Small Tracking Error Research Articles

Robust Control of Exo-Abs, a Wearable Platform for Ubiquitous Respiratory Assistance

Abstract Existing noninvasive breathing assist options compatible with out-of-hospital settings are limited and not appropriate to enable essential everyday activities, thereby deteriorating the quality of life. In our prior work, we developed the Exo-Abs, a novel wearable robotic platform for ubiquitous assistance of respiratory functions in patients with respiratory deficiency. This paper concerns the development of a model-based closed-loop control algorithm for the Exo-Abs to automate its breathing assistance. To facilitate model-based development of closed-loop control algorithms, we developed a control-oriented mathematical model of the Exo-Abs. Then, we developed a robust absolutely stabilizing gain-scheduled proportional-integral control algorithm for automating the breathing assistance with the Exo-Abs, by (i) solving a linear matrix inequality formulation of the Lyapunov stability condition against sector-bounded uncertainty and interindividual variability in the mechanics of the abdomen and the lungs and (ii) augmenting it with a heuristic yet effective gain scheduling algorithm. Using in silico evaluation based on realistic and plausible virtual patients, we demonstrated the efficacy and robustness of the automated breathing assistance of the Exo-Abs under a wide range of variability in spontaneous breathing and Exo-Abs efficiency: the absolutely stabilizing gain-scheduled proportional-integral control resulted in small exhalation trajectory tracking error (<30 ml) with smooth actuation, which was superior to (i) its proportional-integral control counterpart in tracking efficacy and to (ii) its proportional-integral-derivative control counterpart in chattering.

A new hybrid fixed and adaptive gains control algorithm to reduce power losses on LLCL filter-based renewable energy conversion systems with systematic parametrization using Grey Wolf optimizer

Currently, there is a transition in the energy matrix around the world, where traditional sources of energy generation are continually being replaced by energy generation systems based on renewable sources to mitigate the climate crisis. In this bias, this work presents the mathematical modeling of an LLCL filter, used to connect power generation systems based on renewable energy sources to the electrical grid, and presents a novel hybrid fixed-and adaptive gains control strategy for current injection into the grid using this system. The developed hybrid controller is composed of a proportional–integral controller and a direct robust adaptive controller. The first term of the controller guarantees the reference current, while the second term of the controller is used for disturbance rejection. Furthermore, a systematic procedure for the controller’s parametrization based on Grey Wolf Optimizer is also provided. The control of the current injected into the grid is carried out considering the LLCL filter without passive damping resistors in the filter structure to avoid power losses due to the passive filter elements. Additionally, the LLCL filter model considers minimal parasitic resistances to evaluate the controller’s performance and optimize it for the application of interest, aiming to maximize the system performance by ensuring a short transient regime due to the fast closed-loop system response. Simulation results indicate high performance of this optimized control strategy with small tracking error even considering grid impedance variations.

Adaptive synchronous sliding control for a robot manipulator based on neural networks and fuzzy logic

Robot manipulators have become important equipment in production lines, medical fields, and transportation. Improving the quality of trajectory tracking for robot hands is always an attractive topic in the research community. This is a challenging problem because robot manipulators are complex nonlinear systems and are often subject to fluctuations in loads and external disturbances. This article proposes an adaptive synchronous sliding control scheme to improve trajectory tracking performance for a robot manipulator. The proposed controller ensures that the positions of the joints track the desired trajectory, synchronize the errors, and significantly reduces chattering. First, the synchronous tracking errors and synchronous sliding surfaces are presented. Second, the synchronous tracking error dynamics are determined. Third, a robust adaptive control law is designed, the unknown components of the model are estimated online by the neural network, and the parameters of the switching elements are selected by fuzzy logic. The built algorithm ensures that the tracking and approximation errors are ultimately uniformly bounded (UUB). Finally, the effectiveness of the constructed algorithm is demonstrated through simulation and experimental results. Simulation and experimental results show that the proposed controller is effective with small synchronous tracking errors, and the chattering phenomenon is significantly reduced.

