Steady-state Tracking Error Research Articles

Decoupled Active and Reactive Power Predictive Control for PV Applications Using a Grid-Tied Quasi-Z-Source Inverter

This paper proposes a predictive power control algorithm that decouples active and reactive power for grid integration of photovoltaic (PV) systems using a quasi-Z-source inverter. This is important to meet the emerging smart inverter requirements for grid interconnection. The proposed controller uses model predictive control framework to ensure that the maximum available power is harvested from the PV array and that the active and reactive power injected into the grid is controlled to compensate reactive power required by local loads and as need to ensure stable operation of the grid at the point of common coupling. Thus, a power electronics interface is proposed to integrate the PV array to the grid and to work as a reactive power compensator simultaneously. A robust technique is proposed to regulate the impedance network voltage and current according to the maximum operating point of PV panels and grid voltage/current requirements. The proposed controller features a simple structure suitable for practical implementation, fast-dynamic response under changing sky condition, and negligible tracking error in steady state for decoupled active and reactive power control in a typical distributed generation systems. The performance of the proposed controller is verified experimentally; the grid-side power quality analysis is provided and evaluated according to IEEE-519 standard.

Low-Complexity Finite Control Set Model Predictive Control With Current Limit for Linear Induction Machines

In order to limit the armature current within a safe region, this paper proposes a finite control set model predictive control (FCS-MPC) method for linear induction machines (LIMs) by adding a penalty overcurrent term in the cost function. The modulation strategies based on two and three voltage vectors are combined with FCS-MPC so as to reduce the current ripples and steady-state tracking errors. Three different search methods have been developed to help reduce the computational burden by excluding many unsuitable participating voltage vectors and combinations in advance. These search methods are also effective for FCS-MPC with current limit. Finally, some key performance indexes are fully compared for LIMs controlled by different FCS-MPC-based modulation strategies through comprehensive numerical simulation and experiments on a test bench with two 3-kW arc induction motors. It is shown that the proposed low-complexity control strategies can effectively avoid overcurrent under any circumstances.

Extended state observer-based robust non-linear integral dynamic surface control for triaxial MEMS gyroscope

SUMMARYThis paper reports an extended state observer (ESO)-based robust dynamic surface control (DSC) method for triaxial MEMS gyroscope applications. An ESO with non-linear gain function is designed to estimate both velocity and disturbance vectors of the gyroscope dynamics via measured position signals. Using the sector-bounded property of the non-linear gain function, the design of an $\mathcal{L}_2$-robust ESO is phrased as a convex optimization problem in terms of linear matrix inequalities (LMIs). Next, by using the estimated velocity and disturbance, a certainty equivalence tracking controller is designed based on DSC. To achieve an improved robustness and to remove static steady-state tracking errors, new non-linear integral error surfaces are incorporated into the DSC. Based on the energy-to-peak ($\mathcal{L}_2$-$\mathcal{L}_\infty$) performance criterion, a finite number of LMIs are derived to obtain the DSC gains. In order to prevent amplification of the measurement noise in the DSC error dynamics, a multi-objective convex optimization problem, which guarantees a prescribed $\mathcal{L}_2$-$\mathcal{L}_\infty$ performance bound, is considered. Finally, the efficacy of the proposed control method is illustrated by detailed software simulations.

A Parameter Self-Calibration Method for GNSS/INS Deeply Coupled Navigation Systems in Highly Dynamic Environments.

The GNSS/INS (Global Navigation Satellite System/Inertial Navigation System) navigation system has been widely discussed in recent years. Because of the unique INS-aided loop structure, the deeply coupled system performs very well in highly dynamic environments. In practice, vehicle maneuvering has a big influence on the performance of IMUs (Inertial Measurement Unit), and determining whether the selected IMUs and receiver parameters satisfy the loop dynamic requirement is still a critical problem for deeply coupled systems. Aiming at this, a new parameter self-calibration method based on the norm principle is proposed which explains the relationship between IMU precision and the velocity error of the system; the method will also provide a detailed solution to calculate the loop steady-state tracking error, so it will eventually make a judgment about the stability of the tracking loop under present system parameter settings. Lastly, a full digital simulation platform is set up, and the results of simulations show good agreement with the proposed method.

Adaptive Compensation for Infinite Number of Time-Varying Actuator Failures in Fuzzy Tracking Control of Uncertain Nonlinear Systems

The problem of direct adaptive compensation for infinite number of time-varying actuator failures/faults is of both theoretical and practical importance in the fuzzy tracking control of uncertain nonlinear systems. However, due to the technical difficulties, so far, very limited result is available in addressing such an issue, which thus motivates us to propose a new fuzzy control methodology in this paper. The proposed scheme is established from the techniques of projection adaptation design, a new piecewise Lyapunov function analysis, and an optimized fuzzy adaptation. It is shown that all the closed-loop signals are bounded and the steady-state tracking error converges to a residual around zero, irrespective of a possibility that there are infinite number of time-varying actuator failures. Simulations are provided to illustrate the effectiveness and applicability of the proposed scheme.

