ABSTRACT: The Internal ModelControl based approach to design **controller** is used in control applications in industries. It is because, for actual process in industries **PID** **controller** algorithm is simple and robust to handle the model inaccuracies and hence using IMC-**PID** tuning method is a compromise between closed-loop performance and robustness to model inaccuracies is achieved with a single tuning parameter. The IMC-**PID** **controller** allows good set- point tracking for the process with a small **time**-**delay**/**time**-constant ratio. In this paper, modified internal model control (MIMC) will be realized by equivalent **PID** control for **unstable** **first** **order** plus **time** **delay** system. This **controller** will be designed for good dynamic performance and robustness. The **controller** performance will be achieved by analyzing integral absolute error (IAE) and maximum sensitivity (Ms). The cost function (J) will be optimized for different cases of damping ratio on Ms-IAE curve. This will be implementing for different transfer functions for the model of UFOPTD for robust performance.

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The mathematical modeling and simulation of **systems** and processes, based on the description of their properties in terms of fractional derivatives, naturally leads to differential equations of fractional **order** the necessity to solve such equations to obtain the response for a particular input. Thought in existence for more than 300 years, the idea of fractional derivatives and integrals has remained quite a strange topic, very hard to explain, due to absence of a specific tool for the solution of fractional **order** differential equations. Fractional **order** calculus has gained acceptance in last couple of decades. J.Liouville made the **first** major study of fractional calculus in 1832. In 1867, A.K.Grunwald worked on the fractional operations. G. F. B. Riemann developed the theory of fractional integration in 1892. Fractional **order** mathematical phenomena allow us to describe and model a real object more accurately than the classical “integer” methods. Earlier due to lack of available methods, a fractional **order** system was used to be approximated as an integer **order** model. But at the present **time**, there are many available numerical techniques which are used to approximate the fractional **order** derivatives and integrals.

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The **PID** controllers are widely used in industrial control system for several decades since Ziegler and Nichols proposed their **first** **PID** tuning method. This is because the **PID** controllers are simple and it is easier to understand than most other controllers. Design methods leading to an optimal and effective operation of the **PID** controllers are economically vital for process industries. Robust control has been a recent addition to the field of control engineering that primarily deals with obtaining system robustness in presence of uncertainties [1]. **Systems** with delays are common. One reason is that nature is full of transparent delays. Another reason is that **time** **delay** **systems** are often used to model a large class of engineering **systems**, where propagation and transmission of information or material are involved. The presence of **time** delays makes system analysis and control design much more complicated [2]. In **order** for the methods to be applicable in the process control industry, it is particularly important that they can handle **time** delays effectively. And also the **controller** design methods should be simple to understand and easy to manipulate. The methods that depend only on the frequency response of the system eliminate the need for plant model, which may not be available in some applications.

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It is eminent that more than 95% of the control loops are **PID** **controller** type in process control [5]. The **PID** controllers are used in wide range of problems like DC motor, Automotive, Air flight control, etc [7]. A **PID** **controller** calculates an error value on the basis of difference between measured process variable and desired set point. The **controller** attempts to minimize the error by adjusting the tuning **parameters** [4]. These tuning **parameters** can be interpreted in term of **time** proportional (P) which depends on the present error, integral (I) which depends on growth of past value and derivative (D) which predicts the future error. The quality of control in a system depends on settling **time**, rise **time** and overshoot values. The main problem is to optimally reduce such timing **parameters**, avoiding undesirable overshoot, longer settling times and vibrations. To solve this problem, many authors have been proposed different approaches. A **first** approach is the Proportional Integral Derivative (**PID**) controller’s application. They are extensively used in industrial process control application. Vaishnav and Khan, 2007 designed a Ziegler Nichols **PID** **controller** higher **order** **systems** [7]. A tuning method which uses **PID** **controller** has been developed by Shamusuzzoha and Skogestad, 2010 [9]. Such method requires one closed-loop step set point response experiment similar to the classical Ziegler-Nichols experiment. However, in complex **systems** characterized by nonlinearity, large **delay** and **time** variance, the PID’s are of no effect. The design of a **PID** **controller** is generally based on the assumption of exact knowledge about the system. Because the knowledge is not available for the majority of **systems**, many advanced control methods have been introduced. Some of these methods make use of the fuzzy logic which simplifies the control designing for complex models. Fuzzy logic control has been widely implemented for nonlinear, higher **order** and **time** **delay** **systems** [2]. A fuzzy logic **controller** has been proposed with simple approach and smaller set of rules This paper has been organized as following; Section I depicts the introduction of the paper. Section II describes the problem formulation. Section III explains the generalized tuning **parameters** of **PID** **controller**. Section IV describes the design consideration for higher **order** **systems**. Section V reveals the design of **PID** **controller** using Z-N tuning and fine tuning techniques. Section VI describes the design of fuzzy logic **controller** and a summary table of various results obtained through various techniques. Section VII gives general conclusions.

