Steady-state Error Research Articles

Vision-based finite-time prescribed performance control for uncooperative UAV target-tracking subject to field of view constraints

This paper presents a vision-based finite-time prescribed performance controller for unmanned aerial vehicle (UAV) tracking of uncooperative aerial targets. The relative states between UAV and target are estimated by an onboard monocular camera. The inability of visual measurements to accurately determine the initial state of the target renders conventional prescribed performance controllers ineffective in such situations. As a result, it becomes essential to address the problem of prescribed performance control under conditions of uncertain initial values By utilizing an auxiliary transforming function, an Asymmetric Barrier Lyapunov Function (ABLF) and a finite-time prescribed performance function, a robust adaptive controller based on backstepping framework is proposed to deal with state constraints under unknown initial tracking conditions. It is proved that, the closed-loop relative position is capable of reaching the prescribed performance bound before the preset transforming time and converging to the prescribed steady-state error before a finite setting time. Simulation examples are provided to illustrated the effectiveness of the proposed tracking algorithm.

A Novel Assimilate Power Flow Control Technique Based Multiport Converter For Hybrid Power Generation System With Grid-Connected Application

Clean, sufficient energy from renewable resources such as the Sun, Wind, and other natural resources is provided via renewable energy technology. Electricity failure also increases with the electricity demand. Thus, consistent loads may be provided by renewable energy sources. A multiport conversion architecture has been developed for hybrid energy sources such as wind and solar sources. A practical method of producing power is to combine wind and sun resources. This study presents a coordinated control method and dynamic modelling tools for an integrated microgrid scheme that combines fuel cell technology, backup diesel generation, photovoltaic systems, battery generators, and assimilated power flow control (APFC). A unique vibrant filter compensator based on dynamics is employed to achieve a fully balanced integrated system. This ensures minimal inrush current, load excursions, and regulated DC bus voltage while optimizing the utilization of the diesel generator set. Our primary area is to achieve the most efficient operation of the integrated renewable energy sources, including PV panels and fuel cells. Photovoltaic Power System with Backup Fuel Cell Source for Hybrid Power System: The control unit in this hybrid system manages the power from both the fuel and the PV cells. When the control power is activated, it triggers the fuel cell and photovoltaic cell powers. The control device first checks if the photovoltaic cell is generating power. If the PV energy is sufficient to meet the load requirements, the control power links the photovoltaic energy to the load. In cases where the load cannot be fulfilled by photovoltaic power alone, the control system disconnects the photovoltaic cell power and switches to the backup fuel cell power. Afterwards, when the power generated from the photovoltaic cells reaches a sufficient level, the control system promptly switches from the fuel cell to the photovoltaic cells. The fuel cell is integrated with a photovoltaic system and a DC-DC boost conversion in conjunction with the resistive workload. The controller outputs have been fine-tuned, and PWM is generated and subsequently supplied to the converter's switching. The converter's design considers conversion efficiency, power sharing, system stability, and responsiveness in various operational scenarios to ensure successful operation. The effectiveness of the simulated output APFC techniques is evaluated for each parameter, such as steady-state error, THD, and the system's efficiency.

Optimizing power sharing and voltage control in DC microgrids using a novel adaptive droop control strategy based on current consensus algorithm

In DC microgrids, a contradiction between power equalization and bus voltage control exists under conventional droop control. To address this issue, this study proposes a current consensus algorithm-based adaptive droop control for hierarchical controlled DC microgrids. The strategy includes primary, secondary, and current-consensus algorithms. In the primary and secondary control layers, an improved droop control strategy is realized, where the secondary layer provides adaptive parameters for primary control. Also, a current consensus algorithm is suggested to ensure equal current sharing, where the iterative calculation results are sent as the input for two control layers. Based on the novel strategy, a small signal analysis is carried out to investigate the relationship between system stability and controller parameters. Finally, simulation and experiments are conducted to assess the effectiveness of the proposed control strategy in complex operating conditions such as resistive load step-change and plug-and-play situation. Experiment and simulation results indicate that the novel control strategy guarantees accurate bus voltage control with a maximum steady-state error of 1.58 % and simultaneously achieves power equalization regardless of line impedance differences and the abrupt change of system status. Moreover, the comparative experiment between the traditional droop control and the proposed strategy verifies the superiority of this novel method.

