Steady-state Tracking Error Research Articles

Novel auxiliary saturation compensation design for neuroadaptive NTSM tracking control of high speed trains with actuator saturation

In this paper, a novel auxiliary saturation compensation system is constructed to eliminate the negative effect of asymmetric nonlinear actuator saturation (ANAS). Two chatter-free neuroadaptive sliding mode tracking control strategies are proposed by combining nonsingular terminal sliding mode (NTSM) control technique with radial basis function neural network (RBFNN) for high speed trains for resp., the actuator saturation-free and ANAS saturation cases. These two control strategies are used to guarantee that the closed-loop signals are bounded and the steady-state tracking errors converge to a residual around zero. The common assumption that the initial velocities of the train and the desired trajectory are zero, is removed in this paper. In addition, the computationally inexpensive strategy contains an optimized NN adaptation mechanism where only one parameter requires online updating no matter how many neurons are chosen. Finally, numerical examples are provided to demonstrate the validity of the proposed control strategies.

Disturbance-Observer-Based PBC for Static Synchronous Compensator Under System Disturbances

Passivity-based control (PBC) relies on an accurate mathematical model and thus its performance will be degraded by the weak robustness against parameters uncertainties, modeling error, and external disturbances. Moreover, it cannot achieve zero tracking error of the steady-state current under parameter uncertainties and modeling error. This paper proposes a novel disturbance-observer- (DO) based PBC (DO-PBC) for static synchronous compensator (STATCOM) to achieve better stability and dynamic performances against disturbances. A DO that has been introduced into the PBC current loop is used to compensate system disturbances, which can improve the robustness of the control system and eliminate the steady-state tracking error. Moreover, the proposed DO-PBC provides faster responses in handling various kinds of disturbances. Then, the detail design process, stability and robustness analysis, and parameters tuning method are investigated and presented. Also, the proposed method is simple to be implemented by the separation principle. The performance comparisons among the proportional integral, the conventional PBC, and the proposed DO-PBC are carried out to show the effectiveness of the proposed method against disturbances and the precise current tracking, via simulation tests and experimental tests based on a down-scale laboratory prototype experiment of 380 V STATCOM.

Sampled-data internet of connected vehicles control with channel fading and time-varying delay

Abstract This paper is concerned with sampled-data internet of connected vehicles (IOCV) control systems with a communication channel fading and time-varying delay. A hybrid IOCV system model is established, where the communication channel fading and time-varying delay are given full considerations. Based on the model, by employing Lyapunov-Krosovskii functional, a new sampled-data controller method with variable sampling period is derived, which can robustly stabilize the IOCV system with a given level of disturbance attenuation. Furthermore, the obtained sampled-data controller is complemented by additional conditions established to guaranteeing string stability and zero steady state tracking errors. Finally, the effectiveness and superiority of the proposed control strategies are verified by both numerical simulation and experiment with four-laboratory scale cars.

Robust fault-tolerant attitude tracking with guaranteed prescribed performance

The robust fault-tolerant (FT) attitude tracking control problem with guaranteed prescribed performance is addressed in this paper. We consider the actuator fault, misalignment, sensor fault and external disturbance simultaneously and incorporate the L2 control allocation (CA) method to minimize the use of faulty actuators. To guarantee the prescribed performance such as the steady-state tracking error, convergence rate, as well as overshoot and undershoot, the constrained quaternion error is transformed to an unconstrained state, whose stabilization is proven to be sufficient and necessary to guarantee the performance requirement. With the utilization of the transformed state and the compromised angular velocity error suffering from gyro faults, a novel adaptive sliding mode FT control law with CA is developed. Ultimate uniform boundedness of the compromised angular velocity error and transformed state is ensured to satisfy the specified tracking performance. Numerical simulations are conducted on a rigid spacecraft to illustrate the efficiency of the proposed robust FT control law.

Deadbeat Predictive Current Control for Permanent Magnet Synchronous Machines With Closed-Form Error Compensation

Deadbeat predictive current regulator features fast dynamic responses. However, it suffers from the steady-state current tracking error in a practical system due to the plant uncertainties, particularly the inductances. Instead of using observer-based disturbance voltage feedforward methods, this article proposes a new closed-form method to directly compensate the current tracking errors with a simple feedforward term added to the voltage commands. Zero steady-state error is achieved with negligible computation compared to the observer-based methods. The new method is first derived to tackle the inductance mismatch in the surface-mount permanent magnet synchronous motor, then the system close-loop transfer function is established to prove that the proposed method guarantees the zero steady-state error even with mismatches of the stator resistance and rotor flux linkage. Furthermore, based on the proposed compensation method, noise suppression schemes are added and designed to reduce high-frequency noise sensitivities in practical systems. Finally, the proposed method is extended to the interior permanent magnet synchronous motor (IPMSM). IPMSM system simulation and 68.5-kW experimental results are provided to validate the proposed method.