An Adaptive Resonant Regulator for Single-Phase Grid-Tied VSCs

The proportional-resonant (PR) controller is highly popular for controlling grid-connected voltage source converters. The resonant part of this controller provides an infinite gain at the nominal frequency and, in this way, ensures a zero steady-state tracking error when the grid frequency is at its nominal value. In the presence of frequency drifts, nevertheless, a zero tracking error may not be guaranteed. To deal with this problem, the resonance frequency of the PR controller may be updated using the frequency estimated by the synchronization unit, which is often a phase-locked loop. In recent years, however, there is a growing attention toward eliminating the need for a dedicated synchronization unit and designing integrated synchronization and control structures as they benefit from a simpler and more compact structure. In this letter, based on a structural resemblance between a resonant current regulator and second-order generalized integrator-based frequency-locked loop, a frequency-adaptive resonant controller is presented. The tuning procedure of the proposed controller is discussed, and some experimental results are presented to verify its effectiveness.

Robust Design of LCL Filters for Single-Current-Loop-Controlled Grid-Connected Power Converters With Unit PCC Voltage Feedforward

The point of common coupling (PCC) voltage feedforward control is widely employed for LCL-type grid-connected converters to prevent large inrush current during startup, reduce steady-state tracking error, and suppress disturbances of grid voltage. Generally, this feedforward loop is ignored in the system modeling and stability analysis for simplicity. However, the grid impedance would be introduced to the control system through the feedforward loop under practical power grids, leading to a different current loop model from the original one, then conventional LCL filter design for single-current-loop control may be inappropriate. In this paper, the detailed modeling of current control loop with unit PCC voltage feedforward is presented. Based on the established model, it is found that unstable open-loop poles may appear under grid impedance variation, which thus may cause system instability. Therefore, the robust design regions of LCL filters against grid impedance variation are proposed for single-current-loop control schemes. Moreover, another interesting finding is that the feedforward control can help maintain a high current control bandwidth under grid impedance variation. This feature is highly desirable if multiple resonant controllers are employed for harmonic compensation. Experimental results are finally presented to verify the theoretical analysis and robust design presented in this paper.

Prescribed performance-based low-computational cost fuzzy control of a hypersonic vehicle using non-affine models

A novel adaptive fuzzy control approach with low computational costs is addressed for the longitudinal non-affine model of a generic hypersonic vehicle subject to parametric uncertainties, capable of guaranteeing that altitude and velocity tracking errors exhibit prescribed performance. A new performance function is devised to impose preselected bounds on the transient and steady-state tracking error performance, and then a transformed error is constructed, which converts the original “constrained” system into an equivalent “unconstrained” one for the simplicity of control designs. Furthermore, a simplified fuzzy controller is exploited for the altitude subsystem, eliminating the issue of “explosion of complexity” that is associated with back-stepping control. For the velocity subsystem, a prescribed performance-based proportional–integral controller is utilized. The special contributions of the proposed control strategy are that it can guarantee altitude and velocity tracking errors with desired transient and steady-state performance, and meanwhile the computational load is quite low. Finally, numerical simulation results are presented to verify the efficiency of the design.

Adaptive Learning Based Tracking Control of Marine Vessels with Prescribed Performance

A novel adaptive tracking controller of fully actuated marine vessels is proposed with completely unknown dynamics and external disturbances. The model of dominant dynamic behaviors and unknown disturbances of the vessel are learned by a neural network in real time. The controller is designed and it unifies backstepping and adaptive neural network techniques with predefined tracking performance constraints on the tracking convergence rate and the transient and steady-state tracking error. The stability of the proposed adaptive tracking controller of the vessel is proven with a uniformly bounded tracking error. The proposed adaptive tracking controller is shown to be effective in the tracking control of marine vessels by simulations.

Generalized-Extended-State-Observer-Based Repetitive Control for MIMO Systems With Mismatched Disturbances

This paper concerns the problem of designing a modified repetitive-control system based on a generalized extended state observer (GESO) for a class of multi-input, multi-output systems in the form of a nonintegral chain and with mismatched disturbances. A GESO is constructed to estimate a lumped disturbance in a real-time fashion. Then, an improved repetitive control law is developed to attenuate the influence of the lumped disturbance from the output channel. A correction to the amount of the delay of the repetitive controller is introduced to further reduce the steady-state tracking error. A stability criterion and a design algorithm are presented. Finally, simulations and comparisons with other methods demonstrate the validity of this method.

