Steady-state Error Research Articles

Kalman filtering based on dynamic perception of measurement noise

In this work, we focus on the online state estimation problem for linear systems in non-Gaussian measurement noise. Specifically, the measurement noise is modeled as a Gaussian mixture model (GMM). Then, Kalman innovation is used to approximate the current measurement noise, and dynamically perceive its responsiveness to each sub-model of the GMM. The responsiveness from different Gaussian scales is mapped to a new cost function, while the corresponding Kalman filter algorithm is derived. The theoretical steady-state error and computational complexity analysis of the algorithm are also given. The simulation and real experimental results agree with the theoretical predictions and demonstrate the superior performance of the proposed algorithm.

A hybrid optimization algorithm for improving load frequency control in interconnected power systems

The objective of this study is to develop an algorithm named Modified Artificial Bee Colony and Particle Swarm Optimization (MHABC-PSO) to address load frequency control (LFC) challenges in a two-area interconnected power system. The proposed MHABC-PSO algorithm is designed with two key modifications to enhance global exploration capability and improve convergence speed. Hence, a decision block is introduced in the employed bee (EB) phase incorporating a control parameter “limit” to allow each candidate solution (CS) to explore itself up to the “limit” value and boost local exploration. In addition, an introduction of a novel selection mechanism utilizing heuristic information (η) in EBs phase guides the onlooker bee (OB) phase to select better solutions based on success and failure history, thus promoting exploitation and reducing biased exploration. To address the efficacy of the proposed algorithm at the system level, three different two-area power systems are studied, incorporating various complexities, linearity, and non-linearity such as thermal-hydro, reheat thermal, and thermal-hydro-gas turbine configurations with HVDC link, SSSC, and CES. The algorithm is applied to optimize four objective functions (i.e. ITAE, IAE, ISAE, and ITE). The fitness function maximizes controller gains by utilizing the integral time multiplied absolute error (ITAE). Other objective functions like IAE, ISAE, and ITE are employed for a comprehensive analysis. Evaluation of MHABC-PSO effectiveness is conducted through ITAE values, peak deviations, and settling times of frequency and power deviations in different two-area systems. Results demonstrate that MHABC-PSO settles the system more quickly with zero steady-state error under step load perturbations (SLPs) of 1% and 2%. Comparative analysis with ABC, PSO, SFLA-TLBO, and OHABC-PSO using ITAE index and controller settling times shows the superiority of MHABC-PSO for LFC analysis. In conclusion, the proposed MHABC-PSO algorithm proves to be an efficient and effective solution for LFC, outperforming other algorithms in terms of the specified objective functions and exhibiting rapid convergence and optimal gains for controllers, effectively addressing LFC issues by combining exploration and exploitation techniques.

Dynamic fuzzy temperature control with quasi-Newtonian particle swarm optimization for precise air conditioning

Precise air conditioners are renowned for their ability to deliver accurate and stable air output. However, achieving precise temperature control can be challenging due to the complexity of the air conditioner. To address this issue, a dynamic fuzzy control method based on quasi-Newton particle swarm optimization (QNPSO) is put forward for precise air conditioning. The air conditioning dynamics is first modelled using the interconnection of the first-order delayed transfer functions. Incremental fuzzy controllers are then employed to track temperature changes and prevent steady-state errors for all internal components of the conditioner. By employing QNPSO to optimize all control parameters simultaneously, the present method effectively addresses the limitations of particle swarm optimization in poor local search capability, and the sensitivity of the quasi-Newton algorithm to initial values. Additionally, a dynamic adjustment optimization strategy is suggested to accommodate start-up dynamics and meet temperature change requirements. In this way, the precise air conditioning is achieved by regulating internal components in an integrated fashion. The superior performance of the proposed method is validated through model simulation evaluations and prototype conditioner experiments using a water-cooled precise air conditioner. The results demonstrate that the proposed method achieves faster stabilization time and higher control accuracy compared to the state-of-the-art peers.

Temperature Control of Cement Rotary Kiln Sintering Zone Based on FCS-MPC with Soft Constraint of Generalized Triangular Interval

In the new, dry-process method of cement production, the temperature of cement rotary kiln sintering zone is a key factor in ensuring the quality of cement clinker. Based on the auto-regressive with extra inputs model, a finite control set model predictive control with soft constraint of the generalized triangular interval is proposed in this paper for the characteristics of a cement rotary kiln calcination system with multi-variable, multi-time delay, bounded disturbance, and slow dynamic process. Simulation experiments show that the steady-state error of the control algorithm proposed in this paper is smaller with better anti-disturbance performance than that of the traditional reference-trajectory-constrained, predictive control algorithm.

