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Over two decades, the fractional (non-integer) order PID (FOPID or PIλDµ ) controller was introduced and demonstrated to perform the better responses in comparison with the conventional integer order PID (IOPID). In this paper, the design of an optimal FOPID controller for a DC motor speed control system by the flower pollination algorithm (FPA), oneof the most efficient population-based metaheuristic optimization searching techniques, is proposed. Based on the modern optimization framework, five parameters of the FOPID controller are optimized by the FPA to meet the response specifications of the DC motor speed control system and defined as constraint functions. Results obtained by the FOPID controller are compared with those obtained by the IOPID designed by the FPA. As the simulation results show, the FOPID can provide significantly superior speed responses to the IOPID.

The optimal design of the proportional-integral-derivative (PID) controller for an antenna azimuth position control system by using the Levy-flight intensified current search (LFICuS) algorithm is proposed in this paper. The LFICuS is one of the newest and most effective metaheuristic optimization search techniques. Based on the modern optimization context, the error between the desired azimuth angle input and the azimuth angle output is set as the objective function to be minimized by the LFICuS via searching for the optimal parameters of the PID controller. The optimal PID controller designed by the LFICuS is compared with that designed by the Ziegler-Nichols (ZN) tuning rules. As results, an antenna azimuth position control system with the PID controller designed by the LFICuS can provide very satisfactory responses without steady-state error and with less settling time, smaller oscillation and overshoot than that designed by the ZN.

The firefly algorithm (FA) was firstly proposed during 2008–2009 as one of the powerful population-based metaheuristic optimization techniques for solving continuous and combinatorial optimization problems. The FA has been proved and applied to various real-world problems in mostly single objective optimization manner. However, many real-world problems are typically formulated as the multiobjective optimization problems with complex constraints. In this paper, the multiobjective Levy-flight firefly algorithm (mLFFA) is developed for multiobjective optimization. The proposed mLFFA is validated against four standard multiobjective test functions to perform its effectiveness. The simulation results show that the proposed mLFFA algorithm is more efficient than the well-known algorithms from literature reviews including the vector evaluated genetic algorithm (VEGA), non-dominated sorting genetic algorithm II (NSGA-II), differential evolution for multiobjective optimization (DEMO) and multiobjective multipath adaptive tabu search (mMATS).

This paper presents the novel cooperative metaheuristic algorithm including the flower pollination algorithm (FPA) and the adaptive tabu search named the cooperative FPA-ATS. The proposed cooperative FPA-ATS possesses two states. Firstly, it starts the search for the feasible solutions over entire search space by using the FPA’s explorative property. Secondly, it searches for the global solution by using the ATS’s exploitative property. The cooperative FPA-ATS are tested against ten multimodal benchmark functions for global minimum finding in order to perform its search performance. By comparison with the FPA and ATS, it was found that the cooperative FPA-ATS is more efficient than the FPA and ATS, significantly.

The flower pollination algorithm (FPA) was firstly proposed in 2012 as one of the population-based metaheuristic optimization search techniques. It is conceptualized by the pollination behavior of flowering plants. In this paper, the new enhanced version of the original FPA named the modified flower pollination algorithm (MoFPA) is proposed to improve its search performance for function optimization. The switching probability of the original FPA used for selection between local and global pollinations is changed from the fixed manner to the random manner according to the pollination behavior of flowering plants in nature. To perform its effectiveness, the proposed MoFPA is tested against ten standard benchmark functions compared with the original FPA. As simulation results, it was found that the proposed MoFPA performs superior search performance for function optimization to the original FPA with higher success rates and faster search time consumed.

This paper proposes the newest modified version of the original flower pollination algorithm (FPA) named the parallel flower pollination algorithm (PFPA) and its application to the fractional-order (FO) mathematical model identification of the brushless DC (BLDC) motor. Based on the time sharing or the multiple point single strategy (MPSS), the proposed PFPA is suitable for use on a single CPU platform. Some results of the PFPA’s performance test over five standard benchmark functions are reported in this paper. Then, the PFPA is applied to identify the model parameters of the BLDC motor. As results, the PFPA can optimally provide the BLDC motor model parameters of both integer-order (IO) and FO models. However, the FO model performs more accurate than the IO one.