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nonlinear system by using fuzzy logic **controller**. In **order** to synthesise a control system both the **controller** selection and adjustment of **parameters** plays an important role. **PID** **controller** is used in many industries, It doesn’t give acceptable response or performance for system with uncertain **time** delays, performance and nonlinearities. Hence the **parameters** of **PID** **controller** are tuned to get satisfactory response. Therefore tuning of **PID** **controller** is done by Fuzzy logic. Fuzzy control establishes an intelligent control. Fuzzy logic control has been widely used for nonlinear higher **order** and **time** **delay** **systems**. Because of their Knowledge based nonlinear structural characteristics they are applied to nonlinear **systems**. Fuzzy **controller** can perform online and offline parameter operations. Fuzzy **PID** **controller** is designed by fuzzy control principals and techniques. Fuzzy plus **PID** provides good performance when compare to only fuzzy. For fuzzy **controller** simple rule base is used, whereas for Fuzzy **PID** different rule bases are used for proportional, integral and derivative gains to make faster response.

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The proportional-integral-derivative(**PID**) **controller** is widely used in the process industries due to its simplicity, robustness and wide ranges of applicability in the regulatory control layer. However, a very broad class is characterized by aperiodic response. The most important and commonly used category of industrial **systems** can be represented by a **first**-**order** plus dead **time** model given as,

Adaptive system of neuro-fuzzy inference (ANFIS) refers in general to an adaptation network that performs the function of the system of inference fuzzy. The most commonly used ANFIS fuzzy system architecture model is Sugeno since it is less computational and more transparent than other models. The serial membership function of the model (MF) Sugeno can be parameterized by any arbitrary function of neat entries is likely polynomial. Polynomials of zero and **first** **order** are used as the constant and near linear models of Sugeno, respectively. In addition, in the process of defuzzification, Sugeno diffuse model is a simple **calculation** of the weighted average. Fuzzy space is divided by partition grid according to the preceding number MF, and each diffuse area covered by the rule. On the other hand, each fixed and adaptive network node performs a single function or a sub-Sugeno model, so that the overall performance of the network is functionally the same as that of the diffuse model. The network uses an adaptive optimization algorithm to change the **parameters** of the fuzzy inference system. The adaptation process is aimed at obtaining a set of **parameters** for which it minimizes the error between the actual output of the diffuse model and the established target of training data. You can use classic optimization techniques such as backward propagation as well as hybrid algorithms. The total number of modifiable ANFIS **parameters** is the important computational effort required to complete the tuning process. ANFIS combines the advantages of fuzzy **systems** and adaptive networks into a hybrid intellectual paradigm. **Systems** of flexibility and subjectivity with fuzzy inference when added to the optimization of the power of adaptive networks provide a remarkable resistance Amphism simulation, training, nonlinear assignment and pattern recognition.

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It's worthy to note that step response plot is also used to show the correctness of our proposed stabilizing method. The organization of this paper is as follows: In Section 2, the problem is stated. We also state a definition and also two important theorems which help us with getting desired and trustworthy results. Section 3 shows stabilization using a **PID** **controller** method. In this section our approach of design is explained clearly and all stabilizing **PID** **parameters** are determined. Section 4 shows illustrating of the approach by two examples which will be analyzed by MATLAB and simulation results will show the advantages of this approach. Finally, in section 5, the main conclusions are summarized.

