Integral Of Time-weighted Absolute Error Research Articles

Load torque observation and compensation for permanent magnet synchronous motor based on sliding mode observer

Background Permanent magnet synchronous motors (PMSM) are widely used in various industries. However, in practical applications, the time-varying nature of load torque may lead to speed fluctuations, negatively impacting the motor's control performance and stability. To mitigate these issues, this paper proposes a load torque observation method for PMSMs based on a sliding mode observer. Methods The sliding mode observer is designed to estimate the load torque and convert it into a current, which is fed back as a feedforward compensation to the q-axis current in the current closed-loop control system. The observer's dynamic performance is optimized using a genetic algorithm to minimize the Integral of Time-weighted Absolute Error (ITAE) between the observer and the actual system state. Experimental tests are conducted on a motor torque testing platform. After stabilizing the motor at 800rpm, a sudden torque of 0.5Nm is applied. Results Compared to the situation without load torque compensation, the motor speed fluctuations are reduced by approximately 60% after adding load torque compensation. Conclusions This enhancement improves the system's speed control performance during torque variations and increases the system's robustness and disturbance rejection capability.

Robust Fuzzy-PID Technique for the Automatic Generation Control of Interconnected Power System with Integrated Renewable Energy Sources

This paper proposes a robust hybrid fuzzy PID controller, with the PID gain values tuned using the particle swarm optimization (PSO) technique for the automatic generation control (AGC) of the two-area hybrid power system. PSO Algorithm is applied to reduce the integral of time-weighted absolute error (ITAE) of the frequency and tie-line power variations of the two-area interconnected power system. The suggested method’s efficacy is examined on an interconnected two-area power system with Area 1 containing thermal reheat plants, hydropower plants, and diesel generating units, and Area 2 comprising thermal reheat plants and renewable energy sources (RES): wind energy conversion system, solar photovoltaic system, and electric vehicles. The thermal reheat power plants are modelled taking into consideration the governor dead band (GDB) and the generation rate constraints (GRC). The performance of the presented controller is compared with the genetic algorithm-optimized PID AGC and the PSO-optimised PID AGC. The simulation outcomes show superior results of the proposed controller against other controllers. Further, sensitivity analysis reflects that the proposed technique provides better dynamic response and robustness than the other techniques.

Comparative Analysis: Fractional PID vs. PID Controllers for Robotic Arm Using Genetic Algorithm Optimization

This paper presents a comparative analysis of a fractional-order proportional–integral–derivative (FO-PID) controller against the standard proportional–integral–derivative (PID) controller, applied to a nonlinear robotic arm manipulator systems. The genetic algorithm (GA) optimization method was implemented to tune the gain parameters of the FO-PID and PID controllers. The performance of the FO-PID and PID controllers were evaluated though different cost functions, including integral of squared error (ISE), integral of absolute error (IAE), integral of time-weighted absolute error (ITAE), and integral of time-weighted squared error (ITSE). The performance of these controllers was examined via extensive simulations by using MATLAB/SIMULINK for different operating scenarios of the robotic arm manipulator system. Based on the obtained results, a comparative performance matrix is proposed, wherein cost functions ISE, IAE, ITAE, and ITSE are represented as columns while characteristic parameters (overshoot, rising time, and settling time) are represented as rows. The proposed performance matrix facilitates the selection between the PID and FO-PID controllers.

Distributed drive electric vehicle differential assistance particle swarm optimization PID control

To improve the vehicle’s handling stability and enhance the steering assist effect of distributed drive electric vehicles, a differential assist steering control strategy is proposed based on the Particle Swarm Optimization (PSO) algorithm to optimize PID control parameters. A dynamic model of steering torque considering the influence of tire force is established, based on the reference steering torque to calculate the required torque. The PSO algorithm with the Integral of Time-weighted Absolute Error (ITAE) is used to optimize the parameters in the PID steering control, and wheel torque allocation is performed by using the objective function constraint. Simulation results show that the differential assistance can meet the driving requirements of drivers at both high and low speeds, and the proposed control strategy is effective.

An SMC-Based Accurate and Robust Load Speed Control Method for Elastic Servo System

In this paper, a modified sliding mode speed controller is designed in order to improve the load speed control performance of an elastic motor drive system with internal and external disturbances. Firstly, based on the load speed deviation and its first-order and second-order differentials, a two-dimensional sliding surface function is presented. The parameters of the sliding surface are determined by a novel particle swarm optimization (PSO) method. The method has improved inertia weights and evaluation functions, which can improve the accuracy and efficiency of the parameter search and enhance the immunity and robustness of the system. Secondly, on the basis of the integral of time-weighted absolute error (ITAE) criterion, the parameters of the exponential approach law are determined, which improves the tracking accuracy. Finally, the designed sliding mode control (SMC) with high tracking accuracy, fast dynamics, and strong robustness is verified by both simulations and experiments.

