Integral Of Time Multiplied By Absolute Error Research Articles

Modern Optimization Techniques Based PID Controller Tuning for the Speed Control of a DC Motor

In this paper, the optimal configuration of the Proportional Integral Derivative (PID) controller for the speed control of a DC motor are determined and compared using five optimization algorithms. The five optimization algorithms are respectively Ant Lion Optimization (ALO), Grey Wolf Optimizer (GWO), Moth-Flame Optimization (MFO), Multi-Verse Optimization (MVO) and Salp Swarm Optimization (SSO). The objective function uses The Integral of Time multiplied by Absolute Error (ITAE) as the performance index. A comparison of all these methods is done using the following step response parameters - steady-state error, settling time, maximum overshoot and rise time. ALO performed best among all the optimization algorithms.

Optimal design and control loop selection for a STATCOM wide-area damping controller considering communication time delays

Wide-area damping controllers (WADC) have been shown to be effective in damping interarea oscillation modes. The varying nature of power system operating point requires the design of an adaptive WADC. Majority of the existing control design techniques rely on empirical approaches at one or more of their design stages, which makes it difficult to implement in adaptive control techniques. Therefore, the purpose of this study is to provide a systematic procedure based entirely on numerical approaches for designing a STATCOM-based WADC. The proposed procedure involving control loop selection, control design and adaptive time delay compensation, can then be implemented in adaptive WADC schemes. Geometric analysis has been used to choose the STATCOM location. Then, a novel optimization-based signal selection methodology is proposed. The proposed methodology employs a combination of multiple input signals to optimally generate a signal with the required modal objectives like enhancing observability and reducing interaction between different control loops. After that, another optimization problem is formulated to tune the controller parameters using integral of time multiplied by absolute error (ITAE) as the optimization objective. Both optimization problems have been evaluated using two optimization techniques: Particle swarm optimization (PSO) and self-adaptive multi-population elitist Jaya algorithm (SAMPE-JAYA). Finally, an adaptive delay compensator is designed to mitigate the effects of communication time delays. The proposed control strategy is applied on the IEEE 68-bus system and the controller performance is evaluated by modal analysis and multiple time-domain simulation scenarios.

Tuning PID Controllers Based on Hybrid Arithmetic Optimization Algorithm and Artificial Gorilla Troop Optimization for Micro-Robotics Systems

Micro particles have the potentials to be used for many medical purposes in-side the human body such as drug delivery and other operations. This paper attempts to provide a thorough comparison between five meta-heuristic search algorithms: Arithmetic optimization algorithm (AOA), Artificial Gorilla troop’s optimization (GTO), Seagull optimization algorithm (SOA), Parasitism-predation Algorithm (PPA), and hybrid between AOA and GTO (HAOAGTO). These approaches were used to calculate the PID controller optimal indicators with the application of different functions, including Integral Absolute Error (IAE), Integral of Time Multiplied by Square Error (ITSE), Integral Square Time multiplied square Error (ISTES), Integral Square Error (ISE), Integral of Square Time multiplied by square Error ( (ISTSE), and Integral of Time multiplied by Absolute Error (ITAE). Every method of controlling was presented in a MATLAB Simulink numerical model. It is observed that the PPA technique achieves the highest values of best fitness value for simulation results among other control approaches, while the HAOAGTO approach reduces the best fitness function compared to other optimization techniques used. The results indicate that HAOAGTO is the best method among all approaches and that ISTES is the best choice of PID for optimizing the controlling parameters.

Selection of PID controller design plane for time-delay systems using genetic algorithm

The design of a Proportional-Integral-Derivative (PID) controller with proportional, integral, and derivative, gain, k p , k i , and k d , respectively, for a time-delay system, is quite common, particularly in the k i - k d plane, for a fixed k p or in the k p - k i plane, for a fixed k d . These design methods have been widely reported in the literature, however, the process of investigating the effects of using any of these design planes on system performance has not been given serious attention hence the need for this study. The stability region in the k i - k d and k p - k i design plane for a fixed value of k p and k d respectively were determined. For every determined stability region, the optimum value of controller gains in the plane was determined using a genetic algorithm (GA) with the integral of time multiplied by absolute error (ITAE) used as the objective function. The optimum value of the fixed gains was graphically determined by plotting the minimum of ITAE (Min-ITAE) for each stability region against the fixed gains. The overall optimum controller gains are the fixed gain that gives minimum of Min-ITAE (Min (Min-ITAE)) and the gains that resulted in Min-ITAE that yielded the Min (Min-ITAE). Using the determined overall optimum controller gains, the system closed-loop step response was plotted for the two design planes and the time domain performance measures (TDPMs) were determined. Based on TDPMs obtained for examples 1, 2, and 3, the k i -k d design plane yielded a faster response while the k p - k i design plane yielded a response that closely tracks the input irrespective of the system type and order. The study will enable control system designers to select the design plane that will give the best system performance right from the start of controller design without involving trial and error once the system transfer function and design specifications are known.