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This section represents the development of a tuning method of PI D **controller** for **first** **order** plus **time** **delay** system with gain parameter uncertainty structure. All **parameters** of the PI D **controller** are calculated to satisfy the performance of the plant. Five unknown **parameters** of the PI D **controller** are estimated solving five non-linear equations that satisfy five design criteria [12]. Bode plot of FOPTD **systems** with gain parameter uncertainty structure are successfully combined with five design criteria to obtain the PI D **controller**. The phase and amplitude of the plant in frequency domain taken as,

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The **first** attempts to automate the tuning of **PID** controllers were based on iterative manual tuning, and methods based on graphical **time** domain representation using root locus or frequency domain using bode plots [2, 4]. Ziegler and Nichols [5] have proposed their **first** reaction curves tuning rules which is based on calculating the **controller** **parameters** from the model **parameters** determined from the open loop system step response, and the ultimate cycle tuning rules which is based on **calculation** of **controller** **parameters** from the **controller** gain and oscillation period at the ultimate frequency. Then came the well known techniques such as Cohen-Coon method and internal model control method and other techniques which are called optimum methods [1], [2]. Recently, the Ziegler Nichols step response method has been considered by Astrom and Hggalund [6], where they analyzed analytically the power of the method and the recent modified methods based on it. There are many modified tuning methods that have also been proposed recently such as the PI/**PID** **controller** design based on IMC and percentage overshoot specification [7], a plant step response based technique [8], and the IMC-like analytical H∞ design with S/SP mixed sensitivity consideration [9]. Moreover, a recent implementation aspect for building thermal control using **PID** has been considered by Kafetzis et. al. [10]. In addition, tuning rules for fractional PIDs has been proposed by Valerio and Costa [11], similar to the **first** and the second sets of tuning rules proposed by Ziegler and Nichols for integer PIDs.

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38 | P a g e given plants [1]. The **first** step in this method is to calculate two **parameters** T (**time** constant) and L (**delay** **time**) that characterize the plant. These two **parameters** (T, L) can be determined graphically from a measurement of the step response of the plant as illustrated in fig 2. **First**, the point on the step response curve with the maximum slope is determined and the tangent is drawn with the **time** axis. Once T and L are determined, the **PID** **controller** **parameters** are then given in terms of T and L TABLE 1.

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In the present paper, we presented an efficient and straightforward stabilizing **PID** **controller** design method for **time**-**delay** **systems** of neutral type which was free of mathematical complexities. Based on the proposed ap- proach, stability was guaranteed if all the characteristic roots of closed-loop system had negative real parts. For determining the rightmost characteristic roots, the meth- od was presented on the basis of Lambert W function and we managed to determine the stability directly. **Delay** value was chosen τ = 1 for simplicity but the algorithm could produce a plot of the real part of the rightmost root with respect to the **delay** as shown in the **first** illustrative example. Numerical examples with **time** **delay** were pre- sented for illustrating this approach. The results were satisfactory and stabilizing **PID** **parameters** were deter- mined.

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AbdelFattah, Gesraha and Hanafy (2004) developed a **controller** characterized by its robustness against modeling errors and its high disturbance rejection capability for integrating processes with **time** **delay** [6]. Ou, Tang, Gu and Zhang (2005) considered the problem of stabilizing integral plants with **time** **delay** using **PID** controllers and the practical single-parameter **PID** controllers [7]. Matijevic and Stojic (2006) proposed a structure for the Smith predictor based on IMPACT structure for control with long dead **time**. They set the **controller** **parameters** in **order** to achieve robust stability and performance [8]. Camacho, Rojas and Garcia-Gabin (2007) presented a combined approach of predictive structures with sliding mode control for performance and robustness improvement. They applied the structures to processes approximated by a **first**-**order** plus **time** **delay** or an integral **first**-**order** plus **time** **delay** [9]. Shamsuzzoha and Lee (2008) proposed a design technique for an IMC-**PID** **controller** for two integrating processes with **time** **delay**. They used a 2DOF control structure to eliminate the overshoot in the setpoint response and compared their tuning technique with other techniques for the same processes [10]. Saravanakumar and Wahidabanu (2009) proposed a modified Smith predictor for controlling higher- **order** proceses with integral action and long dead **time**. They used an I-PD **controller** where the integral control was in the forward path and the proportional and derivative control were in the feedback [11]. Ruscio (2010) presented analytical results of PI **controller** tuning based on integrator plus **time** **delay** models. They developed analytical relations between the PI **controller** **parameters** and the **time** **delay** error parameter in a way to obtain modified Ziegler-Nichols **parameters** with increased robustness margins [12]. Rao, Rao and Stee (2011) proposed a design for **PID** controllers based on integral model control principles, direct synthesis method and stability analysis method for pure integrating process with **time** **delay**. They compared the performance of the proposed controllers with the controllers designed by some other methods [13]. Alfaro and Vilanova (2012) proposed a robust tuning method of 2DOF PI controllers for integrating controlled processes. Their work was based on the use of a model-reference optimization procedure with servo and regularity closed-loop transfer functions targets [14]. Huba (2013) outlined the performance achievable under PI control using the performance portrait method. He used an IAE cost function of the set point and disturbance _______________________

