Stability Of Closed-loop System Research Articles

DOPH∞-based path-following control for underactuated marine vehicles with multiple disturbances and constraints

This paper presents a new robust path-following (PF) control method for underactuated marine vehicles with multiple disturbances and constraints. To improve the control performance and reduce the conservativeness of many PF control strategies described in the previous literature, which treated the multiple disturbances of the underactuated marine vehicle as a single equivalent disturbance, the multiple disturbances are categorized into two types according to their characteristics in this paper, i.e., the slowly varying disturbance and the H2-norm bounded disturbance. Then, a composite controller combining Disturbance-Observer-based control with H∞ control, which can be abbreviated as DOPH∞-based controller, is constructed for the control model. A disturbance observer is designed for estimating and eliminating the slowly varying disturbance, and the H∞ theory is used to attenuate the H2-norm bounded disturbance. Moreover, to improve the practicability of the control method in engineering applications, the virtual yaw angular velocity constraint and the actuator constraints are considered, and the auxiliary dynamic compensators are used to compensate for them. Finally, the closed-loop stability of the whole system is guaranteed. Simulations and comparative analyses are presented to demonstrate the effectiveness and robustness of the presented strategy.

Trajectory Tracking of UAVs Using Sigmoid Tracking Differentiator and Variable Gain Finite-Time Extended State Observer

The problem of quadrotor attitude and position control is considered in the presence of generally lumped disturbances: external disturbances and model uncertainty. The improved active disturbance rejection controller (ADRC) for quadrotor trajectory tracking is proposed for compensating the lumped disturbances. Firstly, the improved sigmoid tracking differentiator (ISTD), combining improved Sigmoid function and sliding mode terminal attractor is proposed, which can accelerate the global convergence rate and effectively reduce the chattering. Secondly, a novel variable gain finite-time extended state observer (VGFESO) approach is proposed to effectively estimate the lumped disturbances, while the observation errors are convergent to zero in finite time. Then, a super-twisting sliding model controller (STWSMC) is utilized for tracking control of the desired position and attitude. Finally, the convergence of VGFESO and the closed-loop stability of the control system are proved. The results show that the convergence time of the proposed control scheme is the shortest, and the integral absolute error of improved ADRC is reduced from 2.64 to 0.91. The anti-disturbance capability of the proposed controller is fully illustrated when compared with ADRC and robust adaptive nonsingular fast terminal sliding-mode controller (RANFTSMC).

Observer-Based Adaptive Fuzzy Control for Nonlinear State-Constrained Systems Without Involving Feasibility Conditions.

For nonlinear full-state-constrained systems with unmeasured states, an adaptive output feedback control strategy is developed. The main challenge of this article is how to avoid that the unmeasured states exceed the constrained spaces. To achieve a good tracking performance for the considered systems, a stable state observer is structured to estimate unmeasured states which are not available in the control design. In addition, the constraints existing in most practical engineering are the source of reducing control performance and causing the system instability. The main limitation of current barrier Lyapunov functions is the feasibility conditions for intermediate controllers. The nonlinear mappings are used to achieve the satisfaction of full-state constraints directly and avoid feasibility conditions for intermediate controllers. By the Lyapunov theorem, the closed-loop system stability is proven. Simulation results are given to confirm the validity of the developed strategy.

Accurate Parking Control for Urban Rail Trains via Robust Adaptive Backstepping Approach

Nowadays, precise train parking has become a key technology of automatic train operation. Due to the high nonlinearities and various uncertainties existing in the dynamics of urban rail trains (URTs), it is challenging to develop an effective parking controller to achieve high-precision parking. To address this issue, a novel robust adaptive backstepping controller is proposed in the paper, where a robust term is employed to compensate for the system uncertainties caused by the brake shoe, and meanwhile several parametric adaption laws are equipped to estimate the uncertain system parameters as well as the external disturbances. The closed-loop stability of the controlled system is analyzed rigorously by virtue of the Lyapunov theory, and the effectiveness of the proposed control scheme in precise parking of URTs is demonstrated through numerical simulations.

