Design and application of an optimally tuned PID controller for DC motor speed regulation via a novel hybrid Lévy flight distribution and Nelder–Mead algorithm

Abstract

This paper deals with the design of an optimally performed proportional–integral–derivative (PID) controller utilized for speed control of a direct current (DC) motor. To do so, a novel hybrid algorithm was proposed which employs a recent metaheuristic approach, named Lévy flight distribution (LFD) algorithm, and a simplex search method known as Nelder–Mead (NM) algorithm. The proposed algorithm (LFDNM) combines both LFD and NM algorithms in such a way that the good explorative behaviour of LFD and excellent local search capability of NM help to form a novel hybridized version that is well balanced in terms of exploration and exploitation. The promise of the proposed structure was observed through employment of a DC motor with PID controller. Optimum values for PID gains were obtained with the aid of an integral of time multiplied absolute error objective function. To verify the effectiveness of the proposed algorithm, comparative simulations were carried out using cuckoo search algorithm, genetic algorithm and original LFD algorithm. The system behaviour was assessed through analysing the results for statistical and non-parametric tests, transient and frequency responses, robustness, load disturbance, energy and maximum control signals. The respective evaluations showed better performance of the proposed approach. In addition, the better performance of the proposed approach was also demonstrated through experimental verification. Further evaluation to demonstrate better capability was performed by comparing the LFDNM-based PID controller with other state-of-the-art algorithms-based PID controllers with the same system parameters, which have also confirmed the superiority of the proposed approach.

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

“…Those approaches include both PID and FOPID controllers. Table 5 presents the time domain performance comparison of ISMA-FOPID with manta ray foraging optimization based FOPID controller (MRFO-FOPID) (Ekinci et al, 2021b), chaotic atom search optimization algorithm based FOPID (ChASO-FOPID) controller (Hekimoğlu, 2019a), atom search optimization based FOPID (ASO-FOPID) controller (Hekimoğlu, 2019a), stochastic fractal search algorithm based FOPID (SFS-FOPID) controller (Saini et al, 2020), grey wolf optimization based FOPID (GWO-FOPID) controller (Agarwal et al, 2018), Lévy flight distribution with Nelder–Mead algorithm based PID (LFDNM-PID) controller (Izci, 2021), Harris–Hawks optimization based PID (HHO-PID) controller (Ekinci et al, 2020b), Henry gas solubility optimization based PID (HGSO-PID) controller (Ekinci et al, 2021a), SMA based PID (SMA-PID) controller (Izci and Ekinci, 2021), atom search optimization based PID (ASO-PID) controller (Hekimoğlu, 2019a), grey wolf optimization based PID (GWO-PID) controller (Agarwal et al, 2018), stochastic fractal search algorithm based PID (SFS-PID) controller (Bhatt et al, 2019), kidney-inspired algorithm based PID (KA-PID) controller (Hekimoğlu, 2019b), sine–cosine algorithm based PID (SCA-PID) controller (Agarwal et al, 2017), invasive weed optimization algorithm based PID (IWO-PID) controller (Khalilpour et al, 2011), and particle swarm optimization based PID (PSO-PID) controller (Khalilpour et al, 2011).…”

“…Figure 15 illustrates the comparative output speed performance of the DC motor system tuned by different tuning approaches graphically, besides the numerical values provided in Table 5. It is worth noting that Figure 15 only demonstrates the comparative plots of ISMA-FOPID, ChASO-FOPID (Hekimoğlu, 2019a) and LFDNM-PID (Izci, 2021) approaches as those approaches provide the best results, in terms of ZLG quality indicator, among the listed approaches in Table 5. In this way, it was also aimed to avoid confusion and provide a clearer description.…”

“…Considering the existing structures, the PID controllers can be seen to have a huge utilization in terms of speed regulation of DC motors due to their easier implementation (El-Deen et al, 2015; Izci, 2021). Although PID controllers have widely been utilized controller structures with regards to DC motors’ speed regulation, a FOPID controller has been demonstrated to have better flexibility to provide even more efficiency in terms of operation due to the additional fractional order terms that it possesses (Ekinci et al, 2021b).…”

“…The main advantages of optimization algorithms arise from their ability to choose the optimal parameter values of the system under different conditions (Simorgh et al, 2021) without causing a great deal of problems in terms of time consumption (Hashim et al, 2021). The metaheuristic algorithms have so far been demonstrated to be good tools in terms of optimization as they have better ability to avoid local optimum and achieve efficient solutions with less computational costs (Izci, 2021). In terms of metaheuristic optimization techniques, many different algorithms are available to deal with a variety of problems with different domains.…”

“…The proposed ISMA based FOPID controller for DC motor speed control system was compared with 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.…”