Integral Controller Design Research Articles

Design of fractional order proportional integral controller for load frequency control of multi area power system under deregulated environment

The main objective of presented article is here to focus how efficiently minimise the deviations in frequency and area control error caused by load fluctuations and uncertainties in load under the deregulated power system. This work is carried out to eliminate the frequency errors by using fractional order proportional integral (FOPI) controller under deregulated environment by considering the effect of one possible bilateral contract scenario. Because of system nonlinearities, uncertainties and continuously fluctuant load demand the design of these controllers is quite complicated in deregulated environment. The proposed work is to enhance the system parameters like transmitted line power, frequency deviation error, and area control error (ACE) using fractional order PI controller for hydro-thermal system and thermal-thermal system under deregulated environment. The results have been analysed with classical integer order PI controller and FOPI controller. It is observed that the efficacy of the results is satisfied and improved when compared with previous work.

New opposition cuttlefish optimizer based two‐step approach for optimal design of fractional order proportional integral derivative controller for time delay systems

AbstractIn this article, an optimal design of the fractional order proportional integral derivative (FOPID) controller for time delay system is proposed. The proposed optimal design is the combined performance of both the cuttlefish optimizer (CFO) and Opposition‐based learning (OBL) scheme called CFOBL scheme. The proposed CFOBL uses the concept of opposition based population initialization and opposition based position updating to improve its searching behavior, computational speed and convergence profile in the basic CFO. In FOPID controller, apart from the three tuning parameters (GP, GI, and GD) there are two additional tuning parameters that are λ and μ. Here, CFOBL is used to tune the three controller parameters and also to find the optimal values of λ and μ. The uniqueness of the proposed technique is to reduce the FOPID controller's fault in the higher order time delay scheme by the aid of the controller's increase limits. The objective of the proposed technique is chosen by considering the set point parameters and the accomplished parameters from the time delay system. The proposed technique is used to avoid high‐order delays and reliability constraints such as small overruns, time resolution and fixed condition defects. This technique is performed on the MATLAB/Simulink platform and the results are compared with different existing techniques such as Ziegler‐Nichols (ZN) tuning method, curve fitting (CF) technique, Wang technique, and regression technique.

Design of fractional order proportional integral controller using stability and robustness criteria in time delay system

In this paper, a tuning procedure of the parameters of fractional order proportional integral controller is presented for time delay system with arbitrary order. On the basis of obtaining stable solution space by utilizing some stability-domain boundaries which include real-root boundary and σ-stability boundary, the optimal solution can be achieved by applying specific frequency-domain specifications which include gain crossing frequency, phase margin, and robustness constraint. Using the same synthesis by traversing phase angle and phase margin in a given interval, the complete solution space of gain crossing frequency can be obtained and visualized, which is equivalent to demonstrate the complete solution space of optimal parameters of fractional order proportional integral controllers. As a comparison, the tuning procedure of the parameters of integral order proportional integral derivative controller is also discussed. At last, the proposed algorithm is validated by numerical simulation and experimental illustrations. The results show the robustness and advantage of the proposed fractional order proportional integral controller over other controllers.

Fuzzy Gain Scheduled PI-Based Airflow Control of an Oscillating Water Column in Wave Power Generation Plants

Numerous control schemes have been proposed to reach a more efficient power generation using Wells-turbine-based oscillating-water-column power plants. Most of these control strategies aim to avoid the stalling behavior, a feature of the Wells turbine, that limits the generated power. Besides, the plant must be able to maintain its performance despite the input variations due to the intrinsic oscillating nature of the waves and constant climate changes. This paper deals with the modeling and control of the NEREIDA wave power plant installed in the breakwater of Mutriku in the Basque Coast of Spain. In this context, the design of a novel fuzzy gain scheduled proportional integral (FGS-PI) controller is presented to improve the input airflow control. The fuzzy supervisor adequately changes the controller gains to offer the control scheme an adaptive mechanism against input parameter changes. Two study cases were performed to compare the FGS-PI to a conventional PI. The first test is for the output power optimization and the second is to test the robustness against parameter changes. Results show the superior performance of the proposed control providing power generation improvement and higher robustness even with varying input conditions.