Real-Time Implementation of an Enhanced PID Controller Based on Ant Lion Optimizer for Micro-Robotics System

Microparticles have the potentials to be used for many medical purposes in-side the human body such as drug delivery and other operations. This paper offers a comprehensive comparative study of three meta-heuristic search algorithms for controlling the micro-robotics system with a proportional-integral-derivative (PID) controller. Grey Wolf Optimization (GWO), Harmony Search algorithm (HS) and Ant Lion Optimizer (ALO) are the various techniques that this study adopts. The optimum position control can be obtained by employing the former algorithms with different fitness functions, namely Integral Absolute Error (IAE), Integral of Time Multiplied by Square Error (ITSE), Integral Square Time multiplied square Error (ISTES), Integral Square Error (ISE), Integral of Square Time multiplied by square Error ( (ISTSE), and Integral of Time multiplied by Absolute Error (ITAE). In a MATLAB Simulink, each control method was presented, while the experimental measurements were tested and operated by the LabVIEW Software. It is observed that the HS technique achieves the highest values of settling error for both simulation and experimental results among other control approaches, while the ALO approach reduces the settling error by 32.5% compared to former experiments. The results indicate that ALO is the best method among all approaches and that ISTES is the best choice of PID for optimizing the controlling parameters.

MTDC Grids: A Metaheuristic Solution for Nonlinear Control

This scientific paper aims to increase the voltage source converter (VSC) control efficiency in a multi-terminal high voltage direct current (MTDC) network during dynamic operations. In the proposed study, the Mayfly algorithm (MA) is used to modify the control parameters of VSC stations. Traditional strategies that modify VSC control settings using approximate linear models fail to produce optimal results because VSCs are nonlinear characteristics of the MTDC system. Particle swarm optimization (PSO) may produce optimal outcomes, but it is prone to becoming stuck in a local optimum. To modify the proportional-integral (P.I.) control parameters of the VSC station, the Mayfly algorithm, a modified form of PSO, is used. The suggested algorithm’s objective function simultaneously optimizes both the outer and inner control layers. A four-terminal MTDC test system is developed in PSCAD/EMTDC to assess the benefits of the proposed algorithm. For VSCs, a comparison of classical, PSO, and proposed MA-based tuned parameters is carried out. The integral of time multiplied by absolute error (ITAE) criterion is used to compare the performance of classical, PSO, and a proposed algorithm for VSC controller parameters/gains. With an ITAE value of 6.8521 × 10−6, the MA-based proposed algorithm computes the optimal values and outperforms its predecessor to adjust the VSCs controller gains. For (i) wind farm power variation, (ii) AC grid load demand variation, and (iii) ultimate permanent VSC disconnection, steady-state and dynamic performances are evaluated. According to the results, the proposed algorithm based MTDC system performs well during transients.

Design and Optimization of PID Controller using Various Algorithms for Micro-Robotics System

Microparticles have the potentials to be used for many medical purposes in-side the human body such as drug delivery and other operations. This paper attempts to provide a thorough comparison between five meta-heuristic search algorithms: Sparrow Search Algorithm (SSA), Flower Pollination Algorithm (FPA), Slime Mould Algorithm (SMA), Marine Predator Algorithm (MPA), and Multi-Verse Optimizer (MVO). These approaches were used to calculate the PID controller optimal indicators with the application of different functions, including Integral Absolute Error (IAE), Integral of Time Multiplied by Square Error (ITSE), Integral Square Time multiplied square Error (ISTES), Integral Square Error (ISE), Integral of Square Time multiplied by square Error (ISTSE), and Integral of Time multiplied by Absolute Error (ITAE). Every method of controlling was presented in a MATLAB Simulink numerical model, and LABVIEW software was used to run the experimental tests. It is observed that the MPA technique achieves the highest values of settling error for both simulation and experimental results among other control approaches, while the SSA approach reduces the settling error by 50% compared to former experiments. The results indicate that SSA is the best method among all approaches and that ISTES is the best choice of PID for optimizing the controlling parameters.