An Intelligence-Based Controller for Improved Frequency Regulation in Deregulated Power Environment

A methodology for designing and assessing an optimal controller to regulate frequency in a two-area interconnected power system with Renewable Energy Sources (RES) is demonstrated in this paper. The Load Frequency Control (LFC) system makes it possible to restore both system frequency and scheduled tie-line power to their nominal values in a deregulated environment. The introduction of an advanced controller has the potential to improve the LFC mechanism's performance. The present article employs the Inertia Emulation Technique (IET) to demonstrate the potential influence of the novel High Voltage Direct Current (HVDC) tie-line model and converter capacitors. The Integral Time-weighted Absolute Error (ITAE) has been taken as an objective function for the proposed controller. This investigation proposes a novel adaptive control strategy i.e., ANN-based (PIλf + PIλDN) controller for the anticipated LFC mechanism. The modified Quasi-Opposition-learning-based Volleyball Premier League (QOVPL) method is utilized to assess the optimal control parameters with the highest efficacy. The effectiveness of the proposed LFC framework has been evaluated through the implementation of established methodologies for managing step and random load perturbations. The supremacy and effectiveness of the proposed control scheme are validated over recently published work.

Model-Based Optimization Approach for PID Control of Pitch–Roll UAV Orientation

This study focuses on the modeling and control optimization of the pitch–roll angles orientation in a quad-rotor UAV (unmanned aerial vehicle) drone system. To address the control challenge, PID (proportional–integral–derivative) controllers are used, which have been tuned through a model-based optimization approach. A non-linear model of the system is obtained and further validated experimentally. The model is implemented in Simulink to conduct model-based optimization. The controller design uses an IMC (internal model control) model-based approach to establish the initial parameters for a PID controller. In the subsequent design phase, a multiobjective approach is taken, incorporating weighted cost functions that account for IAE (integral absolute error) and ITAE (integral of time-weighted absolute error) forms, along with battery usage. The outcomes of this design are showcased through simulations and real-world platform testing.

Control of Quarter-Car Active Suspension System Based on Optimized Fuzzy Linear Quadratic Regulator Control Method

Vehicle suspension systems, which affect driving performance and passenger comfort, are actively researched with the development of technology and the insufficient quality of passive suspension systems. This paper establishes the suspension model of a quarter of the car and active control is realized. The suspension model was created using the Lagrange–Euler method. LQR, fuzzy logic control (FLC), and fuzzy-LQR control algorithms were developed and applied to the suspension system for active control. The purpose of these controllers is to improve car handling and passenger comfort. Undesirable vibrations occur in passive suspension systems. These vibrations should be reduced using the proposed control methods and a robust system should be developed. To enhance the performance of the fuzzy logic control (FLC) and fuzzy-LQR control methods, the optimal values of the coefficients of the points where the feet of the member functions touch are calculated using the particle swarm optimization (PSO) algorithm. Then, the designed controllers were simulated in the computer environment. The success of the control performance of the applied methods concerning the passive suspension system was compared in percentages. The results are presented and evaluated graphically and numerically. Using the integral time-weighted absolute error (ITAE) criterion, the methods were compared with each other and with the studies in the literature. As a result, it was found that the proposed control method (fuzzy-LQR) is about 84.2% more successful in body motion, 90% in car acceleration, 84.5% in suspension deflection, and 86.7% in tire deflection compared to the studies in the literature. All these results show that the car’s ride comfort has been significantly improved.

Optimal control of wind farm power output with delay compensated nested-loop extreme seeking control

In this paper, we propose to enhance the nested-loop extremum seeking control (NLESC)-based wind farm control strategy with the predictor-based delay compensation in order to improve its convergence characteristics under fluctuating wind. Earlier work has shown the effectiveness of NLESC for region-2 wind farm operation, i.e., maximizing the total power output of cascaded wind turbine array, while its convergence speed is highly limited by the delay of power output for downstream turbines due to wake propagation along the wind direction. By utilizing the delay compensated ESC proposed by Oliveira and Krstic, the delay compensated NLESC (DCNLESC) wind farm control is proposed, allowing the dither frequencies to be of similar magnitude as that in the single-turbine ESC. This can significantly improve the convergence speed of optimum tracking for real-time wind farm control. The wake propagation delay is estimated from turbine power outputs using cross correlation and proper filtering. Using the SimWindFarm platform, the proposed DCNLESC strategy is simulated with both a single-column three-turbine array and a 2 × 3 turbine array, under different wind speeds. The results show that the convergence speed toward the calibrated optimum is significantly improved over the NLESC operation. The convergence time for the upstream turbines' torque gain is reduced by 55%–14% in terms of integral time-weighted absolute error, while the impact on turbine fatigue loads is as low as no more than 3.5% increase on turbine tower and shaft.