A Model-Based Approach of DC-DC Converters Dedicated to Controller Design Applications for Photovoltaic Generators

In this paper, a model-based approach of DC-DC converters dedicated to controller design applications for photovoltaic generators is introduced. The paper provides a mathematic averaging model, based on the state space method for DC-DC converters that is used as an adaptation level in photovoltaic generators. This modeling allows the dynamics of the system to be described by presenting a reliable model to be used for oriented controller design. The two most needed topologies of DC-DC converters are proposed, buck and buck-boost, and an overview of integral state feedback controller design using a model-based approach for a boost converter connected to a photovoltaic generator described in our previous published work is provided. The model-based conception of both converter types is analyzed for optimal use in control-oriented design. The validation of each model is demonstrated by comparative curves represented by a detailed plant model using simscape devices available and implemented in Simulink/Matlab.

Design of Fractional Order PID Controller for Load Frequency Control in Perturbed Two Area Interconnected System

The vital concern of the load frequency control in an interconnected system is to minimize the frequency and tie-line scheduled power variations. A robust controller is required to overcome these concerns in a power system. This paper presents an interval fractional-order proportional integral derivative controller design technique for load frequency control in power system. The controller has been designed for frequency control of two area interconnected system using stability boundary locus method. The controller design involves perturbation in the system parameters (±50%) using the Kharitonov theorem rather than using fixed values. The analysis of the designed controller has been performed by changing system parameters such as governor constant, turbine time constant and step load perturbation (magnitude and location). Further, the performance of the controller has also been monitored under the effect of non-linearities (GRC and GDB). Simulation results illustrate that proposed controller gives better results than the conventional methods.

Model and robust gain‐scheduled PID control of a bio‐inspired morphing UAV based on LPV method

AbstractIn this paper, a linear parameter‐varying (LPV)‐based model and robust gain‐scheduled structural proportion integral and derivative (PID) control design solution are proposed and applied on a bio‐inspired morphing wing unmanned aerial vehicle (UAV) for the morphing process. In the LPV model method, the authors propose an improved modeling method for LPV systems. The method combines partial linearization and function substitution. Using the proposed method, we can choose the varying parameters simply, thus creating a model that is more flexible and applicable. Then, a robust gain‐scheduled structural PID control design method is given by introducing a structural matrix to design a structural PID controller, which is more consistent with the structure of the PID controller used in practice and has a simpler structure than representative ones in the existing literature. The simulation results show that the developed LPV morphing UAV model is able to catch the response of the original nonlinear model with a smaller error than the existing Jacobian linearization method and the designed controller can maintain stable flights in practice with satisfactory robustness and performance.

Optimal integral minus proportional derivative controller design by evolutionary algorithm for thermal‐renewable energy‐hybrid power systems

The goal of this work is to investigate the application of integral minus proportional derivative (IPD) controller for the automatic generation control (AGC) problem comprising of a two-area thermal system integrated with renewable energy (RE)-based sources such as wind, solar and fuel cells. In order to facilitate a realistic environment, each thermal system is equipped with a governor dead band, reheat turbine and generation rate constraint. Moreover, each RE-based power system is modelled by incorporating certain drift and random variations as the key characteristic of RE-based sources. The control performance of IPD is compared with the PID and PI controllers all tuned using an evolutionary technique genetic algorithm by incorporating a step load perturbation in both areas. In order to verify the effectiveness of the control scheme, detailed performance investigations are carried out using random variations in load perturbations and in RE-based power. In addition, sensitivity analysis is also included for wider variations in system parameters in order to test robustness. Based on the extensive simulations for robustness and accuracy, it was observed that IPD outperforms the other controllers and therefore serves as a promising solution to the problem of AGC.

Control of a wastewater treatment plant using relay auto-tuning

Efficient performance of a wastewater treatment plant largely depends on optimal process control. Owing to their complexity and nonlinearity, such processes are difficult to control. In this study, relay auto tuning method is analyzed to design of a proportional integral derivative controller for the activated sludge biological process. The process is estimated as a first-order process with time delay. The key control variable in wastewater treatment is the concentration of dissolved oxygen during the aeration process. The influence of higher order harmonics on the system critical values is considered during the design using preload relay and a modified two-step relay. The system performance was evaluated for both servo and regulatory mechanisms. In addition, the designed controller was tested in the presence of noise for the robustness analysis.

A proportional–integral-based robust state-feedback control method for linear parameter-varying systems and its application to aircraft

The integration of advanced linear parameter-varying and classical proportional–integral–derivative control methods has attracted great attention in control of nonlinear dynamic systems. However, linear parameter-varying proportional–integral–derivative control synthesis is a nonconvex bilinear matrix inequality problem. Although the synthesis conditions can be convexified in the case of proportional–integral control, a strong constraint on the structure of matrix variables usually leads to infeasible solutions. In this paper, a linear parameter-varying proportional–integral control design method is proposed to remove that constraint. The approach is based on the assumption of state-feedback proportional–integral control to guarantee the linear matrix inequality variables to be full matrices instead of block diagonal matrices, and extended linear matrix inequalities are proposed to synthesize the controller. This increases the likelihood of finding feasible linear matrix inequality solutions and reduces the conservatism. The proposed method is applied to control longitudinal and lateral dynamics of an F-16 aircraft and promising simulation results are obtained.

