Метод оптимального налаштування пі-регуляторів із врахуванням обмежень

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.

This work is proposed to continue the discussion of the problems, theoretical foundations and practical features of the construction and synthesis of robust control systems with high gain, allowing us to control multidimensional nonlinear dynamic objects of high dimensional with functional uncertainties. If problems could not be solved at the level where they appeared, it is necessary to rise the level of understanding of the laws of nature, or in the words of master Lui-Shi Chun Qiu (China, 3rd century BC): "The boy of five chi growth leads the bull by the bridle and the bull obeys him in everything. This is because the person in this case follows naturalness" (the laws of nature). The judo philosophy ("soft way") is based on the principles of using the power and energy of the opponent to achieve victory. The purpose of this work is to demonstrate the theoretical aspects and practical features of the methods of synthesis of optimal control systems by the criterion of maximum reproduction accuracy using the example of robust systems, which allow to control dynamic objects with functional uncertainties, including unstable objects, no minimal-phase objects, neutral objects and objects with differentiation properties. The simplicity (at the level of the engineer) and universality, mathematical rigor and physical validity of this approach is based on the judo philosophy: suppressing the dynamics of a functionally uncertain object and external disturbances by the infinitely large gain with the finite control signal and at the same time maintaining sustainability. Theoretically exhaustive solution of the problem of robust control is given by the idea of constructing systems that are stable with an unlimited increase of the gain coefficient. The sustainability properties are valid for optimal systems that were synthesized using quadratic quality functionals that do not explicitly depend on the control signal, and using a restriction on the control signal. It is significant that in contrast to continuous systems with un-measurable disturbances and not well known control object (in which the conditions of invariance imply the use of infinitely large gain), in relay (discontinuous) systems the equivalent effect is achieved with the help of finite control signal. A nice bonus is the highest accuracy which leads to mathematically zero error of regulation, thus all error coefficients (of position, speed, acceleration, acceleration derivative, etc.) is also equal to zero in the presence of external and internal interferences. In fact, the optimal accuracy control system is equivalent to a system with astatism of the n-th order: the regulator contains n serial connected integrators.

Oil is one of the most precious source of energy for the world and has an important role in the global economy. Therefore, the long-term prediction of the crude oil price is an important issue in economy and industry especially in recent years. The purpose of this paper is introducing a new Particle Swarm Optimization (PSO) algorithm to forecast the oil prices. Indeed, the PSO is a population-based optimization method inspired by the flocking behavior of birds. Its original version suffers from tripping in local minima. Here, the PSO is enhanced utilizing a convergence operator, an adaptive inertia weight and linear acceleration coefficients. The numerical results of mathematical test functions, obtained by the proposed algorithm and other variants of the PSO elucidate that this new approach operates competently in terms of the convergence speed, global optimality and solution accuracy. Furthermore, the effective variables on the long-term crude oil price are regarded and utilized as input data to the algorithm. The objective function of the optimization process considered in this research study is the summation of the square of the difference between the actual and the predicted oil prices. Finally, the long-term crude oil prices are accurately forecasted by the proposed strategy which proves its reliability and competence.

The primary function of microgrid (MG) is to share the power accurately among different distributed generation (DG) units according to the load demands. The droop control methods are normally used for appropriate power sharing. However, these control techniques suffer badly due to the feeder impedances and uncontrollable power coupling issues. Many techniques have been proposed to share power accurately, most of them rely on communication link. In this work a localized/communication free signal generating mechanism is proposed. The mechanism injects the transient reactive power in frequency droop characteristics by observing the changes in microgrid. This injection disturbs the actual active power sharing which is helpful for the computation of reactive power sharing errors. These errors are minimized by utilizing the proportional integral (PI) controller. The PI controller modifies the y-intercept and the slop of Q-E (Reactive Power –Voltage) droop characteristic for the correction of reactive power sharing error. Moreover, the parameters of droop and PI controller of inner control loop are optimized by Particle Swarm Optimization (PSO) to obtain high precision and reliability. The proposed technique has the following salient features:1. Accurately shares the reactive power without the information of feeder line impedances2. This accurate reactive power sharing scheme has been started locally without the need of communication signal from the central controller. Thus, there is no delay in monitoring the notable changes in microgrid caused by DGs. 3. The careful selection of PI & droop controller parameters through PSO makes the system more stable as compared to the conventional methods in terms of transients and steady state responses.