Damping of Frequency and Power System Oscillations with DFIG Wind Turbine and DE Optimization

Wind power is one of the most promising renewable energy resources and could become a solution to contribute to the present energy and global warming crisis of the world. The commonly used doubly fed induction generator (DFIG) wind turbines have a general trend of increasing oscillation damping. Unless properly controlled, the high penetration of wind energy will increase the oscillation and affect the control and dynamic interaction of the interconnected generators. This paper discusses power oscillation damping control in the automatic generation control (AGC) of two-area power systems with DFIG wind turbines and Matlab code/Simulink interfacing optimization methods. The differential evolution (DE) optimization technique is used to obtain the controller gain parameters. In the optimization process, a step load perturbation (SLP) of 1% has been considered in Area 1 only, and the integral of time weighted absolute error (ITAE) cost function is used. Three different test studies have been examined on the same power system model with non-reheat turbine thermal power plants. In the first case, the power system model is simulated without a controller. In Case Study 2, the system is simulated with the presence of DFIG and without a controller. In Case Study 3, the system is simulated with a PID controller and DFIG. Most of the studies available in the literature do not optimize the appropriate wind penetrating speed gain parameters for the system and do not consider the ITAE as an objective function to reduce area control error. In this regard, the main contribution and result of this paper is—with the proposed PID+DFIG optimized DE—the ITAE objective function error value in the case study without a controller being 6.7865, which is reduced to 1.6008 in the case study with PID+DFIG-optimized DE. In addition, with the proposed controller methods, the dynamic system time responses such as rise time, settling time, overshoot, and undershoot are improved for system tie-line power, change in frequency, and system area controller error. Similarly, with the proposed controller, fast system convergence and fast system oscillation damping are achieved. Generally, it is inferred that the incorporation of DFIG wind turbines in both areas has appreciably improved the dynamic performance and system stability under consideration.

Predictive Extended State Observer-Based Active Disturbance Rejection Control for Systems with Time Delay

The latest research on disturbance rejection mechanisms has shown active disturbance rejection control (ADRC) to be an effective controller for uncertainties and nonlinear dynamics embedded in systems to be controlled. The significance of the ADRC controller is its model-free nature, as it requires minimal knowledge of the system model. In addition, it can actively estimate and compensate for the impact of internal and external disturbances present, with the aid of its crucial subsystem called the extended state observer (ESO). However, ADRC controller design becomes more challenging owing to different system disturbances, such as output disturbances, measurement noise, and varying time-delays persistent in the system’s communication channels. Most disturbance rejection techniques aim to reduce internal perturbations and external disturbances (input and output disturbance). However, output disturbance rejection with measurement noise under time-delay control is still a challenging problem. This paper presents a novel predictive ESO-based ADRC controller for time-delay systems by employing predictive methods to compensate for the disturbances originating from time delay. The prediction mechanism of the novel (proposed) controller design is greatly attributed to the extended state predictor observer (ESPO) integrated with the delay-based ADRC inside the proposed controller method. Thus, the proposed controller can predict the unknown system dynamics generated during the delay and compensate for these dynamics via disturbance rejection under time-delay control. This approach uses the optimization mechanism to determine controller parameters, where the genetic algorithm (GA) is employed with the integral of time-weighted absolute error (ITAE) as the fitness function. The proposed controller is validated by controlling second-order systems with time delay. Type 0, Type 1, and Type 2 systems are considered as the controlled plants, with disturbances (unknown dynamics due to delay and external disturbance), along with measurement noise present. The proposed controller method is compared with state-of-the-art methods, such as the modified time-delay-based ADRC method and the ESPO-based controller method. The findings indicate that the method proposed in this paper outperforms its existing competitors by compensating for the dynamics during the time delay and shows robust behaviour, improved disturbance rejection, and a fair extent of resilience to noise.

