Optimal Proportional-integral-derivative Controller Research Articles

Dynamic Modeling of Multiple Microgrid Clusters Using Regional Demand Response Programs

Preserving the frequency stability of multiple microgrid clusters is a serious challenge. This work presents a dynamic model of multiple microgrid clusters with different types of distributed energy resources (DERs) and energy storage systems (ESSs) that was used to examine the load frequency control (LFC) of microgrids. The classical proportional integral derivative (PID) controllers were designed to tune the frequency of microgrids. Furthermore, an imperialist competitive algorithm (ICA) was proposed to investigate the frequency deviations of microgrids by considering renewable energy resources (RERs) and their load uncertainties. The simulation results confirmed the performance of the optimized PID controllers under different disturbances. Furthermore, the frequency control of the microgrids was evaluated by applying regional demand response programs (RDRPs). The simulation results showed that applying the RDRPs caused the damping of frequency fluctuations.

Load Frequency Control of Two-area Interconnected Power System Using Optimal Controller, PID Controller and Fuzzy Logic Controller

In this paper, decentralized control scheme for Load Frequency Control (LFC) problem in a two-area interconnected power system with Fuzzy Logic Controller (FLC) is presented and its performance is compared with that of Optimal Controller (OC) and Proportional-Integral-Derivative (PID) Controller used in the same power system. This control scheme is simulated in MATLAB-Simulink for a two-area interconnected power system consisting of two generating units with non-reheat turbines to highlight the performance in terms ofrobustness and optimality. The step response of these control schemes against step load change is analysed and compared.

Design of PID Intelligent Controller Combining Immune Genetic Algorithm

At present, there are many studies on "computer immunology" in the world, and there are many applications of immune genetic algorithm in engineering.The article discusses the immune genetic algorithm in the design of PID intelligent controller.Most objects in the practical industrial process fall in the distributed parameter system (DPS), where the proportional-integral-derivative (PID) control method is used to control the field. In this paper, the PID controller optimization method based on the immune genetic algorithm (IGA) (referred to as the PODM method) is applied to a class of distributed parameter objects to design the optimal controller, which is compared with several controllers based on the conventional tuning formulas. The simulation results suggest that the PID controller designed based on the PODM method can obtain relatively superior control effects in overshoot, tuning time, time integrated time absolute error (ITAE), and other indexes with relatively less control energy. The application of the PODM method to DPS can improve the control level of the PID controller in the industry at present.

Optimization of PID Controller Parameters for First Order plus Time Delay Process

Pressure control could be a key process variable in industrial sector because pressure provides an important condition for air-conditioning, chemical reaction, boiling, extrusion, vacuuming, and distillation. Worse pressure control will cause critical quality, productivity and safety issues at the same time excessive pressure within a closed container will result in dangerous explosion. Hence, it is highly important to maintain the pressure at desirable range even in the presence of disturbance and the change in set point. Usually the pressure is controlled by Proportional Integral Derivative (PID) controller in industries because of its higher performance and simple structure over other controllers. The PID controller was designed using Z-N tuning method. Further the PID values were optimized for higher performance by using Pattern Search and Genetic Algorithm. Finally, the response of optimized PID controller was compared with standard Z-N PID controller. The error performance criteria like ISE, IAE, and IATE were used for comparison

PSO Tabanlı PID Denetimci kullanarak Zaman Gecikmeli AVR Sisteminin Analizi

In this study, a particle swarm optimization (PSO) algorithm-based Proportional-Integral-Derivative (PID) controller is proposed for the Automatic Voltage Regulator (AVR) system terminal tracking problem in the existence of time-delay and varying loads. AVR is a commonly used electronic device for maintaining generator output terminal voltage at a given reference under time-delays and varying load thus introduces a challenging electrical system problem. Time-delays exist in many real-world systems due to the lags in transmission and transport, in general, they have a negative effect on the stability and control design. In this research, the time delay is approximated by Pade approximation leading to the so-called non-minimum phase system. A nonminimum phase system represents the difficulty of controlling due to its zeroes in the complex right half side of the s-plane. To this aim, we utilize a PID controller, its design and application widely studied in real-time systems, thus it is a suitable selection for the AVR system. The optimal controller gains Kp, Ki, and Kd are optimized with the proposed PSO algorithm based on a commonly used error minimization objective function. The PSO-based optimal PID controller’s performance is analyzed with several methods including root locus, bode analysis, robustness, and disturbance rejection. It is demonstrated that the proposed PID controller improves the reference terminal voltage tracking performance of the AVR system. According to the obtained results, it has been revealed that the proposed PSO-based PID controller improves tracking properties under time-delay and load change thus it can be effectively used for synchronous generator automatic voltage regulator (AVR) system terminal voltage stability.