This paper proposes the optimal two-degree-of- freedom proportional-integral-derivative-accelerated (2DOF- PIDA) controller design for the liquid-level system based on the modern optimization by using the modified bat algorithm (MBA). The MBA is the new modified version of the original bat algorithm (BA) developed to improve its exploration and exploitation by using the random number drawn from a Levy- flight distribution as well as new loudness and pulse emission rate functions. Results of the 2DOF-PIDA controller designed by the MBA are compared with those of the one-degree-of- freedom proportional-integral-derivative (1DOF-PID) and 1DOF-PIDA controllers designed by the MBA. As results, the liquid-level controlled system with the 2DOF-PIDA controller designed by the MBA can provide very satisfactory responses superior to that with the 1DOF-PID and 1DOF-PIDA controllers designed by MBA.

Stability is very important in control system design and analysis. This paper presents the stability analysis of the three-phase induction motor speed controlled system with the fractional-order proportional-integral-derivative (FOPID) controller designed by the cuckoo search (CS). Matignon’s stability theorem is one of the most efficient and easiest approaches for stability analysis of the fractional control system. In this paper, Matignon’s stability theorem associated with Riemann surface and Riemann sheets is conducted for stability analysis of the considered fractionalorder control system. As results, it was found that the threephase induction motor speed controlled system with the FOPID controller is stable according to the Matignon’s stability conditions. The system stability can be assured by the responses of the controlled system.

This paper presents the optimal design of the fractional-order proportional-integral-derivative-accelerated (FOPIDA or PIλDμAν) controller by the cuckoo search (CS) for drive train system is presented. As the generalization of the PID controller family, the FOPIDA controller is more flexible in design for a wide range of dynamic systems. Based on the modern optimization, the optimal FOPIDA controller is designed by the CS, one of the most efficient metaheuristic optimization searching techniques, for the drive train usually used in wind turbine systems. Results obtained by the FOPIDA controller are compared with those obtained by the integer-order proportional-integral-derivative (IOPID), fractional- order proportional-integral-derivative (FOPID) and integer-order proportional-integral-derivative-accelerated (IOPIDA) controllers. As results, the drive train controlled system with the FOPIDA controller optimally designed by the CS can provide very satisfactory responses superior to that with the IOPID, FOPID and IOPIDA controllers, significantly.

The three-tank (3-tank) liquid-level control system commonly exists in industries under the proportional-integral-derivative (PID) control loop. However, the proportional-integral-derivative-accelerated (PIDA) can yield better responses than the PID for higher order plant. In this paper, the robust PIDA controller design by the cuckoo search (CS) for the 3-tank liquid-level control system is proposed. Results obtained will be compared with the PID controller designed by the CS. As results, the responses of the 3-tank liquid-level controlled system with the robust PIDA controller optimally designed by the CS are better than the PID controller designed by the CS. Due to model uncertainty within ±10% of each parameter of the nominal plant model, the robust PIDA controller optimized by the CS can provide the very satisfactory responses in both time and frequency domains with robust performance and robust stability.

This paper proposes the artificial intelligence (AI)-based optimal PID controller design optimization of brushless direct current (BLDC) motor speed control with phase advance approach. The proposed control system allows the speed adjustment of the BLDC motor by phase advance technique. In this paper, two selected AI algorithms, i.e., the adaptive tabu search (ATS) and the intensified current search (ICS) are conducted as the optimizer for the PID controller design. The proposed control system is simulated by MATLAB/SIMULINK. Results obtained by the ATS and ICS will be compared with those obtained by the Ziegler-Nichols (ZN) tuning rule and the genetic algorithm (GA). It shows that the speed response of the BLDC motor by phase advance with the PID controller optimized by the ICS outperforms better than the ZN, GA and ATS.

This study presents voltage control with PI controller for four phase interleaved boost converter. The control of voltage control is done by using PI Controller to control output voltage of the four sets of boost converter parallel connected. Each set works interleaving with 90 degree of distance using 586 microhenry inductor, inner resistance of inductor 0.4 ohm/phase, 400 microhenry capacitor, resistance load at the beginning 10 ohm, lowest resistance 2 ohm, input voltage 13.8 volt, output voltage 24 volt. The result of the experiment shows that the circuit maintain the level of output voltage required which is 24 volt, both while changing 10 ohm resistant load to 2 ohm and interchanging. The circuit also still maintain the level of output voltage at 24 volt same.