Dynamic Consensus Tracking of Uncertain Lagrangian Systems With a Switched Command Generator

This paper studies the consensus tracking problem of uncertain Lagrangian systems. In contrast to the existing results where the command signals are sufficiently smooth, we consider a class of nonsmooth command signals generated by a switched command generator, which might be more realistic from the perspective of practical applications. The main technical innovations of this paper are threefold. First, to enable a rigorous problem formulation, some piecewise decaying function sets are defined to precisely describe the steady-state behaviors of the tracking errors. Second, to ensure the stability of the switched nonlinear closed-loop system, a system-based scaling method with the establishment of several lemmas is developed to determine the minimal dwell time of the switching signal. Third, a quantitative analysis is performed to acquire the ultimate bound for the steady-state tracking errors. The proposed control approach is evaluated by a simulation example.

Control Strategy of Single-Phase Hybrid-Mode Ćuk Inverter for LVRT Capability

This article proposes a control strategy for a Cuk module-integrated inverter (MII) with hybrid operation mode for low-voltage ride-through (LVRT) capability. The hybrid-mode Cuk MII operates in unfolding-type power conversion (UPC) mode during normal grid conditions and in two-stage power conversion (TPC) mode during grid faults. It also has the advantages of highly efficient power transfer and LVRT capability but is difficult to control because UPC and TPC modes have distinct system dynamics and suffer from grid voltage disturbances that have different magnitudes. To overcome this control problem, this article proposes a control strategy that corresponds to the operating mode of the hybrid-mode Cuk inverter. To achieve zero steady-state tracking error during the grid disturbance, a repetitive controller (RC) is used in the proposed control scheme. Different phase-lead compensators in the RC compensate for different phase lags caused by distinct system dynamics. To reduce the burden from the RC, different nominal duty ratios are used as the feedforward control input. To minimize the tracking error during grid faults, a proportional-resonant controller is used in parallel with the RC controller in the TPC mode. To analyze the stability of different control systems, a unified control system model is presented for the proposed inverter. The procedure to select control parameters is also presented in detail. Simulation results validate the proposed control scheme in the hybrid-mode Cuk inverter, and experiments are conducted using the 400-VA MII prototype to demonstrate its validity.

H∞ Control for Battery/Supercapacitor Hybrid Energy Storage System Used in Electric Vehicles

This paper proposes a control strategy of a hybrid energy storage system (HESS) based on simplified 2th-order model. The HESS uses a bidirectional DC/DC converter to connect the supercapacitors (SC) with the battery. Two control objectives, the output current of the SC during the traction procedure and the charging current of the SC while regenerative braking, are regulated by using the DC/DC converter. Two H∞ controllers are designed to control the output and charging current of the SC to their reference values, which are generated by the energy management strategy (EMS). Experimental results show that the proposed control method achieves a satisfactory performance, including a low steady-state tracking error and high response speed when the load power varies in a wide range.

Feedback controller designs for an electromagnetic micromanipulator

Magnetic micromanipulators are capable of generating wide range of magnetic forces to manipulate magnetic microparticles for biomedical applications. In this study, a multipole magnetic micromanipulator system including electromagnets, driver circuitry and control unit is designed, modeled and implemented. The micromanipulator can produce a broad range of magnetic forces up to 25 pN on a single magnetic microparticle (1–10 µm diameter) that is 5 mm away from the electromagnet core tip. Both linear and nonlinear controllers are designed and implemented, and the proposed nonlinear controller produces smooth control currents to assure closed-loop stability of the system with 1 s non-overshoot transient response and zero steady-state tracking error. The maximum output current of the driver circuitry is set to 1 A. The single particle at the center is moved at a speed of 5 mm/s. The fully automatic system can be utilized in applications related to single cell or microparticle manipulations.

