Reduced order modelling of linear multivariable systems using particle swarm optimisation technique

In this paper, we present a comprehensive and in-depth investigation on the optimization of Proportional-Integral (PI) controller tuning for achieving stability and desired overshoot in the step response. The main objective of this study is to compare the effectiveness of Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) techniques in finding the optimal parameters for the PI controller. The PI controller is a widely used control algorithm that plays a crucial role in many industrial processes. Its tuning greatly affects the system's performance, particularly in terms of stability and overshoot. Therefore, finding the optimal tuning parameters is of utmost importance. To address this optimization problem, we propose the utilization of two popular metaheuristic algorithms, GA and PSO. These algorithms are known for their ability to efficiently search through large solution spaces and find near-optimal solutions. By applying these algorithms to the PI controller tuning problem, we aim to determine which technique yields better results in terms of stability and overshoot tuning. In our comparative study, we provide a detailed explanation of both GA and PSO algorithms, focusing on their working principles and mathematical formulations. We also describe how these algorithms can be applied to the PI controller tuning problem. Furthermore, we highlight the key differences between GA and PSO, shedding light on their strengths and weaknesses. To assess the performance of GA and PSO, we conduct several experiments using different benchmark functions and step response models. We measure the stability and overshoot metrics for various parameter settings obtained through GA and PSO. By thoroughly analyzing the obtained results, we draw meaningful conclusions regarding the effectiveness of each technique. Our findings demonstrate that both GA and PSO exhibit promising results in optimizing PI controller tuning. These observations provide valuable insights and guidelines for choosing the appropriate algorithm based on specific control requirements. In conclusion, this comparative study is thought to contribute to the field of control systems engineering by offering a comprehensive analysis of GA and PSO techniques in the context of PI controller tuning. By highlighting their strengths and weaknesses, it is aimed to provide researchers and practitioners with valuable information for making informed decisions when optimizing control parameters for stability and overshoot reduction purposes.

In this paper, a self-tuning hierarchical controller in which a Fuzzy logic controller supervises the control actions of a conventional PID has been proposed, implemented and presented. The controller has been applied to a control study of Fluid Catalytic Cracking (FCC) unit riser temperature, and regenerator temperature respectively. Performance comparison of the proposed Fuzzy-PID controller and the conventional PID was made in simulation studies of regulatory and servo performances of the two controller types. Six performance measures: Percent overshoot (OS), settling time (ST), integral absolute error (IAE), integral square error (ISE), integral time absolute error (ITAE) and integral time square error (ITSE) were employed as the tools for performance comparison between the conventional PID and the Fuzzy-PID controller. For the tracking of riser temperature with a set point at 524oC, the performance indicators under PID control gave the following results overshoot (14.5%); settling time (40 seconds) Integral absolute error (8.246), integral square error (3.3); integral time absolute error(1762);integral time square error (43.77) while for the same indicators under Fuzzy-PID control the following values: overshoot (3.3%); settling time (40 seconds) ;Integral absolute error (8.811); integral square error (14.5); integral time absolute error(280),;integral time square error (31.11) .The results allude to the superiority of the fuzzy-PID scheme over the PID scheme in tracking the optimal set point of riser temperature. More so, for tracking the regenerator set point temperature of 746oC, comparative study of step response under the two schemes gave the following results in six performance indicators: overshoot (PID(12.6%)/Fuzzy-PID(6%)); settling time (PID(80 seconds)/Fuzzy-PID(20seconds));Integral absolute error(PID(14.29)/Fuzzy-PID(8.63)); integral square error(PID(6.713).Fuzzy-PID(4.506)); integral time absolute error(PID(2858)/Fuzzy-PID(305.9)), integral time square error (PID(77.55)/Fuzzy-PID(33.05)).Moreover, the fuzzy-PID controller also showed superior performance over the conventional PID controller in terms disturbance rejection (regulatory response) of both riser and regenerator temperature. The results from this study suggest that the application of fuzzy-PID scheme to temperature control offers good promise of improved fluid catalytic cracking unit (FCCU) operations.

