Proportional Integral Derivative Controller Parameters Research Articles

H∞ fuzzy PID control for discrete time-delayed T-S fuzzy systems

This paper is concerned with the H∞ fuzzy proportional-integral-derivative (PID) control problem for delayed Takagi–Sugeno (T-S) fuzzy systems in the discrete-time setting. Based on the current and historical measurement data, a novel T-S fuzzy PID controller is developed with which the integral-loop is generated based on a fixed number of past measurements for the purpose of reducing the computational burden, where a special augmentation scheme is adopted to simplify the closed-loop system. The aim of this paper is to design the PID controller parameters such that the closed-loop T-S fuzzy system is exponentially stable and the prescribed H∞ disturbance attenuation performance is achieved. By adopting the Lyapunov stability theory and the linear matrix inequality technology, sufficient conditions are obtained for the existence of the desired fuzzy PID controllers. In addition, an iterative optimization procedure is proposed to design the controller parameters according to the cone complementarity linearization algorithm. Finally, a numerical simulation example is exploited to demonstrate the usefulness and effectiveness of our proposed design scheme.

Sine-cosine algorithm-based optimization for automatic voltage regulator system

A novel design method, sine-cosine algorithm (SCA) is presented in this paper to determine optimum proportional-integral-derivative (PID) controller parameters of an automatic voltage regulator (AVR) system. The proposed approach is a simple yet effective algorithm that has balanced exploration and exploitation capabilities to search the solutions space effectively to find the best result. The simplicity of the algorithm provides fast and high-quality tuning of optimum PID controller parameters. The proposed SCA-PID controller is validated by using a time domain performance index. The proposed method was found efficient and robust in improving the transient response of AVR system compared with the PID controllers based on Ziegler-Nichols (ZN), differential evolution (DE), artificial bee colony (ABC) and bio-geography-based optimization (BBO) tuning methods.

Load frequency control of a dynamic interconnected power system using generalised Hopfield neural network based self‐adaptive PID controller

A novel generalised Hopfield neural network (GHNN) based self-adaptive proportional–integral–derivative (PID) controller for load frequency control (LFC) is designed for a two-area interconnected power system with nonlinearities of generator rate constraint and governor dead band. The control problem is conceptualised as an optimisation problem with an objective function as an area control error in terms of the PID controller parameters. The differential equations governing the behaviour of the GHNN were solved to obtain the controller parameters Kp, Ki and Kd. To test the feasibility and robustness of the proposed controller, the system is tested in the presence of randomness in load demands, imprecisely modelled system dynamics, nonlinearities in the system model and uncertainties in the system parameter variations. The proposed method is simulated using Matlab R2014b/Simulink and the results obtained have shown that the propounded controller performance is superior to the integral, PID and fuzzy-based proportional–integral controllers. In addition, the Lyapunov stability analysis of the overall closed-loop system was carried out and the controller is implemented in real-time digital simulator run in hardware-in-the-loop to validate the effectiveness of the proposed method. Furthermore, the proposed controller is applied to the three-area power system to test its adaptability.

Optimal tuning of 3 degree-of-freedom proportional-integral-derivative controller for hybrid distributed power system using dragonfly algorithm

The objective of this paper is to study the dynamic stability of a hybrid energy distributed power system (HEDPS) subject to load and wind power variations. A three degree-of-freedom (3-DOF) proportional-integral-derivative (PID) controller is designed and implemented in the HEDPS to stabilize frequency and power fluctuations after the perturbation. For enhancing system dynamics, the parameters of the 3-DOF PID controller are optimized by using dragonfly algorithm (DA). The results are compared with the results obtained by Zeigler–Nichols tuning and some other well-known meta-heuristic algorithms. The efficacy of proposed DA over different reported algorithms is established in terms of convergence rate, minimum fitness value and dynamic performance of the system. The robustness of the 3-DOF PID-controller is ascertained with time-varying step load perturbation, random wind power perturbation, and under system parameter variation. The robust performance of proposed DA has also been established by performing statistical analysis.