Small tracking error correction for moving targets of intelligent electro-optical detection systems

Small tracking error correction for moving targets of intelligent electro-optical detection systems

Fast Finite-Time Composite Controller for Vehicle Steer-by-Wire Systems with Communication Delays

The modern steer-by-wire (SBW) systems represent a revolutionary departure from traditional automotive designs, replacing mechanical linkages with electronic control mechanisms. However, the integration of such cutting-edge technologies is not without its challenges, and one critical aspect that demands thorough consideration is the presence of nonlinear dynamics and communication network time delays. Therefore, to handle the tracking error caused by the challenge of time delays and to overcome the parameter uncertainties and external perturbations, a robust fast finite-time composite controller (FFTCC) is proposed for improving the performance and safety of the SBW systems in the present article. By lumping the uncertainties, parameter variations, and exterior disturbance with input and output time delays as the generalized state, a scaling finite-time extended state observer (SFTESO) is constructed with a scaling gain for quickly estimating the unmeasured velocity and the generalized disturbances within a finite time. With the aid of the SFTESO, the robust FFTCC with the scaling gain is designed not only for ensuring finite-time convergence and strong robustness against time delays and disturbances but also for improving the speed of the convergence as a main novelty. Based on the Lyapunov theorem, the closed-loop stability of the overall SBW system is proven as a global uniform finite-time. Through examination across three specific scenarios, a comprehensive evaluation is aimed to assess the efficiency of the suggested controller strategy, compared with active disturbance rejection control (ADRC) and scaling ADRC (SADRC) methods across these three distinct driving scenarios. The simulated results have confirmed the merits of the proposed control in terms of a fast-tracking rate, small tracking error, and strong system robustness.

Dual-Loop Integral Sliding Mode Control-Based Path Tracking with Reaction Torque for Autonomous Underwater Vehicle

Path tracking control is an important method for a Six-Degree-Of-Freedom Autonomous Underwater Vehicle to perform specific underwater tasks. Therefore, this paper investigates a dual-loop integral sliding mode control (DLISMC)-based tracking controller for an AUV with model uncertainties and external disturbances, and introduces a new reaction torque model for static compensation in order to improve the attitude control capability for AUVs when performing path tracking. In addition, the stability of tracking control law based on DLISMC is demonstrated using the Lyapunov function. Finally, numerical simulations are carried out on MATLAB 2016/Simulink and compared with the Proportion–Integral–Differential (PID) control commonly used in industry as well as the dual-loop Proportion–Integral–Differential (DLPID). Simulation results show that the DLISMC has a smaller tracking error, faster convergence speed, and more robustness against external disturbances and reaction torque.

Data-driven two-dimensional integrated control for nonlinear batch processes

Two-dimensional control has been considered as an effective strategy to accomplish high-accuracy tracking for batch processes because of its excellent learning ability and time-domain stability. However, being a model-based control method, the performance of the two-dimensional control system will inevitably decrease due to unknown uncertainties or unmodeled dynamics. In addition, the high computational cost and complex design process of the control system severely limit its application in batch processes. For this reason, this paper proposes a new data-driven two-dimensional integrated control (DDTDIC) method for nonlinear batch processes. In the presented control scheme, the P-type iterative learning control (ILC) is adopted along the batch-axis to ensure the convergence of the system, and the proportional-integral-differential (PID) control is used in the time-axis to reject the influence of real-time disturbance. The parameters of the PID controller are obtained by utilizing the virtual reference feedback tuning (VRFT) method. The entire design process of the control system only requires the input and output (I/O) data of the batch processes and does not depend on any explicit model information. The simulation results show that compared with the ILC and the two-dimensional control, the presented control method not only has faster convergence speed and smaller tracking error, but also the computational efficiency is improved by more than 40% and 50% respectively.

Learning and Outperforming the Model Predictive Control With a Linear ϵ-Support Vector Machine for Power Converter

This paper presents a linear ϵ error insensitive support vector machine (ϵ-SVM) learned from the model predictive control (MPC) with very limited training samples. Unlike the existing learning-based MPC which takes the same inputs as the MPC, the ϵ-SVM learns from historical data as well. Such structure is found to have both feedforward and feedback elements that improve performance. Besides, using the ϵ error-insensitive tube also increases the noise cancellation capability. The experiment is carried out on a three-phase inverter with an L-C filter and shows that the linear ϵ-SVM-MPC not only has better performance than the artificial neural networks (ANN) MPC, but also outperforms the online MPC in both low THD values and small tracking errors regardless the load conditions. Moreover, the use of the linear kernel significantly reduces the time complexity to <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</i> (1), which is much less than <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</i> (2 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ⁿ</i> ) in either online MPC or ANN-MPC. Therefore, the linear ϵ-SVM-MPC has provided an effective way to implement the MPC and it is preferable for the DSP. This article is accompanied by a video demonstrating the real-time operation.

