Robust Adaptive Sliding Mode Control Research Articles

Design of continuous-time model reference adaptive and super-twisting sliding mode controller

This paper presents a continuous-time Robust Model Reference Adaptive and Super-Twisting Sliding Mode controller and its stability analysis by means of Lyapunov stability theory. The controller law is composed by two control structures: a Robust Model Reference Adaptive Controller (RMRAC) and an Adaptive Super-Twisting Sliding Mode (STSM) Controller. The main benefit of this novel control algorithm is to present, simultaneously, high robustness and fast dynamic response, which are conflicting with each other in conventional adaptive algorithms. Furthermore, as the STSM Controller is also adaptive, the dynamic response has relevant chattering mitigation without additional efforts on controller design, implementation, or execution. Besides, the union of the STSM with RMRAC also improved sliding accuracy in steady state. Thereby, in steady state, the STSM control contribution is almost zero, which avoids the chattering phenomenon, once it acts only in the transient regimes. The stability and robustness analysis of the control structure are presented, in continuous-time, considering the overall plant, that is, in presence of matched and unmatched dynamics. The continuous-time stability analysis is important in an adaptive system, since it features an intermediary step for control system stability analysis in discrete-time and its application in real plants. In addition, to present the feasibility and benefits of the proposed controller, simulations results of two case studies are presented: one is the controller application in an unstable non-minimum phase plant, and the second is its application for current regulation of a single-phase grid-tied power converter with an LCL filter. Moreover, to corroborate the robustness and tracking performance of the proposed controller a comparison with an adaptive first order Sliding Mode is also presented.

Adaptive Disturbance-Observer-Based Continuous Sliding Mode Control for Small Autonomous Underwater Vehicles in the Trans-Atlantic Geotraverse Hydrothermal Field with Trajectory Modeling Based on the Path

Considering intense hydrothermal activities and rugged topography in a near-bottom environment of the trans-Atlantic geotraverse (TAG) hydrothermal mound, a small autonomous underwater vehicle (S-AUV) will suffer from time-varying disturbances, model uncertainties, actuator faults, and input saturations. To handle these issues, a fault-tolerant adaptive robust sliding mode control method is presented in this paper. Firstly, unknown disturbances, model uncertainties, and actuator faults of the S-AUV are synthesized into a lumped uncertain vector. Without requiring the upper bound and gradient of the uncertainties, a continuous adaptive finite-time extended state observer is designed to estimate the lumped uncertain vector. Then, an auxiliary dynamic system composed of continuous functions is introduced to deal with input saturations, thereby contributing to achieving fixed-time trajectory tracking control of S-AUVs. Based on a designed continuous fixed-time nonsingular fast sliding mode surface, the proposed continuous adaptive controller is chattering free. Simulated topography is built according to topographic data of the TAG mound, and a smooth trajectory model is constructed by cubic spline interpolation. Comprehensive simulations performed on an actual S-AUV model are given to validate the effectiveness and superiority of the presented algorithm.

Robust adaptive sliding mode control strategy of uncertain nonlinear systems

This paper presents a robust adaptive sliding mode controller scheme as applied to a class of uncertain nonlinear systems with parametric uncertainties and external disturbances. First, a sliding mode control technique is designed. Then, the proposed robust adaptive control schemes are applied to estimate the parametric uncertainties and the upper bound value of the external disturbances by using adaptive laws, ensure robustness in presence of parametric uncertainties and external disturbances, and reduce chattering problem by introducing an hyperbolic tangent function. Lyapunov stability theory is used to analyze the stability of the closed-loop system. As an exemplar, the schemes have been applied to a quadrotor unmanned aerial vehicle (QUAV) model. Simulation results for the control of the QUAV model are provided to illustrate the performance of the proposed robust adaptive sliding mode control scheme and demonstrate that the proposed method has good tracking performance. The simulation results clearly prove the effectiveness of our approach.