Performance and robustness of optimal fractional fuzzy PID controllers for pitch control of a wind turbine using chaotic optimization algorithms

The most studied controller for pitch control of wind turbines is proportional-integral-derivative (PID) controller. However, due to uncertainties in wind turbine modeling and wind speed profiles, the need for more effective controllers is inevitable. On the other hand, the parameters of PID controller usually are unknown and should be selected by the designer which is neither a straightforward task nor optimal. To cope with these drawbacks, in this paper, two advanced controllers called fuzzy PID (FPID) and fractional-order fuzzy PID (FOFPID) are proposed to improve the pitch control performance. Meanwhile, to find the parameters of the controllers the chaotic evolutionary optimization methods are used. Using evolutionary optimization methods not only gives us the unknown parameters of the controllers but also guarantees the optimality based on the chosen objective function. To improve the performance of the evolutionary algorithms chaotic maps are used. All the optimization procedures are applied to the 2-mass model of 5-MW wind turbine model. The proposed optimal controllers are validated using simulator FAST developed by NREL. Simulation results demonstrate that the FOFPID controller can reach to better performance and robustness while guaranteeing fewer fatigue damages in different wind speeds in comparison to FPID, fractional-order PID (FOPID) and gain-scheduling PID (GSPID) controllers.

A new approach for simplification and control of linear time invariant systems

This study presents a new approach for system simplification and control. This approach is based on the behaviour of growth and reproduction of weed plants namely Invasive Weed Optimization (IWO). The micro system/simplified model of large scale single-input single-output (SISO) continuous time system is attained by optimizing a predefined objective/fitness function by weed optimization algorithm. Performance of the proposed approach is analysed in terms of transient and frequency response parameters such as rise time, peak time, maximum overshoot, gain margin and phase margin, etc. This analysis reveals that the results of this proposed approach are commensurable with other available approaches. Additionally, the application of proposed approach is explored in control of a micro system based on system simplification. The control action is obtained by achieving the unknown parameters of the proportional integral derivative (PID) controller using IWO. Further, the concept of error minimization is being utilised to obtain parameters of PID controller. The simulation results reveal that the PID controller designed by proposed approach has no affect on change of the system. The PID controller for a micro system (second order) exhibits satisfactory performance on the first order simplified system, therefore changing the system does not affect the performance of PID controller. As the proposed approach is being utilised for both micro system’s simplification as well as in controller design, therefore it may be applied in various applications of Microsystems’s analysis and design.

A model predictive functional control based on proportional-integral-derivative (PID) and proportional-integral-proportional-derivative (PIPD) using extended non-minimal state space: Application to a molten carbonate fuel cell process

The performance of most controllers, including proportional-integral-derivative (PID) and proportional-integral-proportional-derivative (PIPD) controllers, depends upon tuning of control parameters. In this study, we propose a novel tuning strategy for PID and PIPD controllers whose control parameters are tuned using the extended non-minimal state space model predictive functional control (ENMSSPFC) scheme based on the auto-regressive moving average (ARMA) model. The proposed control method is applied numerically in the operation of the MCFC process with the parameters of PID and PIPD controllers being optimized by ENMSSPFC based on the ARMA model for the MCFC process. Numerical simulations were carried out to assess the set-point tracking performance and disturbance rejection performance both for the perfect plant model, which represents the ideal case, and for the imperfect plant model, which is usual in practical applications. When there exists uncertainty in the plant model, the PIPD controller exhibits better overall control performance compared to the PID controller.

Research on switch compensation control for maglev flywheel battery

In a maglev flywheel system, an unbalanced interference signal synchronous with the flywheel frequency will be produced because the flywheel rotor is uneven. This signal can reduce system control precision and stability, and make the system produce unbalance force vibration. Therefore, the signal should be filtered to reduce the effects on the control system. A vibration switching compensation control strategy is proposed based on the standard least mean squares (LMS) algorithm and one proportional–integral–derivative (PID) controller. The flywheel's rotational frequency is measured in real time as the switching reference, and different LMS algorithm step sizes and different PID controller parameters are adopted in different rotational frequencies. Simulation and experimental results verify the feasibility and effectiveness of the switch compensation strategy, which can reduce the control current amplitude and make the flywheel rotate around the inertial principal axis as much as possible. © 2018 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

Design and Implementation of a Hierarchical‐Clustering CMAC PID Controller

AbstractIn industrial control processes, proportional‐integral‐derivative (PID) control algorithm is widely employed. Therefore, it is meaningful to design advanced PID controllers, especially for nonlinear control objects. One of the advanced PID controllers is a cerebellar model articulation controller (CMAC) PID controller. In this controller, the PID control parameters are calculated and tuned. The CMAC achieves a higher accuracy by increasing the number of labels of each weight table; this requires a larger memory, and the generalization ability of the controller decreases. On the other hand, if the CMAC requires less memory, the generalization ability increases and accuracy decreases. Hence, in this paper, a novel CMAC in which the accuracy is compatible with the generalization ability is proposed in this paper. In the proposed CMAC, the number of labels of each weight table can be decided by using a hierarchical clustering technology. Moreover, the efficiency of the memory allocation is improved. The effectiveness of the proposed method is verified by experiments.

