Top PDF Design of a Fractional Order CRONE and PID Controllers for Nonlinear Systems using Multimodel Approach

Design of a Fractional Order CRONE and PID Controllers for Nonlinear Systems using Multimodel Approach

Design of a Fractional Order CRONE and PID Controllers for Nonlinear Systems using Multimodel Approach

This paper deals with the output regulation of nonlinear control systems in order to guarantee desired performances in the presence of plant parameters variations. The proposed control law structures are based on the fractional order PI (FOPI) and the CRONE control schemes. By introducing the multimodel approach in the closed-loop system, the presented design methodology of fractional PID control and the CRONE control guarantees desired transients. Then, the multimodel approach is used to analyze the closed-loop system properties and to get explicit expressions for evaluation of the controller parameters. The tuning of the controller parameters is based on a constrained optimization algorithm. Simulation examples are presented to show the effectiveness of the proposed method.
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Multi-objective optimized fuzzy-PID controllers for fourth order nonlinear systems

Multi-objective optimized fuzzy-PID controllers for fourth order nonlinear systems

It is observable from Figs. 20–22 that all the state variables converge to zero and complete stabilization occurs. Moreover, the superiority of this work in comparison with proposed approach in [22] is obvious. In [22] , the cart position and pendu- lum angle reached the final state almost in 7.2 and 7.5 seconds, respectively, while this work can achieve almost 3 seconds for the ball position and 4 seconds for the beam angle and the maximum absolute of the control input is about 8.02 (Point D). The values of design variables relative to point D and objective functions rela- tive to points A, B, C, and D are given in Tables 18 and 19 , respectively.
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Design And Implementation Of Dual Voltage Source Inverter Using Fractional Order Pid Controller

Design And Implementation Of Dual Voltage Source Inverter Using Fractional Order Pid Controller

A FOPID based DVSI scheme is proposed for microgrid systems with enhanced power quality. By using FOPID with DVSI scheme, the AVSI current harmonics are reduces and smoothening the wave forms. FOPID with DVSI scheme decreases the Total Harmonic Distortion (THD). The proposed scheme has the capability to exchange power from distributed generators (DGs) and also to compensate the local unbalanced and nonlinear load. Advantages of FOPID with DVSI scheme are Power quality improvement and the followingReduction in harmonics,Load voltage compensation,Reactive power compensation,It gives more power to the load,Getting optimal values of kp and ki, The performance of the proposed FOPID based DVSI scheme has been validated through simulation studies. Thus, aFOPID based DVSI scheme is a suitable interfacing option for microgrid supplying sensitive loads.the simulation results certified much better performance of FOPID controller in comparison with conventional PI controllers.
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A Conformal Mapping Based Fractional Order Approach for Sub-optimal Tuning of PID Controllers with Guaranteed Dominant Pole Placement

A Conformal Mapping Based Fractional Order Approach for Sub-optimal Tuning of PID Controllers with Guaranteed Dominant Pole Placement

A novel conformal mapping based Fractional Order (FO) methodology is developed in this paper for tuning existing classical (Integer Order) Proportional Integral Derivative (PID) controllers especially for sluggish and oscillatory second order systems. The conventional pole placement tuning via Linear Quadratic Regulator (LQR) method is extended for open loop oscillatory systems as well. The locations of the open loop zeros of a fractional order PID (FOPID or PI λ D μ ) controller have been approximated in this paper vis-à-vis a LQR tuned conventional integer order PID controller, to achieve equivalent integer order PID control system. This approach eases the implementation of analog/digital realization of a FOPID controller with its integer order counterpart along with the advantages of fractional order controller preserved. It is shown here in the paper that decrease in the integro-differential operators of the FOPID/PI λ D μ controller pushes the open loop zeros of the equivalent PID controller towards greater damping regions which gives a trajectory of the controller zeros and dominant closed loop poles. This trajectory is termed as “M-curve”. This phenomena is used to design a two-stage tuning algorithm which reduces the existing PID controller’s effort in a significant manner compared to that with a single stage LQR based pole placement method at a desired closed loop damping and frequency.
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Trends in Fractional Order Controllers