Design of Optimal PID Control with a Sensitivity Function for Resonance Phenomenon-involved Second-order Plus Dead-time System

The present study discusses an optimal design method of a proportional integral derivative (PID) control system for a continuous-time second-order plus dead-time system (SOPDT) that includes an under-damping system. The proposed PID control system is designed to minimize the performance index defined as the tracking performance for the set-point or the regulation performance for the disturbance, where the assigned stability margin is also achieved in order to attain robust stability for the modeling error. Because of the relationship between tracking performance and robust stability, the PID parameters are decided such that the tracking performance is optimized subject to the user-specified stability margin. In the proposed design method, in order to obtain the most general optimal PID possible parameters for controlled plants, we discuss a design method based on a normalized plant model. As a result, the PID parameters are seamlessly optimized between over-damping, critical-damping, and under-damping systems. The effectiveness of the proposed method is demonstrated through numerical examples.

An Intelligent Non-Integer PID Controller-Based Deep Reinforcement Learning: Implementation and Experimental Results

In this article, a noninteger proportional integral derivative (PID)-type controller based on the deep deterministic policy gradient algorithm is developed for the tracking problem of a mobile robot. This robot system is a typical case of nonholonomic plants and is exposed to the measurement noises and external disturbances. To accomplish the control methodology, two control mechanisms are established independently: a kinematic controller (which is designed based on the kinematic model of the vehicle), and a dynamic controller (which is realized according to the physical specifications of the vehicle dynamics). In particular, an optimal noninteger PID controller is initially designed as the primary dynamic controller for the tracking problem of a nonholonomic wheeled mobile robot. Then, a DDPG algorithm with the actor-critic framework is established for the supplementary dynamic controller, which is beneficial to the tracking stabilization by adapting to the uncertainties and disturbances. This strategy implements the supplementary based control to compensate for what the original controller is unable to handle. A prototype of the WMR was also adopted to investigate the applicability of the suggested controller from a real-time platform perspective. The outcomes in experimental environments are presented to affirm the effectiveness of the suggested control methodology.

Optimal fuzzy adaptive robust PID control for an active suspension system

ABSTRACT This work proposes an optimal fuzzy adaptive robust proportional-integral-derivative (PID) controller for a quarter-car model with an active suspension system. To this end, at first, the errors of the relative displacement and acceleration of the chassis and their integrals and derivatives are implemented to design a PID controller. Integral sliding surfaces defined based on the errors and their integrals are utilised to design the adaptation rules via the gradient descent method and the chain derivative rule. Afterwards, a fuzzy system consisted of the singleton fuzzifier, centre average defuzzifier and the product inference engine is applied to regulate the control parameters. Finally, the particle swarm optimisation (PSO) algorithm is utilised to ascertain the optimum gains of the designed controller. The body acceleration and the relative displacement between tire and sprung mass are considered as two objective functions for minimisation by the algorithm. Results show the dominance of the proposed active suspension system over previous published research works.

Application and Modeling of a Novel 4D Memristive Chaotic System for Communication Systems

In this paper, a new four-dimensional (4D) chaotic system which contains an active flux-controlled memristor characterized with a smooth continuous cubic nonlinearity is introduced. The objective is to obtain a 4D chaotic system which contains quadratic terms by using the memristor model which is designed as a new cubic emulator. A new chaotic circuit equation is obtained by using this emulator. The chaotic behavior of the system is observed both theoretically and graphically. The fundamental dynamics of the chaotic system are examined by using equilibrium points, phase portraits, Lyapunov exponents and bifurcation diagrams. The proportional–integral–derivative (PID) control design obtained using optimization algorithms is presented for memristor-based chaotic system. Firefly algorithm and genetic algorithm are used in PID control design for obtaining optimal PID controller gains that provides optimization between master and slave circuits. To verify system performance, this proposed PID-based chaotic circuit is used to communicate communication systems. Experimental results of this system are obtained and presented in real time.

