome this problem. The paper suggests a new method to design a non‐fragile proportional‐integral‐derivative (PID) controller for voltage regulation. This method is carried out by applying a constrained genetic algorithm (GA) as a powerful optimization technique to determine the optimal gains of the PID controller. In addition, new developed conditions from the Routh– Kharitonov theorem are taken into account during the optimization operation to ensure system stability and system response. A new time domain objective function is proposed to establish the optimal permissible limits of controller gains to ensure a constraint of good response. The results of the proposed non‐fragile PID controller are compared with the non‐constrained GA‐based PID controller, artificial bee colony (ABC) algorithm‐based PID controller, and Ziegler Nichols (ZN)‐based PID controller. This achieves better results compared with different methods. The controller gains uncertainties test is applied to ensure the non‐fragility of the proposed controller. Furthermore, the system parameters variation test is applied to check the robustness of the controller based on the suggested method. The designed PID controller by this method is more resilient and less design time is required. The proposed controller and the system are carried out and studied by utilizing MATLAB/Simulink.

Performance evaluation of a novel improved slime mould algorithm for direct current motor and automatic voltage regulator systems

“…Those approaches include PID, FOPID and PIDD 2 controllers. Table 9 presents the time domain performance comparison of ISMA-PIDD 2 with hybrid simulated annealing-Manta ray foraging optimization based PIDD 2 (SA-MRFO-PIDD 2 ) controller (Micev et al, 2021a), improved whale optimization algorithm based PIDD 2 (IWOA-PIDD 2 ) controller (Mokeddem and Mirjalili, 2020), atom search optimization based PIDD 2 (ASO-PIDD 2 ) controller (Ekinci et al, 2020a), whale optimization algorithm based PIDD 2 (WOA-PIDD 2 ) controller (Mosaad et al, 2019), teaching–learning-based optimization based PIDD 2 (TLBO-PIDD 2 ) controller (Mosaad et al, 2018), particle swarm optimization based PIDD 2 (PSO-PIDD 2 ) controller (Sahib, 2015), sine–cosine algorithm based FOPID (SCA-FOPID) controller (Ayas and Sahin, 2021), jaya optimization algorithm based FOPID (JOA-FOPID) controller (Jumani et al, 2020), Henry gas solubility optimization based FOPID (HGSO-FOPID) controller (Ekinci et al, 2020c), chaotic yellow saddle goatfish algorithm based FOPID (C-YSGA-FOPID) controller (Micev et al, 2020), salp swarm optimization algorithm based FOPID (SSA-FOPID) controller (Khan et al, 2019), cuckoo search algorithm based FOPID (CS-FOPID) controller (Sikander et al, 2018), simulated annealing algorithm based FOPID (SA-FOPID) controller (Lahcene et al, 2017), equilibrium optimizer based PID (EO-PID) controller (Micev et al, 2021b), genetic algorithm based PID (GA-PID) controller (Elsisi, 2021), cuckoo search algorithm based PID (CS-PID) controller (Sikander and Thakur, 2020), enhanced crow search algorithm based PID (ECSA-PID) controller (Bhullar et al, 2020a), tree seed algorithm based PID (TSA-PID) controller (Kose, 2020), sine–cosine algorithm based PID (SCA-PID) controller (Hekimoğlu, 2019c), improved kidney-inspired algorithm based PID (IKA-PID) controller (Ekinci and Hekimoğlu, 2019), stochastic fractal search algorithm based PID (SFS-PID) controller (Çelik, 2018), symbiotic organisms search algorithm based PID (SOS-PID) controller (Çelik and Durgut, 2018), grasshopper optimization algorithm based PID (GOA-PID) controller (Hekimoğlu and Ekinci, 2018), jaya optimization algorithm based PID (JOA-PID) controller (Gong, 2019), gravitational search algorithm based PID (GSA-PID) controller (Duman et al, 2016), biogeography-based optimization based PID (BBO-PID) controller (Guvenc et al, 2016), local unimodal sampling algorithm based PID (LUS-PID) controller (Mohanty et...…”