Neural network–based nonaffine control of air-breathing hypersonic vehicles with prescribed performance

This article investigates a novel nonaffine control strategy using neural networks for an air-breathing hypersonic vehicle. Actual actuators are regarded as additional state variables and virtual control inputs are derived from low-computational cost neural approximations, while a new altitude control design independent of affine models is addressed for air-breathing hypersonic vehicles. To further reduce the computational load, an advanced regulation algorithm is applied to devise adaptive laws for neural estimations. Moreover, a new prescribed performance mechanism is exploited, which imposes preselected bounds on the transient and steady-state tracking error performance via developing new performance functions, capable of guaranteeing altitude and velocity tracking errors with small overshoots. Unlike some existing neural control methodologies, the proposed prescribed performance-based nonaffine control approach can ensure tracking errors with preselected transient and steady-state performance. Meanwhile, the complex design procedure of backstepping is also avoided. Finally, simulation results are presented to validate the design.

Robust iterative learning control for multi-phase batch processes: an average dwell-time method with 2D convergence indexes

ABSTRACTIn order to cope with system disturbances in multi-phase batch processes with different dimensions, a hybrid robust control scheme of iterative learning control combined with feedback control is proposed in this paper. First, with a hybrid iterative learning control law designed by introducing the state error, the tracking error and the extended information, the multi-phase batch process is converted into a two-dimensional Fornasini–Marchesini (2D-FM) switched system with different dimensions. Second, a switching signal is designed using the average dwell-time method integrated with the related switching conditions to give sufficient conditions ensuring stable running for the system. Finally, the minimum running time of the subsystems and the control law gains are calculated by solving the linear matrix inequalities. Meanwhile, a compound 2D controller with robust performance is obtained, which includes a robust extended feedback control for ensuring the steady-state tracking error to converge rapidly. The application on an injection molding process displays the effectiveness and superiority of the proposed strategy.

Adaptive fault tolerant control for trajectory tracking of a quadrotor helicopter

In this paper, an adaptive fault tolerant controller based on [Formula: see text] control is developed and applied to the trajectory tracking for a quadrotor helicopter. Both multiplicative and additive actuator faults are considered. The proposed design is based on nonlinear feed-forward compensations and a typical nonlinear quadrotor model with uncertain inertial parameters and external disturbances. The [Formula: see text] adaptive control design is slightly modified to adapt with the position and the attitude error dynamics. The proposed adaptive controller yields uniformly verifiable bounds on the transient and the steady-state tracking error for any designated bounded reference trajectory. In the presence of fast adaptation, the adaptive controller compensates for actuator fault and disturbances in a particular frequency range. Finally, simulation results are included to validate the effectiveness of the proposed design.

Data-driven sliding mode control of unknown MIMO nonlinear discrete-time systems with moving PID sliding surface

This paper investigates the problem of data-driven sliding mode control (DDSMC) for a class of unknown MIMO nonlinear discrete-time systems with both uncertainties and disturbances. Utilizing the non-parametric dynamic linearization technique (NDLT) and the second-order discrete sliding mode observer (2-DSMO), a novel DDSMC law based on the PID sliding surface is developed to achieve faster transient responses with less steady-state tracking errors. A disadvantage of this strategy is that the PID sliding surface design is based on constant coefficients, which may prevent further control performance improvement of the plant. Then, inspired by the fuzzy logic control (FLC) scheme, a moving PID sliding surface is proposed to further enhance the performance of the DDSMC approach, where the PID sliding surface parameters are updated by the proposed data-driven adaptive law. Using the proposed sliding surface, faster dynamic response and less overshoot of the tracking behaviors are achieved with the magnitude of the discontinuous control gain unchanged. Furthermore, the couplings, uncertainties and disturbances are also suppressed owing to the application of the 2-DSMO. Also, the overall closed-loop system is also shown to be asymptotically stable. Finally, numerical and experimental results are given to validate the effectiveness of the proposed approach.

Optimal adaptive reset control with guaranteed transient and steady state tracking error bounds

In this paper, a solution for improvement of transient performance in adaptive control of nonlinear systems is proposed. An optimal adaptive controller based on a reset mechanism and a prescribed performance bound is devised. The suggested controller has the structure of adaptive backstepping controller in which the estimated parameters are reset to an optimal value. The designed controller ensures both the transient bound and the asymptotical convergence of the states. It is shown that the tracking error satisfies the prescribed performance bound all the time, besides the speed of the convergence rate is increased by resetting the estimated parameters. The results have been proved through both the analytical and simulation studies. The proposed method is applied to an Augmented Quarter Car Model as a case study. Simulation results verify the established theoretical consequences that the prescribed performance bound based optimal adaptive reset controller can enhance the transient performance of the adaptive controller.