Virtual Variable Sampling Repetitive Control of Single-Phase DC/AC PWM Converters

Repetitive control (RC) presents an attractive solution to achieve low steady-state tracking error and total harmonic distortion for periodic signals. For the conventional RC (CRC), it requires the ratio of the reference signal period to the fixed sampling period to be an integer. Therefore, the reference signal with a variable frequency or a fractional period ratio will lead to severe performance degradation. Although existing hardware variable sampling (VS) rate methods enable the CRC to be frequency adaptive, the VS frequency will also influence the overall system stability, and they need that the CPU has the VS frequency ability. In this paper, a flexible and easy-to-implement method, virtual VS (VVS), is proposed to enable the RC to be frequency adaptive. The proposed VVS method that creates a virtual delay unit to approximate each VS delay achieves a flexible VS as similar to the hardware-based VS but it does not influence the overall system sampling frequency and stability. Experimental results of a single-phase dc/ac converter system are presented to demonstrate the effectiveness of the proposed VVS-RC.

Design and analysis of output feedback constraint control for antilock braking system based on Burckhardt’s model

PurposeThe purpose of this study is to improve vehicles’ brake stability, the problem of constraint control for an antilock braking system (ABS) with asymmetric slip ratio constraints is concerned. A nonlinear control method based on barrier Lyapunov function (BLF) is proposed not only to track the optimal slip ratio but also to guarantee no violation on slip ratio constraints.Design/methodology/approachA quarter vehicle braking model and Burckhardt’s tire model are considered. The asymmetric BLF is introduced into the controller for solving asymmetric slip ratio constraint problems.FindingsThe proposed controller can implement ABS zero steady-state error tracking of the optimal wheel slip ratio and make slip ratio constraints flexible for various runway surfaces and runway transitions. Simulation and experimental results show that the control scheme can guarantee no violation on slip ratio constraints and avoid self-locking.Originality/valueThe slip rate equation with uncertainties is established, and BLF is introduced into the design process of the constrained controller to realize the slip rate constrained control.

Multirate Resonant Controllers for Grid-Connected Inverters With Harmonic Compensation Function

Resonant controller (RSC) is one of the most popular approaches for ac current/voltage control due to the high performance of zero steady-state tracking error. However, it suffers from heavy computational burden issue when multiple RSCs are demanded to control multiple harmonics. To alleviate this issue, a down-sampled multirate RSCs (MRRSCs) scheme is proposed for controlling power inverters, e.g., grid-connected inverters and active power filters. The proposed control scheme is composed of an inner control loop with a fast sampling rate, which is identical to the switching frequency, and an array of paralleled MRRSCs-based external control loop with a reduced sampling rate. With the reduced sample rate, the MRRSCs can be executed alternatively in the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dq</i> -frame, such that the computational burden can be significantly reduced per cycle. Moreover, to reinforce the wide frequency adaptability of the MRRSC, its central resonant frequency is online updated according to the output of the phase-locked loop. In the paper, the equivalent single-rate closed-loop model of the overall system is developed, based on which the controller parameters are designed employing the Nyquist diagram and root locus. Finally, experiments are performed on a grid-connected inverter to validate the superiority of the proposed scheme.

Robust Quasi-Predictive Control of $LCL$-Filtered Grid Converters

This paper proposes a new control strategy for grid-connected $LCL$ -filtered voltage source converters (VSCs). It is realized by cascading a proportional-resonant (PR) controller, which regulates the grid-side current, and a finite-set model predictive controller (FS-MPC), which is responsible for controlling the filter's capacitor voltage and active damping of the resonance. The overall control circumvents the drawbacks of using only the FS-MPC to control the converter, such as steady state tracking error, weighting factor tuning complexity, and need to use long prediction horizons for optimal performance, but it keeps its advantageous properties. Namely, due to FS-MPC's direct manipulation of the VSC switches, the pulsewidth-modulation delay does not exist, while a high sampling rate leads to only insignificant computational delay. As a consequence, the system achieves far less magnitude and phase roll-off in the high-frequency region that allows considerable increase of dynamic performance compared to conventional control approaches. Moreover, the inner FS-MPC-based regulator exhibits a flat frequency response, which indicates that there is no need for designing a dedicated AD. The overall control design procedure is then largely simplified as only the proportional gain of the PR controller needs to be tuned. These properties are proved using a describing function method where a linear approximation of the FS-MPC regulated VSC and an inner $LC$ filter is derived in the frequency domain and integrated together with the model of the PR controller and grid side inductor. The controller has been analyzed analytically and validated through experimental results, where design correctness and robustness to grid-side inductance variations have been tested.

