Steady-state Accuracy Research Articles

Robust prescribed performance trajectory tracking control with improved fast nonsingular terminal sliding surface of robot manipulators

This paper investigates the high-precision model-free control of robot manipulators. To this end, a model-free robust prescribed performance controller with an improved fast nonsingular terminal sliding mode surface (IFNTSM) and unknown system dynamics estimator (USDE) has been designed. An USDE method is employed to estimate model informations and further to achieve model-free control, which can avoid complex mathematical model calculation. Compared with some other model-free control methods like time-delay control (TDC) and neural-networks control (NNC), the USED does not require acceleration signal and is easy to implement. Then the prescribed performance control (PPC) has been used to limit error trajectory, which means the error can be pre-limit in a constraint band. A new transform function (TF) is designed for PPC, it has unlimited domain and can still maintain stability although tracking error will exceed PPC boundary sometimes, but the PPC with traditional TF will crash in this case. This is a great improvement for the stability of system compared with traditional TF. An improved fast nonsingular terminal sliding mode surface (IFNTSM) with a new adaptive law is proposed to accelerate convergence rate and improve steady-state accuracy on the sliding manifold. Finally, a practical finite-time controller (PFTC) has been constructed to drive sliding variable to a set centered on zero within a finite time, which means the convergence time can be calculated depending on the initial state. The transient response time can be shorten compared with traditional asymptotic stable. Abundant simulations and experimental results also verified the effectiveness of the proposed scheme.

Analysis of thermo-mechanical coupling characteristics of feed system of woodworking center based on fuzzy control algorithm

With the rapid development of science and technology, automatic control systems have been applied in more and more fields. At the same time, the requirements for the stability, accuracy, response speed, and self-regulation ability of the system are also increasing. In the wood processing industry, the heating system of factories is an important link to ensure normal production. Therefore, in order to further improve the production efficiency of the wood processing industry and enhance the stability and controllability of the heating system in wood processing production, this article takes into account the delay and coupling effects in the rapid heating process, and combines fuzzy control with temperature control to study and establish a woodworking thermal mechanical coupling model based on fuzzy control algorithm. The results show that compared with traditional PID control, fuzzy control has advantages such as short response time, small overshoot, high steady-state accuracy, fast steady-state recovery, and good dynamic and static performance. Under the condition of rapid heating, the existence of delay effect weakens the effect of Thermal shock, while the coupling effect not only affects the propagation of thermoelastic waves in the elastic body, but also weakens the weakening effect of delay effect on Thermal shock to a certain extent.

Active Disturbance Rejection Control Method for Marine Permanent-Magnet Propulsion Motor Based on Improved ESO and Nonlinear Switching Function

In the control of marine permanent-magnet propulsion motors, active disturbance rejection control has attracted much attention because it can deal with external load disturbances and uncertainties of motor parameters at the same time. However, the conventional second-order ADRC has the problem of slow disturbance observation speed. To this end, this paper proposes an improved third-order extended state observer using the proportional–integral disturbance update law to improve the tracking performance and anti-external disturbance ability of the motor control system. Then, aiming at the problem that the structure does not effectively use the current information, resulting in large speed fluctuations when the load changes, the measured value of the q-axis current is used as the disturbance feedforward compensation item to further improve the load disturbance suppression ability of the motor. Finally, in order to suppress the influence of the current periodic disturbance caused by unmodeled dynamics on the steady-state accuracy of the motor, a nonlinear switching function with bounded gain and an IIR low-pass filter are designed to suppress the periodic disturbance without affecting the dynamic performance of the system. Combined with the established ship propeller load model, the effectiveness of the method is verified on the motor experimental platform: When suddenly changing 75% of the propeller load, the motor speed decreases by about 20%, and the adjustment time is 0.1 s, which improves the performance by more than 70% compared to PI control and conventional ADRC methods.