Learning Control for Flexible Manipulators with Varying Loads: A Composite Method with Robust Adaptive Dynamic Programming and Robust Sliding Mode Control

This paper focuses on the learning-based motion control for flexible manipulators with varying loads via the singularly perturbed technique. Considering the two-timescale feature of the flexible manipulator, system dynamics are decomposed into fast and slow subsystems, and corresponding sub-controllers are designed with robust adaptive dynamic programming (RADP) and robust sliding mode control (RSMC) methods, respectively. In the proposed composite control framework, an RADP-based sub-controller is developed to realize the trajectory tracking and alleviate the parametric uncertainty utilizing rotating angles in the slow timescale, while an RSMC sub-controller is introduced to improve the vibration suppression in the fast timescale. Finally, the stability of the closed-loop system is guaranteed, and simulations are carried out to show the effectiveness of the proposed control algorithm.

Swing Suppression Task in Double-pendulum Tower Cranes Using Robust Adaptive Sliding Mode Controller

In actual applications, tower crane systems are usually suffered from underactuated characteristic, double-pendulum effect, frictions, model uncertainties and disturbances etc. As a result of these problems, the control of tower cranes for accurate positioning and effective swing suppression becomes more difficult. To this end, we propose a robust adaptive sliding mode controller, which has adaptive gains varying by the system tracking error and adaptive terms to compensate the lumped disturbances in all DOF (degrees of freedom). Therefore, the system convergence rate is effectively increased and the disturbances-related factors are suppressed. Simulation results show that the proposed method can handle the actual conditions better.

A Robust Adaptive Super-Twisting Sliding Mode Controller applied on grid-tied power converter with an LCL filter

This paper presents a new robust adaptive controller, totally developed on discrete-time. This controller is composed by two control structures: a Robust Model Reference Adaptive Controller (RMRAC) and an Adaptive Super-Twisting Sliding Mode (STSM) Controller, constituting a new control structure, nominated Robust Adaptive STSM Controller. The main advantage of this new control proposal is its high adaptability and robust performance, with fast reference tracking without chattering. The stability and robustness analysis, in discrete time, are presented, considering the overall plant, that is, in presence of matched and unmatched dynamics. To evaluate its robustness performance, the proposed controller is designed for grid-injected current control of three-phase grid-tied power converter with an LCL filter under weak grid. To validate it, the plant was partially modeled as a first order transfer function, neglecting capacitor dynamics and considering it as an additive dynamics on control design. Experimental results are presented to corroborate the controller performance and the stability analysis by means of Lyapunov Theory is provided.

Adaptive Door Opening Control Algorithm of Bio-Inspired Mobile Manipulator Based on Synchronous Sensing.

At present, the research of robot door opening method is basically realized by identifying the door handle through the synchronous sensing system on the premise that the bio-inspired mobile manipulator is located in front of the door. An adaptive door opening strategy of a bio-inspired mobile manipulator based on a synchronous sensing system is proposed. Firstly, the random delay distribution in clock synchronization technology is analyzed in detail, and its distribution is verified on the experimental platform of adjacent nodes. Based on the Gaussian distribution of random delay, the relative frequency offset and relative phase offset of adjacent nodes are calculated. The clock synchronization of network cable sensor nodes is realized. Secondly, based on the information data of synchronous sensing system, this article realizes target detection and tracking based on depth network. In addition, based on the sliding mode control theory, the dynamic model of the nonholonomic bio-inspired mobile manipulator is applied. Finally, a robust adaptive sliding mode control method for nonlinear systems with input gain uncertainty and unmatched uncertainty is proposed by combining adaptive backstepping with sliding mode control. By adding sliding mode control in the last step of adaptive backstepping, the uncertainty of the system is compensated, and the system trajectory is maintained on the specified sliding mode manifold. The tracking control and stability control of the nonholonomic bio-inspired mobile manipulator are simulated. The experimental and simulation results show that the control method proposed in this article is effective and feasible.

Design and Stability Analysis of a Robust-Adaptive Sliding Mode Control Applied on a Robot Arm with Flexible Links