Concurrent PI Controller Design for Indirect Vector Controlled Induction Motor

AbstractIn this work, a concurrent proportional integral (PI) controller design technique is addressed for indirect vector controlled induction motor (IVCIM). For this, a full‐order induction motor (IM) model is employed that includes the stator current dynamics. The current‐loop proportional integral (PI) controllers are tuned to use the attributes of such dynamics. The robustness against load torque and rotor resistance variations are incorporated in the design problem. This method is implemented using a static output feedback scheme in which iterative linear matrix inequality (ILMI) based H∞ control technique is applied. The simulation and experimental comparison with existing designs show the superiority of proposed method and practical interest for industry use.

Modified Integral Sliding Mode Controller Design based Neural Network and Optimization Algorithms for Two Wheeled Self Balancing Robot

Modified Integral Sliding Mode Controller Design based Neural Network and Optimization Algorithms for Two Wheeled Self Balancing Robot

Design and Implementation of a Discrete-Time Proportional Integral (PI) Controller for the Temperature Control of a Heating Pad.

Contact heat evoked potentials (CHEPs) are recorded from the brain by giving thermal stimulations through heating pads kept on the surface of the skin. CHEP signals have crucial diagnostic implications in human pain activation studies. This work proposes a novel design of a digital proportional integral (PI) controller based on Arduino microcontroller with a view to explore the suitability of an electric heating pad for use as a thermode in a custom-made, cost-effective CHEP stimulator. The purpose of PI controller is to set, regulate, and deliver desired temperatures on the surface of the heating pad in a user-defined pattern. The transfer function of the heating system has been deduced using the parametric system identification method, and the design parameters of the controller have been identified using the root locus technique. The efficiency of the proposed PI controller in circumventing the well-known integrator windup problem (error in the integral term builds excessively, leading to large transients in the controller output) in tracking the reference input and the controller effort (CE) in rejecting output disturbances to maintain the set temperature of the heating pad have been found to be superior compared with the conventional PI controller and two of the existing anti-windup models.

Design of an Optimal Integral Backstepping Controller for a Quadcopter

In this paper, an Integral Backstepping Controller (IBC) is designed and optimized for full control, of rotational and translational dynamics, of an unmanned Quadcopter (QC). Before designing the controller, a mathematical model for the QC is developed in a form appropriate for the IBC design. Due to the underactuated property of the QC, it is possible to control the QC Cartesian positions (X, Y, and Z) and the yaw angle through ordering the desired values for them. As for the pitch and roll angles, they are generated by the position controllers. Backstepping Controller (BC) is a practical nonlinear control scheme based on Lyapunov design approach, which can, therefore, guarantee the convergence of the position tracking error to zero. To improve controller capability in the steady state against disturbances, an integral action is used with the BC. To determine the optimal values of the IBC parameters, the Particle Swarm Optimization (PSO) is used. In the algorithm, the controller parameters are computed by minimizing a cost function that depends on the Integral Time Absolute Error (ITAE) performance index.
 Finally, different numerical simulations are provided in order to illustrate the performances of the designed controller. And for comparison purposes, a PID controller is designed and optimized using the PSO to control the quadcopter. The obtainediresults indicated a superiority in performance for the IBC over the PID controller based on some points among which are: a 13.3% and 30.5% lesser settling times for X and Y consequently, the ability to perform critical maneuvers that the quadcopter failed to do using the PID controller, and the capability of fast following up and conforming the changes of pitch (

Robust PID controller design for rigid uncertain spacecraft using Kharitonov theorem and vectored particle swarm optimization

This paper presents a robust Proportional Integral Derivative controller design methodology for three axis attitude control of a rigid spacecraft with parametric uncertainty using a combination of Kharitonov theorem and vectored particle swarm optimization based approaches. A controller is designed for each of the three axes using a systematic graphical approach. Here, a plot of the stability boundary loci in the integral gain versus proportional gain parameter plane, for the specified gain and phase margins for each of the Kharitonov interval plants is used to determine the region representing the set of all PID controllers that satisfy the desired performance and stability requirements. Vectored particle swarm optimization technique is used to determine the optimized proportional and integral gain values. The spacecraft attitude control system is simulated using Matlab-Simulink tool which shows that the designed controller provides stability, robustness, good reference pointing and disturbance rejection for perturbations within the specific bounds.