Tuning optimal PID controllers for open loop unstable first order plus time delay systems by minimizing ITAE criterion

The present paper gives an optimal tuning procedure for design of Proportional Integral Derivative (PID) controllers for open loop unstable First Order plus Time Delay systems. Estimation of the optimal PID controller parameters: kc, τI and τD is carried out by minimizing the time integral performance criteria:ITAE(Integral of Time-weighted Absolute Error) for a setpoint tracking problem. Results of the simulation for linear transfer functions and nonlinear isothermal CSTR reveals the proposed tuning approach provides enhanced performance for the set-point tracking and disturbance rejection with improved time domain specifications. To evaluate the superiority of the proposed method over others, robustness analysis with complimentary sensitivity function is carried out.

Optimal Control of AVR System With Tree Seed Algorithm-Based PID Controller

In this study, an optimal Tree-Seed Algorithm (TSA) algorithm-based Proportional-Integral-Derivative (PID) controller is proposed for automatic voltage regulator (AVR) system terminal tracking problem. PID controller gains Kp, Ki, and Kd are optimized with the proposed TSA algorithm based on different objective functions. The TSA-based optimal PID controller's performance is compared with numerous PID controllers, which were developed using different meta-hermetic optimization algorithms in the literature. Several analysis methods including root locus, bode analysis, robustness, and disturbance rejection are studied and compared with reported works in the literature. It is shown that there is still a research gap to improve the tracking performance of the AVR system due to its importance in electrical systems. According to the obtained comparison results, it has been revealed that the proposed TSA-based PID controller improves tracking properties under load change thus it can be effectively used for synchronous generator automatic voltage regulator terminal voltage stability.

A new control method based on fuzzy controller, time delay estimation, deep learning, and non-dominated sorting genetic algorithm-III for powertrain mount system

This article presents a new control method based on fuzzy controller, time delay estimation, deep learning, and non-dominated sorting genetic algorithm-III for the nonlinear active mount systems. The proposed method, intelligent adapter fractions proportional–integral–derivative controller, is a smart combination of the time delay estimation control and intelligent fractions proportional–integral–derivative with adaptive control parameters following the speed range of engine rotation via the deep neural network with the optimal non-dominated sorting genetic algorithm-III deep learning algorithm. Besides, we proposed optimal fuzzy logic controller with optimal parameters via particle swarm optimization algorithm to control reciprocal compensation to eliminate errors for intelligent adapter fractions proportional–integral–derivative controller. The control objective is to deal with the classical conflict between minimizing engine vibration impacts on the chassis to increase the ride comfort and keeping the dynamic wheel load small to ensure the ride safety. The results of this control method are compared with that of traditional proportional–integral–derivative controller systems, optimal proportional–integral–derivative controller parameter adjustment using genetic algorithms, linear–quadratic regulator control algorithms, and passive drive system mounts. The results are tested in both time and frequency domains to verify the success of the proposed optimal fuzzy logic controller–intelligent adapter fractions proportional–integral–derivative control system. The results show that the proposed optimal fuzzy logic controller–intelligent adapter fractions proportional–integral–derivative control system of the active engine mount system gives very good results in comfort and softness when riding compared with other controllers.

Self‐adaptive fractional‐order LQ‐PID voltage controller for robust disturbance compensation in DC‐DC buck converters

