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Abstract A single-step procedure to obtain first and higher order discrete-time models in terms of infinite impulse response templates of the fractional order Laplacian operator s α , where 0 < α < 1 , is proposed in this paper. The Moth Flame Optimization (MFO) algorithm based rational approximations are generated using a discretization operator-free method. Solution accuracy and the convergence performance of MFO are extensively compared with several other advanced evolutionary algorithms. Simulations justify the improved modelling accuracy of the proposed models over the recently published designs. The effects due to the finite word length leading to truncated filter coefficients are also considered, and the design stability robustness is demonstrated. The efficacy of the proposed model as a fractional order proportional-derivative controller is also validated. [ABSTRACT FROM AUTHOR]

In this paper, a recently proposed metaheuristic optimization technique called hybrid flower pollination algorithm (HFPA) is applied to design wideband infinite impulse response digital differentiators (DDs) and digital integrators (DIs). In recent years, benchmark nature-inspired optimization algorithms such as particle swarm optimization (PSO), simulated annealing, and genetic algorithm have been employed for the design of wideband DDs and DIs. However, individually, these algorithms show major drawbacks such as premature convergence, thus leading to a sub-optimal solution. HFPA, however, is a hybrid approach which combines the efficient exploitation and exploration capabilities of two different metaheuristics, namely PSO and flower pollination algorithm (FPA), respectively. The HFPA-based designs have been compared with real-coded genetic algorithm, PSO, differential evolution, success-history-based adaptive differential evolution with linear population size reduction (L-SHADE), self-adaptive differential evolution (jDE), and FPA-based designs with respect to the solution quality, robustness, convergence, and optimization time. Simulation results demonstrate that among all the algorithms, the HFPA-based designs consistently achieve superior performances in the least number of function evaluations. Exhaustive experimentations are conducted to determine the best values of the control parameters of HFPA for the optimal design of DDs and DIs. The proposed designs also outperform the recently reported designs based on non-optimal, classical, and nature-inspired optimization approaches in terms of magnitude response. The lower orders of the proposed designs render them suitable for real-time applications. [ABSTRACT FROM AUTHOR]

Design of wideband infinite impulse response (IIR) digital fractional order integrators (DFOIs) based on a bio-inspired metaheuristic optimization approach called the cat swarm optimization (CSO) algorithm is presented in this paper. To investigate the efficiency of the proposed approach, the CSO-based DFOIs are evaluated against those of the approximations designed using real-coded genetic algorithm (RGA), standard particle swarm optimization (PSO), and differential evolution (DE) by different magnitude and phase response error metrics. Simulation results reveal the better frequency response of the CSO-based DFOIs in comparison with the competing designs. Both parametric and nonparametric statistical hypothesis tests validate the performance consistency of CSO. Comparisons with the cited literature confirm the efficacy of the proposed models. [ABSTRACT FROM AUTHOR]

This paper presents an efficient approach to design stable, wideband, and infinite impulse response digital integrators (DIs) and digital differentiators (DDs) of first, second, third, and fourth order using an evolutionary optimization algorithm called harmony search (HS). In recent years, although wideband DIs and DDs have been designed using metaheuristic optimization techniques such as simulated annealing, genetic algorithm, and particle swarm optimization (PSO), these algorithms lead to sub-optimal solutions because of stagnation and premature convergence. HS algorithm, however, promises an enhanced frequency response for DIs and DDs because of the better exploration and exploitation of the search space. Simulation results demonstrate the superiority of HS-based designs as compared with three well-known benchmark evolutionary optimization algorithms, namely real coded genetic algorithm (RGA), PSO, and differential evolution (DE) based designs by yielding the least values of different magnitude response error metrics. Parametric and non-parametric statistical hypothesis tests are also conducted to compare the consistency in the performance of HS-based DIs and DDs with those of the designs based on RGA, PSO, and DE. The proposed HS-based designs also outperform those of the designs based on both classical and evolutionary optimization approaches reported in recent literature in terms of the maximum absolute magnitude error metric. [ABSTRACT FROM AUTHOR]

A precise control in the stopband attenuation characteristics can be achieved by using the fractional-step filters instead of the traditional integer-order filters. In this paper, nine nature-inspired optimization algorithms, such as five advanced variants of differential evolution (DE), three advanced variants of particle swarm optimization (PSO), and an efficient evolutionary strategy method (CMA-ES-RIS) are employed to design the fractional-step low pass Butterworth filter (FLBF). The proposed (1 + α) and (2 + α) order models, where α ∈ (0 , ​ 1) , are optimally approximated as an integer-order transfer function by using the magnitude-frequency information of the ideal FLBF. Comparisons regarding the solution quality and robustness reveal an improved accuracy for the DE variants and CMA-ES-RIS over all the PSO variants. Results from the pair-wise Wilcoxon rank-sum test demonstrate the superiority of enhanced fitness-adaptive differential evolution (EFADE) algorithm as the most efficient optimization tool for solving this problem. Comparisons with the state-of-the-art approaches also confirm the superior modelling accuracy of the proposed FLBFs. The canonical structure circuit realization of the FLBFs using current feedback operational amplifiers is presented. Simulations carried out in OrCAD PSPICE platform suggest proximity in the magnitude responses between the proposed and the theoretical models. The optimal design of stable, minimum-phase (2 + α) order FLBFs is also presented for the first time without employing the cascading concept involving the integer-order Butterworth polynomials. [ABSTRACT FROM AUTHOR]

• The paper benefits from Reinforcement Learning in industrial control applications. • TD3 policy gradient is implemented to learn optimal PI controller dynamics. • The actor-network learns the optimal PI dynamics using the reward mechanism. • The performance of the optimal PI dynamics is compared with the other results. To benefit from the advantages of Reinforcement Learning (RL) in industrial control applications, RL methods can be used for optimal tuning of the classical controllers based on the simulation scenarios of operating conditions. In this study, the Twin Delay Deep Deterministic (TD3) policy gradient method, which is an effective actor-critic RL strategy, is implemented to learn optimal Proportional Integral (PI) controller dynamics from a Direct Current (DC) motor speed control simulation environment. For this purpose, the PI controller dynamics are introduced to the actor-network by using the PI-based observer states from the control simulation environment. A suitable Simulink simulation environment is adapted to perform the training process of the TD3 algorithm. The actor-network learns the optimal PI controller dynamics by using the reward mechanism that implements the minimization of the optimal control objective function. A setpoint filter is used to describe the desired setpoint response, and step disturbance signals with random amplitude are incorporated in the simulation environment to improve disturbance rejection control skills with the help of experience based learning in the designed control simulation environment. When the training task is completed, the optimal PI controller coefficients are obtained from the weight coefficients of the actor-network. The performance of the optimal PI dynamics, which were learned by using the TD3 algorithm and Deep Deterministic Policy Gradient algorithm, are compared. Moreover, control performance improvement of this RL based PI controller tuning method (RL-PI) is demonstrated relative to performances of both integer and fractional order PI controllers that were tuned by using several popular metaheuristic optimization algorithms such as Genetic Algorithm, Particle Swarm Optimization, Grey Wolf Optimization and Differential Evolution. [ABSTRACT FROM AUTHOR]