“…The efficacy of the proposed approach for the DC motor system was compared to other available and effective approaches of manta ray foraging optimization (Ekinci et al, 2021b), chaotic atom search optimization algorithm (Hekimoğlu, 2019a), atom search optimization (Hekimoğlu, 2019a), stochastic fractal search algorithm (Saini et al, 2020), grey wolf optimization (Agarwal et al, 2018) based FOPID controllers and Lévy flight distribution with Nelder–Mead algorithm (Izci, 2021), Harris–Hawks optimization (Ekinci et al, 2020b), Henry gas solubility optimization (Ekinci et al, 2021a), SMA (Izci and Ekinci, 2021), atom search optimization (Hekimoğlu, 2019a), grey wolf optimization (Agarwal et al, 2018), stochastic fractal search algorithm (Bhatt et al, 2019), kidney-inspired algorithm (Hekimoğlu, 2019b), sine–cosine algorithm (Agarwal et al, 2017), invasive weed optimization algorithm (Khalilpour et al, 2011), and particle swarm optimization (Khalilpour et al, 2011) based PID controllers for further assessment. Likewise, the proposed approach for the AVR control system was compared with other available and effective approaches of hybrid simulated annealing–Manta ray foraging optimization (Micev et al, 2021a), improved whale optimization algorithm (Mokeddem and Mirjalili, 2020), atom search optimization (Ekinci et al, 2020a), whale optimization algorithm (Mosaad et al, 2019), teaching–learning-based optimization (Mosaad et al, 2018), particle swarm optimization (Sahib, 2015) based PIDD 2 controllers and sine–cosine algorithm (Ayas and Sahin, 2021), jaya optimization algorithm (Jumani et al, 2020), Henry gas solubility optimization (Ekinci et al, 2020c), chaotic yellow saddle goatfish algorithm (Micev et al, 2020), salp swarm optimization algorithm (Khan et al, 2019), cuckoo search algorithm (Sikander et al, 2018), simulated annealing algorithm (Lahcene et al, 2017) based FOPID controllers along with equilibrium optimizer (Micev et al, 2021b), genetic algorithm (Elsisi, 2021), cuckoo search algorithm (Sikander and Thakur, 2020), enhanced crow search algorithm (Bhullar et al, 2020a), tree seed algorithm (…”

“…The proposed ISMA based PIDD 2 controller for the AVR control system was compared with other available and effective approaches of hybrid simulated annealing–Manta ray foraging optimization (Micev et al, 2021a), improved whale optimization algorithm (Mokeddem and Mirjalili, 2020), atom search optimization (Ekinci et al, 2020a), whale optimization algorithm (Mosaad et al, 2019), teaching–learning optimization (Mosaad et al, 2018), particle swarm optimization (Sahib, 2015) based PIDD 2 controllers and sine–cosine algorithm (Ayas and Sahin, 2021), jaya optimization algorithm (Jumani et al, 2020), Henry gas solubility optimization (Ekinci et al, 2020c), chaotic yellow saddle goatfish algorithm (Micev et al, 2020), salp swarm optimization algorithm (Khan et al, 2019), cuckoo search algorithm (Sikander et al, 2018), simulated annealing algorithm (Lahcene et al, 2017) based FOPID controllers along with equilibrium optimization (Micev et al, 2021b), genetic algorithm (Elsisi, 2021), cuckoo search algorithm (Sikander and Thakur, 2020), enhanced crow search algorithm (Bhullar et al, 2020a), tree seed algorithm (Kose, 2020), sine–cosine algorithm (Hekimoğlu, 2019c), improved kidney-inspired algorithm (Ekinci and Hekimoğlu, 2019), stochastic fractal search algorithm (Çelik, 2018), symbiotic organisms search algorithm (Çelik and Durgut, 2018), grasshopper optimization algorithm (Hekimoğlu and Ekinci, 2018), jaya optimization algorithm (Gong, 2019), gravitational search algorithm (Duman et al, 2016), biogeography-based optimization (Guvenc et al, 2016), local unimodal sampling algorithm (Mohanty et al, 2014), many optimizing liaisons algorithm (Panda et al, 2012), artificial bee colony algorithm (Gozde and Taplamacioglu, 2011), and neural network (Pongfai et al, 2020) based PID controllers.…”

Modified neural network algorithm based robust design of AVR system using the Kharitonov theorem

“…NNA, is a recently developed metaheuristic algorithm 45 which is inspired by biological nervous system and behavior of ANNs. The best obtained solution at each iteration in NNA is considered as target data.…”

“…One such recently developed (2018) optimization algorithm is the neural network algorithm (NNA) which is inspired by the concepts of artificial neural networks (ANNs) and biological nervous systems and employs the structure and concept of ANNs to generate new candidate solutions. 45 NNA has been used in the optimization of PEM fuel cell problem recently. 46,47 This paper comprises nine sections.…”