Current Controller Design of Grid-Connected Inverter with Incomplete Observation Considering L-/LC-Type Grid Impedance

This paper presents a current control design for stabilizing an inductive-capacitive-inductive (LCL)-filtered grid-connected inverter (GCI) system under uncertain grid impedance and distorted grid environment. To deal with the negative impact of grid impedance, LC-type grid impedance is considered in both the system model derivation and controller design process of an LCL-filtered GCI system. In addition, the integral and resonant control terms are also augmented into the system model in the synchronous reference frame to guarantee the reference tracking of zero steady-state error and good harmonic disturbance compensation of the grid-injected currents from GCI. By considering the effect of grid impedance on the control design process, an incomplete state feedback controller will be designed based on the linear-quadratic regulator (LQR) without damaging the asymptotic stabilization and robustness of the GCI system under uncertain grid impedance. By means of the closed-loop pole map evaluation, the asymptotic stability, robustness, and resonance-damping capability of the proposed current control scheme are confirmed even when all the system states are not available. In order to reduce the number of required sensors for the realization of the controller, a discrete-time current-type full-state observer is employed in this paper to estimate the system state variables with high precision. The feasibility and effectiveness of the proposed control scheme are demonstrated by the PSIM simulations and experiments by using a three-phase GCI prototype system under adverse grid conditions. The comprehensive evaluation results show that the designed control scheme maintains the stability and robustness of the LCL-filtered GCI when connecting to unexpected grids, such as harmonic distortion and L-type and LC-type grid impedances. As a result, the proposed control scheme successfully stabilizes the entire GCI system with high-quality grid-injected currents even when the GCI faces severe grid distortions and an extra grid dynamic caused by the L-type or LC-type grid impedance. Furthermore, low-order distortion harmonics come from the background grid voltages and are maintained as acceptable limits according to the IEEE Std. 1547-2003. Comparative test result with the conventional one also confirms the effectiveness of the proposed control scheme under LC-type grid impedance thanks to the consideration of LC grid impedance in the design process.

Prescribed performance under input saturation for uncertain strict-feedback systems: A switching control approach

We consider the problem of achieving prescribed performance metrics on the output tracking error, for uncertain strict-feedback systems, while satisfying inelastic control input constraints in the form of magnitude saturation. Inspired by the prescribed performance control (PPC) methodology, we propose a switching control strategy comprised of two operational units: a traditional PPC and a Safety Controller. The former enforces the output error to evolve strictly inside a user-defined performance envelope that incorporates all the desired performance characteristics. However, in the presence of input saturation this envelope can be easily violated, leading to PPC instability. On the other hand, the Safety Controller enables the safe escaping, thus avoiding the appearance of this internal instability phenomenon. We prove that the closed-loop system solution is complete and non-zeno. Furthermore, we show that the tracking error evolves inside a modified performance envelope, guaranteeing a prescribed minimum convergence rate and a controlled maximum steady-state error. Simulation studies clarify and verify the theoretical findings.

Research on an Intelligent Vehicle Trajectory Tracking Method Based on Optimal Control Theory

This study aims to explore an intelligent vehicle trajectory tracking control method based on optimal control theory. Considering the limitations of existing control strategies in dealing with signal delays and communication lags, a control strategy combining an anthropomorphic forward-looking reference path and longitudinal velocity closure is proposed to improve the accuracy and stability of intelligent vehicle trajectory tracking. Firstly, according to the vehicle dynamic error tracking model, a linear quadratic regulator (LQR) transverse controller is designed based on the optimal control principle, and a feedforward control strategy is added to reduce the system steady-state error. Secondly, an anthropomorphic look-ahead prediction model is established to mimic human driving behavior to compensate for the signal lag. The double proportional–integral–derivative (DPID) control algorithm is used to track the longitudinal speed reference value. Finally, a joint simulation is conducted based on MatLab/Simulink2021b and CarSim2019.0 software, and the effectiveness of the control strategy proposed in this paper is verified by constructing a semi-physical experimental platform and carrying out a hardware-in-the-loop test. The simulation and test results show that the control strategy can significantly improve the accuracy and stability of vehicle path tracking, which provides a new idea for future intelligent vehicle control system design.