Multi-missile Coordination High Precision Guidance and Control Method for Beam-riding Guidance

Due to the limitation of target indication error and steady-state tracking error, it is difficult for the existing beam-riding guidance weapon system to attack long-range and high-maneuvering targets accurately. In order to solve this problem, this paper proposes a high precision guidance and control method for beam-riding guidance multi missile coordination: through sharing error information between multiple missiles in the same guiding beam, correcting the center line of guided beam and eliminating the steady-state error in the process of missile tracking target, thus the strike capability of the guided missile for long distance and high maneuvering target is enhanced. The six degree of freedom controlled trajectory simulation is used to verify this method. The simulation results show that the guidance and control method is correct and effective. Compared with the existing beam-riding guidance system, it has a higher hit precision and better application prospect.

An Artificial Tissue Homeostasis Circuit Designed via Analog Circuit Techniques.

Tissue homeostasis (feedback control) is an important mechanism that regulates the population of different cell types within a tissue. In type-1 diabetes, auto-immune attack and consequent death of pancreatic β cells result in the failure of homeostasis and loss of organ function. Synthetically engineered adult stem cells with homeostatic control based on digital logic have been proposed as a solution for regenerating β cells. Such previously proposed homeostatic control circuits have thus far been unable to reliably control both stem-cell proliferation and stem-cell differentiation. Using analog circuits and feedback systems analysis, we have designed an in silico circuit that performs homeostatic control by utilizing a novel scheme with both symmetric and asymmetric division of stem cells. The use of a variety of feedback systems analysis techniques, which is common in analog circuit design, including root-locus techniques, Bode plots of feedback-loop frequency response, compensation techniques for improving stability, and robustness analysis help us choose design parameters to meet desirable specifications. For example, we show that lead compensation in analog circuits instantiated as an incoherent feed-forward loop in the biological circuit improves stability, whereas simultaneously reducing steady-state tracking error. Our symmetric and asymmetric division scheme also improves phase margin in the feedback loop, and thus improves robustness. This paper could be useful in porting an analog-circuit design framework to synthetic biological applications of the future.

Dynamic Adaptive Hybrid Impedance Control for Dynamic Contact Force Tracking in Uncertain Environments

The importance of robot contact operation control has been increasing recently due to a need for robots to interact more with the outside world. However, traditional robot compliance control cannot take both transient contact force overshoots and steady-state force tracking error problems into account. To address this problem, this paper aims to design a dynamic adaptive hybrid impedance (DAHI) controller to deal with dynamic contact force tracking in uncertain environments (e.g., polishing scenarios). Under the premise of analyzing the transient response and steady-state error in the hybrid impedance control (HI) and adaptive hybrid impedance (AHI) control, the DAHI control, which combines the advantages from HI and AHI control, is applied to improve the performance of AHI controller. The main goal of such a controller is to avoid force overshoots in the contact stage while maintaining force tracking error in the dynamic tracking stage. The proposed controller is capable of adapting its update rate parameter online in order to track a reference force in uncertain environments. Besides, it does not require any modeling or estimation of an environment's dynamics or the robot's dynamics. The simulation and experimental results both show the achieved control performance. The results have also been compared with the previous control methods.

Double-Loop Integral Terminal Sliding Mode Tracking Control for UUVs With Adaptive Dynamic Compensation of Uncertainties and Disturbances

This paper focuses on the trajectory tracking control of unmanned underwater vehicles (UUVs) in the presence of dynamic uncertainties and time-varying external disturbances. Two adaptive integral terminal sliding mode control schemes, namely, adaptive integral terminal sliding mode control (AITSMC) scheme and adaptive fast integral terminal sliding mode control (AFITSMC) scheme are proposed for UUVs based on integral terminal sliding mode (ITSM) and fast ITSM (FITSM), respectively. Each control scheme is double-looped: composed of a kinematic controller and a dynamic controller. First, a kinematic controller is designed for each of the two control schemes. The two kinematic controllers are based on ITSM and FITSM, respectively. These kinematic controllers yield local finite-time convergence of the position tracking errors to zero meanwhile avoid the singularity problem in the conventional terminal sliding mode control (TSMC). Then, using the output of the kinematic controller as a reference velocity command, a dynamic controller is developed for each of the two control schemes. The two dynamic controllers are also based on ITSM and FITSM, respectively. An adaptive mechanism is introduced to estimate the unknown parameters of the upper bound of the lumped system uncertainty which consists of dynamic uncertainties and time-varying external disturbances so that the prior knowledge of the upper bound of the lumped system uncertainty is not required. The estimated parameters are then used as controller parameters to eliminate the effects of the lumped system uncertainty. The convergence rate of the integral terminal sliding variable vector is investigated and the local finite-time convergence of the velocity tracking errors to zero in the ITSM or FITSM is obtained. Finally, based on the designed kinematic and dynamic controllers, the finite-time stability of the full closed-loop cascaded system is shown. The two proposed control schemes improve the tracking accuracy over the existing globally finite-time stable tracking control (GFTSTC) and adaptive nonsingular TSMC schemes, and enhance the robustness against parameter uncertainties and external disturbances over the GFTSTC scheme. Compared with the conventional adaptive integral sliding mode control (AISMC) scheme, the two proposed control schemes offer faster convergence rate and stronger robustness against dynamic uncertainties and time-varying external disturbances for the trajectory tracking control of UUVs due to involving the fractional integrator. Comparative numerical simulations are performed on the dynamic model of the Omni Directional Intelligent Navigator UUV for two trajectory tracking cases. The convergence rate and robustness to uncertainties and disturbances are quantified as the convergent time and bounds of the steady-state position and velocity tracking errors, respectively. The results show that the two proposed control schemes improve at least 20s in convergence rate and enhance about 2% robustness in position tracking and 20% robustness in velocity tracking over the AISMC scheme.