Trends in Fractional Order Controllers

385 Robust regulators with fractional structure and fractional order state equations for the control of visco-elastic damped structures was presented in year 1991 [24, 25]. The concept of tilt-integral-derivative (TID) (refer fig. 2) was presented and patent was registered in 1994 [26]. The first practical application of CRONE (refer to CRONE Group‘s introduction and the demo of MATLAB CRONE Toolbox) control was presented in year 1995 [27]. Fractional order lead-lag compensator was presented in year 2000 [28]. Application of fractional calculus in control theory was accelerated after year 2002. In the year 2002 a special issue on fractional order calculus and its applications was published in an international journal of Nonlinear Dynamics and Chaos in Engineering Systems [29]. A tutorial Workshop in IEEE International Conference on Fractional Order Calculus in Control and Robotics was organized in Las Vegas in the year 2002 [30]. Tuning of PI λ D μ controllers is a new research subject during last few years. Some important articles on design and parameter optimization of fractional controllers are presented here.
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Performance comparison of optimal fractional order hybrid fuzzy PID controllers for handling oscillatory fractional order processes with dead time

Performance comparison of optimal fractional order hybrid fuzzy PID controllers for handling oscillatory fractional order processes with dead time

Fuzzy logic controllers (FLC) have been traditionally used for efficient control of nonlinear, time varying and vague systems with little knowledge of the process to be controlled. Conventional FLCs work with the loop error and its integer order differ- integral [4] and have been proved to be an effective means over conventional PID controllers. The FLC based PID controllers have certain advantages as it combines the potential of both FLC and conventional PID controller. Tuning of such fuzzy PID controllers can be done to meet the design specifications. The tuning parameters of a fuzzy PID controller can be the input-output scaling factors, rule base, shape and degree of overlap of the membership functions (MF) etc. It has been suggested in Woo et al. [5] that the output scaling factors can be considered as the effective gains of the FLC based PID controllers. Also, these SFs have the highest impact on the control performance over the other FLC parameters. So, tuning of the input-output SFs based on fixed MFs and rule-base can be a logical approach as shown in [5]-[7]. Moreover, similar to the different decomposed structure of conventional PID controller [8]-[9], fuzzy PID controllers have been categorized in this paper to produce enhanced closed loop performance. Golob [8] studied various decomposed and hybrid fuzzy PID structures and their relative merits in closed loop control design which has been extended in the present work with its fractional order enhancements.
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Stability of closed-loop fractional-order systems and definition of damping contours for the design of controllers

Stability of closed-loop fractional-order systems and definition of damping contours for the design of controllers

stability. Section 2 shows the properties of a sys- tem whose open loop transfer function is defined by a pure complex order integrator. Section 3 explains how the complex order integrator can be band- limited and how to obtain integrators whose order has a high imaginary part. Section 4 presents how the band-limitation of the integrator can mod- ify the closed loop pole location. Section 5 shows how these contours can be used to design a sim- ple PID robust controller. Then it is explained how the contours can be taken into account to design robust controllers using either the CRONE or QFT methodology.
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Optimum Weight Selection Based LQR Formulation for the Design of Fractional Order PIλDμ Controllers to Handle a Class of Fractional Order Systems

Optimum Weight Selection Based LQR Formulation for the Design of Fractional Order PIλDμ Controllers to Handle a Class of Fractional Order Systems

Modern optimal control theory proposes several analytical tools to design not only control strategies satisfying desirable characteristics according to the designer’s specifications, but also gives the best possible way to do so [1]. The Linear Quadratic Regulator is one such design methodology whereby quadratic performance indices involving the control signal and the state variables are minimized in an optimal fashion. Till date, PID controllers are used widely in industrial process control applications due to their simple structure, tuning, ease of applicability and reliability [2]. Some efforts have been directed towards tuning PID controller with LQR technique as in He et al. [3] and Yu and Hwang [4], considering the error and integral of error as the state variables. The LQR based technique has also been extended for tuning PID controllers for sluggish over-damped second order processes in [3] by canceling one of the real system poles with a zero of the PID controller. Thus, the approach, presented in [3] does not give
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Satisfactory optimization design for fractional order PID controller

Satisfactory optimization design for fractional order PID controller

This paper presents a new parameters optimization approach for fractional or- der PID controllers, which uses a satisfactory optimization model. To fulfill different design performance specifications and constrains of systems, the appli- cation of multi-criterion satisfactory optimization to fractional control systems is considered. At the same time, the performance of fractional control systems controlled by fractional order controller and integer order controller is discussed. The simulation illustrates the effectiveness of the proposed method and the su- periority of the fractional order controller in both time domain and frequency domain.
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Design Templates for Some Fractional Order Control Systems