Enhancing pressure control of low-friction pneumatic actuator with eddy current damper via valve dead-zone compensation

This article addresses the high-performance pressure control of a pneumatic actuator that incorporates an air-bearing piston and an eddy current damper (ECD). After optimizing the pneumatic actuator, achieving precise pressure control relies on maintaining an accurate and stable airflow through the control valve. A terminal sliding mode adaptive control method (TSMAC) is proposed, proficiently integrating considerations for dead zone nonlinearities in the proportional valve and the effects of unmodeled disturbances in the pneumatic actuator. Using the opening area of the proportional valve as the input to the pneumatic system greatly simplifies the control process and reduces the workload required for valve parameter calibration. The Lyapunov-based stability analysis demonstrates that excellent asymptotic output tracking can be achieved with low steady-state error simply by knowing the boundaries of the valve opening area. The control effect of the proposed control strategy is compared with an adaptive backstepping sliding mode control method based on a linearly fitted proportional valve model on an established constant pressure control test bench. Experimental results under various loads and operating conditions illustrate the effectiveness of the proposed approach.

Surge-Elimination Strategy for Aero-Engine Transient Control

Abstract The fundamental principle of the transient state control method for turbofan engines, which is based on the acceleration ratio of high-pressure rotational speed (N-dot), involves sacrificing a portion of the safety margin to obtain satisfactory acceleration performance. However, it could induce surge in the engine's compressor. To prevent the destructive damage caused by surge to both the engine and its components, a surge-elimination control strategy for the engine based on an N-dot controller is proposed. First, the engine mathematical model, which incorporates the effects of engine volumetric dynamics, stall zone characteristics, and combustion chamber flameout characteristics, is established to simulate surge mechanism. Subsequently, the acceleration schedule of the N-dot is calculated by employing sequential quadratic programming (SQP) algorithm to solve the multiconstraint optimization problem, while designing the transition state controller of N-dot based on a high-order filter. Finally, the surge detection logic and surge-elimination strategy based on the μ-correction method are proposed and designed to realize active control of surge elimination. The simulation results demonstrate that the N-dot control method offers significant advantages in mitigating the steady-state errors resulting from inevitable engine degradations. The surge state is effectively suppressed by the proposed surge-elimination control method, and the surge duration is significantly shorten during the acceleration phases. Furthermore, compared to the one without any surge-elimination control, the proposed method decreases the acceleration time by 5.53%.

Pyrolysis process control: temperature control design and application for optimum process operation

Fast pyrolysis in auger reactor gains attention for efficient bio-oil production. Due to the quick nature of the process, precise temperature control using the proportional-integral-derivative (PID) algorithm is paramount. This study harnesses various PID tuning approaches through modelling and experimental validation to optimize continuous and precise pyrolysis temperature. System identification was done to investigate the process dynamic with fit accuracy above 93% and design a suitable PID control. Comparison with the experiment data shows a favorable result with rise time and settling time match above 75%. Ziegler-Nichols (ZN) and Cohen-Coon (CC) tuning methods were implemented in the system with undistinguished results, yielding steady-state error (SSE) below 1% and settling time around 4,300 to 4,800 seconds. The heuristic fine-tuning method improved the rise time and settling time by stabilizing before 3,600 seconds. Furthermore, the robustness of PID controllers was verified with a disturbance rejection test, keeping the SSE deviation inside the boundary of 2%. Finally, the setup could support maximum pyrolytic oil production by 69.6% at 500 °C. The result implies that the PID controller could provide a stable and rugged response to support a productive and sustainable pyrolysis plant operation.

Multiple Discrete Adaptive Filter Based Position Error Reduction for Sensorless IPMSM Drives

The inverter nonlinearity and the flux spatial harmonics will lead to noticeable (6κ±1) harmonics in the observed back electromotive force (EMF), causing (6κ) pulsations in the rotor position estimation error and deteriorating the performance of sensorless interior permanent magnet synchronous motor (IPMSM) drives. To improve the sensorless IPMSM control accuracy, a multiple discrete adaptive filter (MDAF) embedded between sliding mode observer (SMO) and normalized quadrature phase-locked loop (PLL) is adopted to solve the above problem in this paper. The MDAF consists of a fundamental extraction block and a harmonic cancellation block. Harmonic cancellation works similarly to fundamental extraction, simply by removing the dominant 5th and 7th harmonics from the distorted back-EMF in a frequency multiplicative manner. The proposed algorithm is designed directly in the discrete domain, avoiding the complex discretization process. The open-loop amplitude-frequency characteristic curves show that the method is able to achieve infinite gain exactly at the expected frequency, thus allowing closed-loop zero steady-state error tracking of the back-EMF and providing higher precision for harmonic estimation. The excellent performance of the suggested method is validated based on a 1.5kW sensorless IPMSM control system.