AbstractThis paper presents a state‐dependent self‐tuning fractional control strategy for a DC‐DC buck converter in order to enhance its output voltage regulation and disturbance attenuation capability. The proposed control scheme primarily employs a ubiquitous proportional‐integral‐derivative (PID) controller, where gains are optimally selected using a linear‐quadratic state‐space tuning approach. The optimal PID controller is then augmented with fractional‐order integral and derivative operators in order to improve the controller's degrees‐of‐freedom as well as the system's overall time‐domain performance. The fractional controller's robustness against bounded exogenous disturbances, contributed by the input fluctuations and load‐step transients, is further enhanced by adaptively modulating the fractional‐orders of the integro‐differential operators as a smooth nonlinear function of controlled‐variable's error‐dynamics. An online dynamic adjustment law, comprising of a zero‐mean Gaussian function of error and its derivative, is used to individually update the two fractional orders after every sampling interval. The error derivative is evaluated by measuring the output capacitor's current in order to compensate the noise injected by parasitic impedance. The other controller parameters are tuned via particle‐swarm‐optimization algorithm. The proposed self‐adaptive control strategy renders rapid transits, minimum transient recovery time, and minimal fluctuations around steady state in the response. Its efficacy is validated through hardware in‐the‐loop experiments conducted on a buck converter prototype.

Design of Robust Trackers and Unknown Nonlinear Perturbation Estimators for a Class of Nonlinear Systems: HTRDNA Algorithm for Tracker Optimization

A robust linear quadratic analog tracker (LQAT) consisting of proportional-integral-derivative (PID) controller, sliding mode control (SMC), and perturbation estimator is proposed for a class of nonlinear systems with unknown nonlinear perturbation and direct feed-through term. Since the derivative type (D-type) controller is very sensitive to the state varying, a new D-type controller design algorithm is developed to avoid an unreasonable large value of the controller gain. Moreover, the boundary of D-type controller is discussed. To cope with the unknown perturbation effect, SMC is utilized. Based on the fast response of SMC controlled systems, the proposed perturbation estimator can estimate unknown nonlinear perturbation and improve the tracking performance. Furthermore, in order to tune the PID controller gains in the designed tracker, the nonlinear perturbation is eliminated by the SMC-based perturbation estimator first, then a hybrid Taguchi real coded DNA (HTRDNA) algorithm is newly proposed for the PID controller optimization. Compared with traditional DNA, a new HTRDNA is developed to improve the convergence performance and effectiveness. Numerical simulations are given to demonstrate the performance of the proposed method.

A robust firefly–swarm hybrid optimization for frequency control in wind/PV/FC based microgrid

This paper presents frequency regulation in a microgrid consisting of wind, photovoltaic (PV), fuel cell (FC) and diesel engine generator (DEG) along with the energy storage system such as flywheel energy storage (FES) and battery energy storage (BES). In this study, firefly and particle swarm (FF–PSO) based hybrid optimization technique is proposed to tune parameters the proportional–integral–derivative (PID) controller to minimize the frequency deviation in microgrid system under different operating conditions such as variation in wind speed, and load demand. Further, a comparative analysis for tuning of the PID controller is performed using particle swarm optimization (PSO), and firefly algorithms (FFA) to minimize the deviation in frequency. The power management as well as frequency control in microgrid is studied with the help of the performance indices; integral absolute errors (IAE), peak overshoots, settling times and standard deviation (SD). In addition, the effect of communication delay with higher non-linearity is tested to assess the performance of the controllers. Further, the frequency control is validated in real-time digital simulation environment using OPAL-RT. The qualitative, quantitative and real-time analysis reflects the improvements in frequency deviation in microgrid using the proposed hybrid FF–PSO optimized PID as comparison to the PSO/FF optimized PID controllers.

Optimal Fuzzy Sliding Mode Controller Design using Bee Algorithm for Dynamic Voltage Restorer System

This paper proposes an application of the bee algorithm (BA) in order to design an optimal proportional-integral-derivative (PID) controller, a sliding mode (SM) controller, and a fuzzy sliding mode (FSM) controller for a dynamic voltage restorer (DVR) system. The DVR is an electronic device, which has excellent dynamic capabilities and is well-suited in protecting critical or sensitive loads from short duration voltage sags or swells. The parameters of the optimal PID, SM, and FSM controllers are automatically tuned by the BA to compensate for the magnitude of load voltage by injecting the compensating voltages when the source voltage sags and swells. In order to confirm these concepts and to show that the proposed strategy outperforms other strategies when it is compared to others using the trial and error method, experimental and simulation setups were implemented in various cases.