Intelligent control based on single-input interval type-2 fuzzy iPI and super twisting nonlinear sliding mode compensator for regulating PEMFC output voltage

The control of Proton Exchange Membrane Fuel Cell (PEMFC) is exceptionally challenging due to its complex nonlinearity, slow dynamics and load disturbance. In this paper, an Adaptive Model Free Control (AMFC) approach is introduced for regulating the PEMFC output voltage under load perturbation and measurement noise conditions. The proposed method consists of four sub-elements. Firstly, an Extended State Observer (ESO) based on a Single-Input Interval Type-2 Fuzzy intelligent PI (SI-IT-2-FLC-iPI) scheme is designed to enhance the performance of PEMFC. Secondly, a Nonlinear Sliding Mode Control-based Super Twisting Algorithm (NSMC-STA) is used as an auxiliary control approach to reduce the estimation error and ameliorate the system robustness. Thirdly, a Forgotten Recursive Least Square Error (FRLSE) is applied for adjusting the physical parameter of MFC and further ameliorating the control response. Finally, all these elements are merged together within what it is called Ultra Local Model (ULM).Through extensive simulation, the efficacy of the proposed regulator in accurately tracking the output signal is showcased, outperforming conventional controllers with remarkable improvements. The system achieves 0.001 steady-state error, 0% overshoot and settling time of approximately 8.9 s, which is good enough in the context of standalone fuel cell applications.

Application of pseudo-parameter iteration method to nonlinear deflection analysis of an infinite beam with variable beam cross-sections on a nonlinear elastic foundation

In this study, the nonlinear deflection of an infinite beam with variable beam cross-sections on a nonlinear elastic foundation was analyzed using the pseudo-parameter iteration method (PIM), which is a novel iterative semi-analytic method for solving ordinary/partial differential equations. To do this, we set six types of infinite beams with concave and convex shapes under static loading conditions. To calculate the nonlinear deflection of the infinite beam with variable cross-sections, the Bernoulli-Euler beam equation (fourth-order ordinary differential equation) considering changing beam flexural rigidity was introduced, and the PIM was adopted to this equation. Through the numerical experiment, it was confirmed that the nonlinear deflections calculated via the PIM are quite close to the exact solution within a few iterations. In addition, the graph of error quickly reaches the steady state error for all cases as the number of iterations increases.

Phase Error Criterion Based Adaptive Algorithm for Frequency Estimation

A simple phase error criterion (PEC-)-based adaptive algorithm for estimating the frequency of a complex sinusoidal signal in additive white Gaussian and impulsive noises is proposed. The proposed technique makes use of the instantaneous phase response of a first-order complex linear predictor (CLP) as a driving function to update the frequency parameter of the CLP. The proposed PEC is attractive due to its simplicity and high impulsive noise robustness. Theoretical analysis for the mean value of the estimated frequency and the steady-state mean square error (MSE) of the frequency estimate are derived in closed forms. Computer simulations are drawn to show the performance of the proposed frequency estimator.

Combining hybrid metaheuristic algorithms and reinforcement learning to improve the optimal control of nonlinear continuous-time systems with input constraints

This paper proposes an innovative method for achieving optimal tracking control in nonlinear continuous-time systems with input constraints. The method combines reinforcement learning and hybrid metaheuristics to enhance the controller’s performance. Specifically, a hybrid metaheuristic algorithm is employed to optimize the hyperparameters of a critic neural network, which serves as the system’s controller. The proposed approach is evaluated through extensive simulation studies on a nonlinear system with input constraints. Results demonstrate its superiority over traditional control techniques in terms of accuracy, timeliness, and stability. Notably, the approach effectively eliminates overshoot and steady-state error while providing precise and prompt tracking and showcasing remarkable robustness against model uncertainties. By synergistically integrating reinforcement learning and hybrid metaheuristics, this approach represents a significant advancement in enhancing the control performance of complex nonlinear systems. The simulation studies confirm superiority of the proposed approach over existing techniques, offering a promising solution for achieving optimal tracking control in nonlinear systems with input constraints. This approach holds potential for a wide range of applications, including robotics, aerospace, and manufacturing, where precise and prompt tracking control is critical.