The modern vehicles with complex control algorithms have widely used the intelligent suspension systems as the controller. The objective for designed controller of vehicle suspension system is to gain the comfort sensed by passengers covering on the road-profile deflection. In this paper, it presents the design of the proportional-integral-derivative) PID (controllerby the Cuckoo search) CS(, one of the metaheuristic optimization searching techniques on the population-based algorithm. For comparison with CS-based design approach, the results obtained by the PID controller will be compared with those obtained by the PI and PD controllers. The results came out that the CS can give optimal PI, PD and PID controllers for a given suspension system. The PID controller yielded very satisfactory response superior to PI and PD, respectively.

In heavy-duty truck control, the reliable and effective breaking system is one of the most important parts. Such the design problem is very complicate because it is subject to variations of dead time, changes of input function and variations of parameters. The truck breaking control system design can be formulated as one of the constrained optimization problems. Based on the modern optimization, the proportional-integral-derivative-accelerated (PIDA) controller designed by the flower pollination algorithm (FPA) is presented in this paper. To perform its effectiveness, results obtained by the PIDA controller will be compared with those obtained by the PID designed by the FPA. As results, it was shown that the FPA has an outstanding performance for the optimal truck breaking control system design. In command-tracking and load-regulating purposes, the PIDA controller can provide smoother and faster response than the PID controller.

The four phase interleaved boost converter has been widely implemented in various studies, for example, solar cell application, fuel cell energy and application with electric motor driving. Due to various applications of the four-phase interleaved boost converter, this study presents another possible simulation of four-phase interleaved boost converter with inductor $586.5 \mu \mathrm{H}$ and inner resistant of inductor $0.4 \Omega /$ phase, capacitor $400 \mu \mathrm{F}$, resistant load when start $10 \Omega$, lowest resistant load $2 \Omega$, input voltage 13.8 volt, output voltage 24 volt, duty cycle for mosfet switching 42.5% and frequency switch 25 kH z for reducing ripple of input current, ripple of output current, ripple of output voltage. This is also to support the increasing of load power. The results compare two types of boost and another type of single phase boost converter using large inductor. It found that the four-phase interleaved boost converter can reduce the ripple of input, output current and output voltage like using a large inductor and also provided the circuit response faster than traditional single phase boost converter. In summary, the proposed system is capable of simulating for the circuit operation.

In various industries, the high efficiency and endurance of a Brushless DC (BLDC) motor. It is an important component in control system of electromechanics speed. A Brushless DC motor has been commonly used in various industries because of its high efficiency, endurance. Appropriate controller design in the response mode of BLDC motor speed enhances the efficiency in controlling motor speed. The objective of this research is to propose the Proportional Integral (PI) controller to stabilize the motor speed. A PI controller can be formulated in terms of K P and K I , a proportional and an integral gain parameters, respectively. The increase in proportional gain results in the system’s response is increasing. For suitable integral gain parameter of system, the exceeding steady-state error in the system can be eliminated by the increase of integral gain. The increase of high efficiency of motor’s response to control the motor can be applied to DSP TMS320F28335 board. For testing and simulation of controlling BLDC motor speed, the experiment’s parameters were determined as follows: 24 V, 350 W, and rotational speed of motor 3,000 rpm. The experiment of the system was based on state space model. The experimental result showed that controlling non-load motor speed would be adjusted by PI controller during steady state with reference signal varying with time. When the load was supplied the motor, the rotational speed of motor would decrease and return to its steady state in which the motor response was faster active in the reference signal system. Consequently, the PI controller of controlling BLDC motor’s rational speed is an alternative and efficiency.

This paper proposes the fractional-order proportional-integral-derivative (FOPID or $\mathbf { P } \mathbf { I } ^ { \lambda } \mathbf { D } ^ { \mu }$) controller design optimization for a stable fractional order (FO) system by using the flower pollination algorithm (FPA), one of the most efficient metaheuristic optimization search techniques. FPA is applied to design an optimal FOPID controller by searching for the 5 appropriate parameters to meet the response specifications of the system. Results obtained by this method will be compared with those obtained by the conventional controller or integer-order proportional-integral-derivative (IOPID or PID) controller. By comparison, the optimal FOPID controller yields very satisfactory responses superior than the IOPID controller with faster and very small steady-state error of unit step response. MATLAB and FOMCON programs are used to conduct this research.