System-level simulation and experiment for levitation control of micromachined electrostatically suspended accelerometer

It is proposed in this paper a micromachined electrostatically suspended accelerometer (MESA) based on non-silicon micro-electromechanical systems technology. The MESA is designed in sandwich-like structure, which was composed of three main parts: proof mass, upper stator and lower stator. The system design of levitation control base on centralized control strategy is also presented which including the multiplex frequency detection way and six degree of freedom (six-DOFs) control. The control voltages reflect the input acceleration. The control with bias voltage is used for the initial levitation along axial direction for the approximate linear model can be constructed near the null position. In order to levitate the PM along Z-axis, the levitation control based on de-centralized control strategy was introduced, which was based on proportional integral derivative (PID) control for the MESA. The damping coefficient along Z-axis was calculated by analytical solution. According to the Routh criterion analysis of the characteristic equation, the scopes of PID control parameters were defined. An Achitect/Coventorware model was built to simulate the initial levitation, 10 Hz square wave time response and 0.5 g acceleration disturbance input response. The design of the control system which including detection and control modules is introduced and circuit design is also presented. Experiment show that the control principle is reasonable. The pulse input acceleration experiment and simulation also proves that the MESA can act as multi-axis accelerometer. The quick-response performance and global stability are in agreement with the dynamic simulation.

An Approach for Setting Parameters for Two-Degree-of-Freedom PID Controllers

In this paper, a new tuning method is proposed, based on the desired dynamics equation (DDE) and the generalized frequency method (GFM), for a two-degree-of-freedom proportional-integral-derivative (PID) controller. The DDE method builds a quantitative relationship between the performance and the two-degree-of-freedom PID controller parameters and guarantees the desired dynamic, but it cannot guarantee the stability margin. So, we have developed the proposed tuning method, which guarantees not only the desired dynamic but also the stability margin. Based on the DDE and the GFM, several simple formulas are deduced to calculate directly the controller parameters. In addition, it performs almost no overshooting setpoint response. Compared with Panagopoulos’ method, the proposed methodology is proven to be effective.

Flight Motion Controller Design using Genetic Algorithm for a Quadcopter

In this study, the Genetic Algorithm operability is assigned to optimize the proportional–integral–derivative controller parameters for both simulation and real-time operation of quadcopter flight motion. The optimized proportional–integral–derivative gains, using Genetic Algorithm to minimum the fitness function via the integral of time multiplied by absolute error criterion, are then integrated to control the quadcopter flight motion. In addition, the proposed controller design is successfully implemented to the experimental real-time flight motion. The performance results are proven that the highly effective stability operation and the reliable of waypoint tracking.

Wind Turbine Tower Modeling and Vibration Control Under Different Types of Loads Using Ant Colony Optimized PID Controller

Vibration in the wind turbine tower disturbs the reliability and increases the possibility of structural damage. Design and optimization of vibration controller are a key goal for wind turbine tower to achieve optimal performance. In this study, a proportional integral derivative (PID) is designed and optimized using nature technology to find optimal required force for actuators and therefore, reducing wind turbine tower vibration. PID controller parameters are optimized with ant colony optimization (ACO) and compared with traditional tuning methods such as Ziegler–Nichols and Tyreus–Luyben methods to ensure its effectiveness in minimizing wind turbine tower vibration. The optimized active vibration controller shows better performance than traditional method in terms of vibration reduction rate, ability to adapt when frequency varies and computational time. This paper also investigated finite difference method for wind turbine tower modeling, and its efficacy is compared with another well-known numerical finite element method based on mean squared error, fit to estimated data and cross signature assurance criterion. The performance of ACO optimized PID controller is investigated for wind turbine tower under four different types of disturbances and compared with uncontrolled and passive controlled system. Results show that 98, 84, 92 and 98% of displacement of the tower are reduced under simulated blade/rotor imbalance, impact, wind and turbulence disturbances, respectively, using ACO optimized PID controller.