Robust frequency control in a renewable penetrated power system: an adaptive fractional order-fuzzy approach

PurposeLoad frequency control (LFC) in today’s modern power system is getting complex, due to intermittency in the output power of renewable energy sources along with substantial changes in the system parameters and loads. To address this problem, this paper proposes an adaptive fractional order (FO)-fuzzy-PID controller for LFC of a renewable penetrated power system.Design/methodology/approachTo examine the performance of the proposed adaptive FO-fuzzy-PID controller, four different types of controllers that includes optimal proportional-integral-derivative (PID) controller, optimal fractional order (FO)-PID controller, optimal fuzzy PID controller, optimal FO-fuzzy PID controller are compared with the proposed approach. The dynamic response of the system relies upon the parameters of these controllers, which are optimized by using teaching-learning based optimization (TLBO) algorithm. The simulations are carried out using MATLAB/SIMULINK software.FindingsThe simulation outcomes reveal the supremacy of the proposed approach in dynamic performance improvement (in terms of settling time, overshoot and error reduction) over other controllers in the literature under different scenarios.Originality/valueIn this paper, an adaptive FO-fuzzy-PID controller is proposed for LFC of a renewable penetrated power system. The main contribution of this work is, a maiden application has been made to tune all the possible parameters of fuzzy controller and FO-PID controller simultaneously to handle the uncertainties caused by renewable sources, load and parametric variations.

Robust Fine Tuning of Optimal PID Controller With Guaranteed Robustness

The proportional-integral-derivative (PID) controller is a widely used controller in automation industries. Several advanced PID tuning/design methods, such as response-based design, internal model control, and controller optimization by stochastic algorithms, have been proposed in the literature. However, regardless of the advantages and accuracy of developed tuning methods, due to the process modeling error and parametric uncertainties, the experimental response always differs from the theoretical response, which required online fine-tuning of the PID parameter. Manual adjustment of three PID parameters disturbs the robustness of the controller from its desired value; also, it does not guarantee the stability of the process. Therefore, this paper focuses on online PID controller tuning with the guaranteed robustness of the controller. A new single variable tuning method is developed for the online robustness and performance adjustment. Moreover, the proposed rules only depend upon the previously optimized PID parameters. The proposed method is an additional feature to all existing PID tuning methods, including optimal PID controller with stochastic optimization algorithms. The proposed method is validated with the help of optimal PID controller design by existing optimal tuning rules, optimized PID with particle swarm optimization and experimental validation on the canonical tank system.

Extreme learning‐based non‐linear model predictive controller for an autonomous underwater vehicle: simulation and experimental results

In this study, an extreme learning-based non-linear model predictive controller (NMPC) is proposed for path following planning of an autonomous underwater vehicle (AUV) using horizontal way-points. The proposed controller comprises a kinematic controller and a dynamic controller. The kinematic controller is designed by using back-stepping approach whilst the dynamic controller is designed by employing the NMPC approach. The dynamics of the AUV is identified in real-time by employing an extreme learning machine (ELM) structure. In view of achieving improved performance of the ELM structure, its hidden layer parameters are optimally determined by applying Jaya optimisation algorithm. The resulting ELM model is then used to design a NMPC considering the constraint on rudder planes. The tracking performance of the proposed controller is compared with that of two recently reported control algorithms namely, $H_\infty $ H ∞ state feedback controller and inverse optimal self-tuning proportional–integral–derivative (PID) controller. The proposed controller is implemented using MATLAB and then in real-time on a prototype AUV developed in the authors’ laboratory. From both the simulation and experimental results obtained, it is observed that the proposed controller exhibits superior tracking performance compared to both $H_\infty $ H ∞ state feedback controller and inverse optimal self-tuning PID controller.

Deep learning framework for controlling an active suspension system

In this paper, a feed-forward deep neural network (DNN) and automated search method for optimum network structure are developed to control an active suspension system (ASS). The network was trained through supervised learning using the backpropagation algorithm. The training data were generated from an optimal proportional–integral–derivative controller tuned based on a full state feedback optimal controller. The trained network was implemented in an ASS test rig for a quarter-car model and was initially tested in simulation under parameter uncertainties. Experimental results showed that the developed DNN controller outperforms the optimal controller under uncertainties in terms of reducing the sprung mass acceleration and actuator energy consumption, with a 4% and 14% reduction, respectively.