Linear Matrix Inequality-Based Multivariable Controller Design for Boost Cascaded Charge-Pump-Based Double-Input DC–DC Converter

An analysis and controller design of double-input dc–dc converter (DIDDC) is introduced in this article. This converter is integrated with buck and boost converters at the front-end and a charge pump on the back-end. Salient features of this topology are as follows: (i) ripple content is low in source currents, (ii) both the dc sources are connected through an inductor, which gives rise to a smooth source current waveform, (iii) both the sources supply power to load either in standalone or simultaneously together, and (iv) two control–loops (one for source current regulation, while the second one for load voltage regulation) are sufficient enough to ensure power transfer/management from dc sources to load. To ensure power management on the input dc sources while keeping a stable closed-loop converter system, a multivariable diagonal controller is designed. The first diagonal controller performs the load voltage regulation task, while the second controller regulates input of source-2 dc current. From the control point of view, the double-input single-output converter becomes a two-input two-output control problem and exhibits control–loop interactions due to the power flow from two different sources to load through common elements. The impact of off-diagonal elements’ interactions is accounted by using decouplers. The <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> robust control theory and linear matrix inequality (LMI) principles are adopted to design reliable controllers. The structured controller of fixed order (PID) is designed by enforcing the necessary type LMIs. To demonstrate the feasibility and effectiveness of multivariable controllers of the DIDDC, a 60/24 V to 48 V, 150 W, 50 kHz topology prototype is constructed, and the power management aspects are investigated experimentally. Load voltage regulation, source current regulation, load sharing on the input dc sources, and power management aspects of LMI-based controllers were tested extensively for all possible disturbances. In all these test cases, the closed-loop double-input converter system is stable and robust in rejecting a variety of disturbances created.

An event-triggered mechanism to observer-based sliding mode control of fractional-order uncertain switched systems

This paper is dealing with the problem of observer-based event-triggered sliding mode control for fractional-order uncertain switched systems with a positive order less than one. Firstly, a fractional-order state observer is designed, based on which a fractional-order integral sliding surface function is proposed. Then, utilizing the estimated observer error and sliding mode error vectors, an event-triggered condition is constructed to decide whether the current control signal should be updated or not. Besides, sufficient conditions are derived in the forms of linear matrix inequalities (LMIs) to ensure finite-time stability of the augmented closed-loop system by adopting an average dwell time approach. Thereafter, to avoid the occurrence of infinite triggers within finite time, this paper also discusses the Zeno behavior and refines the results in the previous literature. Finally, to illustrate the effectiveness and superiority of the proposed method, three numerical simulations are provided.

Lyapunov-Based Nonlinear Model Predictive Control for Attitude Trajectory Tracking of Unmanned Aerial Vehicles

This paper presents a new Lyapunov-based nonlinear model predictive controller (LNMPC) for the attitude control problem of unmanned aerial vehicles (UAVs), which is essential for their functioning operation. The controller is designed based on a quadratic cost function integrating UAV dynamics and system constraints. An additional contraction constraint is then introduced to ensure closed-loop system stability. That constraint is fulfilled via a Lyapunov function derived from a sliding mode controller (SMC). The feasibility and stability of the LNMPC are finally proved. Simulation and comparison results show that the proposed controller guarantees the system stability and outperforms other state-of-the-art nonlinear controllers such as the backstepping controller (BSC) and SMC. In addition, the proposed controller can be integrated into an existing UAV model in the Gazebo simulator to perform software-in-the-loop tests. The results show that the LNMPC is better than the built-in PID controller of the UAV, which confirms the validity and applicability of our proposed approach.

Finite time non-singular sliding mode control for spinning tether system with prescribed performance under artificial gravity mission

In this paper, the spinning tether system (STS) is applied to produce the artificial gravity overload with a proposed spin-up scheme in elliptical transfer orbits. To improve the comfort of the astronauts during spinning, the combined control scheme with tension and thrust is designed for spin-up. Then, based on the novel performance function and sliding mode technology, a finite time prescribed performance controller is proposed to track angular velocity for the desired artificial gravity overload. Compared with the existing works, the tracking error is controlled within the preset transient performance and converged to the origin within finite time even in the presence of unknown external disturbance. The stability of closed-loop tracking system is proved by Lyapunov theorem. Finally, the numerical simulations are given to demonstrate the effectiveness and robustness of the proposed controllers in the artificial gravity mission.