PID speed control of DC motor using meta-heuristic algorithms

This paper presents archimedes optimization algorithm(AOA) and dispersive flies optimization(DFO) to optimally tune gain parameters of PID control scheme in order to regulate DC motor’s speed. These suggested techniques tune the controller by the minimization of the fitness function represented by the integral of time multiplied by absolute error (ITAE). The modelling and simulation are carried out in MATLAB/Simulink. The transient response of unit step input obtained from AOA-PID-ITAE andDFO-PID-ITAE controllers were compared to those obtained from Ziegler-Nichols (ZN) method and particle swarm optimization(PSO). The results indicate that AOA-PID-ITAE and DFO-PID-ITAE are more efficient than ZN method and PSO in reducing rise time and settling time. Likewise, DFOconverge faster to the optimal solution with lower overshoot than AOA and PSO.

A hybrid grey wolf optimisation and pattern search algorithm for automatic generation control of multi-area interconnected power systems

A hybrid grey wolf optimisation-pattern search (hGWO-PS) algorithm has been proposed to optimise the parameters of two degree of freedom-proportional integral derivative (2DOF-PID) controllers in multi-area power systems for automatic generation control. The integral of time multiplied by absolute error (ITAE) has been considered as an objective function in the present work. Firstly, this algorithm has been applied to a two-area non-reheat thermal power system; secondly, the analysis of ITAE, dynamic responses and robustness of the same has also been carried out. The dynamic behaviour of the system optimised by the proposed approach hardly alters with the broad changes in the load and system parameters within the range [−50%, +50%]. The proposed algorithm has also been applied extensively to a three-area hydro-thermal power system with appropriate generation rate constraints (GRC). The simulation results show that the proposed algorithm performs better when compared with recently published approaches in terms of less ITAE value, settling time, overshoot and faster system ability to return at zero frequency and tie line power deviations.

A hybrid grey wolf optimisation and pattern search algorithm for automatic generation control of multi-area interconnected power systems

A hybrid grey wolf optimisation-pattern search (hGWO-PS) algorithm has been proposed to optimise the parameters of two degree of freedom-proportional integral derivative (2DOF-PID) controllers in multi-area power systems for automatic generation control. The integral of time multiplied by absolute error (ITAE) has been considered as an objective function in the present work. Firstly, this algorithm has been applied to a two-area non-reheat thermal power system; secondly, the analysis of ITAE, dynamic responses and robustness of the same has also been carried out. The dynamic behaviour of the system optimised by the proposed approach hardly alters with the broad changes in the load and system parameters within the range [−50%, +50%]. The proposed algorithm has also been applied extensively to a three-area hydro-thermal power system with appropriate generation rate constraints (GRC). The simulation results show that the proposed algorithm performs better when compared with recently published approaches in terms of less ITAE value, settling time, overshoot and faster system ability to return at zero frequency and tie line power deviations.

Design of Fractional Order PID Controller Using Genetic Algorithm Optimization Technique for Nonlinear System

AbstractIn this paper, fractional order PID controller, as well as integer order PID controller, is designed for non-linear system to enhance the system’s performance and gain the stability. The novelty of the work is achieved by the development of a new methodology for integer order PID and fractional order PID control tuning by optimizing the parameters of controllers using the Genetic Algorithms optimization technique. The performance of any system mainly depends upon how efficiently the controller will be working and hence that’s how most crucial part of the designing of FOPID controller or any controller is the tuning of its parameters. The uniquely designed and tuned parameters of the FOPID controller which is obtained by optimizing all the five parameters by using an evolutionary algorithm optimization technique i. e. a genetic algorithm which is a very powerful search tool and carrying heuristic characteristics. This method of tuning the FOPID controller which is designed and has been applied over the conical tank (nonlinear) system. The most important step in applying genetic algorithm is the selection of the fitness function and hence Integral of time multiplied by absolute error (ITAE) have been used here as the fitness function. Each chromosome comprised of all the five parameters of FOPID controller, which have been further optimised using above mentioned fitness function. From the simulation results, it can be observed that the solutions which are obtained optimally, presents an excellent performance for the system studied, by improving the behaviour of the system satisfactorily. Simulation results also show that the proposed FOPID controller gives improved performance over classical PID controller in terms of IAE and TV.