Improved Adaptive CCS-MPCC for Distorted Model Parameters Mitigation of IPMSM Drives

In this study, a robust adaptive model continuous-control-set model predictive current control (CCS-MPCC) method is proposed for interior permanent magnet synchronous motors (IPMSMs) considering the existing disturbances, unmodeled dynamics, and parameter variations. The novel aspect of this research is that it merges the improved dynamic, useful properties of model predictive control (MPC), which includes easy implementation and fast dynamic response, together with the most effective criterion of an adaptive controller (i.e., robustness to model uncertainties), that result in enhanced dynamic and steady-state control performance despite unknown and changing disturbances. Unlike the conventional CCS-MPCC approach that heavily depends on the accurate knowledge of the system model to attain improved control performance, the proposed method achieves satisfactory control performance (e.g., fast dynamic response, smaller steady-state error, and low stator current THD) by stabilizing the state errors to approach zero and compensating for variations in the model parameters using the designed feedback control terms and adaptive control terms, respectively. The stability of the proposed control method is ensured by the state errors asymptotically decaying to zero. The proposed approach was simulated and then implemented on a PSIM simulation tool and a prototype IPMSM test bench using TI TMS320F28335 DSP, respectively, to confirm its feasibility.

An Analysis of Sliding Mode Speed Controller for a Differential Drive Wheel Mobile Robot

In this study, we present a systematically designed Sliding Mode Speed Controller (SMSC) tailored for motors utilized in a Differential Drive Wheel Mobile Robot (DDWMR). Our analysis delves into the critical parameters of the SMSC, including convergence and reaching rates, alongside simulation configurations such as time step. We concurrently consider metrics like rising time, steady-state error, and control ripple factors to optimize performance. Through comprehensive evaluation across various case studies, we demonstrate the efficacy of the fine-tuned SMSC in enhancing the overall performance of the DDWMR. Our simulation results underscore the significance of meticulous parameter tuning, particularly emphasizing the role of time step settings. We find that a smaller time step mitigates chattering phenomena and improves performance, albeit at the cost of increased computational demands and potentially heightened hardware requirements.

Adaptive backstepping control for uncertain semiconductor refrigeration systems considering even-order input

Temperature control technique has received much attention in the field of semiconductor thermal management. This paper presents a novel adaptive backstepping-based temperature control strategy for semiconductor refrigeration systems considering unmodeled dynamics. The inherent non-affine problem caused by the even-order input signal is solved by combining a novel smooth function into the command filtered backstepping method. And then, the adaptive observer is also employed to improve the system performance under unmodeled dynamic deviations. The stability of the closed-loop system is analyzed based on the Lyapunov theory, and simulation experiments are given to verify our control method. The simulation results show that the method can realize the accurate control of temperature under unmodeled dynamics. Under the disturbance of ambient temperature changes and model errors, the steady state error of the system remains below 0.1 °C. In comparison with the traditional control methods, our strategy has a stronger ability to suppress the uncertainty effects.

Reliability evaluation method for PID feedback control system considering performance degradation

The reliability of proportional-integration-derivative (PID) feedback control systems is crucial for products due to their critical functions. Traditional reliability evaluation methods of PID feedback control systems usually pose difficulties in comprehensively considering the performance compensation property of feedback mechanisms and the degradation phenomenon in operating processes. This paper proposes a new reliability evaluation method for the PID control system under the framework of belief reliability theory to consider both deterministic and uncertain laws regarding functional logics and degradation effects. For deterministic laws, the interdisciplinary, degradation, and margin equations are established with respect to the steady state error. Various internal and external influencing factors are integrated into these equations by modeling state space and characterizing degradation mechanisms. For uncertain laws, the metric equation is constructed accordingly considering diverse uncertain factors. A Monte Carlo-based algorithm and an analysis framework are further developed to calculate the belief reliability. Finally, the proposed method is implemented to an aero-power hydraulic servo control system as a specific illustration, demonstrating its effectiveness and rationality.