Minimal-Approximation-Based Adaptive Event-Triggered Control of Switched Nonlinear Systems with Unknown Control Direction

In this paper, the adaptive neural network event-triggered tracking problem is investigated for a class of uncertain switched nonlinear systems with unknown control direction and average dwell time switching. To reduce the communication network traffic, an event-triggering mechanism based on the tracking error is explored in the controller-to-actuator channel. Additionally, the minimal approximation technology, which designs virtual control laws as the unavailable intermediate signals, is introduced to reduce the difficulty of the controller design process. Compared with the existing adaptive backstepping designs using the filtering technology, the virtual controllers are recursed into a lumped nonlinear function to settle the explosion of complexity, and one neural network is employed in the recursive process. Meanwhile, a boundedness lemma on Nussbaum function is given to address the unknown control direction under the minimal approximation design framework. The stability of the overall closed-loop system is rigorously proved by the Lyapunov stability theory, and the rationality of the proposed strategy is verified by a simulation example. According to the proposed event-triggered mechanism, 81.25% of the communication resources are saved in the simulation example.

Model‐free adaptive optimal control of continuous‐time nonlinear non‐zero‐sum games based on reinforcement learning

In this paper, two novel algorithms to find the Nash equilibrium solution of the non-zero-sum games for continuous-time input-affine nonlinear systems are presented. Based on integral reinforcement learning method, the integral-exploration-coupled Hamilton-Jacobi (HJ) equations are derived, which does not contain any information of the system dynamics. Then, based on neural networks approximation, two different adaptive tuning law of weights are given to estimate the approximate solution of the coupled HJ equations. Both two algorithms can estimate the value function and the policy without knowing or identifying the system dynamics. The closed-loop system stability and the convergence of weights are guaranteed based on Lyapunov analysis. Finally, the simulation results of a two-player non-zero-sum game demonstrate the effectiveness of our algorithms.

Adaptive coupled attitude-servo control for moving mass flight vehicles with high-mass-ratio

Moving mass flight vehicles (MMFVs) with high-mass-ratio suffer from a more severe nonlinear attitude-servo coupling than the traditional configurations that are under particle moving mass hypothesis. Therefore, the coupled attitude-servo control problem is investigated in this paper, and an adaptive backstepping sliding mode controller with extended state observers and neural-networks (ABSMC-ENN) is proposed. Based on the formulated control model with strict-feedback form, a sliding mode control law (SMC) with exponential reaching rate and a nonsingular terminal sliding mode control law (NTSMC) are combined to perform the fast and robust tracking of the command angle-of-attack. Considering the disturbances and uncertainties existing in the coupled dynamics, two nonlinear extended state observers (ESOs) are utilized to estimate the total disturbances online for compensation. To further enhance the adaptiveness and dynamic response performances of the controller in various flight conditions, two radial basis function neural networks (RBFNNs) are exploited to optimize the switching gains of the controller in real-time with performance indexes being the functions of tracking errors. Closed-loop stability of the whole system is proved via Lyapunov methodology. Comparison simulation studies considering multiple disturbances, various flight conditions, and different controllers successfully demonstrate the superiority of the ABSMC-ENN in robustness and adaptiveness.

An Adaptive Prescribed Performance Tracking Motion Control Methodology for Robotic Manipulators with Global Finite-Time Stability.

In this paper, the problem of an APPTMC for manipulators is investigated. During the robot’s operation, the error states should be kept within an outlined range to ensure a steady-state and dynamic attitude. Firstly, we propose the modified PPFs. Afterward, a series of transformed errors is used to convert “constrained” systems into equivalent “unconstrained” ones, to facilitate control design. The modified PPFs ensure position tracking errors are managed in a pre-designed performance domain. Especially, the SSE boundaries will be symmetrical to zero, so when the transformed error is zero, the tracking error will be as well. Secondly, a modified NISMS based on the transformed errors allows for determining the highest acceptable range of the tracking errors in the steady-state, finite-time convergence index, and singularity elimination. Thirdly, a fixed-time USOSMO is proposed to directly estimate the lumped uncertainty. Fourthly, an ASTwCL is applied to deal with observer output errors and chattering. Finally, an observer-based-control solution is synthesized from the above techniques to achieve PCP in the sense of finite-time Lyapunov stability. In addition, the precision, robustness, as well as harmful chattering reduction of the proposed APPTMC are improved significantly. The Lyapunov theory is used to analyze the stability of closed-loop systems. Throughout simulations, the proposed PPTMC has been shown to perform well and be effective.