LMI-based design of an I-PD+PD type LPV state feedback controller for a gantry crane

In this paper, an alternative gain-scheduled PID tuning procedure is proposed for gantry crane control systems. In order to avoid excessive overshoot and aggressive control action due to the proportional kick and/or derivative kick effects, an I-PD+PD type control law is considered. The scheduling parameter is considered the cable length due to the payload lifting and lowering movements. A linear parameter-varying (LPV) gantry crane model is constructed to enable gain-scheduled controller design with a linear matrix inequalities (LMIs) framework. Based on the LPV model, a convex optimization problem is formulized to minimize L2 gain under regional pole location constraints. Then, a fixed gain L2 gain state feedback I-PD+PD type controller and a conventional pole placement state feedback I-PD+PD controller are designed to investigate the efficiency of the proposed controller. A pole placement controller is tuned to minimize the very common ITAE (integral of time multiplied by absolute error) performance index. Simulation results show that the proposed controller has superior tracking performance under time-varying cable length, when compared with nominal fixed gain controllers.

A Fuzzy-Based PI Controller for Power Management of a Grid-Connected PV-SOFC Hybrid System

Solar power generation is intermittent in nature. It is nearly impossible for a photovoltaic (PV) system to supply power continuously and consistently to a varying load. Operating a controllable source like a fuel cell in parallel with PV can be a solution to supply power to variable loads. In order to coordinate the power supply from fuel cells and PVs, a power management system needs to be designed for the microgrid system. This paper presents a power management system for a grid-connected PV and solid oxide fuel cell (SOFC), considering variation in the load and solar radiation. The objective of the proposed system is to minimize the power drawn from the grid and operate the SOFC within a specific power range. Since the PV is operated at the maximum power point, the power management involves the control of SOFC active power where a proportional and integral (PI) controller is used. The control parameters of the PI controller Kp (proportional constant) and Ti (integral time constant) are determined by the genetic algorithm (GA) and simplex method. In addition, a fuzzy logic controller is also developed to generate appropriate control parameters for the PI controller. The performance of the controllers is evaluated by minimizing the integral of time multiplied by absolute error (ITAE) criterion. Simulation results showed that the fuzzy-based PI controller outperforms the PI controller tuned by the GA and simplex method in managing the power from the hybrid source effectively under variations of load and solar radiation.

Optimal PID controller design with Kalman filter for Qball-X4 quad-rotor unmanned aerial vehicle

In this paper, we used a Qball-X4 quad-rotor unmanned aerial vehicle (UAV) which was developed by the Quanser Company as the experimental platform. First, a fundamental mathematical model of the Qball-X4 quad-rotor UAV was built and a simulation model was set up based on the proposed mathematical model; then, a double closed-loop optimal proportional–integral–derivative (PID) controller based on integral of time multiplied by absolute error (ITAE) indices was designed according to the model structure. In consideration of the possible system error and data delay, we designed a corresponding Kalman filter, which can estimate the target trajectory and be put before the proposed PID controller to ensure their validity. Finally, simulation results of the system with presented PID controller and Kalman filter were shown to verify their effectiveness.

English

PID controllers are most popular controllers because of simplicity of implementation and broad applicability. In order to obtain the desired control performance correct tuning of PID controller is very important. There are many tuning algorithms available for tuning the PID controller. Most of the tuning processes are implemented manually. These processes are difficult and time consuming. Soft computing techniques have been widely used to tune the parameters of PID. In this paper parameters of PID controller are tuned using two sets of soft computing techniques which are Differential Evolution (DE) and Hybrid Differential Evolution (HDE). The optimal PID control parameters are applied for a composition control system. The performance of two techniques is evaluated by setting its objective function with Integral Square Error (ISE), Integral Absolute Error (IAE), Integral of Time multiplied by Absolute Error (ITAE). This paper also compares performance of tuned PID controller using DE and HDE methods with Ziegler-Nichols method.

Optimal PI controller design for active power in grid-connected SOFC DG system

This paper is concerned with optimal control of grid-connected solid oxide fuel cell (SOFC) stack based on a model developed and validated in the literature. Recent studies have shown that control of SOFC is challenging due to its slow dynamics and firm operating limits. For an SOFC, while the primary objective is to supply the demand active power, it is crucial to operate fuel cell within its safe operating constraints. In order to meet these requirements, a proper control strategy is developed in this study. This control strategy employs an optimal robust PI controller to control active power of the plant and at the same time satisfies physical and operating constraints via employing two proportional-gained controllers, of fuel utilization factor controller and anode–cathode pressure difference controller in such a way to maintain the fuel utilization factor at its optimal value of 85% and also keep pressure difference between anode and cathode within the safe bound of 0–0.08atm under transient conditions. A distributed generation (DG) system including an SOFC stack connected to the power grid through an IGBT inverter is implemented in MATLAB/SIMULINK™ environment. Moreover, dynamics of fuel processor are included. In addition, differential evolution (DE) algorithm evaluated by integral of time multiplied by absolute error (ITAE) criterion is used to search for optimal values of PI controller parameters. Dynamics of the DG system are analyzed for the cases of conventional and proposed PI controllers under different load changes and short circuit condition to verify the performance of proposed PI controller. Simulation results show that the proposed controller can provide satisfactory performance for load changes and short circuit condition at the cost of keeping the SOFC performance beyond its operating constraints.