Robust Proportional Integral Derivative Controller Design for Various Processes Using Novel Hybrid Metaheuristic Algorithms

This paper compares the effectiveness of the proposed hybrid metaheuristic algorithms for a class of unstable systems with time delay to that of the existing ones. The local search and global methods of optimization are combined to yield more effective hybrid metaheuristic algorithms. These algorithms are used to tune the proportional–integral–derivative (PID) controllers, satisfying the robust stabilizing vector gain margin (VGM). Six global heuristic algorithms namely ant colony optimization (ACO), particle swarm optimization (PSO), biogeography-based optimization (BBO), population-based incremental learning (PBIL), evolution strategy (ES), and stud genetic algorithms (StudGA) are combined with the local search property of derivative free optimization methods such as simplex derivative based pattern search (SDPS) and implicit filtering (IMF) to yield hybrid metaheuristic algorithms. The efficacy of the proposed control schemes in terms of various time domain specifications and stabilizing VGM are compared with some existing methods for unstable process with time delay (UPTD) systems. The performance of the proposed control schemes particularly in the context of uncertainty in the plant is demonstrated using a case study. The efficacy of the proposed control scheme is illustrated with a nontransfer function based multibody vehicle autosteer control design problem.

Robust adaptive fractional order proportional integral derivative controller design for uncertain fractional order nonlinear systems using sliding mode control

This article presents a robust adaptive fractional order proportional integral derivative controller for a class of uncertain fractional order nonlinear systems using fractional order sliding mode control. The goal is to achieve closed-loop control system robustness against the system uncertainty and external disturbance. The fractional order proportional integral derivative controller gains are adjustable and will be updated using the gradient method from a proper sliding surface. A supervisory controller is used to guarantee the stability of the closed-loop fractional order proportional integral derivative control system. Finally, fractional order Duffing–Holmes system is used to verify the proposed method.

Design and performance of final optics assembly in SG-II Upgrade laser facility

In high power laser facility for inertial confinement fusion research, final optics assembly (FOA) plays a critical role in the frequency conversion, beam focusing, color separation, beam sampling and debris shielding. The design and performance of FOA in SG-II Upgrade laser facility are mainly introduced here. Due to the limited space and short focal length, a coaxial aspheric wedged focus lens is designed and applied in the FOA configuration. Then the ghost image analysis, the focus characteristic analysis, the B integral control design and the optomechanical design are carried out in the FOA design phase. In order to ensure the FOA performance, two key technologies are developed including measurement and adjustment technique of the wedged focus lens and the stray light management technique based on ground glass. Experimental results show that the design specifications including laser fluence, frequency conversion efficiency and perforation efficiency of the focus spot have been achieved, which meet the requirements of physical experiments well.

Robust speed control design for electric motors using the Kharitonov theorem and genetic algorithms: an experimental study

Electric motor drives are subjected to severe oscillations that might cause motor shaft fatigue and consequent breakdown during system operation. In this paper, a design of robust proportional integral (PI) controller for induction motor (IM) drives is presented. Uncertainties due to different load conditions of the drive system are modelled by a transfer function with interval coefficients. Instead of stabilising an infinite number of polynomials, the Kharitonov theorem is used to design a robust controller by simultaneous stabilisation of only four polynomials. The controller parameters are optimised so that the maximum eigenvalue among the four polynomials is pushed to the left in the complex plane. This is accomplished using genetic algorithm (GA) optimisation to achieve the maximum possible rapidity of the system. The proposed controller is tested experimentally using the hardware-in-the-loop (HIL) technique. The simulation and experimental results show the validity and effectiveness of the proposed controller as compared to the auto-tuned PID control at different loading conditions.

Evolutionary Optimization Based Fractional Order controller for Web Transport Systems in Process Industries

This investigation presents an optimisation-based design of fractional order proportional integral (FO-PI) controller for web transport systems used in paper industries. The objective of the optimisation algorithm is to reduce the integral absolute error of the closed loop web transport systems considering the underlying physical and operating constraints. The resulting optimisation problem is nonlinear, and to compute the controller parameters, evolutionary algorithms - particle swarm optimisation (PSO) and bacterial foraging optimisation (BFO) are used. The performance improvements achieved using FOC is compared with traditional proportional integral derivative controller. Our results show that BFO tuned FOC shows better performance.