Design of Synchronization Tracking Adaptive Control for Bilateral Teleoperation System with Time-Varying Delays.

The performances of position synchronization and force interaction of the teleoperation system provide a safe and efficient way for operators to perform tasks in remote, hazardous environments. In practice, however, communication delays and dynamic uncertainties can impair the performance of position synchronization controls. Under the above factors, it is necessary to study and design appropriate bilateral control methods to achieve stable and effective position synchronization control. In this paper, a new adaptive control architecture based on velocity feedback filter and radial basis function neural network is proposed. In the proposed control scheme, only the position signal is transmitted during the communication process, and the speed feedback filter and compensation method are designed and adopted to avoid the use of acceleration signals. In addition, a new auxiliary variable with a tracking error integral term is used to reduce the steady-state error of position tracking under nonzero external environmental forces. Using the Lyapunov–Krasovskii method, the stability of closed-loop remote operating systems is demonstrated. In the simulation and experiment sections, the algorithm was verified separately and compared with other algorithms. The results of a master–slave robot system verify the tracking performance of our proposed control scheme.

Elimination of the Voltage Output Fluctuations of a Vienna Active Rectifier-I Integrated Under Unsymmetrical Faults Based Wind Power Plant

In this article, a fault ride-through controller is proposed with the use of proportional-integral compensator and electronic sensors for riding-through alternative current faults in a wind power plant collection grid connected with a permanent magnet synchronous generator. Three parallel-connected wind energy conversion units supplying a direct current (DC) load are simulated and discussed. It is found that the sub-module will directly adjust the transmission of power and protect the generator from overheating, which can occur due to voltage fluctuation. Furthermore, a DC voltage controller is designed to ensure a stable closed-loop system, and the system stability is verified using bode plots. The dynamic response of the system is demonstrated with the use of power simulator (PowerSim, Rockville, USA) software to verify the reliability of the proposed rectifier topology.

Online recorded data-based finite-time composite neural trajectory tracking control for underactuated MSVs.

This paper presents an online recorded data-based composite neural finite-time control scheme for underactuated marine surface vessels (MSVs) subject to uncertain dynamics and time-varying external disturbances. The underactuation problem of the MSVs was solved by introducing the line-of-sight (LOS) method. The uncertain dynamics of MSVs are approximated by the composite neural networks (NNs). A modified prediction error signal is designed by virtue of online recorded data. The weight updating law of NN is driven by both tracking error and prediction error, introducing additional correction information to the weights of NN, thus improving the learning ability of the NN. Furthermore, disturbance observers can be devised to estimate the compound disturbances consisting of the approximation errors of NNs and external disturbances. Moreover, the smooth function is inserted into the design of the control scheme, and the finite-time composite neural trajectory tracking control of MSVs is achieved. The stability of the MSVs trajectory tracking closed-loop control system is guaranteed rigorously by the Lyapunov approach, and the tracking error will converge to the set of residuals around zero within a finite time. The simulation tests on an MSV verify the effectiveness of the proposed control scheme.

Nonsingular Terminal Sliding-Mode Controller Based on Extended State Observer for Two-Mode Vibration of a Piezoelectric Plate: Design, Analysis and Experiments

Considering the internal and external disturbances, i.e. coupling effect, model uncertainties, and external excitation of an all-clamped piezoelectric plate, a two-loop nonsingular terminal sliding-mode controller (NTSMC) based on extended state observer (ESO) is developed to suppress the two-mode structural vibration. First, a state space model of the structure is established based on system identification with an auxiliary variable method. Second, a three-order ESO of each individual mode is drawn to estimate and compensate the lumped disturbances via feedforward channel in real-time. Third, the NTSMC based on ESO for each single mode is designed to obtain vibration suppressing performance. In addition, the two-mode vibration control is decoupled into single-mode independent control through the proposed ESO. The stability of whole closed-loop system is analyzed by using a Lyapunov stability criterion. Finally, the experimental platform based on NI-PCIe device for a piezoelectric structural vibration control is set up to verify the effectiveness and superiority of the proposed two-mode vibration control method. Compared with the conventional ESO-based sliding-mode control (SMC) method, the experimental results of two-mode structural vibration demonstrate that the vibration suppression performance of first two modes is improved from 8.94[Formula: see text]dB to 11.7[Formula: see text]dB and 9.2[Formula: see text]dB to 14.75[Formula: see text]dB, respectively.