Modelling errors and robust stabilization/tracking problems under parameter and model uncertainties complicate the control of the flexible underactuated systems. Chattering-free sliding-mode-based input-output control law realizes robustness against the structured and unstructured uncertainties in the system dynamics and avoids the excitation of unmodeled dynamics. The main purpose of this paper was to propose a robust adaptive solution for stabilizing and tracking direct-drive (DD) flexible robot arms under parameter and model uncertainties, as well as external disturbances. A lightweight robot arm subject to external and internal dynamic effects was taken into consideration. The challenges were compensating actuator dynamics with the inverter switching effects and torque ripples, stabilizing the zero dynamics under parameter/model uncertainties and disturbances while precisely tracking the predefined reference position. The precise control of this kind of system demands an accurate system model and knowledge of all sources that excite unmodeled dynamics. For this purpose, equations of motion for a flexible robot arm were derived and formulated for the large motion via Lagrange’s method. The goals were determined to achieve high-speed, precise position control, and satisfied accuracy by compensating the unwanted torque ripple and friction that degrades performance through an adaptive robust control approach. The actuator dynamics and their effect on the torque output were investigated due to the transmitted torque to the load side. The high-performance goals, precision and robustness issues, and stability concerns were satisfied by using robust-adaptive input-output linearization-based control law combining chattering-free sliding mode control (SMC) while avoiding the excitation of unmodeled dynamics. The following highlights are covered: A 2-DOF flexible robot arm considering actuator dynamics was modelled; the theoretical implication of the chattering-free sliding mode-adaptive linearizing algorithm, which ensures robust stabilization and precise tracking control, was designed based on the full system model including actuator dynamics with computer simulations. Stability analysis of the zero dynamics originated from the Lyapunov theorem was performed. The conceptual design necessity of nonlinear observers for the estimation of immeasurable variables and parameters required for the control algorithms was emphasized.

Lyapunov stability analysis of discrete-time robust adaptive super-twisting sliding mode controller

This paper presents a discrete-time Robust Adaptive Super-Twisting Sliding Mode controller and its stability analysis by means of Lyapunov stability theory. The control law is composed by two different control structures: a Robust Model Reference Adaptive Controller (RMRAC) and an Adaptive Super-Twisting Sliding Mode (STSM) Controller. The main advantage of the control structure is its robust performance and high adaptability in face of unmodelled dynamics, presenting a fast reference tracking without chattering, since it uses a second-order Sliding Mode action into adaptive control structure. The stability and robustness analysis of the control structure are presented in discrete time, considering the overall plant, that is, in presence of matched and unmatched dynamics. In addition, the control structure performance is corroborated with simulation results, considering a non-minimum phase unstable plant. Moreover, the presented results are compared with an adaptive first-order SM control-based RMRAC, which can be clearly seen that proposed controller has better performance, mainly by means of chattering mitigation.

Attitude stability control of micro-nano satellite orbit maneuver based on bias momentum

In this paper, an attitude stability control strategy based on cold air micro propulsion microsatellite orbital maneuver is designed. Firstly, the influence of environmental disturbance moment, uncertainty of rotational moment of inertia and thrust eccentricity moment on the attitude stability of the micro-nano-satellite is considered, and the attitude dynamics model of the micro-nano-satellite based on biased momentum wheel and magnetic moment device is established. Then, the disturbance moments such as environmental disturbance moments, rotational inertia uncertainty and thrust eccentricity moments are analyzed. In order to suppress the influence of various internal and external disturbance factors on the stability of the micro-nano-satellite during the deorbiting process, a robust adaptive sliding mode variable structure controller is designed. The designed robust adaptive sliding mode controller is able to compensate for various disturbances adaptively. The robust adaptive sliding-mode variable structure controller is designed with a reasonable distribution of torque considering the characteristics of bias momentum wheel control and magnetic control. Finally, numerical simulations are performed, and the simulation results show that the system has good robustness.

Robust Adaptive Sliding Mode Control Based on Iterative Learning for Quadrotor UAV

In order to improve the anti-disturbance ability and reduce the sensitivity to faults for the quadrotor UAV, the robust sliding mode adaptive control strategy based on iterative learning is designed in this paper. Firstly, the dynamic model of the quadrotor UAV is established. Secondly, the iterative learning observer is designed to track the states of the UAV system, and the convergence analysis of the observer is given. Thirdly, for the attitude system of the quadrotor UAV, a robust adaptive sliding mode control strategy based on iterative learning is proposed, and the stability is proved by the Lyapunov theory. Finally, by the simulation for the UAV attitude system, the validity of the iterative learning observer and robust adaptive sliding mode control strategy based on iterative learning is verified.