Real Time Control For Time Delay System

A Computer Package for the Synthesis of Optimal Control Systems with Arbitrary Performance Index

This paper presents a modern approach for speed control of an induction motor (IM) using the particle swarm optimization (PSO) method for determining the optimal parameters, Kp and Ki, of the integral proportional (IP) controller. The use of PSO as an optimization algorithm makes the drive robust, with faster dynamic response, higher accuracy and insensitive to load variation. Comparison between different controllers is achieved, using an IP controller which is tuned by two methods, firstly manually and secondly using the PSO technique. Integral time absolute error, integral absolute error and integral square error performance indices are considered to satisfy the required criteria in output speed of an IM. From the simulation results it is observed that the IP controller designed with PSO yields better results when compared to the traditional method in terms of performance index.

A Static Synchronous Compensator (STATCOM) is one of the Flexible AC Transmission System (FACTS) device which plays an vital role in power system network in alleviation of small and large transient disturbances and better voltage regulation. This paper proposed a self tuning Proportional-Integral (PI) controller for STATCOM which provided a voltage support at point of common coupling (PCC). Self tuning of PI controller was achieved by adapting PI controller gains with system parameters by using Bats Echolocation controller which mimics the Bats Echolocation behavior. In the proposed controller, the system voltage (parameter) at point of common coupling compared with reference voltage and then Bats Echolocation Controller updates the PI controller gains according to the variation obtained between them. This paper also proposed a Cascaded Multilevel Inverter (CMLI) instead of conventional Voltage Source Inverter (VSI) for STATCOM to obtain better voltage regulation at point of common coupling. The voltage imbalance between H-bridge cells in CMLI was rectified by prosing Multicarrier Pulse Width Modulation (PWM) techniques, The proposed controller was validated by comparing the simulation results with fixed gain PI controller and Self tuning PI controller using Neural controller and Particle Swarm Optimization.

This paper presents a load frequency control (LFC) of five areas connected to same tie-line and it consist of non-conventional main power grids (Thermal-Hydro) and micro-grids (Wind-Diesel). Performance of conventional PI controllers is compared with PSO (Particle Swarm Optimization) tuned PI controller in a regulated and deregulated environment. A five area power system model has been made using Matlab/simulink to analyse load frequency control measures under different conditions based on participation factors, load disturbances and variations in local load demands. Simulation results shows that PSO(Particle Swarm Optimization) tuned PI(Proportional & Integral) controller's gains give much better performance than the conventional PI controller parameters which are more difficult to determine and time-consuming. The effect of DFIG (Doubly fed Induction Generator) in the power system which helps to smooth the tie line power is also been described.

The main problem of using a Proportional Integral (PI) Controller in Brushless Direct Current (BLDC) motor speed control is tuning the PI’s parameter and its performance cannot adapt to the system behavior changes. Particle Swarm Optimization (PSO) has been chosen to optimize the tuning. Fuzzy Logic Controller (FLC) is used to online tuning PI’s parameters to adapt to system conditions. Optimal adaptive PI, which combines the PSO method and FLC method to tune PI, is proposed. It was successfully implemented in the simulation environment. The test was carried out in three conditions: step responses, set-point changes, and disturbance rejection. The proposed algorithm is superior with no overshoot/undershoot. Whereas in terms of settling time is in between PI and PI-PSO. PI controller has the smallest control effort. However, the other parameter is the worst. PI-PSO is superior in terms of settling time and Integral of Absolute Error (IAE) except for the step response test. The proposed method has lower IAE and higher control effort by 78.73 % and 60 % compared to PI control. On the other hand, it has a higher IAE dan lower control effort by 11.82 % and 33.88 % compared to PI-PSO. Therefore, the optimal adaptive PI control can reduce energy consumption compared to optimal PI with better performance than PI control.

