Integral Performance Criterion Research Articles

PID Controller Design for a Fractional Order System using Bode’s Ideal Transfer Function

In this paper, an optimization method is proposed to design a fractional order system with PID controller by taking Bode’s ideal transfer function as reference model. In the study, PID controllers are preferred because of their simplicity, reliability and robustness. PID controller parameters can be obtained by optimization method. In order to obtain the desired time response, it is sufficient to set two parameters in the Bode’s ideal transfer function. The Bode's ideal transfer function was considered as the reference model and compared with the generated model. The error in the output signal is minimized by the integral performance criteria, and the PID controller parameters are optimized. Integral performance criteria are frequently used in evaluating the performance of control systems. In Simulink model, Matsuda's 4th order integer approximation model is used for fractional order control system. Finally, the success of the optimization method is seen in the given numerical example.

Integral Performance Criterion of Self-Propagating High-Temperature Synthesis Ferrosilid for Optimization of Charge Composition

An algorithm of optimization of the charge for metal-containing waste processing of metallurgical and foundry industries was developed. The processing method is based on the phenomenon of self-propagating high-temperature synthesis (SHS) of ferroalloys of the composition of dispersed waste without the use of external sources of heat due to internal energy.

Tuning of Fractional Order PID Controllers Based on Integral Performance Criteria Using Fourier Series Method

This paper presents a time domain tuning technique for a fractional order PID controller based on optimizing an integral performance criterion. A Fourier series based method (FSM) is used to calculate accurately the step response of the closed loop control systems so as to determine the exact value of the error function performance criterion. The initial guesses for the FOPID controller parameters to be optimized are found using the analytical solution for integral squared error optimization for an integer order PID controller. The proposed method is used for two test plant transfer functions by comparing different optimal FOPID controllers. The results show that the design technique based on optimization of different integral performance criteria give good step responses for FOPID controller.

Kinematic problem of optimal nonlinear stabilization of angular motion of a rigid body

The problem of optimal transfer of a rigid body to a prescribed trajectory of preset angular motion is considered in the nonlinear statement. (The control is the vector of absolute angular velocity of the rigid body.) The functional to be minimized is a mixed integral quadratic performance criterion characterizing the general energy expenditure on the control and deviations in the state coordinates.

Tuning of Fractional Order PI Controller for Cascade Control System using Genetic Algorithm

Background/Objectives: The main objective of this research work is to design a cascade control system with fractional order proportional plus integral controller as the primary controller and proportional controller as the secondary controller. The best optimal values for fractional order PI controller (FOPI) controller are obtained by minimizing time integral performance criteria i.e IAE using genetic algorithm. Methods/Statistical Analysis: Cascade control scheme is one of the most popular control schemes in process industries because of its improved disturbance rejection and easy implementation. Research have been done by various researchers in designing the conventional controller for a cascade control system, but the emergence of fractional calculus in the field of control area paved the idea to replace conventional integer order controllers by fractional order controllers. Findings: The cascade control system is always designed using conventional controllers. An attempt is made to replace conventional integer order controllers in the primary loop with fractional order controllers in order to improve the performance and get better disturbance rejection. Applications/ Improvements: Simulation results show the effectiveness of the proposed controller. The performance indices tabulated and compared to indicate the improvement.

Multiobjective robust PID controller design for various industrial processes

In this paper, Non-dominated Sorting Particle Swarm Optimization (NSPSO) is applied to design multiobjective ro- bust Proportional-Integral-Derivative (PID) controllers for various industrial processes such as distillation column plant, liquid level control system and DC servo motor control system. Multiobjective robust PID controller design problem is formulated by minimizing Integral Squared Error (ISE) and balanced robust performance criteria. The performance of various optimal PID controllers is compared in terms of ISE and robust criteria. For the purpose of comparison, NSPSO and Non-dominated Sorting Genetic Algorithm-II (NSGA-II) methods are considered. The performance of PID controllers obtained using NSPSO is better than that of NSGA-II. The results reveal that NSPSO yields better robustness and consistency in terms of integral squared error (ISE) and balanced robust performance criteria than NSGA-II for various industrial processes.

Model of Evaluation of the Management Effectiveness of State Corporate Rights of Industrial Enterprises in Ukraine

This paper proposes a method for increasing the efficiency of state corporate rights management of industrial enterprises by clarifying the evaluation of the efficiency of their management. This method is a model of comprehensive evaluation of enterprises on the basis of data that resulted in the reporting documents. Three groups of indicators were adopted and included: commercial, non-commercial and managing criteria. Integral performance criterion is the weighted sum of those three groups. Model performance evaluation was built using ordinal regression. Based on this model estimate the efficiency of state corporate rights management of industrial enterprises was obtained more accurately, providing a wide range of estimates.