Sway and disturbance rejection control for varying rope tower cranes suffering from friction and unknown payload mass

Tower cranes are well-known underactuated systems, where the design of controllers for them with time-varying rope length was weak in the past because of their complex dynamic characteristic. The payload oscillation will become worse when the jib slew angle, the trolley position and the rope length are changed simultaneously. The proposed method is designed based on robust adaptive sliding mode control via tracking nonzero initial reference trajectories, in which frictions and lumped disturbances in the crane system are eliminated, and unknown payload mass is effectively estimated online. Lyapunov technique is combined with LaSalle’s invariance theorem to design controller and analyze stability. Various and strict simulations are applied, which validate the effectiveness and extreme robustness of the proposed method.

Adaptive sliding mode control of hydraulic systems with the event trigger and finite-time disturbance observer

This paper studies a class of hydraulic servo system control problems with digital communication constraints and model uncertainty. A cooperative design method of adaptive robust sliding mode controller with event trigger strategy and the finite time disturbance observer is proposed. The introduced event trigger strategy can remove a large amount of redundant data and release the communication bandwidth. Besides, the non-matching interference can be accurately estimated by the finite time disturbance observer, and the uncertainty of the matching parameter can be online through the proposed parameter adaptation update. Theoretical analysis shows that the control algorithm not only maintains the asymptotic stability of the hemisphere but also enables the reachability of a given sliding surface. Finally, the simulation results also verify the feasibility and validity of the theoretical resultss.

Robust Adaptive Control of a Quadruple Tank Process with Sliding Mode and Pole Placement Control Strategies

Many industrial processes have challenging issues such as complex nonlinear nature, high sensitivity to disturbances and existence of parametric uncertainties. A Quadruple Tank Process (QTP) is used in the laboratory as a scaled representation of many industrial processes involving liquid level control problems. Conventional controllers are relatively slow in tracking the reference inputs and in reacting to disturbances, and they tend to lack the ability in dealing with parametric changes in the QTP. The aim of this paper is to design and test an Adaptive Pole Placement Controller (APPC) and a robust Adaptive Sliding Mode Controller (ASMC) with the purpose of high-efficacy control of a minimum phase QTP. The controllers are tested via simulations and performance indices resulting from the simulation of these controllers are compared with a PID controller in terms of the three cases of robustness to set point variations, rejection of disturbance inputs, and robustness to parametric uncertainties. Simulation results reveal that the proposed adaptive control configurations perform better than the PID controller with lower performance indices and faster settling times due to the paramater estimation method used in the design processes. ASMC outperforms APPC in different variations of inputs and in regulation performances due to the invariant nature of the Sliding Mode Control (SMC). The results show that a decentralized ASMC can be used to improve the rapidity and robustness of many multivariable industrial process control systems.

Robust output feedback adaptive sliding mode control for a class of uncertain nonlinear systems using robust adaptive fuzzy observer

This article presents a new robust adaptive sliding mode controller for a class of uncertain nonlinear systems whereas only the system output is measurable. Firstly, a robust adaptive fuzzy observer is designed for the system in order to estimate its state variables. The robust asymptotic convergence of the proposed observer is proven by Lyapunov direct method. Then based on the observation states, a robust adaptive sliding mode controller is suggested such that the closed loop system to be asymptotically stable. Robust asymptotic stability of the overall system suggested by the controller is also confirmed based on Lyapunov theory. Simulation results illustrate practicality and effectiveness of the proposed technique for controlling uncertain nonlinear systems.

A New Robust Adaptive Sliding Mode Control for Discrete-Time Systems With Time-Varying State Delay

This article proposes a novel robust adaptive sliding control mode law for time unknown varying delay in state uncertain systems. In this work, the upper limit of disruption and uncertainty is assumed to be unknown. The model is adjusted so that the system looks like a certain one with unknown added disturbances on the bounds of which are unknown too. Accordingly, new control law for this kind of systems has been defined based on a Lypunov function choice. The main results of this paper are that the conditions for the existence of linear sliding surfaces are derived within the linear matrix inequalities (LMIs) framework by employing the free weighting matrices and the determination of the control law based on a sliding surface will converge to zero. This proposed approach has been validated in simulation on an uncertain system with comparative study proved the efficiency of the proposed resulting methodology after has been validated in real system.