Event-triggered impulsive observer with [formula omitted]-asymptotic gain for DC microgrids

This paper studies the problem of the state estimate of a class of DC microgrids with both disturbed states and disturbed outputs via event-triggered impulsive observer (ETIO). First, a mathematical model is established for such class of DC microgrids, and then the notion of impulsive observer including impulsive observer with K-asymptotic gain is proposed. Then, by using two Lyapunov-like functions, a scheme of event-triggered impulsive control (ETIC) via three layers of event-triggering conditions is designed for ETIO to track the state of the DC microgrid. And an algorithm is given for the implementation of ETIC in practice. The ETIC scheme is then extended to the sampling-based ETIC (S-ETIC) to reduce the calculation and improve the effectiveness of the ETIC. Both theoretical proofs and numerical simulations are given to show that the proposed ETIO via both ETIC and S-ETIC can track the state of the DC microgrid within K-asymptotic gain. Specifically, when the disturbance tends to zero, the tracking is accurate. Moreover, the simulation is given for comparisons between ETIO and other observers including the classic impulsive observer, Luenberger observer, sliding mode observer, and extended state observer. It is shown that the designed ETIO has advantages of lower impulse frequency, lower control cost, and smaller tracking error than the other observers.

Linear Active Disturbance Rejection Lateral Controller for Unmanned All-Terrain Vehicle

Abstract: To address the disturbance of model uncertainty, a linear active disturbance rejection controller (LADRC) was designed for robust lateral control of unmanned all-terrain vehicle. In terms of relative motion of target node and current state, first-order lateral tracking model is established. According to the developed model, linear tracking differentiator (LTD), linear extended state observer (LESO) and linear state error feedback (LSEF) are designed in turn. LESO could observe the uncertainty of system and LSEF could compensate the uncertainty to make system robust. In order to verify the effectiveness, two typical scenarios, circle and double lane tracking, were designed for test. And the uncertainties of wheelbase and steering ratio were considered. Results illustrate that the designed LADRC can stably control the unmanned all-terrain vehicle tracking reference trajectory under both scenarios and has the advantages of small tracking error and small overshoot compared with the conventional pure tracking methods.

Disturbance observer–based backstepping sliding mode cascade control of 2–degrees of freedom hydraulic tunneling robot

For the 2–degrees of freedom position tracking problem of the robotized hydraulic-driven roadheader with high nonlinearities and strong uncertainties, a practical disturbance observer–based backstepping sliding cascade control method together with an adaptive compensator is proposed and investigated. The presented methodology mainly includes a continuous nonsingular fast terminal sliding mode with the backstepping technique and the power reaching law with time-varying coefficients used to achieve satisfactory performance against the multi-source disturbances, two disturbance observers used to approximately estimate the unknown dynamics in the mechanical and hydraulic subsystem, respectively. Simultaneously, a continuous robustifying term is also utilized to compensate for the residual disturbances and enhance the robustness. The presented control method doesn’t need the precise model thanks to the auxiliary disturbance observer, and can ensure fast convergence and small tracking error thanks to the backstepping sliding cascade control and the adaptive robust compensator. Based on Lyapunov theory, stability of the overall closed-loop system is proved rigorously, and asymptotically bounded tracking performance of the robotic manipulator is guaranteed. Finally, 2–degrees of freedom trajectory tracking experiments are conducted, and comparative results effectively verify the superiorities of the proposed method.

Time‐varying state constrained estimators‐based command filtered quantized consensus control for nonlinear multiagent systems

AbstractThis article investigates the command filtered backstepping quantized consensus control for the time‐varying full‐state constrained nonlinear multiagent systems based on unknown system dynamics estimators (USDE). First, different from the intelligent control and the USDE‐based control methods, a novel time‐varying state constrained (TVSC)‐USDE is developed to estimate the unknown nonlinear dynamics and disturbances exactly with fewer parameters, where the states in TVSC‐USDE satisfy the state constraints requirements. The proposed TVSC‐USDE can reduce the computational burdens that caused by the online estimation of weights. Second, distinguish from current state constraints methods, by designing the integral barrier Lyapunov functions (IBLFs), the conservatism feasibility conditions are removed, which is more reasonable for the physical multiagent systems. Furthermore, the explosion of complexity (EOC) is a vital issue to tackle under the IBLFs backstepping control schemes. For this purpose, this article designs the command filters to gain the derivatives and handle the EOC problem. Further, to counterbalance the filtering errors, the error compensation signals are first developed in IBLFs‐based control method. Finally, the input quantized signals are introduced for the limited bandwidth problem in multiagent network systems, and the proposed control approach can attain consensus tracking under low communication rates and small tracking errors.