The control of a dc motor drive system is performed using two Proportional-Integral (PI) controllers, mostly comprising the outer (speed) and inner (torque) loops. However, the tuning of the PI controllers is challenging, because of the significant overshoot and substantial settling time. The overshoot cannot be absolutely removed without sacrificing the speediness. In this paper, an experimental implementation of Adaptive Neuro-Fuzzy Inference System (ANFIS) based high-precision controllers for a dc motor drive system is presented for eliminating the overshoot contemporaneously improving the settling time. In this regard, for fair comparison, Bode Plot method is used for obtaining most satisfactory values of Kp and Ki of both the controllers and the performance of the proposed ANFIS controllers is compared with the tuned PI controllers. For the sake of validation, an experimental setup, a 2-quadrant dc motor drive based on DS1104 R&D controller board from dSPACE is used. The designed ANFIS controllers are implemented and also authenticated using simulations. The obtained simulation as well as experimental results indicated that the ANFIS controller successfully eliminates the overshoot and significantly improves settling time. Thereby, outclass the tuned PI controllers by giving experimental results as 0% overshoot and just 0.18 s settling time.

A new tuning rule is proposed for PI controllers and first-order plants with time delay. The tuning presents a set of equations based on a multi-objective optimization with a closed-loop robustness criterion for both input and output disturbances rejection. The equations allow the control engineer to select the weight given to each response in order to cope with the compromise between input and output disturbance rejection optimality.

This paper proposes optimal tuning of Proportional Integral (PI) controller using Grey Wolf Optimizer (GWO) to overcome the slow convergence into local optimum associated with the Particle Swarm Optimization (PSO), and Genetic Algorithm (GA) tuning methods. The optimal gains of the PI controller obtained from tuning using GWO, PSO and GA were implemented in the pitch angle control of the fixed speed Wind Turbine integrated into the distribution system. The objectives are to enhance the efficiency and reduced the fluctuation in the Wind Turbine output. Similarly, the Ziegler Nichols (ZN) tuned PI controller, the PI-fuzzy logic and Fuzzy Logic controllers were implemented in the same distribution system. The implementation of the tuned PI controllers has enhanced the output power of the Wind Turbine compared to the value obtained using the Hybrid or Fuzzy controllers. Furthermore, the GWO tuned PI controller recorded the high average output power of the Wind Turbine with low mean power error compared to other controllers. Also, it recorded the second-position in smoothing the Wind Turbine output power. The significance of the research is it has enhanced the efficiency and smoothing the output power of the fixed speed Wind Turbine.

Greenhouse system (GHS) is the worldwide fastest growing phenomenon in agricultural sector. Greenhouse models are essential for improving control efficiencies. The Relative Gain Analysis (RGA) reveals that the GHS control is complex due to 1) high nonlinear interactions between the biological subsystem and the physical subsystem and 2) strong coupling between the process variables such as temperature and humidity. In this paper, a decoupled linear cooling model has been developed using a feedback-feed forward linearization technique. Further, based on the model developed Internal Model Control (IMC) based Proportional Integrator (PI) controller parameters are optimized using Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) to achieve minimum Integral Square Error (ISE). The closed loop control is carried out using the above control schemes for set-point change and disturbance rejection. Finally, closed loop servo and servo-regulatory responses of GHS are compared quantitatively as well as qualitatively. The results implicate that IMC based PI controller using PSO provides better performance than the IMC based PI controller using GA. Also, it is observed that the disturbance introduced in one loop will not affect the other loop due to feedback-feed forward linearization and decoupling. Such a control scheme used for GHS would result in better yield in production of crops such as tomato, lettuce and broccoli.

Recently, the Gravitational-Search Algorithm (GSA) has been presented as a promising physics-inspired stochastic global optimization technique. It takes its derivation and features from laws of gravitation. This paper applies the GSA to design optimal controllers of a nonlinear system consisting of a doubly-fed induction generator (DFIG) driven by a wind turbine. Both the active and the reactive power are controlled and processed through a back-to-back converter. The active power control loop consists of two cascaded proportional integral (PI) controllers. Another PI controller is used to set the q-component of the rotor voltage by compensating the generated reactive power. The GSA is used to simultaneously tune the parameters of the three PI controllers. A time-weighted absolute error (ITAE) is used in the objective function to stabilize the system and increase its damping when subjected to different disturbances. Simulation results will demonstrate that the optimal GSA-based coordinated controllers can efficiently damp system oscillations under severe disturbances. Moreover, simulation results will show that the designed optimal controllers obtained using the GSA perform better than the optimal controllers obtained using two commonly used global optimization techniques, which are the Genetic Algorithm (GA) and Particle Swarm Optimization (PSO).