Calculation of PID Controller Parameters for Unstable First Order Time Delay Systems

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Study of Design of MIMC-PID for Unstable First Order Time Delay Process

Study of Design of MIMC-PID for Unstable First Order Time Delay Process

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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Analysis of Fractional PID Controller Parameters on Time Domain Specifications using Nelder Mead Algorithm & Interior Point Algorithm

Analysis of Fractional PID Controller Parameters on Time Domain Specifications using Nelder Mead Algorithm & Interior Point Algorithm

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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A PID Controller Design Approach for Robust Stability of Arbitrary Order Plants with Time Delays

A PID Controller Design Approach for Robust Stability of Arbitrary Order Plants with Time Delays

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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SIMULATION PERFORMANCE OF PID AND FUZZY LOGIC CONTROLLER FOR HIGHER ORDER SYSTEMS

SIMULATION PERFORMANCE OF PID AND FUZZY LOGIC CONTROLLER FOR HIGHER ORDER SYSTEMS

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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Controlling Of Nonlinear System by Using Fuzzy Logic Controller

Controlling Of Nonlinear System by Using Fuzzy Logic Controller

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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Computation of Simple Robust PI/PID Controller Design for Time Delay Systems using Numerical Optimization Approach

Computation of Simple Robust PI/PID Controller Design for Time Delay Systems using Numerical Optimization Approach

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,

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IMPLEMENTATION AND PERFORMANCE ANALYSIS OF BLDC MOTOR DRIVE BY PID, FUZZY AND ANFIS CONTROLLER

IMPLEMENTATION AND PERFORMANCE ANALYSIS OF BLDC MOTOR DRIVE BY PID, FUZZY AND ANFIS CONTROLLER

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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Computation of All Stabilizing PID Controllers for High- Order Systems with Time Delay in a Graphica
                 

Computation of All Stabilizing PID Controllers for High- Order Systems with Time Delay in a Graphica  

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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Analysis of Fractional order PID controller for Ceramic Infrared Heater

Analysis of Fractional order PID controller for Ceramic Infrared Heater

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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Optimum Tuning of the PID Controller for Stable and Unstable Systems Using Nonlinear Optimization Technique

Optimum Tuning of the PID Controller for Stable and Unstable Systems Using Nonlinear Optimization Technique

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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Stability Region Analysis of PID and Series Leading Correction PID Controllers for the Time Delay Systems

Stability Region Analysis of PID and Series Leading Correction PID Controllers for the Time Delay Systems

delay on system performance and the stability region of PID controller for first and second order systems with time delay are analysed in [4]. The recent designing approaches are proposed in [6, 7]. To improve the system performance, a new PID controller with series leading correction is described in [5]. Many new PID control strategies are discussed in [8-14] based on some intelligent algorithms. But these algorithms require lot of prior knowledge about control objects and difficult to use in actual applications. The SLC-PID controller model has only one adjustable parameter. The mathematical model of SLC-PID controller is given by equation.3
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COMPARISON OF PID TUNING METHODS FOR FIRST ORDER PLUS TIME-DELAY SYSTEM

COMPARISON OF PID TUNING METHODS FOR FIRST ORDER PLUS TIME-DELAY SYSTEM

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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PID Stabilization of Linear Neutral Time Delay Systems in a Numerical Approach

PID Stabilization of Linear Neutral Time Delay Systems in a Numerical Approach

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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Tuning Of A Pd-Pi Controller Used With An Integrating Plus Time Delay Process

Tuning Of A Pd-Pi Controller Used With An Integrating Plus Time Delay Process

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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Real time implementation of first order model reference adaptive control 
		(MRAC) without integral on regulating temperature of glycerin bleaching 
		process

Real time implementation of first order model reference adaptive control (MRAC) without integral on regulating temperature of glycerin bleaching process

controller capability in compensating the nonlinearities of the system and promote robust temperature regulation for glycerin bleaching process. The established Lyapunov approach in [10] is designed by assuming that there are no nonlinearities involve in the process and this MRAC approach is working well as well as be able to achieve the desired performance[11]. However, during actual operating, most of the control systems face nonlinear characteristics such as actuator constraint. The occurrence of actuator saturation will lead MRAC to instability problems due to divergence of adaptation gain when process output is mismatch with reference model. This situation is initiates by the existence of integral term in adaptation law that are continuously accumulates the integral gain due to integration of error that caused the controller output accumulates beyond the maximum and minimum operating point of the actuator. This situation is also known as windup phenomenon.
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Design and Implementation of Intelligent Controller for a Continuous Stirred Tank Reactor System

Design and Implementation of Intelligent Controller for a Continuous Stirred Tank Reactor System

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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Comparative analysis of controllers designed for a load  frequency control

Comparative analysis of controllers designed for a load frequency control

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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Lab 4: Root Locus For Controller Design

Lab 4: Root Locus For Controller Design

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.

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PSO based PID Controller for Bidirectional Inductive Power Transfer System

PSO based PID Controller for Bidirectional Inductive Power Transfer System

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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Social Spider Optimization (SSO) for Tuning PID Controller on DC Motors

Social Spider Optimization (SSO) for Tuning PID Controller on DC Motors

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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