Adaptive Integral Extended State Observer-Based Improved Multistep FCS-MPCC for PMSM

In this article, an improved multi-step finite control set model predictive current control (FCS-MPCC) based on adaptive integral extended state observer (AIESO) is proposed for permanent magnet synchronous motor (PMSM). The improved multi-step FCS-MPCC based on sector is introduced in the current loop. The elements of the voltage vector set are reduced with different sector division method, so it could reduce the computational burden to some extent. Meanwhile, considering that the high gain extended state observer (ESO) will obtain faster convergence, better tracking accuracy in theory and the system disturbance rejection can be enhanced, but the noise suppression performance will become poor. Thus, the adaptive extended state observer (AESO) is proposed to balance the disturbance rejection and noise suppression. When system subject to disturbance, the adaptive gain will increase to enhance the system disturbance rejection and become small to improve the noise suppression in steady-state. However, disturbed by time-varying disturbance, the small gain in the steady state will lead to poor steady-state tracking accuracy. To improve the steady-state tracking accuracy, AIESO is proposed by adding the integral term into AESO. Finally, in order to avoid the sector misjudgment caused by parameter mismatch, the strategy based on extended state observer is used for disturbance compensation. However the selection of inductance is closed related to the estimated burden of the observer. Thus, the inductance parameter estimation method is proposed to update the initial inductance value to reduce the estimated burden, which can help to suppress the parameter mismatches with a smaller estimated burden of the observer. The simulation and experimental results verify the effectiveness of the proposed method.

Pump-Controlled AGC Micro-Displacement Position Control of Lithium Battery Pole Strip Mill Based on Friction Model

Electrode roll-forming refers to rolling a battery electrode into a preset thickness through the electro-hydraulic servo pump-controlled hydraulic roll gap thickness automatic control system (known to as pump-controlled AGC). Compared with the motor servo system, the friction problem of the electro-hydraulic servo system is more serious and the friction problem of the actuator itself is very prominent. Moreover, low-speed performance is one of its core indicators, the friction phenomenon is the most abundant during the low-speed stage and the impact on the servo system is also the most obvious. Therefore, for high-performance electro-hydraulic servo control, friction compensation is not only unavoidable, but also a very difficult problem. Aiming to influence the friction on the position control of the pump-controlled system of a lithium battery pole strip mill, the rolling mechanism and process procedure under micro-displacement position control based on the friction model were studied and compared from the perspective of considering friction factors, and a friction compensation controller based on the LuGre model was designed. The control precision of a pump-controlled AGC system was improved through combination with an adaptive robust controller. Because of the diversity of unmeasurable states of the system, a dual observer was designed, and the known model of the system was added to the observer. In the final comparative experiment, the steady-state accuracy of the friction adaptive robust compensation controller system based on the LuGre model reached ±0.3 μm, which is superior to the fuzzy IMC compensation and traditional PID control strategies.

Robust multitask diffusion normalized M-estimate subband adaptive filter algorithm over adaptive networks

In recent years, the multitask diffusion least mean square (MD-LMS) algorithm has been extensively applied in distributed parameter estimation and target tracking of multitask network. However, its performance degrades under colored input signals or impulsive noises. To overcome these two drawbacks, this paper introduces the subband adaptive filter (SAF) into a multitask network for the first time, and a robust multitask diffusion normalized M-estimate subband adaptive filtering (MD-NMSAF) algorithm is proposed, which solves the global network optimization problem based on the modified Huber (MH) function in a distributed manner, achieves robustness to impulsive noise, and significantly improves the convergence performance of the MD-LMS algorithm. Compared with existing robust multitask diffusion affine projection algorithms (MD-APAs), the computational complexity of the proposed MD-NMSAF algorithm is greatly reduced. In addition, we analyze the mean and mean-square stability conditions of MD-NMSAF, provide theoretical models characterizing the network mean square deviation (MSD) behaviors of transient and steady-state, and further verify their correctness by computer simulations. Simulation results under different network topologies, input signals, filter lengths and impulsive noise types fully demonstrate the performance advantages of the proposed MD-NMSAF algorithm over its competitors in terms of steady-state estimation accuracy and convergence speed.

A Novel Closed-Loop Structure for Drag-Free Control Systems with ESKF and LQR.

