Genetic algorithm **based** **optimal** **time** **domain** **tuning** of a **novel** **fractional** **order** **fuzzy** **PID** **controller** is attempted in this paper while minimizing a weighted sum of various **integral** **performance** **indices** and the control signal. Small magnitude of control signal is a necessity in some typical safety critical process control applications like [49] where the chance of actuator saturation and **its** undesirable results like **integral** wind-up is highly detrimental and also increases the cost involved for large actuator size as a preventive measure. In the present study four different **integral** **performance** **indices** [43], [47] have been studied while designing the proposed **fuzzy** FOPID along with **its** simpler versions like **fuzzy** **PID**, PI D λ μ , **fuzzy** **PID** and **PID** satisfying the same set of optimality criteria. It is observed that the **controller** **performance** depends on the type of process to be controlled and also on the choice of **integral** **performance** **indices**. More degrees of freedom in the **controller** parameters do not necessarily imply better **performance** in all cases if the **performance** index is not chosen judiciously. Also for **fuzzy** enhanced **PID** controllers it is well known [4] that change in output scaling factor for example has more effect on the **controller** **performance** than changes in the membership functions or fuzzification-inferencing-defuzzification mechanism. Thus all the **tuning** parameters of **fuzzy** **PID** **controller** are not equally potent in affecting the overall **performance** of the control loop. Our present approach gives additional design parameters viz. the differ- **integral** orders of a nominal FLC-**PID** to the designer which can have significant effect on the **performance** and hence make the applicability of these types of controllers to meet various control objectives.

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error signal does not resemble the integer **order** calculus or conventional differentiation and integration in a pure mathematical sense. Rather it reflects an operator’s experience which gives extra freedom for **tuning** of control loops. Thus, the control signal generated as a result of his actions may be approximated by appropriate mathematical operations which have the required compensation characteristics. The rationale behind incorporating **fractional** **order** operators in the conventional hybrid **fuzzy** **PID** input and output can be visualized like a heuristic reasoning for an observation of a particular rate of change in error (not in mathematical sense) by a human operator and the corresponding actions he takes over **time** which is not static in nature since the **fractional** differ-integration involves the past history of the integrand and as if the integrand is continuously changing over **time** [2]. Since, human brain does not observe the rate of change of a variable and **its** **time** evolution as classical integer **order** numerical differentiation and integration, the **fractional** **order** of differ-integration perhaps puts some extra flexibility to map information in a more easily decipherable form. Considering these flexibilities incorporated in the **fuzzy** inference input and output, the present study extends the idea with different hybrid structures of the FLC **based** FOPID **controller** and their comparative merits in closed loop control with fixed MF type and rule base and **fuzzy** inferencing.

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the ﬁrst **time**, using a new metaheuristic optimization Bat algorithm (BA) inspired by the echoloca- tion behavior to improve power system stability. The problem of FOPID-PSS design is transformed as an optimization problem **based** on **performance** **indices** (PI), including **Integral** Absolute Error (IAE), **Integral** Squared Error (ISE), **Integral** of the **Time**-Weighted Absolute Error (ITAE) and **Integral** of **Time** multiplied by the Squared Error (ITSE), where, BA is employed to obtain the opti- mal stabilizer parameters. In **order** to examine the robustness of FOPID-PSS, it has been tested on a Single Machine Inﬁnite Bus (SMIB) power system under different disturbances and operating con- ditions. The **performance** of the system with FOPID-PSS **controller** is compared with a **PID**-PSS and PSS. Further, the simulation results obtained with the proposed BA **based** FOPID-PSS are compared with those obtained with FireFly algorithm (FFA) **based** FOPID-PSS. Simulation results show the effectiveness of BA for FOPID-PSS design, and superior robust **performance** for enhance- ment power system stability compared to other with different cases.

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The continuous and discrete **time** Linear Quadratic Regulator (LQR) theory has been used in this paper for the design of **optimal** analog and discrete **PID** controllers respectively. The **PID** **controller** gains are formulated as the **optimal** state-feedback gains, corresponding to the standard quadratic cost function involving the state variables and the **controller** effort. A real coded Genetic Algorithm (GA) has been used next to optimally find out the weighting matrices, associated with the respective **optimal** state-feedback regulator design while minimizing another **time** **domain** **integral** **performance** index, comprising of a weighted sum of **Integral** of **Time** multiplied Squared Error (ITSE) and the **controller** effort. The proposed methodology is extended for a new kind of **fractional** **order** (FO) **integral** **performance** **indices**. The impact of **fractional** **order** (as any arbitrary real **order**) cost function on the LQR tuned **PID** control loops is highlighted in the present work, along with the achievable cost of control. Guidelines for the choice of **integral** **order** of the **performance** index are given depending on the characteristics of the process, to be controlled.