Prediction-based Adaptive Robust Control for a Class of Uncertain Time-delay Systems

This paper presents an integrated control design approach for a class of dynamical systems that satisfy a certain matching condition subject to known input time-delay, unknown parameters, and time-varying disturbances, simultaneously. A novel nonlinear predictor adaptive robust control (PARC) is proposed to track a desired state trajectory. The controller uses predictor-based model compensation to attenuate the effect of input time-delay, gradient type projection with prediction-based learning mechanisms to reduce the parameter uncertainties, and prediction-based nonlinear robust feedback to attenuate the effect of model approximation errors and disturbances, simultaneously. The controller guarantees a prescribed transient performance (with global exponential convergence) and final steady-state tracking error with an ultimate bound proportional to the time-delay, the disturbances, and the switching gain. The effectiveness of the proposed control design is illustrated with a simple tumor growth example.

Analysis and controller design for stand‐alone VSIs in synchronous reference frame

The common practice for controlling the stand-alone voltage source inverters (VSIs) is to transform abc voltage and current signals to DC signals using the dq transformation, which makes it possible to control the new DC voltage and current signals just using simple proportional-integral controllers with a zero steady-state tracking error. However, the transformation causes coupling terms between d- and q-axis components in both current control loops and voltage control loops, which deteriorate the dynamic and steady-state performance of the control system. This study presents a step-by-step graphical analysis and design approach for a three-phase stand-alone VSI system in the dq reference frame, which provides a clear systematic decoupling process to design the inner- and outer-loop current and voltage controllers, respectively. The closed-loop d- and q-axis output impedances of the stand-alone VSI system by considering the coupling effects between axes are also formulated, modelled, and evaluated. The study investigates how the decoupling and compensating terms added in the current and voltage controllers affect the dynamic performance and output dq impedances of the VSI system. Simulation and hardware results verify the effectiveness of the graphic design and analysis strategy.

Simulation of FPGA controlled Single Stage Boost Inverter for the Applications of Grid Connected Photovoltaic System

Improving the efficiency, reducing the cost and maintaining the power quality of a grid tied with Photovoltaic (PV) system are the important aspects of the present day research. The efficiency of power conversion can be improved by reducing the number of stages. In this paper, a single stage boost inverter topology fed from PV array is used and connected to a single phase grid. Less number of switching components is used in this topology compared to conventional technique and hence, the converter losses are reduced. This can also be very well extended to utility grid system. Further, the proposed topology includes battery backup unit which consists of a DC-DC converter to overcome the variations of Voltage based Maximum Power Point (VMPP) of PV array because of the variations in solar irradiance. The proposed system uses the current control approach which has zero steady state tracking error to control the single stage boost inverter. The proposed system offers many advantages such as low cost, high efficiency, compactness and high quality of output power. Design procedure and simulation results are obtained from MATLAB/SIMULINK and the experimental results are obtained from the model developed in the laboratory. The entire system is controlled by SPATRAN 3A FPGA board.

Robust variable step-size sign subband adaptive filter algorithm against impulsive noise

The main drawback of the sign subband adaptive filter algorithm (SSAF) is its large steady-state error and poor tracking capability. A robust variable step-size SSAF algorithm is presented to improve the performance, which uses the optimal step-size for each subband by minimizing the mean square deviation. Since the step-size contains the variance of noise-free priori error, the shrinkage denoising method is used to estimate the noise-free error signal. With the step-size adaptation influenced by the variance of error signal for each subband, the proposed algorithm is shown to achieve a significant improvement in both the convergence rate and the steady-state error than the SSAF algorithms. Besides, the proposed algorithm offers robust performance with respect to impulsive noise and good ability of tracking unknown system. Finally, simulation results demonstrate that these features of the proposed algorithm in system identification and echo-cancellation applications.

Deadbeat Weighted Average Current Control With Corrective Feed-Forward Compensation for Microgrid Converters With Nonstandard LCL Filter

Microgrid converters are required to have the capability of both grid-tied mode and islanding mode operation. For this dual-mode operation, large shunt capacitors are often used in the interfacing converter output LCL filter, as it can help to stabilize supply voltage and to reduce switching ripple pollutions to sensitive loads during autonomous islanding operation. At the same time, this modification causes a few challenges, including the low-frequency harmonic distortions, the steady-state tracking errors and the slow dynamic response, to the line current regulation during grid-tied operation. To overcome these drawbacks, a modified weighted average current controller is developed. First, to realize a fast line current response, a deadbeat control of weighted average current is developed based on a reduced-order virtual filter plant. Second, a grid voltage feed-forward term is added to the weighted average current reference to mitigate the steady-state line current tracking errors. Note that this compensation term is directly added to the current reference, thus, it is very well decoupled from the closed-loop current regulator. In addition, it can be seen that the low-order line current harmonics caused by grid voltage distortion is inherently compensated by this proposed corrective feed-forward control.