Space-borne gravitational wave detection satellite confronts many uncertain perturbations, such as solar pressure, dilute atmospheric drag, etc. To realize an ultra-static and ultra-stable inertial benchmark achieved by a test-mass (TM) being free to move inside a spacecraft (S/C), the drag-free control system of S/C requires super high steady-state accuracies and dynamic performances. The Active Disturbance Rejection Control (ADRC) technique has a certain capability in solving problems with common perturbations, while there is still room for optimization in dealing with the complicated drag-free control problem. When faced with complex noises, the steady-state accuracy of the traditional control method is not good enough and the convergence speed of regulating process is not fast enough. In this paper, the optimized Active Disturbance Rejection Control technique is applied. With the extended state Kalman filter (ESKF) estimating the states and disturbances in real time, a novel closed-loop control structure is designed by combining the linear quadratic regulator (LQR) and ESKF, which can satisfy the design targets competently. The comparative analysis and simulation results show that the LQR controller designed in this paper has a faster response and a higher accuracy compared with the traditional nonlinear state error feedback (NSEF), which uses a deformation of weighting components of classical PID. The new drag-free control structure proposed in the paper can be used in future gravitational wave detection satellites.

Adaptive Backstepping Integral Sliding Mode Control of a MIMO Separately Excited DC Motor

This research proposes a robust nonlinear hybrid control approach to the speed control of a multi-input-and-multi-output separately excited DC motor (SEDCM). The motor that was under consideration experienced parametric uncertainties and load disturbances in the weak field region. The proposed technique aims to merge the benefits of adaptive backstepping (AB) and integral sliding mode control (ISMC) to enhance the overall system’s robustness. The unknown parameters with load disturbances are estimated using an adaptation law. These estimated parameters are incorporated into the controller design, to achieve a highly robust controller. The theoretical stability of the system is proved using the Lyapunov stability criteria. The effectiveness of the proposed AB–ISMC was demonstrated by simulation, to track the reference speed under parametric uncertainties and load disturbances. The control performance of the proposed technique was compared to that of feedback linearization (FBL), conventional sliding mode control (SMC), and AB control laws without and with the adaptation law. Regression parameters, such as integral square error, integral absolute error, and integral time absolute error, were calculated to quantitatively analyze the tracking performance and robustness of the implemented nonlinear control techniques. The simulation results demonstrated that the proposed controller could accurately track the reference speed and exhibited robustness, with steady-state error accuracy. Moreover, AB–ISMC overperformed, compared to the FBL, SMC, AB controller without adaptation law and AB controller with adaptation law, in reducing the settling time by factors of 27%, 67%, 23%, and 21%, respectively, thus highlighting the superior performance of the proposed controller.

A speed loop control method of a laser tracing measurement control system

In a laser tracking control system, a motor drives the load to achieve continuous forward and reverse rotation speed control, and the magnitude of the load changes periodically during the motor rotation to realize tracking. Based on these characteristics, we propose an integral-separated improved variable universe fuzzy proportional-integral (PI) control method with torque feedforward compensation method in this study. The proposed method achieves the control performances of fast response, high steady-state accuracy, and strong anti-interference. The conventional fuzzy PI control method achieves good performance only in the unidirectional acceleration of a motor; therefore, we have improved its fuzzy rules, and designed a novel universe contraction–expansion factor. Additionally, a load torque observer is introduced to observe and compensate for the external load and to further improve the anti-interference performance of the tracking control system. The experimental results demonstrate that the integral-separated improved variable-universe fuzzy PI control method achieves better performance in the forward and reverse speed regulation processes of the motor. The overshoot is 92% less than that of the conventional PI control when the target speed is set to ±500 rpm. The Luenberger observer is introduced to observe and compensate for the load torque. After the stabilizing the speed and applying an external load of 0.2 N m to the motor, the maximum speed reduction is observed to be 59% less than that obtained using the conventional PI control. The improved PI control method satisfies the speed loop control requirements of the laser tracking control system and can improve the steady-state tracking accuracy and robustness of the system.