Nonlinear Model Predictive Control with aggregated constraints

This paper presents a constraint aggregation approach for Nonlinear Model Predictive Control (NMPC). Constraint aggregation functions provide an approximation of the feasible region with a reduced number of nonlinear constraints. The effect of the aggregation on the closed-loop system performance and stability is studied using tools from sensitivity analysis. Numerical results for the control of a 20th order flexible aircraft model show that significant computational savings can be achieved. The proposed method can facilitate the implementation of NMPC solutions for large-scale systems.

Hybrid Half-Gaussian Selectively Adaptive Fuzzy Control of an Actuated Ankle–Foot Orthosis

To control an actuated ankle–foot orthosis (AAFO) during walking, a selectively adaptive hybrid fuzzy control employing particle-swarm optimization was used in conjunction with a Lyapunov-theory-based adaptive fuzzy-logic control. Adaptation (a computationally expensive process) was performed only when the tracking error exceeded a certain half-Gaussian function. The stability of the overall closed-loop system was proved using Lyapunov theory. The proposed control strategy was verified both by simulations and by experiments with five healthy subjects. The proposed control strategy significantly reduced both tracking error and required control torque when compared to other competing control schemes.

Dual-Loop Dynamic Control of Cable-Driven Parallel Robots Without Online Tension Distribution

Achieving high-precision position control while maintaining positive cable tensions is the most challenging issue for the motion control of cable-driven parallel robots, which should be considered significantly. Different from the existing control schemes with online tension distribution that needs real-time computing in each control cycle, a novel dual-loop dynamic control scheme is proposed in this article, where a paralleled dual-loop tracking strategy is introduced to provide a more compatible scheme, which consists of two tracking loops: 1) the tension control loop and 2) the position control loop. In the former loop, the offline tension distribution is adopted to avoid cable hanging loosely and the real-time feasibility of the distribution method is no longer a necessary demand. In the latter loop, due to the complex dynamics characterized by the cable-driven form, the cooperative motion relation among multiple cables and inevitable external disturbances are investigated comprehensively, and the robust synchronization method is included to guarantee the high-precision position control. Afterward, the Lyapunov method is adopted to analyze the strict stability of the whole closed-loop system with both the position and tension control feedback. The experiments indicate that by synthesizing the two control loops, the proposed scheme can dramatically reduce the tracking errors in the trajectory tracking while avoiding the cable relaxation, and particularly, has a satisfactory control effect when the velocity and acceleration of the trajectory have significant oscillations. Additionally, the strong disturbance rejection ability is also validated via robustness experiments.

Personalized hybrid artificial pancreas using unidirectional sliding-modes control algorithm

This paper presents an artificial pancreas algorithm implemented with a discrete-time sliding-mode method combined with a nonlinear block controllable form using a unidirectional control law and a discrete adaptive observer. The algorithm is both unidirectional, using insulin as unique input, and hybrid with a percentage of the pre-meal bolus administered in advance to complement the control action. Personalisation combines patient clustering and individual gain calculation after analysing glucose time-in-range. The stability of the complete closed-loop system involving the observer bounds is tested using the Lyapunov methodology. The performance of the algorithm is evaluated with 256 patients, simulated using Hovorka’s model. The evaluation defines two scenarios (closed-loop and open loop with continuous subcutaneous insulin infusion, CSII), divided into three 1-week intervals, to respectively compare the impact of glucose control under the expected meal plan as a result of changes in carbohydrates quantities and meal schedule, and in response to more extreme events.The performance of time-in-range in each period obtained with CSII is improved by hybrid closed-loop in all cases, i.e., with the expected meals (weekdays 74.9 vs 78.4; weekends 71.5 vs 73.4), with meal variability (weekdays 74.3 vs 77.6; weekend 71.6 vs 72.7), and in the presence of transgressions (forgetting meal announcement: 50.1 vs 63.4; meal omission: 78.2 vs 82.03; copious meal: 60.1 vs 63.4). Compared to CSII, the personalised nonlinear block controller was able to increase the time-in-range without glucose presence in time below range level 2 for 98 % of the cohort for expected meals, meal variability, and transgressions.