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In recent literature many evolutionary optimization algorithms are proposed for **tuning** **PID** **controller** in the AVR system such as Anarchic Society Optimization [16], reinforcement learning automata optimization approach [17], real coded GA with **fuzzy** logic technique [18], Choatic ant swarm algorithm [19], Artificial Bee Colony algorithm [20], Hybrid GA-Bacterial Foraging (BF) algorithm [21] and local unimodal sampling algorithm [22]. GA and Ant Colony Optimization techniques are proposed to tune the parameters of FOPID **controller** in controlling of AVR system. In some of the research papers **novel** **performance** criteria has been proposed for **optimal** **tuning** of **PID** and FOPID **controller** in AVR control system. A **novel** **performance** criterion comprises of overshoot, settling **time**, steady state error and mean of **time** weighted **integral** absolute error has been proposed for **optimal** **tuning** of **PID** **controller** in AVR system using cuckoo search algorithm [23]. A. Sikander et. al, 2018 has proposed a cuckoo search algorithm **based** **fractional** **order** **PID** **controller** for AVR system with **performance** criterion which was proposed by Gaing et. al in 2004 [24]. In this research work, Cuckoo search (CS) and particle swarm optimization (PSO) algorithms are proposed to find the **optimal** parameters of **PID** **controller** in the control of automatic voltage regulator (AVR) system with new **performance** criterion comprises of **Integral** absolute error, rise **time**, settling **time** and peak overshoot. The **performance** of this new proposed **performance** criterion is compared with **performance** of other **performance** criterion such as ITAE, ITSE, ISE, MSE and IAE. The paper is mainly organized such that section two describes about the Automatic Voltage Regulator (AVR) system; section three examines the Cuckoo search (CS) algorithm and particle swarm optimization (PSO) algorithms; section four and five concentrate on the application of CS-**PID**, PSO-**PID** and conventional **tuning** method (Ziegler-Nichols) in **optimal** **tuning** **PID** **controller** for both servo and regulatory control of AVR system. Additionally, section six describes conclusions of the study.

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A particle swarm optimized I-PD **controller** of Second **Order** **Time** Delayed System has been suggested by Suji Prasad et al. [24] . Optimization was **based** on the presentation **indices** like settling **time**, rise **time**, peak overshoot, ISE (**integral** square error) and IAE (**integral** absolute error). **PID** control- lers and **its** alternatives are most commonly used, although there are important improvements in the control systems in industrial processes. If the parameter of **controller** was not appropriately planned, next needed control output may not succeed. Compared with Ziegler Nichols and Arvanitis **tuning**, they have conﬁrmed that their simulation results with opti- mized I-PD **controller** to be speciﬁed enhanced presentations. A **PID** **controller** for **time** delay systems has been explained by Rama Reddy et al. [25] . Their suggested technique pre´cised the stable areas of **PID** and a **novel** **PID** with cycle leading cor- rection (SLC) for network control systems with **time** delay. The latest **PID** **controller** has a modiﬁcation parameter ‘b’. They have obtained that relation of the parameters of the sys- tem. The outcome of plant parameters on constancy areas of **PID** controllers and SLC-**PID** controllers in ﬁrst-**order** and second-**order** systems with **time** delay is moreover pre´cised. Finally, an open-loop zero was introduced into the plant- unstable second **order** system with **time** delay so that the con- stancy areas of **PID** and SLC-**PID** controllers get competently made bigger.

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As discussed previously, the most common shapes of membership functions used are triangular, trapezoidal, Gaussian and bell curves, but the shape is generally less important than the number of curves and their placement. The major components to strategy the **fuzzy** logic control are Fuzzification, knowledge base, decision making logic and Defuzzification

This paper presents a **tuning** approach **based** on Continuous firefly algorithm (CFA) to obtain the proportional-**integral**- derivative (**PID**) **controller** parameters in Automatic Voltage Regulator system (AVR). In the **tuning** processes the CFA is iterated to reach the **optimal** or the near **optimal** of **PID** **controller** parameters when the main goal is to improve the AVR step response characteristics. Conducted simulations show the effectiveness and the efficiency of the proposed approach. Furthermore the proposed approach can improve the dynamic of the AVR system. Compared with particle swarm optimization (PSO), the new CFA **tuning** method has better control system **performance** in terms of **time** **domain** specifications and set-point tracking.