SPEED CONTROL OF PERMANENT MAGNET SYNCHRONOUS MOTOR IN SLIDING MODE

The paper examines a series of speed control algorithms for a synchronous permanent magnet motor in sliding mode, providing asymptotic stability of the first, second, and third order. In the sliding mode, the control system exhibits properties that are unattainable with classical continuous control algorithms. The control algorithms are developed based on the inverse dynamics method combined with the minimization of local instantaneous energy functionals. The key idea of the method lies in the reversibility of the direct Lyapunov method for stability analysis. The closed-loop control system has a predefined Lyapunov function, represented by the instantaneous energy. Notably, the control algorithms do not require knowledge of the object's parameters or differentiation operations, which facilitates their practical implementation. The regulator parameters consist solely of coefficients used to specify the desired duration and shape of current and motor speed transient processes. The vector speed control system comprises two controllers for the stator current components and the motor speed controller. All regulators operate in sliding mode. The output signals of the stator current component controllers and speed vary discontinuously from maximum to minimum values. Simulation results demonstrate the effectiveness and high-quality performance of the control algorithms. To determine the control performance indicators for the three synthesized speed controllers, the motor startup trajectory is formed from characteristic segments of constant, linearly increasing, and parabolic signals. The speed control algorithm with a first-order asymptote ensures zero tracking error only for a constant reference signal. With a linearly increasing reference signal, the steady-state relative tracking error is 2,5 %, while for a parabolic reference signal, the error varies between zero and 2,5 %. The second-order asymptotic speed control algorithm ensures zero steady-state tracking error for constant and linearly increasing reference signals, and for a parabolic reference signal, the steady-state relative tracking error is 0,125 %. The third-order asymptotic speed control algorithm ensures zero steady-state tracking error for constant, linearly increasing, and parabolic reference signals, with a maximum dynamic relative tracking error of 0,05 %.

Using Fractional-order Technique and Non-linear Surface to Improve the Performance of the Backstepping Control of Multi-rotor Wind Power Systems

In this study, an effective solution is given to overcome the drawbacks of backstepping command (BC) for a doubly-fed induction generator based on multi-rotor wind power system, where both fractional calculus and non-linear surface were used for this purpose. This suggested approach differs from the classical BC method and demonstrates strong efficacy, displaying resilience against both external and internal factors of the system. This command was suggested to command the machine-side inverter to increase power quality and reduce steady-state error (SSE). Therefore, the characteristics of this suggested BC were verified compared with the conventional BC method using MATLAB in different operating situations. This proposed strategy demonstrates a distinctive performance in improving system characteristics, as evidenced by the reduction rates compared to the BC technique. Active power undulations were minimized by 47.36% in the first test and 41.74% in the second test compared to BC. Also, The SSE value of reactive power was minimized by approximately 41.66% and 45.83% in both tests compared to the BC strategy. Moreover, the value of harmonic distortion improved significantly compared to the BC, with high ratios estimated at 68.57% and 55.30% in the same testes. These ratios indicate that the current quality is high when the suggested command is used. This indicates that in the future, this control method is poised to become one of the leading solutions trusted in the field of control.

Adaptive fuzzy control for tendon-sheath actuated bending-tip system with unknown friction for robotic flexible endoscope.