Design Templates for Some Fractional Order Control Systems

area mutually connected thermal power plant with generation rate constraint; group hunting search algorithm is adopted to explore the gain parameters of the controllers [13]. In [14], PI controller design is performed by using optimization for FOSs; first, controller parameters for a stable control are calculated by using the stability boundary locus method and then optimization is used to provide the best control. In [15], a new robust FOPID controller to stabilize a perturbed nonlinear chaotic system on one of its unstable fixed points is proposed based on the PID actions using the bifurcation diagram. In [16], fractional-order discrete synchronization of a new fourth -order memristor chaotic oscillator and the dynamic properties of the fractional-order discrete system are investigated; a new method for synchronizing is proposed and validated. In spite of the existence of a great deal of publications about FOSs some of which have just been mentioned above, most of the present analysis and design techniques deal with sophisticated and rather special applications [17-24]. Although the step response characteristics such as rise time, settling time, delay time, overshoot and some others are well known by explicit formulas for simple integer order systems [25], such formulas are not available for FOSs. And a compact publication yielding the relations between the design parameters and the step response characteristics of even simple FOSs are not yet present. The purpose of this paper is to fulfill this vacancy and to supply some design tools for simple order FOSs.
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Design and Analysis of fuzzy PID Controllers using Genetic Algorithm

Design and Analysis of fuzzy PID Controllers using Genetic Algorithm

Jouda Arfaoui , ElyesFeki , Abdelkader Mami have Discussed the Genetic algorithm which is generally used in the various best possible problems . This paper propose an another method for designing fuzzy logic controller for temperature control inside the cavity of refrigeration. This paper compare the result of GA FLC with Conventional PID and GA PID with respect to stability ,settling time and energy consumption . The result of this paper shows GA- FLC has good response compare with the other. GA_FLC reduced the consumption energy of about 1.3401kWh.[4]
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Design and Optimization of Fractional Order Proportional Integral Derivative Controllers for Hard- Disk Drive Servo Systems

Design and Optimization of Fractional Order Proportional Integral Derivative Controllers for Hard- Disk Drive Servo Systems

The rest of this brief is organized as follows. In section II the HDD- actuator system modelling is presented. The basic concepts of fractional order calculus and control are given in section III. In section IV the tuning process for FO-PID controllers is given. In section V the implementation details of FOPID controllers on the HDD model are given. In section VI simulation results are shown for the validation of the method discussed. Conclusions are given in section VII.

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Self Tuning Of Pid Parameters Using Fuzzy Logic Vs Nonlinear Controllers

Self Tuning Of Pid Parameters Using Fuzzy Logic Vs Nonlinear Controllers

The PID controller is the most common form of feedback. It became the standard tool. PID controllers are today found in all areas where control is used. The controllers come in many different forms. PID control is often combined with logic, sequential functions, selectors, and simple function blocks to build the complicated automation systems used for energy production, transportation, and manufacturing. PID controllers have survived many changes in technology, from mechanics and pneumatics to microprocessors via electronic tubes, transistors, integrated circuits. The microprocessor has had a significant influence on the PID controller. Practically all PID controllers made today are based on microprocessors. This has given opportunities to provide additional features like automatic tuning, gain scheduling, and continuous adaptation.[1]
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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  

Abstract — In the present paper, the problem of computation of all stabilizing high-order time delay systems using well known and efficient proportional- integral-derivative (PID) controller is investigated in a graphical approach. An efficient approach to this important problem is presented. Based on this approach, all PID controllers that will ensure stability are determined in a ( k p , k i , k d ) plane and then the stability boundary in a ( k i , k d ) plane for a constant value of k p is determined and analytically described. It is shown that the stabilizing ( k i , k d ) plane consists of triangular regions. The generalized Hermite- Biehler theorem which is applicable to quasipolynomials and finite root boundaries which will be described in detail in continuation are studied to establish results for this design and also determining region of stability of designed PID controllers. Bode diagram criterion is used to show the stabilizing PID gain and phase margins. Step response is also used to show the correctness and advantage of the approach in two examples which are given to illustrate the method.
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Fractional sliding mode control design for robust synchronization and anti-synchronization of fractional order nonlinear chaotic systems in finite time

Fractional sliding mode control design for robust synchronization and anti-synchronization of fractional order nonlinear chaotic systems in finite time

Chaotic system is a nonlinear deterministic system with complex and unpredictable behavior. Chaotic behavior as is known to all, is a prevalent phenomenon which can be appeared in nonlinear systems. It has been also seen in a variety of real system in laboratory such as electrical circuits, chemical reactions and fluid dynamics and so forth [1]. Based on chaos theory, the prominent features of chaotic systems are that the highly sensitivity to initial conditions. Chaos synchronization is a phenomenon that may happen when two, or more, dissipative chaotic systems are coupled. Moreover, Synchronization control is one of the important research area in chaos theory and it is simply means that things occur at the same time. The main problem related to the synchronization
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Controller Design for Fractional-Order Systems