SOSPD Controllers Tuning by Means of an Evolutionary Algorithm

The Proportional Integral Derivative (PID) controller is the most widely used industrial device to monitoring and controlling processes. There are numerous methods for estimating the controller parameters, in general, resolving particular cases. Current trends in parameter estimation minimize an integral performance criterion. Therefore, the calculation of the controller parameters is proposed as an optimization problem. Although there are alternatives to the traditional rules of tuning, there is not yet a study showing that the use of heuristic algorithms it is indeed better than using the classic methods of optimal tuning. In this paper, the evolutionary algorithm MAGO is used as a tool to optimize the controller parameters. The procedure is applied to a range of standard plants modeled as a Second Order System plus Time Delay. Better results than traditional methods of optimal tuning, regardless of the operating mode of the controller, are yielded.

Multi-step mode signal conversion algorithms in hall sensor devices

This paper presents a numerical and experimental based data analysis of electromagnetic noise immunity in magnetic field measurement devices on Hall sensor transducers. Relevance of this problem takes place in sensor networks with autonomous low-powered sources, magnetic field mapping devices for charged particle accelerators fusion reactors, etc. The proposed algorithm is based on averaging of several step by step signals, especially, acquired by three consecutive measurements in time interval: (t + dt), (t), (t – dt). In (t + dt) and (t – dt) time intervals a Hall sensor current pulse magnitude and directions are the same. Contrary to these, in (t) time interval the Hall sensor current has the opposite direction. It is shown that the efficiency of triple step measurements is three times higher than in double step measurement. The integral performance criterion concept of the signal converter effectiveness is introduced. The performance criterion factor is defined as a ratio of signal converter electromagnetic noise immunity to its energy consumption. A signal transducer optimized to noise immunity study, its operating modes and Hall sensor parameters are described. Both calculation and experiment results show that the performance criterion factor in triple step measurements is twice higher than in double step measurements.

Design of non-parametric process-specific optimal tuning rules for PID control of flow loops

The problem of designing optimal process-specific rules for non-parametric tuning is undertaken in the paper. It is shown that producing non-parametric process-specific optimal tuning rules for PID controllers leads to the problem that can be characterized as optimization under uncertainty. This happens due to the fact that tuning rules, unlike tuning constants, are produced not for a particular process or plant model but for a set of models from a certain domain. The novelty of the proposed approach is that the problem of obtaining optimal tuning rules for a flow process is formulated and solved as a problem of optimization of an integral performance criterion parametrized through values that define the domain of available process models. The considered non-parametric tuning assumes the use of the modified relay feedback test (MRFT) recently proposed in the literature. It allows one to tune the PID controller satisfying the requirements to gain or phase margins that is achieved through coordinated selection of tuning rules and test parameters. This approach constitutes a holistic approach to tuning. In the present paper, optimal tuning rules coupled with MRFT, for flow loops, are proposed. Final results are presented in the form of tables containing coefficients of optimal tuning rules for the PI controller, obtained for a number of specified gain margins. The produced non-parametric tuning rules well agree with the practice of loop tuning.

Analysis of the Integral Efficiency Indicator for Information Systems of the Cyclic Type Accounting for Weights

The article is dedicated to the task of developing efficient means to analyze functioning of an information system of the cyclic type based on determining the integral performance criterion. We consider the subject area related to the analysis of moments of peak loads in teaching (admissions, conducting tests and examinations, accreditation of a university, etc.). The criterion is developed based on the analysis of all the processes occurring in the information system (IS) of a university and based on the selection of main factors affecting the change in the effective functioning of the university departments. Certain qualitative and quantitative parameters affecting the integral index of efficiency are considered at various times, since functioning of the whole system is cyclical. A weight for each criterion is accounted for in the integral indicator of efficiency. The proposed approach will allow for simplification of the research of efficiency characteristics of the information systems of the cyclic type based on the analysis of the integral coefficient.

SINTONIZACIÓN DE CONTROLADORES PI Y PID UTILIZANDO LOS CRITERIOS INTEGRALES IAE E ITAE

Se plantea en general el problema de la determinación de los parámetros óptimos de controladores bajo los criteriosintegrales y se describen las características de los métodos de sintonización de controladores de López, Rovira, y deKaya y Sheib.Se presentan nuevas ecuaciones para el cálculo de los parámetros óptimos para controladores PI y PID bajo loscriterios integrales IAE e ITAE.Mediante pruebas comparativas por simulación, se muestran las ventajas obtenidas con las nuevas ecuacionespresentadas.

Multi-objective robust PID controller tuning using two lbests multi-objective particle swarm optimization

In this paper, two lbests multi-objective particle swarm optimization (2LB-MOPSO) is applied to design multi-objective robust Proportional-integral-derivative (PID) controllers for two MIMO systems, namely, distillation column plant and longitudinal control system of the super maneuverable F18/HARV fighter aircraft. Multi-objective robust PID controller design problem is formulated by minimizing integral squared error (ISE) and balanced robust performance criteria. During the search, 2LB-MOPSO can focus on small regions in the parameter space in the vicinity of the best existing fronts. As the lbests are chosen from the top fronts in a non-domination sorted external archive of reasonably large size, the offspring obtained can be more diverse with good fitness. The performance of various optimal PID controllers is compared in terms of the sum of ISE and balanced robust performance criteria. For the purpose of comparison, 2LB-MOPSO, NSGA-II as well as earlier reported Riccati, IGA and OSA methods are considered. The performance of PID controllers obtained using 2LB-MOPSO is better than that of others. In addition, Hypervolume-based comparisons are carried out to show the superior performance of 2LB-MOPSO over NSGA-II. The results reveal that 2LB-MOPSO yields better robustness and consistency in terms of the sum of ISE and balanced robust performance criteria than various optimal PID controllers.