This paper strives to present a model order reduction (MOR) method for complex high order linear time-invariant (LTI) single input-single output (SISO) systems. The recommended method utilises the benefits of pole clustering method and differential evolution algorithm. In this suggested method, approximated denominator polynomial is obtained by pole clustering method whereas; approximated numerator is obtained using differential evolution algorithm. To indicate the effectiveness of the suggested method over existing MOR techniques, a comparison on the basis of a performance index known as integral square error (ISE) is depicted in this paper by using simulation graphs and in tabular form. Further, the suggested method is extended for MIMO systems also. Numerical examples are solved to give better understanding of the propound technique for SISO and MIMO systems. The recommended method derives and guarantees a stable approximated ROM if the original higher order system (HOS) is stable.

There has been ongoing experiments on a two-wheeled self-balancing robot for several years, and it is almost similar to the model of an inverted pendulum on a cart. The presented paper describes the model, design, working and simulation of a two-wheeled self-balancing robot. Properties of the system under study are extremely non-linear. Moreover, there is a great deal of instability in the controller of proposed system. To improve the stability of mobile robots, this paper introduces fractional order PID (FOPID) or PI <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">λ</sup> D <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">μ</sup> controller for a non-linear and high-order system and compares it with the conventional PID. FOPID controller is designed specifically to adjust the parameters of the system more accurately according to desired specifications. The factorrs of the considered controller are optimized using both Nelder-Mead (N-M) technique and Particle Swarm Optimization (PSO) technique. The results obtained by N-M technique are compared with those of PSO technique. N-M tuned FOPID controller significantly improves the quality of controller in contrast to PSO technique. Simulation results also indicate that Nelder-Mead tuned FOPID is a better and more stable controller as compared to classical PID or PSO tuned FOPID, for a non-linear system like a two-wheeled self-balancing robot.

&lt;p&gt;Order reduction of linear-time invariant systems employing two methods; one using the advantages of Routh approximation and other by an evolutionary technique is presented in this paper. In Routh approximation method the denominator of the reduced order model is obtained using Routh approximation while the numerator of the reduced order model is determined using the indirect approach of retaining the time moments and/or Markov parameters of original system. By this method the reduced order model guarantees stability if the original high order model is stable. In the second method Particle Swarm Optimization (PSO) is employed to reduce the higher order model. PSO method is based on the minimization of the Integral Squared Error (ISE) between the transient responses of original higher order model and the reduced order model pertaining to a unit step input. Both the methods are illustrated through numerical examples.&lt;/p&gt;

This paper presents performance comparative study of various particle swarm optimization (PSO) techniques for the placement of generator units in the distributed generation (DG) system. For the installation of generator units in the distributed generation system, it is very important to know the generator sizing and its placement in the network system for reducing the line losses and hence the cost. Various PSO techniques such as Canonical PSO, Hierarchical PSO (HPSO), Time varying acceleration coefficient (TVAC) PSO, Self-organizing hierarchical particle swarm optimizer with time-varying acceleration coefficients (HPSO-TVAC), Stochastic inertia weight (Sto-IW) PSO and Time varying inertia weight (TVIW) PSO have been used for comparative study. Here the main objective function (OF) is to minimize the system cost. These techniques have been tested on the standard IEEE-14 bus, IEEE-30 bus and IEEE-57 bus network system by the use of MATLAB software.

In the modern world with the advancement of technologies in solid-state electronics, the use of power electronics devices is playing a crucial role in the conversion and control of electric power. By using these innovative devices in 3-phase voltage source inverters, precise and smooth control over the conversion of electrical power can be achieved. But on the other hand, this leads to Total Harmonic Distortion (THD) leading to an adverse effect on the overall system performance. The optimization technique has emerged as a newly popular method for selective harmonic elimination. The main focus of this paper is on simulation study for harmonic analysis of 3-phase voltage source inverter by using particle swarm optimization (PSO) technique. By considering the expression of THD as an objective function, optimization is achieved in the PSO algorithm. This paper also discusses the harmonic analysis of the proposed inverter for conventional PWM techniques such as sinusoidal pulse width modulation (SPWM) and trapezoidal pulse width modulation (TPWM). The harmonic spectrum of the output voltage of the inverter is compared for SPWM, TPWM, and PSO by using MATLAB. From THD analysis, it is observed that PSO gives better performance than other conventional techniques.