Dynamic Modeling and Controller Design for a Parabolic Trough Solar Collector

The current study unveils an analytical dynamic model of a parabolic trough solar collector (PTSC) and subsequently presents the process to derive the transfer function of the PTSC system. The presented generalized transfer function derivation can be utilized to relate different operating parameters with the output temperature for any PTSC module. Presented model and derivation are applied on a PTSC module tested by Sandia National Laboratory, USA and a transfer function relating the outlet temperature of heat transfer fluid (HTF) with flowrate is derived. PID controller is designed to maintain the HTF outlet temperature by manipulating the flowrate. Controller tuning is performed <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">via</i> nature-inspired algorithms (NIAs) which is rare in the context of the control systems for PTSCs. Two NIAs namely Self-adaptive Differential Evolution (SaDE) and African Vultures Optimization Algorithm (AVOA) were used for tuning with minimization of integral of time-weighted absolute error (ITAE) as an objective. It is concluded that SaDE-PID tuned controller outperforms AVOA-PID tuned controller with lower ITAE and in terms of other controller characteristics. Also, the designed controller is examined on various grounds as transient response characteristics and performance indexes. This completes the investigation of the integrity of the presented model, process, and controller.

Study on an adaptive multi-model predictive controller for the thermal management of a SOFC-GT hybrid system

A SOFC temperature control system based on adaptive multimodel predictive control (MMPC) method is designed for a solid oxide fuel cell-gas turbine (SOFC-GT) hybrid system with anode and cathode ejectors. Two multi-input and multi-output MPCs (under 100% and 90% load) are designed to control the anode and cathode inlet temperatures. The accuracy of the identified linear models are both more than 95%. The control performance of the designed MMPC is compared with a single MPC and traditional PI. The comparison results demonstrate that the proposed MMPC is most effective and competitive in SOFC thermal management. During the load following, the controller overshoot is less than 1.19K. The settling time is about 2000s, and the integral of time-weighted absolute error is less than 472.

Extended Approach to Analytical Triangular Decoupling Internal Model Control of Square Stable Multivariable Systems With Delays and Right-Half-Plane Zeros

The Analytical Triangular Decoupling Internal Model Control (ATDIMC) technique for 2×2 systems is generalized to <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> × <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> systems ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> ≥2) with delays and right-half-plane (RHP) transmission zeros. The formulation is done by first creating a triangular closed-loop transfer function matrix corresponding to the achievement of the triangular decoupling objective of restraining inverse-response and control-loop-interaction characteristics to a single plant output. Subsequently, the corresponding multivariable internal model controller is calculated, with transfer-function approximations made using optimization algorithm that minimizes the Integral Time-Weighted Absolute Error (ITAE) of the difference between the step responses of the original and reduced expressions. It is shown that <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> ATDIMC designs emerge that achieve the shifting of inverse responses and interactions to a least-desired output, with delays retained for all outputs and asymptotic tracking of setpoints achieved for all <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> outputs of each design. To mitigate the possible effect of severe interaction on the least-desired output, a modification of this formulation is performed to spread inverse-response behavior to a second output, while minimizing the interaction of that output with the initial least-desired output. Simulation results for selected 3×3 and 4×4 systems show the effectiveness of these propositions.

THE WINDER DANCER POSITION CONTROL MODEL USING DIFFERENT PID CONTROL STRUCTURES AND MICROLOGIX PLC

In the cable industry, improper regulation of the winding speed of the conductor cable, i.e. the position of the tensioner (dancer) leads to improper stretching of the conductor, which significantly affects the characteristics of the final product. Winding speed control is directly related to tensioning which is an additional problem. This paper presents a system for control a cable winding device using a linear PID controller with and without control signal limitation. The system parameters were determined using integral time-weighted absolute error (ITAE) criteria and realized using a conventional PLC controller.

Study on Setpoint Tracking Performance of the PID SISO and MIMO Under Noise and Disturbance for Nonlinear Time-Delay Dynamic Systems

This paper presents a case study of the setpoint tracking performance of the proportional integral derivative (PID) controller on the Single-Input Single-Output (SISO) and Multi-Input Multi-Output (MIMO) nonlinear digital plants under Gaussian white noise and constant load disturbance for the nonlinear time-delay dynamic system. With the objective of getting a better understanding of the nonlinear discrete-time PID controller, we proposed a case study using two SISO and two MIMO digital plants, and then do the numerical simulations along with the addition of Gaussian white noise and load disturbance to simulate the real environment. In this paper, we compare the results of the system working with and without noise and load disturbance. The study result of this paper shows that on the discrete-time digital nonlinear plant, the PID controller is working well to follow the nonlinear setpoint even under heavy noise and load disturbance. The study compared the performance indexes of the controllers in terms of the maximum error, the Root mean square error (RMSE), the Integral square error (ISE), the Integral absolute error (IAE), and the Integral of time-weighted absolute error (ITAE).