Performance analysis of robust stable PID controllers using dominant pole placement for SOPTD process models

This paper derives new formulations for designing dominant pole placement based proportional-integral-derivative (PID) controllers to handle second order processes with time delays (SOPTD). Previously, similar attempts have been made for pole placement in delay-free systems. The presence of the time delay term manifests itself as a higher order system with variable number of interlaced poles and zeros upon Pade approximation, which makes it difficult to achieve precise pole placement control. We here report the analytical expressions to constrain the closed loop dominant and non-dominant poles at the desired locations in the complex s-plane, using a third order Pade approximation for the delay term. However, invariance of the closed loop performance with different time delay approximation has also been verified using increasing order of Pade, representing a closed to reality higher order delay dynamics. The choice of the nature of non-dominant poles e.g. all being complex, real or a combination of them modifies the characteristic equation and influences the achievable stability regions. The effect of different types of non-dominant poles and the corresponding stability regions are obtained for nine test-bench processes indicating different levels of open-loop damping and lag to delay ratio. Next, we investigate which expression yields a wider stability region in the design parameter space by using Monte Carlo simulations while uniformly sampling a chosen design parameter space. The accepted data-points from the stabilizing region in the design parameter space can then be mapped on to the PID controller parameter space, relating these two sets of parameters. The widest stability region is then used to find out the most robust solution which are investigated using an unsupervised data clustering algorithm yielding the optimal centroid location of the arbitrary shaped stability regions. Various time and frequency domain control performance parameters are investigated next, as well as their deviations with uncertain process parameters, using thousands of Monte Carlo simulations, around the robust stable solution for each of the nine test-bench processes. We also report, PID controller tuning rules for the robust stable solutions using the test-bench processes while also providing computational complexity analysis of the algorithm and carry out hypothesis testing for the distribution of sampled data-points for different classes of process dynamics and non-dominant pole types.

Stabilising PID tuning for a class of fourth-order integrating nonminimum-phase systems

ABSTRACTFed-batch fermentation processes are commonly used in bioprocessing industry. A fed-batch fermentation process often exhibits integrating/unstable type of dynamics with multiple right-half plane zeros. A class of fourth-order integrating model can be used to adequately represent such a complex dynamics of the fed-batch fermentation process. In this paper, rigorous stability analysis of proportional-integral-derivative (PID) controller based on the Routh-Hurwitz criteria for the fourth-order integrating system is presented. A set of all stabilising PID controller parameter regions is established. Based on these stabilising regions, a general PID controller tuning procedure is proposed for the fourth-order integrating system with two right-half plane zeros. Numerical study shows that based on the proposed tuning procedure, a low-order PID controller can outperform a fifth-order optimal LQG controller in terms of servo and regulatory controls.

Experimental Evaluation of an Autonomous Surface Craft for Shallow-Water Bathymetry

AbstractVast coastal water bodies such as mangroves and wetlands, despite their enormous importance, are inaccessible to even the smallest aquatic vehicles, which are not capable of navigating the extremely shallow environments. To understand their behavior and the transport and exchange processes with both sea and land, it is crucial to study local hydrodynamics, which are highly dependent on bathymetric configuration. In order to obtain accurate and high spatial resolution bathymetric samples, an existing small surface vehicle instrumented with GPS and echosounder was implemented with an autopilot system to achieve autonomy. A description of the autonomous system together with the evaluation of the whole vehicle's performance in a natural coastal environment (e.g., affected by the wind, waves, and currents that exist in coastal regions) is presented. The navigation system is based on an autopilot system, which follows a set of user-selected waypoints to drive the vehicle through a previously designed path. The trajectory is self-corrected to achieve sufficient accuracy (the limits are also defined by the user) using real-time kinematics. The tracking is performed by two independent proportional-integral-derivative (PID) control systems: the boat's displacement speed and the bearing control. A simple experimental procedure to tune the low-level PID control parameters is presented. Comparisons between the bathymetric maps obtained with the system and with other standard bathymetric surveys from a selected coastal site (ship-towed echosounder) are presented to test both the precision of the boat's navigation and the fine structure of the bottom topography. The results confirm the system's capability as a valuable tool for surveying large and very shallow environments.