Adaptive sliding mode controller based on fuzzy rules for a typical excavator electro-hydraulic position control system

In order to improve the trajectory tracking accuracy and robustness of a typical heavy electro-hydraulic position system, a fuzzy adaptive sliding mode controller is proposed. A potential-like function is introduced to design a new sliding surface with non-linear integral term. An adaptive controller is designed to approximate the equivalent controller in sliding mode control. Stability of the controller is demonstrated by Lyapunov method, and the chattering phenomenon caused by the nonlinear switching term is reduced by using the fuzzy switching method, 25 fuzzy rules are given to adjust the sliding mode switching controller. Simulations with sinusoidal, ramp and step signals, and experiments with leveling operation at different speeds are carried out. The proposed controller can follow the reference trajectory quickly and smoothly, and has certain anti-interference ability. Compared with the traditional sliding mode controller, the proposed controller has small tracking error, fast response and good tracking performances.

Adaptive dynamic programming for data-based optimal state regulation with experience replay

Traditional model-based control methods require accurate system dynamics. However, the dynamics are usually unknown and it is challenging to tune the control parameters manually when controlling a complex nonlinear system. In this paper, we propose a novel reinforcement learning method that combines the advantages of a model-based method, namely Adaptive Dynamic Programming (ADP), with the actor-critic method. Specifically, a linear approximate model is chosen to obtain the estimated dynamics as part of the optimal policy. Then, a designed actor-critic structure is used to obtain the sub–policy. We provide the theoretical proof of convergence and validate the proposed method through simulation experiments. The experimental results demonstrate the effectiveness of the proposed method with smaller tracking errors and faster learning speed compared with the controller trained by the actor-critic method.

A self-adjusting multi-objective control approach for quadrotors

The quadrotor represents a class of highly nonlinear dynamic systems and its controllability features are challenging. Hence, it serves as an ideal unmanned aerial vehicle platform to validate many artificial intelligence-based research investigations. Nonetheless, most of the offline tuning approaches devote efforts to find near optimal control gains to regulate individually the decoupled motion directions. This work adopts a multi-objective self-adjusting search mechanism to actuate the motions of a quadrotor via deciding the control gains of the interacting loops simultaneously. This algorithm employs a first order low pass filter transfer function as an accepting approach for the tunning mechanism. The proposed approach is compared with a Genetic Algorithm and another nonlinear Proportional-Integral-Derivative approach to highlight the usefulness of the proposed mechanism. It was founded that quadrotor follows the desired trajectory with a small tracking error of less than 2% in the X-Y plane and less than 1 % error tracking error in the altitude Z. Also, it is recorded that MONLTA can overcome the simulated wind disturbances of 0.1 N.m as a disturbance torque.

Disturbance Observer-Based Terminal Sliding Mode Tracking Control for a Class of Nonlinear SISO Systems with Input Saturation

This paper focuses on the trajectory tracking control for general nonlinear single-input single-output (SISO) systems in which the output is not directly related to the control input. To address the tracking problem with the consideration of possible model uncertainty, external disturbance, and control input saturation, we employ the input-output feedback linearization technique and design a finite-time disturbance observer-based terminal sliding mode controller to improve the tracking performance and enhance the robustness. The stability analysis is carried out by using the Lyapunov method. To alleviate the chattering while achieving an acceptable control performance, a boundary layer method is adopted for the trade-off between the high-frequency control actions and the bounded unavoidable nonzero steady-state error. The proposed method is evaluated on the two typical nonlinear systems, which are fully linearizable and partially linearizable, respectively, and compared to the state-of-the-art method in terms of tracking and robustness through comprehensive numerical simulations. The results show that the proposed method not only renders the estimated disturbance error tends to be zero in finite time, but also has superiority in the fast reaction to disturbance and small tracking error without high-frequency chattering.