Modeling and robust quantitative control for AUV-tow-load system

This paper models a point-mass load tethered to a single autonomous underwater vehicle (AUV) and proposes a quantitative control strategy, which is able to drive the load to track the desired trajectory closely. The AUV-tow-load system is modeled as three connected subsystems: load position subsystem, cable direction subsystem, and AUV attitude subsystem. Improving on the current prescribed performance control methods, where the transient-state and steady-state tracking behaviors cannot be preassigned accurately, a quantitative controller is designed for the point-mass load position, achieving predefined tracking performance without violating user-defined quantitative indices including overshoot, convergence time, and steady-state accuracy. An uncertainties and disturbances estimator (UDE) is designed and incorporated into the control inputs to compensate for the effects of uncertain dynamics and external disturbances. Rigorous theoretical proof is presented, showing that all tracking errors converge to the neighborhood of zero with quantitatively designed tracking behaviors, obtaining uniformly ultimately boundedness. Simulation results are provided to validate the efficiency of the proposed method.

A switched extremum seeking control without steady-state oscillation using gradient-based adaptive-amplitude perturbation

To enhance the steady-state and dynamic performance of the extremum seeking control (ESC), a switched ESC scheme is proposed in this paper. Firstly, to solve nonconvex optimization problems, a novel adaptive law for perturbation is established utilizing the hybrid gradient information to accomplish a trade-off between the dynamic and steady-state performance. It is shown that the adaptive-amplitude ESC achieves global optimization despite the existence of local extrema. Then, to overcome the adverse effect of inaccurate gradient estimation on steady-state accuracy, a Lyapunov-based switched strategy is employed to start the bisection-based ESC. The plant output converges to the equilibrium rapidly and accurately without steady-state oscillation. Furthermore, the stability of the proposed scheme is theoretically proved. Numerical simulation examples are carried out to demonstrate the effectiveness of the proposed scheme.

State of Charge Estimation for Lithium-Ion Battery Based on Unscented Kalman Filter and Long Short-Term Memory Neural Network

State of charge (SOC) estimation is the core algorithm of the battery management system. However, the commonly used model-based, data-driven, or experiment-based methods struggle to independently achieve accurate SOC estimation under different working conditions and temperatures, which affects battery performance and safety. To this end, this paper proposes an online SOC estimation method that combines the model-driven and double-data-driven approaches. The unscented Kalman filter (UKF) based on the first-order RC model is used to achieve robust SOC estimation, while the data-driven long short-term memory (LSTM) neural network is used to achieve fast SOC estimation. The former model has an excellent dynamic performance and the latter has high steady-state accuracy. The SOC estimation results are input into the SOC estimation model of series LSTM so that the stable but inaccurate SOC values estimated by UKF in the first part and the accurate but fluctuating SOC values estimated by LSTM can be correlated and corrected, achieving a fast and accurate SOC estimation under various working conditions. The estimation results show that the above method has strong robustness and high accuracy, and effectively reduces model complexity and data redundancy. In addition, the root mean square error of SOC estimation under different working conditions is controlled within 1–2.3% at 0 °C, 25 °C, and 45 °C, which is better than the traditional single-SOC estimation method.

Control-oriented modeling of a LiBr/H[formula omitted]O absorption heat pumping device and experimental validation

Absorption heat pumping devices (AHPDs, comprising absorption heat pumps and chillers) are devices that use thermal energy instead of electricity to generate heating and cooling, thereby facilitating the use of waste heat and renewable energy sources such as solar or geothermal energy. Despite this benefit, widespread use of AHPDs is still limited. One reason for this is partly unsatisfactory control performance under varying operating conditions, which can result in poor modulation and part load capability. A promising approach to tackle this issue is using dynamic, model-based control strategies, whose effectiveness, however, strongly depend on the model being used. This paper therefore focuses on the derivation of a viable dynamic model to be used for such model-based control strategies for AHPDs such as state feedback or model-predictive control. The derived model is experimentally validated, showing good modeling accuracy. Its modeling accuracy is also compared to alternative model versions, that contain other heat transfer correlations, as a benchmark. Although the derived model is mathematically simple, it does have the structure of a nonlinear differential–algebraic system of equations. To obtain an even simpler model structure, linearization at an operating point is discussed to derive a model in linear state space representation. The experimental validation shows that the linear model does have slightly worse steady-state accuracy, but that the dynamic accuracy seems to be almost unaffected by the linearization. The presented new modeling approach is considered suitable to be used as a basis for the design of advanced, model-based control strategies, ultimately aiming to improve the modulation and part load capability of AHPDs.