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Conventional **PID** controllers have been a wide range of use in industry because of **its** simple structure and acceptable **performance**. This **controller** deals with both **time** response and frequency response improvements if they are properly tuned. But as the demands increases to control the different systems in industries, **performance** of conventional controllers are tend to degrade. Now systems are getting complicated day by day introducing higher **order** plants. There is drastic change in the **performance** of controllers with the introduction of **Fuzzy** systems and so the **Fuzzy** controllers (PD and **PID**) has been designed and tuned for third **order** system which is difficult to control by the use of conventional controllers. FLC has been widely used for nonlinear, high **order** & high dead **time** plants. This paper has three main considerations. Firstly, a **PID** **controller** has been designed for nonlinear unstable third **order** plant using Zeigler Nichols **tuning** method I & **its** **performance** is analyzed. Secondly, for the same system a FLC has been proposed with simple approach and smaller number of rules(four rules) as it gives the same **performance** by the larger set rule II . Even though modern control methods are very promising for non-linear control applications, they require substantial computational power because of complex decision making processes. For example FLC has to deal with fuzzification, rule base storage, inference mechanism and defuzzification operations. Larger set of rules yields more accurate control at the expense of longer computational **time**. Therefore it may not be practical because there are many implementation aspects that must be addressed, namely real-**time** response, communication bandwidth, computational capacity and onboard battery. The use of NN is also thought to be impractical due to **its** unpredictability, particularly when real **time** self-**tuning** is considered. Despite these issues, it is known that FLC requires simpler mathematics and offers higher degree of freedom in **tuning** **its** control parameters compared to other nonlinear controllers. In this paper, the Single Input **Fuzzy** **Controller**

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The concept of **fuzzy** derivative was ﬁrst introduced by Chang and Zadeh [1]. Kaleva [2], Puri and Ralescu [3] introduced the notion of **fuzzy** derivative as an extension of the Hukuhara derivative and the **fuzzy** **integral**, which was the same as that proposed by Dubois and Prade [4]. There has been a signiﬁcant development in the study of **fuzzy** dif- ferential and **integral** equations (see, for example, [5–8], and the references therein). Under suitable conditions, it was proved in [9] that the boundedness of solutions of the following **fuzzy** **integral** equation:

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Traditionally the **PID** **controller** has been used in the AVR loop due to **its** simplicity and ease of implementation [5]. However, recently the **fractional** **order** **PID** (FOPID) **controller** have been used in the design of AVR systems and have been shown to outperform the **PID** in many cases [6], [7]. In Zamani et al. [8], the FOPID has been tuned for an AVR system using the Particle Swarm Optimisation (PSO) algorithm employing **time** **domain** criterion like the **Integral** of Absolute Error (IAE), percentage overshoot, rise **time**, settling **time**, steady state error, **controller** effort etc. In Tang et al. [6], the **optimal** parameters of the FOPID **controller** for the AVR system, has been found using a chaotic ant swarm algorithm. In [6] a customised objective function has been designed using the peak overshoot, steady state error, rise **time** and the settling **time**. The above mentioned literatures perform optimisation considering only a single objective. But in a practical control system design multiple objectives need to be addressed. In the study by Pan and Das [9], the AVR design problem has been cast as a multi- objective problem and the efficacy of the **PID** and the FOPID controllers are compared with respect to different contradictory objective functions like the **Integral** of **Time** Multiplied Squared Error (ITSE) and the **controller** effort etc. However, the optimisation is done in the **time** **domain** and the obtained **controller** values are checked for robustness against gain variation by varying different parameters of the control loop. All these above mentioned literatures which employ **time** **domain** optimisation techniques cannot guarantee a certain degree of gain or phase margins which are important for the plant operator. These margins are useful from a control practitioner’s view point as they can give an estimate of how much uncertainty the system can tolerate before

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Summary The paper demonstrates about melioration of integer **order** and **fractional** **order** model of heating furnace. Both models are being placed in closed loop along with the propor- tional **integral** derivative (**PID**) **controller** and **fractional** **order** proportional **integral** derivative (FOPID) **controller** so that the various **time** **domain** **performance** characteristics of the heating furnace can be meliorated. The **tuning** parameters (K p , Ki and Kd ) of the controllers has been found using the Astrom-Hagglund **tuning** technique and the differ-integrals ( and ) are found using the Nelder-Mead optimisation technique.