Development of a neural network model predictive controller for the fluidized bed biomass gasification process

In this study, an advanced controller for the fluidized bed biomass gasification (FBG) process is proposed. The controller is based on the model predictive control method, utilizing a long short-term memory neural network to accurately predict the controlled variable in the FBG process. Then, employing a gradient-based optimization algorithm, it optimizes the inputs to achieve the desired control objective. The controller specifically aims for temperature regulation in three spatial regions (fluidized bed, freeboard and outlet), using primary air, secondary air, and biomass flow rates as input variables. Open-loop simulations are used to fine-tune the controller's parameters (prediction and control horizon). For unbiased controller testing, a computational fluid dynamics (CFD) model of the FBG process is also developed, which is integrated with the controller in a closed-loop system, simulating real-process feedback for performance evaluation. The proposed controller effectively maintains temperatures (steady state error < 1.5 %) at desired set points (800–900 °C) with a short prediction horizon of 24 time steps, reducing response time to under 5 s, making it suitable for real-time FBG process control.

Control strategies for inverted pendulum: A comparative analysis of linear, nonlinear, and artificial intelligence approaches.

An inverted pendulum is a challenging underactuated system characterized by nonlinear behavior. Defining an effective control strategy for such a system is challenging. This paper presents an overview of the IP control system augmented by a comparative analysis of multiple control strategies. Linear techniques such as linear quadratic regulators (LQR) and progressing to nonlinear methods such as Sliding Mode Control (SMC) and back-stepping (BS), as well as artificial intelligence (AI) methods such as Fuzzy Logic Controllers (FLC) and SMC based Neural Networks (SMCNN). These strategies are studied and analyzed based on multiple parameters. Nonlinear techniques and AI-based approaches play key roles in mitigating IP nonlinearity and stabilizing its unbalanced form. The aforementioned algorithms are simulated and compared by conducting a comprehensive literature study. The results demonstrate that the SMCNN controller outperforms the LQR, SMC, FLC, and BS in terms of settling time, overshoot, and steady-state error. Furthermore, SMCNN exhibit superior performance for IP systems, albeit with a complexity trade-off compared to other techniques. This comparative analysis sheds light on the complexity involved in controlling the IP while also providing insights into the optimal performance achieved by the SMCNN controller and the potential of neural network for inverted pendulum stabilization.

Field-Weakening Strategy with Modulated Predictive Current Control Applied to Six-Phase Induction Machines

The predictive current controller has arisen as a practicable technique for operating multiphase machines due to its fast dynamic response, control flexibility, and overall good performance. However, this type of controller has limitations, e.g., it tends to suffer from steady-state tracking errors in (d−q) currents; high computational burden; and high (x−y) currents, which become more pronounced at higher speeds, thereby worsening its sustainability. While some proposals have addressed these limitations by incorporating modulation stages and new cost functions, there is still room for improvement, particularly at higher speeds. In line with the pursuit of sustainable advancements, this article explores the integration of a field-weakening strategy with a modulated predictive current controller applied to a six-phase induction machine to improve its performance at current tracking for higher speed ranges. Experimental tests were conducted to validate the effectiveness of the proposed controller, assessing stator current tracking, reduction in the (x−y) currents, and the total harmonic distortion.

Development of AVR controller performance using exponential distribution and transit search optimization techniques

This paper attempts to obtain the optimal solution to enhance the performance of the Automatic Voltage Regulator (AVR) Controller, as it is an essential tool to control the synchronous generator output voltage. The controller improves AVR system stability and response time; moreover, it is demonstrated that the Proportional Integral Derivative (PID) controller achieves the goal by applying two artificial intelligence techniques to design the optimal values of the Automatic Voltage Regulator (AVR) PID controller for a single area model. The first is the Exponential Distribution Optimization Algorithm (EDO), and the second is the Transit Search Optimization Algorithm (TS). EDO and TS are used to determine the best PID controller parameters and have also recently been developed in the breadth of optimization problems and associated computational complexities field. The objective function, Integrated Square Error (ISE), minimizes the error voltage for improved stability and response. The outcomes are compared to various optimization techniques to prove the validation of the two proposed methods. The results show that the EDO and TS proved their superiority through their stability level to the AVR system and their steady-state error improvement. Moreover, the dominant effect of damping frequency decreases the oscillation and the reduced maximum overshoot that protects the loads from being subjected to non-permissible over-voltage levels. Finally, a robustness test is applied to the two proposed optimization methods to prove their reliability and effectiveness.