This paper proposes the proportional-integral-derivative (PID) controller design optimization for the air-gap position control of the magnetically levitated (Maglev) vehicles by using the bat-inspired algorithm (BA). Considered as the constrained optimization problem, the BA is applied to design an optimal PID controller by searching for the appropriate values of the controller gains. Results obtained by the PID controller designed by the BA will be compared with those obtained by the conventional controller from literatures. As results, the BA can provide an optimal PID controller for the Maglev air-gap position controlled system. By comparison, the PID controller yields very satisfactory responses superior to the conventional controller without steady-state error of the command-tracking and load-regulating responses.

This paper presents an application of the spiritual search (SS), one of the newest and most efficient metaheuristic optimization algorithms, to optimally design the proportional-integral-derivative-accelerated (PIDA) controller for regulating the heart rate of the cardiac pacemaker in the cardiovascular system. For this biomedical engineering problem, designing of the PIDA controller can be considered as one of the constrained optimization problems. With the proposed SS-based design approach, results obtained by the PIDA controller will be compared with those obtained by the PID controller. Simulation results show that the PID and PIDA controllers for the cardiac pacemaker are optimally designed by the SS. The PIDA can provide faster and smoother response than the PID controller, significantly.

This paper proposes a design of optimal PI(D) controller for brushless DC (BLDC) motor speed control by the particle swarm optimization (PSO), one of the powerful metaheuristic optimization search techniques. The proposed control system is implemented on the TMS320F28335 DSP board interfacing to MATLAB/SIMULINK. With Back EMF detection, the proposed system is considered as a class of sensorless control. This scheme leads to the speed adjustment of the BLDC motor by PWM. In this work, the BLDC motor of 100 watt is conducted to investigate the control performance. As results, it was found that the speed response of BLDC motor can be regulated at the operating speed of 800 and 1200 rpm in both no load and full load conditions. Very satisfactory responses of the BLDC system can be successfully achieved by the proposed control structure and PSO-based design approach.

The I-PD controller, one of the modified versions of the PID controller, was proposed for eliminating the set-point kick caused by proportional and derivative terms appeared during set point change. In this paper, the optimal I-PD controller design for DC motor speed control system by the cuckoo search (CS), one of the most efficient metaheuristic optimization techniques, is proposed. The simulation results show that the I-PD parameters can be optimized by the CS. The controlled system with the I-PD provides better responses with smaller overshoot and faster regulating time once compared to that with the parallel PID controller.

A Brushless Direct Current (BLDC) motor has been widely used due to the high efficiency, durability, easy maintenance, and winding dynamically faster than a brushed direct current motor. The objectives of this research are to investigate and analyze the efficiency of function and the response of BLDC motor in the neighbor of speed response. The simulation of BLDC motor was established in the mathematical model as the state space model which was in the first order of differential equations as well as the analysis in time domain and in the signal with Multi MIMO simulation. The investigation in the behavior of BLDC motor is classified to two cases, load motor and non-load motor, with testing for BLDC motor, rated voltage (24 V), rotational speed (3,000 rmp). The simulation results showed that the load supply for motor resulted in the decrease in the rotational speed but the increase in the current. Therefore, the load supplied for BLDC motor affects the motor's response behavior in term of rotational speed decreasing and current increasing.

Firefly algorithm (FA) was firstly proposed by Yang in 2008 as one of the most powerful population-based metaheuristic optimization techniques for solving the hardest optimization problems including real-world engineering practices. In this paper, the FA is applied to design an optimal proportional-integral-derivative-accelerated (PIDA) controller for the automatic voltage regulator (AVR) system. Based on the optimization context, the sum-squared errors between referent input voltage and actual terminal output voltage of the controlled system are performed as the objective function to be minimized. As results, the optimum PIDA controller for the AVR system is successfully obtained by the FA. Moreover, the FA-based design approach performs high robustness once parameter variations are occurred.

This paper proposes an application of the bat-inspired algorithm to optimal proportional-integral-derivative-accelerated (PIDA) controller for the liquid-level system widely used in industry. The bat-inspired algorithm (called BA), firstly proposed in 2010 by Yang, is one of the most efficient population-based metaheuristic optimization search techniques. Based on the echolocation behavior of bats, the BA has been successfully applied to single-and multi-objective engineering optimization problems. In this work, the BA is conducted to optimally design the PIDA controller for the liquid-level system. The system specifications, consisting of rise time, maximum overshoot, settling time and steady-state error, are set as the proposed objective function to be minimized. The optimal PIDA controller designed by the BA is compared to the classical PID controller. As results, the PIDA controller provides the faster and smoother responses of the liquid-level controlled system than the PID controller, significantly.