An optimal initialisation for robust model reference adaptive PI controller for grid-tied power systems under unbalanced grid conditions

This paper presents an Optimal Robust Model Reference Adaptive Proportional–Integral controller for grid-tied power systems, which is automatically parametrised using a Genetic Algorithm. The task of choosing the adaptation rate and the controller’s initial gains set is now performed in a computational and automatic way, saving design time and ensuring satisfactory transient regimes.The use of a Genetic Algorithm for complete parametrisation of robust adaptive controllers applied to renewable energy power generation systems with LCL filter is first here explored. Five cost functions are considered in the optimisation process. A comparison of simulation results applying the optimised controller in a grid-tied Voltage Source Inverter with LCL filter points out the benefits and drawbacks of using each cost function. A framework for performance analysis and an in-depth discussion are provided. The function determined as the best one, which is integral of absolute error, is used in the controller implemented experimentally, ensuring suitable tracking of grid current references and rejection of grid voltage harmonics, even under unbalanced grid voltage conditions. An experimental comparison in a three-phase 6.75 kW power converter with the non-optimised controller is also provided, where the optimised controller obtains a reduction in the overshoot in all transient regimes and smaller tracking error, resulting in a reduction in the mean error of 14.31% and 60.30% in α and β coordinates, respectively. In addition, the optimised controller reduces total harmonic content, improving energy quality. This parametrisation procedure can be immediately extended to the control of any other power converter systems.

A composite adaptive robust control for pneumatic servo systems with time-varying inertia

This article proposes a composite adaptive robust control for a pneumatic servo system with time-varying inertia to achieve a good tracking performance. The proposed design not only preserves the merits of both direct adaptive robust control and indirect adaptive robust control but also obtains a better performance of the working condition with time-varying inertias. Firstly, prescribed tracking performance is guaranteed without knowing the bounds of parametric and non-parametric uncertainties by leveraging a discontinuous projection and deterministic robust control technique. And a nonlinear tracking differentiator is used to obviate differential signal in backstepping. Secondly, the online parametric estimation algorithm is developed by intelligently integrating tracking error dynamics and physical plant dynamics. By effectively using the information of both tracking error and prediction error, a high adaptation gain can be used for achieving a faster parameter convergence and smaller tracking error. Moreover, exponential convergence of both tracking error and prediction error can be obtained under certain conditions. Lastly, comparative experiments on different conditions are carried out for a single-rod pneumatic cylinder driven by a proportional directional valve to demonstrate the superiority of the proposed method.

A composite adaptive robust control for nonlinear systems with model uncertainties

AbstractThis article is concerned with a composite adaptive robust control (CARC) for non‐strict feedback nonlinear systems with model uncertainties including parametric uncertainties and uncertain nonlinearities. It is assumed that the model uncertainties of the nonlinear system are bounded but unknown. Firstly, prescribed tracking performance is achieved by the CARC control law even the unknown parameters are time‐varying. This is accomplished firstly by designing a discontinuous projection that confines the unknown parameters in an estimated region. Then the robustness of the closed‐loop system is guaranteed by leveraging the deterministic robust control philosophy. Also, a command filter has been designed to avoid computing complex derivatives of virtual control law in the backstepping procedure. Secondly, a composite adaptation law that intelligently integrates information of both tracking error and prediction error is constructed for improving the performance of controllers. The high adaptation gain of CARC leads to higher parameter convergence speed and smaller tracking errors. Moreover, if the actual parameters are within the design range, asymptotic stability can be achieved in presence of parametric uncertainties only. In addition, exponential convergence of tracking errors and parameters can be shown under certain conditions. Finally, numerical examples are made to validate the superiority and effectiveness of the proposed control scheme.

Adaptive fuzzy fast terminal sliding mode control for inverted pendulum-cart system with actuator faults

In this work, the adaptive fuzzy fast terminal sliding mode control (AFFTSMC) is used to create a robust fault-tolerant control system for the care and swing-up control problem of the inverted pendulum-cart system is developed in the presence of actuator faults and external disturbances. The proposed controller has the benefit of the fast terminal sliding mode control (FTSMC) method to guarantee faults and uncertainties compensation, small tracking error, chattering phenomenon reduction, and fast transient response. To compensate for the uncertainties and actuator faults effects that can happen in practical tasks of an inverted pendulum-cart system, a new adaptive FTSMC method is proposed, where the prior knowledge of external perturbation and uncertainties is not required. In addition, the developed controller reduces the chattering phenomenon without disappearing the tracking precision and robustness property. Stability demonstration has been effectuated utilizing Lyapunov method. Practical results prove the efficiency of the suggested control algorithm.