A variable diagonal-matrix-step-size APA robust to impulsive noises

This study introduces a variable diagonal-matrix-step-size affine projection algorithm (APA), which shows robustness against to impulsive noises. Unlike the normal scalar step-size method, the independent step size for each input vector is used as the entry of the diagonal matrix, and the optimal step size at each time step is ascertained by conducting mean-square-deviation (MSD) analysis. In addition, a recursive equation of weight update has been derived without approximating posteriori error as priori error. Using the Lagrange multiplier method, we formulate a scalar step size affine projection algorithm that shows resilience to impulsive noises. This algorithm emerges as a solution to a constrained optimization problem. To further enhance convergence performance, a diagonal-matrix-step size is introduced and its MSD is analyzed. The step size at each time step is optimized by interpreting the MSD mathematically, resulting in the variable diagonal-matrix-step size APA (VDMSS-APA). Various simulations exhibit low steady-state error and fast convergence rate of the proposed algorithm.

Experimental and Simulative Evaluation of a Reinforcement Learning Based Cold Gas Thrust Chamber Pressure Controller

At DLR neural networks, as potential future controller for rocket engines, are studied. A neural network-based chamber pressure controller for a simplified cold gas thruster is presented and analyzed in simulation and experiment. The goal of the controller is twofold: It can track a trajectory with different changes of setpoints and it allows to set and control a wide variety of steady state chamber pressures. The neural network gets feeding line pressure measurement data as input and calculates valve positions as output values. The training phase of the controller is done with a reinforcement learning algorithm in an EcosimPro/ESPSS simulation, that is validated with data from the corresponding experimental set up. To increase the robustness and to allow a transfer from the simulation directly to the test facility domain randomization is applied. The controller is evaluated in simulations and experiment. It was found that – in the range of physically possible operation points – the controller achieves a constantly high reward which corresponds to a low error and a good control performance. In the simulation the controller was able to adjust all required set points with a steady state error of less than 0.1bar while retaining a small overshoot and an optimal settling time. It is found that the controller is also able to regulate all desired set points in the real experiment. A reference trajectory with different steps, linear and sinus changes in target pressure is tested in simulation and experiment. The controller was in both cases able to successfully follow the given trajectory.

Improving Steady State Accuracy in Field-Weakened Six-Phase Induction Machines with Integrator and Modulated Predictive Control

Finite-control-set model predictive control techniques are considered an exciting option for high-performance control multiphase drives due to their fast dynamic response, ability to handle multiple targets and constraints, and adaptability to different power converters or machine models. However, these techniques have some drawbacks, such as poor current reduction (x−y) and steady-state error (d−q), especially in the field weakening zone. Although some proposals have addressed these issues by adding modulation stages or designing new cost functions, there is still room for improvement, especially in steady-state error reduction. Therefore, this article proposes to include an integrator attached to a modulated predictive current controller applied to a six-phase induction machine to improve its performance throughout the entire speed range regarding steady-state error mitigation. Experimental tests were carried out to validate the effectiveness of the proposed controller. Tests were carried out evaluating the reduction of the steady-state error (d−q), the current tracking, the (x−y) currents reduction and the total harmonic distortion.

Design and implementation of facility intelligent carbon dioxide incubator control system based on POA optimized fuzzy PID

To solve the problem that traditional carbon dioxide incubators are difficult to accurately control the required carbon dioxide environment to the detriment of experimental cultivation, and given the difficulties of time lag, nonlinearity, time-varying, and poor adaptive ability of the incubator control system, this study designs a set of intelligent carbon dioxide incubator control system suitable for laboratory cultivation. The system is based on the POA (Pelican optimization algorithm) to optimize the fuzzy PID (Proportional Integral Derivative) control to regulate the opening degree of the solenoid valve to accurately control the carbon dioxide concentration in the incubator to the set range. In this study, the simulation and comparison tests of POA-based optimized fuzzy PID control, PID control, and fuzzy PID control are carried out by MATLAB/Simulink, and it is found that the overshooting amount of the system is reduced by 11.6%, the regulating time is shortened by 69.3 s, and the steady state error is reduced by 0.1% compared with that of the traditional fuzzy PID control. It can be obtained through practical tests that the accuracy, response, and stability of the optimized fuzzy PID control of the pelican algorithm are better than those of the fuzzy PID control method, and it has better robustness. Therefore, the carbon dioxide incubator control system has high practical application value.