Robust augmented complex-valued normalized M-estimate subband adaptive filtering algorithm against colored non-circular inputs and impulsive noise

Recently, the augmented complex-valued normalized subband adaptive filtering (ACNSAF) algorithm has been proposed to process colored non-circular signals. However, its performance will deteriorate severely under impulsive noise interference. To overcome this issue, a robust augmented complex-valued normalized M-estimate subband adaptive filtering (ACNMSAF) algorithm is proposed, which is obtained by modifying the subband constraints of the ACNSAF algorithm using the complex-valued modified Huber (MH) function and is derived based on CR calculus and Lagrange multipliers. In order to improve both the convergence speed and steady-state accuracy of the fixed step size ACNMSAF algorithm, a variable step size (VSS) strategy based on the minimum mean squared deviation (MSD) criterion is devised, which allocates individual adaptive step size to each subband, fully exploiting the structural advantages of SAF and significantly improving the convergence performance of the ACNMSAF algorithm as well as its tracking capability in non-stationary environment. Then, the stability, transient and steady-state MSD performance of the ACNMSAF algorithm in the presence of colored non-circular inputs and impulsive noise are analyzed, and the stability conditions, transient and steady-state MSD formulas are also derived. Computer simulations in impulsive noise environments verify the accuracy of theoretical analysis results and the effectiveness of the proposed algorithms compared to other existing complex-valued adaptive algorithms.

Reinforcement Learning Based Sliding Mode Control for a Hybrid-STATCOM

The hybrid static synchronous compensator (hybrid-STATCOM) is characterized with a wide compensation range and low dc-link voltage, which is a cost-effective reactive power compensator for medium voltage level application. However, the coupling part of the hybrid-STATCOM is time-varying, and its system model is nonlinear, which causes a great challenge for the controller design. This paper proposes a model-free reinforcement learning (RL) based sliding mode control (RL-SMC), which provides the inverter voltage as the control action of the hybrid-STATCOM to compensate the load reactive power and harmonic. The proposed RL-SMC is computationally efficient with high steady-state accuracy, fast response, and good robustness. First, an agent-environment framework (AEF) is proposed to enable RL. Then, the comprehensive design procedure of the RL-SMC is proposed. Finally, simulation and experimental results are carried out to verify the validity and effectiveness of the proposed RL-SMC under different load and grid conditions.

Robust Flight-Path Angle Consensus Tracking Control for Non-Minimum Phase Unmanned Fixed-Wing Aircraft Formation in the Presence of Measurement Errors

The robust flight-path angle consensus tracking control problem for multiple unmanned fixed-wing aircrafts is investigated in this paper, where the non-minimum phase properties and the presence of measurement errors are systematically addressed. A three-module control scheme is proposed for each aircraft: a Distributed Observer that obtains the available information from the reference system and the neighbor aircraft to provide the estimates of the reference states; a Casual Stable Inversion that calculates the bounded estimates of the desired input, desired external states, and most importantly, desired internal states to resolve the divergence issues caused by the non-minimum phase properties; and a Local Measurement Error Rejection Controller that includes a measurement error estimator (MEE) to actively compensate for the adverse effect of measurement errors to achieve robust consensus tracking control. Stability, convergence, and robustness of the proposed control are analyzed, showing that (1) the non-minimum phase issue can be systematically resolved by the designed Casual Stable Inversion to ensure aircraft internal stability and flight safety, and (2) the consensus tracking accuracy can be improved by tuning a single MEE parameter, which is favorable in practical applications to large-scale unmanned aircraft formations. Comparative simulation results with classic PID-based consensus control demonstrate the advantage of the proposed control in transient oscillations, steady-state tracking accuracy, and robustness against measurement errors.