A Robustness Analysis of a Fuzzy Fractional Order PID Controller Based on Genetic Algorithm for a DC-DC Boost Converter

In this paper, a new topology of a Fractional Order PID (FOPID) controller is proposed to control a boost DC-DC converter with minimum over/undershoot. The fractional controller parameters are tuned using a genetic algorithm (GA) with a combined cost function composed of the Integral of Time-Weighted Absolute Error (ITAE) and the Integral of Time-Weighted Square Error (ITSE). Despite adding moderate complexity to the control structure, the simulation results reveal that the GA-based FOPID controller tuning provided better performance for the setpoint tracking both under load variations and parameters deviation due to the prolonged use. The proposed FOPID shows a wide operational range concerning load disturbances, and capacitance/inductance deviations of ±30% and ±50% from nominal values, achieving functionality and voltage stability even with output power 50% higher than the converter power specification. The assessment was made considering operation in voltage mode and the performance was compared to conventional Proportional-Integral (PI), Type II and current mode controllers. Finally, a fuzzy fractional-order PID (FFOPID) was designed to outperform the FOPID during disturbances in the control variable.

Iterative Approach for Tuning Multiple Converter-Integrated DER in Microgrids

This paper proposes an iterative approach to adjust the control parameters of multiple power converters within a microgrid, which operates in grid-connected and grid-islanded modes. The adequate control parameters are determined using an optimisation-based strategy, local measurements, and results obtained in previous algorithm iterations. The proposed objective function is based on the integral time-weighted absolute error (ITAE), modified to improve the microgrid control performance. The proposed approach addresses the control tuning complexity by considering an incremental strategy, starting from adjusting basic microgrids, continuing to the setting of intermediate microgrids, and finalising when the target microgrid control is fine adjusted. The results obtained at the CIGRE LV benchmark microgrid validate the proposal, obtaining during faults, the maximum deviations from rated frequency around 2.2% and 0.3% in grid-islanded or grid-connected cases, respectively. Also, voltage and power references are adequately followed during steady-state regardless of the microgrid operation mode, where the steady voltage profile is below 10% variation. The obtained results demonstrate the proposed approach advantages, which straightforwardly adjust multiple converters integrated into a microgrid. The main contributions are as follows: (a) the microgrid model is not required, and (b) only measurements at the point of common coupling of the distributed energy resource are used; consequently, the proposed tuning approach is especially applicable to complex microgrids. Finally, finely adjusted microgrids are required for further operation or protection studies where complex system configurations are commonly required.

Improved PID controller design for an unstable second order plus time delay non-minimum phase systems

Principally the fundamental limitations for achieving better control performance is caused due to the existence of positive zeros. This study proposes a method to stabilize the unstable non-minimum phase Second Order Plus Time Delay (SOPTD) process. It adopts the Taylor series expansion to produce the equal order of numerator and denominator for the closed loop transfer function. The coefficient of corresponding powers of s, s2 and s3 in numerators are equated to α, β, γ times of the denominator and solved for PID controller setting using multi-objective optimization problems. The stability of the controller is then analysed by minimizing the Integral Time weighted Absolute Error (ITAE) and maximum sensitivity function using MATLAB solvers. The observations from various simulation studies clearly suggests that the proposed method provides significant superior responses when compared with the methods reported.

Comparison of sliding mode controller application for buck-boost converter based on linear sliding surface

In the utilization of photovoltaic (PV), the output voltage produced is unstable because the conditions of irradiation received by PV is not uniform. Therefore, a direct current (DC) voltage converter is needed as an output voltage regulator. In this research, buck-boost converter is proposed to regulate the desired output voltage. The proposed controller in this research is a sliding mode controller (SMC) and employ a linear sliding surface to maintain the regulated voltage stable. This research was conducted by determining the component parameters and state space model of the buck-boost converter. Proportional integral derivative (PID) controller with integral of time-weighted absolute error (ITAE) method is used as a comparison of the proposed method. The performance results were observed from the buck-boost converter by performing 3 fault scenarios, variation in supply voltage, resistor in load side, and the desired output voltage. The results obtained of SMC has a faster settling time than PID controller. The voltage deviation of buck-boost converter exhibits that SMC is smaller than the PID control. In addition, under some experiment conditions, the PID control could not or did not fit in some scenarios while the output control values of SMC matched the changes in the entire scenarios.