Design and implementation of EP-based PID controller for chaos synchronization of Rikitake circuit systems

This article addresses an evolutionary programming (EP) algorithm technique-based and proportional-integral-derivative (PID) control methods are established to guarantee synchronization of the master and slave Rikitake chaotic systems. For PID synchronous control, the evolutionary programming (EP) algorithm is used to find the optimal PID controller parameters kp, ki, kd by integrated absolute error (IAE) method for the convergence conditions. In order to verify the system performance, the basic electronic components containing operational amplifiers (OPAs), resistors, and capacitors are used to implement the proposed chaotic Rikitake systems. Finally, the experimental results validate the proposed Rikitake chaotic synchronization approach.

Reinforcement learning based PID controller design for LFC in a microgrid

PurposeThis paper aims to propose an improved reinforcement learning-based fuzzy-PID controller for load frequency control (LFC) of an island microgrid.Design/methodology/approachTo evaluate the performance of the proposed controller, three different types of controllers including optimal proportional-integral-derivative (PID) controller, optimal fuzzy PID controller and the proposed reinforcement learning-based fuzzy-PID controller are compared. Optimal PID controller and classic fuzzy-PID controller parameters are tuned using Non-dominated Sorting Genetic Algorithm-II algorithm to minimize overshoot, settling time and integral square error over a wide range of load variations. The simulations are carried out using MATLAB/SIMULINK package.FindingsSimulation results indicated the superiority of the proposed reinforcement learning-based controller over fuzzy-PID and optimal-PID controllers in the same operational conditions.Originality/valueIn this paper, an improved reinforcement learning-based fuzzy-PID controller is proposed for LFC of an island microgrid. The main advantage of the reinforcement learning-based controllers is their hardiness behavior along with uncertainties and parameters variations. Also, they do not need any knowledge about the system under control; thus, they can control any large system with high nonlinearities.

Hybrid BFPSO Approach for Effective Tuning of PID Controller for Load Frequency Control Application in an Interconnected Power System

Penetration of renewable energy sources makes the modern interconnected power systems to have more intelligence and flexibility in the control. Hence, it is essential to maintain the system frequency and tie-line power exchange at nominal values using Load Frequency Control (LFC) for efficient, economic and reliable operation of power systems. In this paper, intelligent tuning of the Proportional Integral Derivative (PID) controller for LFC in an interconnected power system is considered as a main objective. The chosen problem is formulated as an optimization problem and the optimal gain parameters of PID controllers are computed with three innovative swarm intelligent algorithms named Particle Swarm Optimization (PSO), Bacterial Foraging Optimization Algorithm (BFOA) and hybrid Bacterial Foraging Particle Swarm Optimization (BFPSO) and a comparative study is made between them. A new objective function designed with necessary time domain specifications using weighted sum approach is also offered in this report and compared with conventional objective functions. All the simulation results clearly reveal that, the hybrid BFPSO tuned PID controller with proposed objective function has better control performances over other optimization methodologies.

Performance Analysis Stability Of Speed Control Of BLDC Motor Using PID-BAT Algorithm In Electric Vehicle

The research on the development of electric vehicles includes such as power electronics, energy storage capability that the higher the battery, reducing fuel emissions, and the motor efficiency. The electric motor efficiency requires the automatic control on the main parameters such as speed, position, and acceleration. The performance setting of speed Brushless DC (BLDC) Motor can be improved by using the controller Proportional Integral Derivative (PID), a combination of PID using nature inspired optimization algorithms such as Bat Algorithm (BA). BA is one of the optimization algorithm that mimics the behavior of bats on the move using a vibration or sound pulses emitted a very loud (echolocation) and listen to the echoes that bounce back from the object to determine the circumstances surrounding vicinity 
 In this paper, simulate of Bat Algorithm to find the best value PID controller parameter to speed control BLDC motor and analyze performance such as the value of overshoot, steady state. The result simulation shows that values for the PID parameters without using algorithm bat is Kp = 208.1177, Ki = 1767, and Kd = -8.6025. While using the algorithm bat got value Kp = 5.4303e+04, Ki = -1.3059e+06, and Kd = 3.0193e+04. The performance of the motor obtained through value rise time of 0. 282, settling time of 1.5, overshoot value of 20.5% and the peak value of 1.21.