Controller Design for Fractional-Order Systems

Fractional calculus provides an excellent instrument for the description of memory and hereditary properties of various materials and processes. This is the primary advantage of fractional derivatives in comparison to classical integer order models, where such dynamics not taken into account. The advantages of fractional derivatives become more appealing in the modeling of mechanical, electrical and electro-mechanical properties of real materials, as well as in the description of rheological properties of rocks, and in many other fields. Recent times have wide application of field fractional integrals and derivatives also in the theory of control of dynamical systems, where the controlled system or/and the controller is described by a set of fractional differential equations. 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. For this reason, this mathematical tool could be judged “far from reality”. But many physical phenomena have “intrinsic” fractional order description and so fractional order calculus is necessary to replicate their input-output characteristics.
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Frequency Domain Design of Fractional Order PID Controller for AVR System Using Chaotic Multi-objective Optimization

Frequency Domain Design of Fractional Order PID Controller for AVR System Using Chaotic Multi-objective Optimization

numbers from a normal or uniform distribution, similar to the case of single objective cases in [28]. Since NSGA-II is a widely accepted multi-objective optimisation algorithm, therefore it has been chosen in this paper and has been improved by applying a chaotic map. The other newly introduced multi-objective optimization algorithms like Multi-objective Evolutionary Algorithm based on Decomposition (MOEA/D) has improvements in run time complexity over NSGA-II, but the performance improvements in obtaining better Pareto fronts is slight or almost similar [35]. The objective of the present paper is more applied in nature and geared towards the improvement in the power system control side using a harmonious blend of fractional order control techniques and multi-objective optimization based design trade- offs. The paper does not aim to propose a new algorithm or provide a comparison of a set of MOEA algorithms for test bench functions. Therefore, chaotic map augmented NSGA-II algorithm is highlighted to be used as a tool for an important frequency domain design aspect for AVR systems.
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Performance of Two Loop Controlled Micro Gird Scheme with Fractional Order PID and Hysteresis controllers

Performance of Two Loop Controlled Micro Gird Scheme with Fractional Order PID and Hysteresis controllers

Microgrid is a blend of small scale generators, energy-storage -frameworks and burdens. The control techniques of Micro grids are acknowledged by the control of converters. The control methodologies of converters are unique in relation to AC Micro grids to DC- Micro grids. A survey on organize procedures of AC/DC Micro grid was recommended. “Microgrid grid outage management (GOM) using (MA) multi-agent-frameworks” was given. Demonstrating and examination of the AC/DC hybrid micro-grid with bidirectional power stream controller was exhibited. In view of MPPT controller incorporates two phases, the principal phase was the notable Incremental Conductance calculation as well as the second-phase depends going on the prescient hysteresis controller [5]-[9]. “Execution correlation of hysteresis (HC) &resonant-current-controllers (RCC) on behalf of a multifunctional (GCI) grid-connected-inverter” was displayed. ‘PQ (Power-quality) improvement utilizing distributed generation (DG) inverters by dynamic power-control’ was introduced. “Objective-arranged-PQ (power-quality) pay of multifunctional-grid–tied inverters &its purpose in Micro grids” was created [10]-[14]. Finding the ideal structure as per an inventive energy the executive’s framework that explores the primary parameters which would influence the framework execution was researched. Energy-management for a grid-associated hybrid-sustainable power source framework was given [15]-[16].
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Positive Solutions for Multi-Order Nonlinear Fractional Systems

Positive Solutions for Multi-Order Nonlinear Fractional Systems

Abstract. In this paper, we study the existence of positive solutions for a class of multi-order systems of fractional differential equations with nonlocal conditions. The main tool used is Schauder fixed point theorem and upper and lower solutions method. The results obtained are illustrated by a numerical example.

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Self-balancing Robot Control Using Fractional-Order PID Controller

Self-balancing Robot Control Using Fractional-Order PID Controller

balancing robot has been studied on this paper. The proper FOPID parameters obtained by FOMCON toolbox for MAT- LAB based on proper integer-order PID parameters to achieving system performance and stability using MATLAB and SIMULINK. The realize implementation on Raspberry Pi concept for both controllers has been introduced using IIR cascaded second-order section form II transfer function in filter form on CODESYS V3.5, In theoretical term. simulated results show that the FOPID controller can stabilize the system and improve transient response with less percent overshoot and rise time than PID controller. Whereas the implementation of PID controller on real robot system can keep the robot stable better than FOPID controller because of this implementation on raspberry or microcontroller using numerical method of filter l ead t o o ver c omputing a nd slow overall process. The FOPID implementation on Raspberry Pi has been studying in the future.
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