With the increasing complexity of high-order dynamical systems (HOS), significant challenges arise in its analysis and controller design. Classical pole-zero clustering has been investigated for several decades, yet its conventional form provides only limited approximation accuracy on the reduced order (RO) approximant. This work extends the clustering approach by introducing a novel weighting vector concept coupled with an optimization stage. The problem of finding the optimal values of elements of the vector is framed in an optimization framework where the objective function represents the integral square error (ISE) between the response of the original HOS and that of the final reduced order system (ROS). Comparative analysis of the proposed algorithm has been carried out using performance indicators namely ISE, integral absolute error (IAE), integral time-weighted absolute error (ITAE), and relative integral square error (RISE) for stable / unstable / non minimum phase (NMP) SISO / MIMO benchmark systems. The comparative analysis results validate the efficacy of the proposed algorithm, and the resultant reduced order model (ROM) shows an improved approximation accuracy over that given in the existing literature, making it a viable process for obtaining a RO approximant for HOS SISO / MIMO systems preserving its original characteristics in the ROS. The results confirm that even though the pole clustering concept is classical, the integration of a pole / zero weighting scheme in an optimization framework provides a meaningful and modern enhancement that makes the method competitive with the recent state-of-the-art approaches.

In this paper differentiation method is proposed for driving reduced order model (ROM) of Multi-input multi - output (MIMO) linear dynamic system. The proposed method is based on differentiation of polynomials numerator and denominators. The reduction procedure is very simple given better response when compared with other reduction techniques and original high order system. Also, the proposed method guarantees given stability of the reduced models of MIMO system if the original high order MIMO system is stable. The proposed approach of MIMO system order reduction model is illustrated with the help of an Two-input and Two-output (2×2) transfer function matrix and the results of MIMO transfer function matrix are compared with the recently published reduction modal order techniques.

Investigating a hybrid of Tone-Model and Particle Swarm Optimization techniques in transcribing polyphonic guitar sound

This paper deals with a new method for model order reduction of linear continuous time interval system. This new method is based on the Kharitonov’s theorem, the Stability equation method and the error minimization by Differential Evolution. The reduced order interval model is determined by using Kharitonov’s polynomials, which make use of the Kharitonov’s theorem and general form of the stability equation method for denominator, while the numerator is obtained by minimizing the integral square error between the transient responses of original and reduced order models using Differential Evolution algorithm. This method generates stable reduced order interval system if the original higher order system is stable and retains the steady-state value. The proposed method is illustrated with the help of typical numerical example considered from the literature.

Segmentation is an important step in iris recognition system because the accuracy of the iris recognition system is affected by the segmentation of the iris. In this paper, an efficient method has been proposed for the segmentation of non-ideal iris images captured under uncooperative conditions. A fuzzy c-means clustering algorithm based on Particle Swarm Optimization (PSO) technique has been employed as a pre-segmentation step in the iris recognition framework. The fuzzy c-means clustering method delimits the iris and eliminates the unwanted portions of an image. The particle swarm optimization technique is incorporated to avoid FCM fall into local minimum. The segmentation accuracy of the proposed method is implemented by considering CASIA v3 Interval and UBIRIS databases. The proposed method is compared with the classical segmentation methods and has an encouraging performance.

Glioma detection based on multi-fractal features of segmented brain MRI by particle swarm optimization techniques

PurposeThis paper aims to employ particle swarm optimization (PSO) technique for optimum design of single‐phase induction motor (SPIM) on the basis of maximizing the efficiency of the motor simultaneously satisfying a set of performance constraints.Design/methodology/approachThe design problem of a SPIM is presented as a nonlinear optimization problem on the basis of maximizing the efficiency of the motor. A set of performance constraints are imposed in the optimization procedure. Particle swarm optimization technique is used as an optimization tool for obtaining the motor dimensions corresponding to maximum efficiency. Incorporation of PSO as a derivative free optimization technique in solving SPIM optimum design problem significantly relieves the assumptions imposed on the optimized objective function.FindingsThis approach has been applied to two sample motors and the results are compared with the evolutionary programming (EP) results. It is observed that the proposed approach is effective and robust.Originality/valueThe fields of application of SPIMs are expanding day by day. The emphasis on energy conservation demands an improvement of the efficiency of single‐phase induction motors. Hence, the design optimization of these motors with efficiency as objective function assumes great importance.

In this paper, an optical fiber alignment system based on the particle swarm optimization (PSO) technique is developed and presented. The PSO algorithm is used for locating the optimal coupling position with the highest optical power with two-degrees of freedom alignment. This algorithm yields interesting results without a need to go through the complex mathematical modeling of the alignment system. The proposed algorithm is validated considering the alignment of two Single Mode Fibers (SMF) and the alignment of SMF and Photonic Crystal Fiber (PCF) fibers.