The multipath adaptive tabu search (MATS) has been proposed as one of the most powerful metaheuristic optimization search techniques for solving the combinatorial and continuous optimization problems. The MATS employing the adaptive tabu search (ATS) as the search core has been proved and applied to various real-world engineering problems in single objective optimization manner. However, many design problems in engineering are typically multiobjective under complex nonlinear constraints. In this paper, the multiobjective multipath adaptive tabu search (mMATS) is proposed. The mMATS is validated against a set of multiobjective test functions, and then applied to design an optimal PID controller of the automatic voltage regulator (AVR) system. As results, the mMATS can provide very satisfactory solutions for all test functions as well as the control application.

This paper presents a design and implementation of Brushless DC (BLDC) motor speed control based on the TMS320F28335 DSP board interfacing to MATLAB/SIMULINK. To obtain the optimal tracking and regulating responses, the PI controller is conducted and designed by pole placement technique. With Back EMF detection, the proposed system is considered as a class of sensorless control. This scheme leads to the speed adjustment of the BLDC motor by PWM. This experiment aims to examine the effectiveness of BLDC motor by testing the BLDC motor of 100 watt. It was found that the speed response of BLDC motor can be regulated at the operating speed of 700 rpm and 1400 rpm at no load and full load conditions.

The brushless dc (BLDC) motor has been increasingly used in industrial automation, automotive, aerospace, instrumentation and appliances. Analysis and design of the BLDC motor efficiently require its accurate model and parameters. In this paper, the parameter identification of the BLDC motor model via well-known metaheuristic optimization search techniques is proposed. Two trajectory-based methods, i.e. adaptive tabu search (ATS) and intensified current search (ICS) are employed to estimate the BLDC motor parameters. As simulation results of model identification and validation, both ATS and ICS can provide optimal BLDC model parameters. The BLDC models obtained show a very good agreement to actual system dynamics. However, the ICS can pro-vide optimal model parameters faster than the ATS.

Flower pollination algorithm (FPA) is one of the most efficient population-based nature-inspired metaheuristic optimization algorithms based on the flower pollination process of flowering plants. With Levy distribution, the FPA can control the balance of exploration and exploitation properties with a proposed switch probability. This leads the FPA efficiently escape from local entrapment and reach global optimal rapidly. In this paper, the application of FPA to parameter identification of a direct current (DC) motor model is proposed. Under testing, the DC motor system was excited by the step input to generate the specific level of the motor speed considered as the output of the system. As results of parameter identification and validation, it was found that the FPA can provide the optimal parameters of DC motor model representing system dynamics accurately. Very good agreement between actual system dynamics behavior and model parameters obtained by the FPA is completely confirmed.

The brushless DC motor is widely used in various industrial fields because of low maintenance, high power density and high efficiency. The permanent magnets in the rotor generate a constant magnetic flux which is limited by the motor speed range. Mathematical modelling of brushless DC motor is necessary for realizing the dynamic behaviour. This paper presents a phase advanced angle for brushless DC motor to extend speed range of brushless DC motor beyond the rate top speed. The experimental designed system is simulated. The simulated results show that a phase advanced angle in the designed system can extend speed range. Finally, it can improve the ability of the proposed system, efficiently.

A novel fractional-order PIλDμAν controller involving fractional-order integrator, fractional-order differentiator and fractional-order accelerator is proposed for higher-order systems. The proposed PIλDμAν controller is a successor of the fractional-order PIλDμ and the integer-order PIDA controllers. In this paper, time-domain and frequency-domain responses of the PIλDμAν controller are characterized. With the design optimization framework, seven parameters of the PIλDμAν controller, i.e. proportional gain, integral gain, derivative gain, accelerated gain, fractional order of integrator, fractional order of differentiator and fractional order of accelerator, are optimized by the spiritual search (SS), one of the most efficient hybrid metaheuristic optimizers. To perform its benefits and effectiveness, the PIλDμAν controller and its SS-based design optimization are applied to three real-world higher-order control systems. Results obtained by the PIλDμAν controller are compared with those obtained by the PIDA and PIλDμA controllers. As results, it was found that the proposed PIλDμAν controller exhibits very satisfactory responses superior to the PIDA and PIλDμA controllers, significantly.