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By using Equation (20, 21, 22, 25, 28) five unknown parameter K K K p , i , d , and can be solved by using FMINCON optimization toolbox of Mat Lab. Equation (21) is considered as a main equation and other equations are taken as non-linear constraints for optimization. Value of the all five unknown parameters are calculated to obtain the PI D **controller** to control the ceramic IR heater as Kp=0.6073 , Ki=6.1194,Kd=0.2045, =0.7815, =0.4454 and transfer function of **fractional** **order** **PID** **controller** given as

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The BLDC motor has been widely used in many applications such as, industrial automation, medical, electric traction, consumer, aerospace, road vehicles, aircraft, military equipment, hard disk, etc. It has the advantages of high reliability, good efficiency, high power density, lower weight, low maintenance requirements, and wide speed range. On the other hand, the developments in power semiconductor technology, power electronic technology and microprocessors/logic ICs make the BLDC motor gaining popularity[1,2]. BLDC motors do not have brushes for commutation, Instead they are electronically commutated using three phase bridge inverter with feedback rotor position. The rotor position feedback is necessary for starting and providing proper commutation to turn on the inverter. The BLDC motor consists of permanent magnet rotor and distributed stator winding which are wound such that the back emf's is trapezoidal. The phase current, typically quisi - squar shape, is synchronized with the back emf to produce constant torque at constant speed. The BLDC motor is operated when two phases are ON at any **time** while the third phase is floating.

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ABSTRACT: Many controllers have been implemented in a Liquid Level System by control engineers such as conventional **PID** **controller**, fussy logic. But with development of **Fractional** calculus the control technique are also being improved. The thesis work deals with design of **Fractional** **Order** **PID** [FOPID] and a Robust **Fractional** **order** **PID** **controller** for the Liquid Level System.

literature reviews [4-8] In section II, we will discuss theories related to this paper include of **fractional** calculus, **fractional** **order** PI λ D µ **controller**, digital IIR filter, and Kalman filter that necessary to eliminate the measurement error from the tilt sensor. Section III discusses in mechanical structure, mathematical model, and state - space of the robot. Section IV demonstrates **PID** and FOPID **controller** design and their simulation results. Section V demonstrates to realization implemented both controllers on the real system and result of **PID** **controller** on the real system.

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Abdelaty, Ahmed and Ouda (2018) studied the analysis and design of a set point weighting 2DOF **PID** **controller**. They used a 2/2 sub-**controller** receiving the reference input signal with set point weight on the proportional and derivative terms and a **PID** sub-**controller** in the forward path receiving the error signal of the control system with filter on **its** derivative part [8]. Hassaan (2018) studied the **tuning** process of a 2DOF **PID** **controller** for use with second-**order**-like processes. He used a 2DOF **controller** consisting of PD sub-**controller** receiving a reference input signal and set in a feedforward loop and a **PID** sub-**controller** set in the forward path of the control system receiving the error signal of the system. He tuned the **controller** for use with second **order**-like processes of damping ratio from 0.05 to 2 and a natural frequency up to 10 rad/s [9].

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Abstract:- This paper presents a method for **tuning** of conventional **PID** **controller**. Simplicity, robustness, wide range of applicability and near-**optimal** **performance** are some of the reasons that have made **PID** control so popular in the academic and industry sectors. Recently, it has been noticed that **PID** controllers are often poorly tuned and some efforts have been made to systematically resolve this matter. Thus **Fuzzy** logi c can be used in context to vary the parameters values during the transient response, in **order** to improve the step response performances. Simulation analysis has been carried out for the different processes by conventional and different defuzzification techniques and the results indicate that the values of percentage overshoot are reduced by using **fuzzy** logic mechanism.

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ABSTRACT: Measurement of Pressure is one of the very essential parameter in a process station which needs to be controlled. This paper deals with obtaining the real **time** response of a pressure process from which the system transfer function is identified using two point method. The identified model is in the form of first **order** plus dead **time** (FOPTD). **PID** controllers are effectively used in controlling liner feedback systems with the suitable **tuning** methods. Predominantly available **tuning** methods like Ziegler Nicholas method (Z-N), and Internal Model Control (IMC), are used here to compare the responses using software LabVIEW to get the optimum **controller** for the pressure process.

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Multivariable system control is known to be more challenging to design when compared to scalar processes. This is primarily due to the presence of interactions and directionality in such systems. This limits the scope of application of most parametric model-**based** design algorithms to Single Input Single Output (SISO) applications (Huang, et al., 2003). Over the past decades, several methods of solving multivariable control issues have been proposed for conventional **PID** controllers (Loh, et al., 1993; Luyben, 1986). Niederlinski modified Ziegler-Nichol’s **tuning** rule for MIMO processes by introducing a detuning factor to meet the stability and **performance** of the multi-loop control system. Luyben introduced the Biggest Log-modulus **Tuning** (BLT) method which is a frequency **domain** **PID** **controller** design method. It uses a detuning factor (F) iteratively to decouple an interactive MIMO system (Luyben, 1986). A detailed review of some multivariable **PID** design methods was published by Shiu and Hwang (Shiu & Hwang, 1998). One common limitation of these design methods is that all the algorithms are limited to conventional **PID** controllers and do not address **fractional**- **order** controllers.

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