Suppression of chaos in the spin-orbit problem of Enceladus via robust adaptive sliding mode control

This paper proposes a new robust adaptive sliding mode control (RASMC) technique and investigates the control of chaos in the two-dimensional uncertain spin-orbit problem of Enceladus (SOPE) in the presence of external disturbances and model uncertainties. The external disturbances, model uncertainties, and nonlinear terms of the system are bounded and unknown. The proposed RASMC technique: 1) accomplishes oscillation free and fast convergence of the state variables to the origin; 2) suppresses chattering in the control inputs. The Lyapunov stability theory verifies the convergence behaviour and guarantees the robust asymptotic stability of the equilibrium point at the origin. In the sense of Lyapunov function, this article also provides parameters adaptation laws that confirm the convergence of uncertain parameters to some constants. The computer simulation results verify the theoretical findings and provide comparative analysis. The results of this study could be beneficial in the area of space sciences.

Finite-Time Stability of MIMO Nonlinear Systems Based on Robust Adaptive Sliding Control: Methodology and Application to Stabilize Chaotic Motions

This paper introduces a robust adaptive sliding mode control to solve a finite-time stability of the uncertain nonlinear systems with multiple inputs and multiple outputs (MIMO). The proposed algorithm guarantees a strict robustness and fast convergence of the system trajectories to zero in a finite time under the negative effects of uncertainties and/or external disturbances. The fundamental methodology is based on an improved modification of the super-twisting sliding technique to alleviate an undesirable influence of the chattering phenomenon. In addition, a nonlinear adaptive law is constructed to ensure a strict stability of the control system even without prior awareness of the upper bounds of uncertainties and disturbances. A general stability of the closed-loop disturbed MIMO nonlinear system is achieved by the Lyapunov theorem. Lastly, the proposed algorithm is applied to stabilize the typical chaotic behaviors of Duffing - Holmes system and Lorenz system. The advantages and effectiveness of the proposed method are clearly demonstrated through the results of numerical simulations compared with other existent methods.

Development of an Intention-Based Adaptive Neural Cooperative Control Strategy for Upper-Limb Robotic Rehabilitation

Robotic rehabilitation therapy has become an important technology to recover the motor ability of disabled individuals. Clinical studies indicate that involving the active intention of patient into rehabilitation training contributes to promoting the performance of therapies. An adaptive neural cooperative control strategy is developed in this letter to realize intention-based human-cooperative rehabilitation training. The human motion intention is estimated by fusing the human-robot interaction forces and the muscular forces into a Gaussian radial basis function network. A biological force estimation method is proposed to obtain the muscular forces of biceps and triceps based on surface electromyography signals and Kalman filter. A robust adaptive sliding mode controller is integrated into the cooperative control scheme to ensure the accuracy and stability of inner position control loop with uncertainties. The minimum jerk cost principle is used to improve the smoothness and continuity of trajectory. To evaluate the effectiveness of the proposed control scheme, further experimental investigations are conducted on a planar upper-limb rehabilitation robot with ten volunteers. The results indicate that the proposed control strategy has significant potential to modulate the interaction compliance and cooperation process during training.

Passivity‐based robust adaptive sliding mode control for singular time‐delay systems with uncertainties in both derivative matrix and some other system matrices

SummaryThis article addresses the passivity analysis and passification problems for a class of nonlinear singular time‐varying delay systems with the special forms of uncertainties in both derivative matrix and some other system matrices by adopting adaptive sliding mode control (SMC) strategy. First, a distinctive state augmentation technique, which keeps the admissibility and the robust passivity unchanged, is employed due to “left‐singular” form uncertainty in the derivative matrix (ie, ). Next, an integral‐type sliding surface, which involves the SMC gain matrix K, is constructed. By designing an appropriate Lyapunov‐Krasovskii functional and introducing slack matrix approach, in which the slack matrix is not constrained in contrast to most existing literatures, a new sufficient condition is derived to ensure that the resulting sliding mode dynamics is admissible and robustly passive for all admissible uncertainties. Additionally, for the passification problem, a delay‐dependent sufficient condition is proposed in the form of strict linear matrix inequality (LMI), which not only removes the equality constraint but also makes the SMC gain matrix K solvable. Then a novel adaptive SMC law, which does not need to use the assumption that bounds of nonlinear perturbation function and external disturbance are known constants, is synthesized such that the finite‐time reachability can be guaranteed. And the state information before and after state augmented transformation is utilized in SMC law design to help achieve better performance. Finally, four examples are presented to illustrate the effectiveness, superiority, and less conservativeness of the proposed scheme.