Design of decoupling and tracking controllers for continuous-time transfer function matrices with multiple time delays

This paper presents an extended adjoint decoupling method together with a reference model-based sliding mode tracking method, to design a decoupling and tracking controller for continuous-time transfer function matrices with multiple (integer/fractional) time delays in both denominators and numerators. First, for obtaining the diagonally decoupled subsystems, a decoupler is designed by utilizing the extended adjoint decoupling method. Then, by using sampled data from the unit-step response of the decoupled subsystems, the conventional balanced model-reduction method is carried out to obtain the approximated delay-free/single-delay continuous-time models for the decoupled subsystems with multiple time delays. For the integral of time multiplied by absolute error (ITAE) reference model tracking, a chain observer is designed to establish the virtual estimated states for the decoupled subsystems by utilizing the obtained approximated continuous-time models. At last, we develop a sliding mode tracking controller together with a disturbance observer (DOB), to achieve reference model tracking and disturbance rejection. Illustrative examples are given to demonstrate the effectiveness of the proposed method.

Nonlinear Control of Magnetically-geared Drive-trains

The paper considers certain impedimental issues related to the use of magnetic gearbox and magnetic coupling technologies in high performance servo control systems. A prototype magnetic coupling is used as a basis for demonstrating that the underlying torque transfer characteristic is significantly nonlinear when transmitted torque approaches the maximum designed pull-out torque of the device. It is shown that linear controllers for speed control proportional plus integral (PI) and position control proportional plus derivative (PD) result in acceptable performance provided the magnetic coupling operates below 80 % of designed pull-out torque. To fully compensate for the inherent nonlinearity of the torque transfer characteristic, feedback linearizing control laws and state transformations are derived resulting in exactly linear input-output characteristic for position and speed control of magnetically-geared drive-trains. With the addition of state feedback, the closed-loop dynamics for both position and speed control of a magnetically-geared drive-train can be designed to satisfy the integral of time multiplied by absolute error (ITAE) optimized linear response for a step input. Outstanding results are demonstrated through simulation and experimental real-time implementation on a demonstrator magnetically-geared drive-train.

Optimized proportional integral derivative (PID) controller for the exhaust temperature control of a gas turbine system using particle swarm optimization

In this paper, the particle swarm optimization (PSO) technique is used in optimising theproportional integral derivative (PID) controller parameters for the exhaust temperature control of a gas turbine system. The performance of the PID controller whose parameters are tuned based on the PSO method (PSO-PID) is compared with the conventional PID (CPID) controller that employs the Ziegler-Nichols method. A new performance criterion, known as multipurpose performance criterion (MPPC) is proposed and used in the PSO algorithm. Time domain performance of the PSO-PID controller, such as the maximum overshoot QUOTE , rise time QUOTE , settling time QUOTE and absolute error (AE) are being optimized based on the MPPC and compared with other performance criteria such as the integral of time multiplied by absolute error (ITAE), integral of time multiplied by square error (ITSE), integral square error (ISE) and integral of absolute error (IAE). Result shows that the PSO technique, combined with the MPPC performance criterion is very effective to yield optimal transient response of the gas turbine exhaust temperature. An adjustable weighting factor in the MPPC technique makes it more reliable, consistent and flexible as compared to the commonly used performance criteria. Key words: Proportional integral derivative (PID) controller, particle swarm optimization, multipurpose performance criterion, gas turbine exhaust temperature.

Trajectory tracking control system for ship

The conventional way-point guidance system has two main operation modes: the course-keeping mode at straight trajectory segments and the course changing mode in the way-points. This paper presents the design of a course and a turning controllers which have high steering performance and are robust due to ship dynamics' variations. The bases for the design are simple, linear ship dynamics models of the 1st and 2nd order (Nomoto models). The controllers have fixed structure and theirs coefficients are selected using the performance indices: the settling time and integral performance index ITAE (the integral of time multiplied by absolute error).