The tendon-sheath actuated bending-tip system (TAB) has been widely applied to long-distance transmission scenes due to its high maneuverability, safety, and compliance, such as in exoskeleton robots, rescue robots, and surgical robots design. Due to the suitability of operation in a narrow or tortuous environment, TAB has demonstrated great application potential in the area of minimally invasive surgery. However, TAB involves highly non-linear behavior due to hysteresis, creepage, and non-linear friction existing on the tendon routing, which is an enormous challenge for accurate control. Considering the difficulties in the precise modeling of non-linearity friction, this paper proposes a novel fuzzy control scheme for the Euler-Lagrange dynamics model of TAB for achieving tracking performance and providing accurate friction compensation. Finally, the asymptotic stability of the closed-loop system is proved theoretically and the effectiveness of the controller is verified by numerical simulation carried out in MATLAB/Simulink. The desired angle can be reached quickly within 3 s by adopting the proposed controller without overshoot or oscillation in Tracking Experiment, demonstrating the regulation performance of the proposed control scheme. The proposed method still achieves the desired trajectory rapidly and accurately without steady-state errors in Varying-friction Experiment. The angle errors generated by external disturbances are < 1 deg under the proposed controller, which returns to zero in 2 s in Anti-disturbance Experiment. In contrast, comparative controllers take more time to be steady and are accompanied by oscillating and residual errors in all experiments. The proposed method is model-free control and has no strict requirement for the dynamics model and friction model. It is proved that advanced tracking performance and real-time response can be guaranteed under the presence of unknown bounded non-linear friction and time-varying non-linear dynamics.

Robust multimodulus blind equalization algorithm for multilevel QAM signals in impulsive noise

As a blind equalization algorithm, the fractional lower-order statistics based multimodulus algorithm (FLOS-MMA) is suitable for equalizing multilevel quadrature amplitude modulation (QAM) signals in impulsive noise. However, the equalization performance of FLOS-MMA is severely degraded in strong impulsive noise because the first-order gradient of the cost function constrains the ability of FLOS to suppress large outliers in the equalizer output signal and is sensitive to large outliers in the equalizer input signal. To enhance the robustness of multimodulus blind equalization algorithm against impulsive noise, a FLOS based momentum fractional-order multimodulus algorithm (FLOS-MFOMMA) is proposed in this paper. The proposed algorithm mitigates the adverse effects of impulsive noise on the updating of equalizer coefficients by utilizing the fractional-order gradient and accelerates the convergence speed by incorporating a momentum term. Then, the steady-state excess mean square error and the computational complexity of FLOS-MFOMMA are analyzed theoretically. Finally, numerical simulations, for equalizing 16-QAM signals under impulsive noise environments, show that the proposed algorithm is superior to FLOS-MMA in terms of robustness and convergence speed.

Designing a fixed-time observer-based adaptive non-singular sliding mode controller for flexible spacecraft

This paper investigates the stabilization problem with a fixed-time approach for a flexible spacecraft subject to vibrations of flexible modes, unknown bounded disturbance, and inherent uncertainty. To estimate the modal variables of a flexible spacecraft which are often unmeasurable in practice, an observer with guaranteed fixed-time convergence is designed. Using the estimated modal variables, a fixed-time non-singular sliding mode controller is designed so that the desired attitude can be reached before a pre-specified time threshold regardless of the spacecraft's initial attitude. By incorporating the estimated modal variables in the control design, significant reduction in the steady-state error of the system response is achieved. The proposed control system is further enhanced with an adaptive law to increase robustness against unknown external disturbances and uncertainties. Stability analysis based on Lyapunov theory guarantees the convergence of observer estimation error and spacecraft attitude error to a pre-determined set before a fixed threshold. Simulation results validate the promising performance of the proposed control system, highlighting its effectiveness in achieving accurate and robust attitude control for flexible spacecraft.

A flexible mixed-optimization with H∞ control for coupled twin rotor MIMO system based on the method of inequality (MOI)- An experimental study.

This article introduces a cutting-edge H∞ model-based control method for uncertain Multi Input Multi Output (MIMO) systems, specifically focusing on UAVs, through a flexible mixed-optimization framework using the Method of Inequality (MOI). The proposed approach adaptively addresses crucial challenges such as unmodeled dynamics, noise interference, and parameter variations. Central to the design is a two-step controller development process. The first step involves Nonlinear Dynamic Inversion (NDI) and system decoupling for simplification, while the second step integrates H∞ control with MOI for optimal response tuning. This strategy is distinguished by its adaptability and focus on balancing robust stability and performance, effectively managing the intricate cross-coupling dynamics in UAV systems. The effectiveness of the proposed approach is validated through simulations conducted in MATLAB/Simulink environment. Results demonstrated the efficiency of the proposed robust control approach as evidenced by reduced steady-state error, diminished overshoot, and faster system response times, thus significantly outperforming traditional control methods.