Disturbance Observer based Dynamic Surface Sliding Mode Control for Manipulator Arm with Adaptive RBF Networks

For the rotation position control of automatic loading manipulator arm with uncertain problems of load change and external disturbances, an adaptive radial basis function networks (RBF) dynamic surface sliding mode control (DSMC) strategy based on disturbance observer (DOB) is proposed. The value of the external disturbance, which is estimated by the DOB on line, is added to the output of the proposed controller for feedforward compensation. The dynamic performance of the controller is ensured by introducing the adaptive RBF networks while the stability of the controller is verified by designing the Lyapunov function. Comparison between the results of the proposed control strategy and those of the conventional sliding mode control (SMC) shows that the controller has better dynamic tracking characteristics, steady-state accuracy and strong robustness under load changes.

Distributed hierarchical economic optimization approach of microgrid based on multi-agent leader-following consensus

Considering the higher generation operation cost of distributed generations (DGs) and power purchase cost in microgrid, the discrete-time mean consensus protocol (DMCP) is improved by bringing in the power offset elimination term in this paper. Then an improved multi-agent leader-following consensus algorithm (IMLCA) is proposed. The total power balance can be realized by the algorithm, which make the incremental cost (IC) of DGs converge to the consensus value quickly. Besides, the active power output objective of DGs is optimized and the overall generation operation cost of the AC microgrid is lessened. Afterwards, the distributed hierarchical economic optimization approach of microgrid based on multi-agent leader-following consensus is studied. In this approach, a distributed hierarchical framework is constructed. The economic optimization management level emits the optimal active power output objective of DGs to the droop control level. Meantime, the optimal active power output objective computed by IMLCA is carried out by using the droop control level. Thus, the active power output of DGs is apportioned reasonably. Finally, the simulation model of five-DG operation is constructed for research. The simulation results suggest that the approach can achieve the economic cost optimization goal of the grid-connected microgrid and the IMLCA possesses the better transient response performance and steady-state computation accuracy.

Collaborative estimations of state of energy and maximum available energy of lithium-ion batteries with optimized time windows considering instantaneous energy efficiencies

The state of energy (SOE) of the lithium-ion battery indicates the driving range of electric vehicles, which is affected by its maximum available energy (MAEgy). Meanwhile, the energy efficiency is of great significance to improve the estimation accuracy. In this paper, a collaborative estimation method of the SOE and MAEgy with optimized time windows considering energy efficiency is proposed. Firstly, based on the Thevenin model of the battery, the forgetting factor recursive least squares is used to identify its parameters. The state space equations of the SOE and MAEgy are established respectively and two extended Kalman filters are leveraged to estimate them with different time windows. To reduce calculations and improve estimation accuracy, the multi-objective genetic algorithm is applied to optimize the time windows for the transient scheme and steady scheme, respectively. Then the optimal time windows of the initial and convergence phase are derived from these two schemes by the entropy weight method. Finally, the instantaneous energy efficiency is deduced, and the influences of four different calculation methods on the estimation performances are discussed. The results show that the proposed method has better transient performances and steady-state accuracy under dynamic driving condition and is robust against incorrect initial values.

Motion Control of Autonomous Underwater Helicopter Based on Linear Active Disturbance Rejection Control with Tracking Differentiator

As a new disk-shaped autonomous underwater vehicle (AUV), the autonomous underwater helicopter (AUH) is devoted to subsea operations, usually diving into the seabed and docking with a subsea docking system. Due to the motion control’s performance, the AUH’s stability and steady-state accuracy are affected remarkably while docking. Moreover, considering the difficulties of hydrodynamic modeling of AUHs, the classical model-based control method is unsuitable for AUHs. Moreover, there is a large gap between the hydrodynamic simulation results and real situations. Hence, based on the data-driven principle, the linear active disturbance rejection control with a tracking differentiator (LADRC-TD) algorithm is employed for AUH depths and heading control. As the simulation experiments prove, LADRC and LADRC-TD have better anti-interference performance when compared with PID. According to the pool experiments, overshoots of the LADRC-TD are 20 cm and 3° for the depth control and heading control, respectively, which are superior to PID and LADRC. Meanwhile, the steady-state accuracy of the LADRC-TD is ±21 cm and ±2.5° for the depth and heading control, respectively, which is inferior to PID and the same as LADRC.