Direct Torque and Suspension Force Control for Bearingless Induction Motors Based on Active Disturbance Rejection Control Scheme

The bearingless induction motor (BIM) system has the characteristics of non-linear, strongly coupled, and highly accurate. To achieve the stable and accurate control of BIM, the methods of direct torque control (DTC) and direct suspension force control (DSFC) based on space vector modulation (SVM) are introduced first. However, the dynamic performance and uncertain anti-jamming robustness of the system need to be further researched. Based on the BIM control system, the active disturbance rejection control (ADRC) technology is selected in this paper. The total disturbance of the system is estimated in real time by using the extended state observer (ESO). According to the estimated value of the ESO, the disturbance can be compensated by the ADRC in time to eliminate the steady-state tracking error to achieve good anti-interference performance. The ADRC-based direct torque and suspension force control system for the BIM is designed and simulated by the MATLAB software. The simulation and experiment results show that the ADRC technology can effectively suppress the impact of load disturbance, reduce the overshoot, and have strong robustness.

Robust Deadbeat Predictive Power Control With a Discrete-Time Disturbance Observer for PWM Rectifiers Under Unbalanced Grid Conditions

This paper presents a robust deadbeat predictive power control (DPPC) for pulsewidth modulation (PWM) rectifiers with the consideration of parameter mismatches under unbalanced grid conditions. First, conventional DPPC is modified to extend its application to both ideal and unbalanced grid conditions. Second, a tracking error of the modified DPPC with inaccurate grid-side impedance is analyzed. Third, a discrete-time power disturbance observer (DPDO) is designed to achieve accurate power control with mismatched parameters. The designed DPDO can predict complex power at the next sampling instant and estimate system disturbance simultaneously. Therefore, the DPDO can contribute to eliminate the steady-state tracking error resulting from disturbances caused by inaccurate parameters and compensate one-step delay in digital implementation. Although satisfactory steady-state performance can be obtained with modified DPPC and DPDO, transient performance still deteriorates significantly with an inaccurate value of the grid-side inductance. Thus, an online adaptive method to estimate mismatched inductance is finally developed based on the proposed DPDO. Both DPPC and DPDO are implemented in the stationary reference frame without coordinate transformation. Theoretical analysis confirms that the proposed DPDO can track disturbance without phase lag or magnitude error. Experimental tests and comparative studies with a prior DPPC on a two-level PWM rectifier validate the effectiveness of the proposed scheme.

Passive Fault Tolerant Control System Using Feed-forward Neural Network for Two-Tank Interacting Conical Level Control System Against Partial Actuator Failures and Disturbances

Abstract A novel approach for passive fault-tolerant control (PFTC) system design against actuator faults is proposed. The scheme is based on Feed-forward Neural Network (FFNN) plus conventional PI controller, during the fault occurred into system FFNN will give additional control output to the system according to fault magnitude. The FFNN will trained using back-propagation algorithm. To eliminate the steady-state tracking error, the PI controller is also incorporated. The following fault type and input signals are considered: abrupt, step, sine, and trapezoidal trajectory inputs. The effectiveness and the superiority of the proposed approach are demonstrated using Two-Tank Interacting Conical Level Control System (TTICLCS) example. The simulation performed in MATLAB Simulink platform, also different integral errors like IAE, ISE and IATE are presented to validate the proposed approach.