Design of robust-optimal output feedback controllers for linear uncertain systems using LMI-based approach and genetic algorithm

This paper considers the robust-optimal design problems of output feedback controllers for linear systems with both time-varying elemental (structured) and norm-bounded (unstructured) parameter uncertainties. Two new sufficient conditions are proposed in terms of linear-matrix-inequalities (LMIs) for ensuring that the linear output feedback systems with both time-varying elemental and norm-bounded parameter uncertainties are asymptotically stable, where the mixed quadratically-coupled parameter uncertainties are directly considered in the problem formulation. A numerical example is given to show that the presented sufficient conditions are less conservative than existing ones reported recently. Then, by integrating the hybrid Taguchi-genetic algorithm (HTGA) and the proposed LMI-based sufficient conditions, a new integrative approach is presented to find the output feedback controllers of the linear systems with both time-varying elemental and norm-bounded parameter uncertainties such that the control objective of minimizing a quadratic integral performance criterion subject to the stability robustness constraint is achieved. A design example of the robust-optimal output feedback controller for the AFTI/F-16 aircraft control system with the time-varying elemental parameter uncertainties is given to demonstrate the applicability of the proposed new integrative approach.

Development of a Model Predictive Controller for Tankless Water Heaters

This paper describes the development of a novel approach to temperature control of tankless water heaters (TWHs). Conventional methods of controlling TWHs typically allow a high degree of error in the outlet water temperature when subjected to disturbances in flow rate or inlet water temperature. Poor control affects comfort, safety, and energy consumption associated with TWHs. The novel control approach presented here uses model predictive control (MPC) to minimize the outlet temperature error. A dynamic heat transfer model of an electric TWH is developed and validated and used within a MPC-based controller. The controller is interfaced to a physical prototype TWH and tested using an experimental test bed developed for this project. An integral performance criterion is used to compare performance and to tune the MPC in a standardized series of tests, also developed for this project. MPC is shown to provide excellent control of the prototype TWH.

Design of PID controller with incomplete derivation based on differential evolution algorithm

To determine the optimal or near optimal parameters of PID controller with incomplete derivation, a novel design method based on differential evolution (DE) algorithm is presented. The controller is called DE-PID controller. To overcome the disadvantages of the integral performance criteria in the frequency domain such as IAE, ISE, and ITSE, a new performance criterion in the time domain is proposed. The optimization procedures employing the DE algorithm to search the optimal or near optimal PID controller parameters of a control system are demonstrated in detail. Three typical control systems are chosen to test and evaluate the adaptation and robustness of the proposed DE-PID controller. The simulation results show that the proposed approach has superior features of easy implementation, stable convergence characteristic, and good computational efficiency. Compared with the ZN, GA, and ASA, the proposed design method is indeed more efficient and robust in improving the step response of a control system.

An Optimal Control Problem with a Small Parameter

A controlled object with small nonlinearity and two boundary conditions is considered. An integral performance criterion is established. The behavior of optimal value of such an extremal problem is studied as the small parameter tends to zero.

Estimates for the Norm of Green's Matrix Based on the Integral Performance Criterion for Dichotomy and Hausdorff Set Bounds

For a system of ordinary differential equations of the form \(du/dt = Au + f(t)\), \( - \infty < t < \infty \), we obtain new upper bounds for the second norm of Green's matrix using the integral performance criterion for dichotomy and bounds of the Hausdorff set of the matrix A. These estimates are considerably better for many applications than some well-known ones.

Optimal tuning of PID controllers for integral and unstable processes

Tuning formulas for PID controllers applied to integral and unstable processes are presented. In particular, the controller parameters are determined, based on the process model, to minimise integral performance criteria such as ISE, ITSE and ISTE. Results have been obtained by means of genetic algorthms, in order to avoid local minima in the optimisation procedure. Both the set-point following and the load disturbance rejection design specifications are addressed. The achieved results can be adopted both for tuning purposes and for the evaluation of the performances of a pre-existing PID controller.

Fuzzy Adaptive Control of a Plug Flow Tubular Reactor

A self-organizing, fuzzy controller is proposed for the adaptive control of a tubular reactor. Its design is based on a heuristic approach and it involves two functions: creating and modifying the control rules for a fuzzy logic controller and adjusting the universe of discourse based on system performance observed. The proposed controller is compared against a conventional PID controller which is tuned by two methods: either by the process reaction tuning method or by minimising the IAE time integral performance criterion. The proposed self-organizing controller, exhibits a superior performance in comparison with the PID tuned through the process and an equivalent, if not better performance than the PID controller whose parameters are adjusted optimally for minimising the IAE dynamic criterion.