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Abstract: All the industrial process applications require the solutions of a specific chemical strength of the chemicals or fluids considered for analysis. Continuous Stirred Tank Reactor (CSTR) is one of the common used reactors in chemical process. Such specific concentrations are achieved by mixing of a full strength solution with water in the desired proportions. In this paper, a **controller** is designed for controlling the concentration of one chemical with the help of other. This paper features the influence of different controllers like PI, **PID**, Fuzzy logic **controller** and Genetic algorithm (GA) upon the process model. Model design and simulation are done in the MATLAB/ SIMULINK software. The concentration control is found better controlled with the addition of Genetic algorithm (GA) instead of fuzzy logic and conventional **PID** controllers. The improvement of the process is observed.

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This paper **PID** **controller** design for third **order** system using Ziegler-Nichols technique [28-29] (closed loop method), and performing parameter can be observed. The Ziegler-Nichols technique is a most popular technique in the **PID** tuning techniques. It is suitable only when system input is step. The main drawback of Ziegler-Nichols method show higher percentage overshoot. So Honeywell [30-31] technique preferred to minimize the overshoot of the system but Honeywell technique consist second **order** process [32]. The Ziegler-Nichols and Honeywell are designed **controller** **parameters** with tuning to show satisfactory performance and results. In this Direct Synthesis (DS) impenitence [33-34], the composition is founded on a cherished closed loop transfer function for an exclusive second-**order**-plus-dead-**time** (SOPDT) system. From such a Direct Synthesis (DS) **controller**, **PID** **controller** designed with varied prescript [35]. Generally Internal Model Control (IMC) based **PID** **controller** with **first** **order** filter is a promoted technology to optimize higher **order** system to low **order** system and system is deficient sophisticated and all **parameters** (percentage overshoot, settling **time**, rise **time** and steady state error) of the system is less than Ziegler-Nichols, Honeywell tuned **controller**, Direct Synthesis (DS) **controller** and Internal Model Control based **PID** Control without changing **parameters** of FOPDT, SOPDT and third **order** process. Many advanced control strategies improve and implement in load frequency control and automatic generation control of single area Power system, double and multi area Power system [36-40].

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This is second **order** system with two real poles, located at -5 and -6. Our general goal will be to speed up the response of the system and produce a system with a position error for a unit step input of 0.1 or less, a percent overshoot of 10% or less, and a settling **time** of less than 1 second. To keep things reasonable, assume we want k ≤ 10 for all designs. You must write down the values of , and for each of the following designs and include these in the captions for the figures.

integral-derivative (**PID**) **controller** for a Bidirectional inductive power transfer (IPT) system using multiobjective Particle Swarm Optimization (PSO). The objective of the paper is to analyze the power flow in Bidirectional inductive power transfer **systems** and to design and implement the optimal **parameters** of **PID** **controller**. The optimal **PID** control **parameters** are applied for a composition control system. The performance of PSO- tuned **controller** is dependent on nature of the objective function and with the determination of **parameters** of **PID** **controller** based PSO is observed. Simulated performance analysis of the proposed PSO-based **PID** **controller** is compared with other well-known tuning method to investigate the optimal response and the best balance between performance and robustness. Finally, design **parameters** for bidirectional IPT system, implemented with a PSO-based **PID** **controller**, which uses a multiobjective fitness function, are presented to demonstrate the validity, performance and effectiveness of the optimum **controller** design.

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Definition of optimization means searching for an alternative options that promising most cost effective or better feasible performance under different constraints. Optimization has been applied in many fields of science, including engineering, economics and logistics where optimal decisions need to be chosen. In essence, optimization means the selection of a best element with regard to some criterions or issues from variety set of available alternatives solutions. In addition, algorithm would continuously search for the best solution until certain criteria are met. Nevertheless, in **order** to tend totally exploit and explore the search space, the optimization algorithm must have a system to balance between local search and global search [3].

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