Optimization of RST Controller for Speed Control of Linear Induction Motor Using Genetic Algorithm

Background: In this study, a new model of linear induction motor, along with the impact of end-effect on motor performance, is proposed. Moreover, a new strategy of control approach based on the polynomial RST controller is suggested and investigated. Objective: The proposed approach can provide a robust control strategy and overcome the limitations imposed by the proportional-integral (PI) regulator in the FOC technique. RST controller has a two-degree of freedom structure and consists of three polynomials, namely R, S and T, which are determined by the pole placement method and resolving of a Diophantine equation. Despite this, the implementation of this method is usually difficult and becomes more complicated with the complexity of the controlled plants. Methods: This study proposes the genetic algorithm (GA) optimization strategy for tuning RST controller parameters (adjust the controller coefficients) in order to achieve an adequate response time by minimizing the different objective functions, such as steady-state error, settling time, and rise time. Results: The accuracy and control performance of the proposed technique are checked and validated using Matlab /Simulink environment software tool. Simulation results reported that the proposed method (RST-GA) could provide robust solutions with perfect reference tracking and efficient disturbance rejection. Conclusion: These significant results make the proposed approach a promising technique for the design of a high-performance controller, which is highly suitable for industrial and electrical applications.

Grey Wolf Optimization Algorithm for Embedded Adaptive Filtering Applications

Nowadays, meta-heuristic algorithms have been emerged as a potential solution in adaptive filtering applications since they offer good convergence properties. Nonetheless, most of them fall into local minimum since their optimization is based on single-solution technique. As a consequence, these algorithms present a high misadjustment level and require a large population to find the optimal solution. Recently, the grey wolf optimization (GWO) algorithm have emerged as a potential solution since it requires a smaller population and possesses a stronger global optimization ability with lesser control parameters. From an engineering perspective, its compactness is an attractive feature. Therefore, this opens new horizons in the implementation of this algorithm in resource-constrained devices. In this paper, we present for the first time the use of the GWO algorithm for system identification and acoustic echo canceller (AEC) and its implementation in a field programmable gate array (FPGA) device to validate its effectiveness. Our results show that the use of the GWO algorithm achieves lower steady-state mean square error (MSE) and requires less computational resources when compared with one of the most used meta-heuristic algorithm.

Improved ADRC With a Cascade Extended State Observer Based on Quasi-Generalized Integrator for PMSM Current Disturbances Attenuation

Traditional active disturbance rejection control (ADRC) is not adequately capable to deal with current disturbances including periodic harmonics of permanent magnet synchronous motor (PMSM). Thus, an improved ADRC with a cascade extended state observer (CESO) based on quasi-generalized integrator (QGI) is proposed to attenuate the periodic and aperiodic disturbances in the current loop. In the proposed strategy, a CESO with two cascaded levels is designed to enhance the estimation accuracy of aperiodic disturbances and decrease the steady-state observation error of periodic harmonics. The QGI is embedded into the second cascade level of CESO to improve its estimation accuracy harmonic disturbances. With the periodic harmonics accurately estimated, the subsequent improved ADRC based on feedback control law can effectively enhance the rejection of such disturbances. The theoretical analysis is comprehensively conducted to investigate the disturbances estimation performance, stability, disturbances rejection capability and robustness, while the parameter tuning strategy is studied based on the control bandwidth. Finally, the effectiveness and superiority of the proposed scheme are verified on a PMSM bench through the experiments.

Predictive controllers for synchronous reluctance motor drive systems

This paper proposes the design and implementation of predictive controllers for synchronous reluctance motor drive systems to enhance their dynamic responses. The predictive speed and current controllers in this paper are designed in systematic procedures. The predictive speed controller is implemented by using Laguerre function procedure. The Laguerre function is used to simplify the algorithm and to minimize the execution time of the digital signal processor. For predictive current controller, a finite control set method improves the current tracking ability. The measured currents are used to predict the future phase-current based on the motor model. The optimal control inputs of both predictive controllers are determined by using a cost function minimization method. Experimental results show the proposed drive system provides a wide adjustable speed range, from 2 r/min to 1800 r/min. It has better performance than a proportional-integral (PI) controller including fast rise time, which is 0.9 second, small steady state error, which is 0.32 r/min, and small current ripples. A 32-bit floating-point digital signal processor, TMS-320-F-28335 DSP, is employed to implement the control algorithms.