Adaptive super-twisting fractional-order nonsingular terminal sliding mode control of cable-driven manipulators

Time-delay control scheme with adaptive fixed-time convergent super-twisting fractional-order nonsingular terminal sliding mode for piezoelectric displacement amplifier

Piezoelectric displacement amplifiers (PDAs) have been widely used in precision positioning fields. However, the inherent hysteresis and creep nonlinear effect of piezoelectric actuators (PEAs) and time-varying lumped disturbances bring extreme challenges to the precise motion control of PDAs. Although various control schemes based on PEAs have been developed and have shown significant results. However, due to the high sensitivity of precision positioning to environmental variations, the development and identification of accurate models and the control timeliness often become obstacles in engineering. To realize precise motion control of PDAs under complex lumped disturbances, a new time-delay control scheme (AFSTA-FONTSM) using an adaptive fixed-time convergent super-twisting algorithm (AFSTA) and a fractional-order nonsingular terminal sliding mode (FONTSM) is proposed. Specifically, the time-delay information obtained by time-delay estimation technology is used to estimate the lumped dynamic characteristic of the system, thus establishing a simple control framework without a system dynamic model. FONSTM is constructed as a sliding mode manifold, and satisfactory error dynamic characteristic is obtained. A new AFSTA is designed as the reaching law in the sliding mode phase. AFSTA has fixed-time convergence when the upper bound of lumped disturbances exists, which ensures the control timeliness. Benefiting from the newly designed adaptive algorithm, the upper bound value of lumped disturbances is no longer needed to determine the control gains, which effectively prevents overestimation of the control gains. Correspondingly, the convergence time of AFSTA is estimated, and the stability of the closed-loop system is analyzed by the Lyapunov theory. Three existing time-delay control schemes, namely MSTA-FONTSM, AMSTA-FONTSM, and ASTA-FONTSM are selected, and four scenes are designed for comparative experiments. The experimental results show that MSTA-FONTSM has the worst control performance among the four control schemes. For the step, and continuous cosine trajectories with periods of T = 1 s and T = 2 s, the root-mean-square error of the proposed AFSTA-FONTSM is reduced by 56.86%, 54.03%, and 50.24% compared with MSTA-FONTSM. For disturbance experiments under different loads, the control performance of the proposed AFSTA-FONTSM is still superior to the other three control schemes without load.

Hybrid adaptive disturbance rejection control for inflatable robotic arms

This paper aims to tackle the controller design issue of highly nonlinear and stochastic inflatable robotic arms (IRAs). A novel control scheme, i.e., hybrid adaptive disturbance rejection control (HADRC), is devised to handle the challenging tracking control of hard-to-model IRAs. The model-free adaptive control (MFAC) that linearizes the dynamics by leveraging solely the online input and output (I/O) data of plants is analytically enhanced for superlinear convergence. Both internal and external disturbances are rejected via the active disturbance rejection control (ADRC) that requires little prior model information. The fuzzy logic control (FLC) is subsequently implemented to correlate the two sub-controllers and contribute to attaining smooth motions. The superiority of the proposed scheme is demonstrated by the comparative simulations and experiments on a 2-degree-of-freedom (DOF) IRA.

Dynamic Modeling and Robust Adaptive Sliding Mode Controller for Marine Cable-Driven Parallel Derusting Robot

Ship derusting has the characteristics of a complex operation environment, high labor intensity and low efficiency. In order to better cope with this situation, a new type of cable-driven parallel derusting robot (CDPDR) is proposed in this article. To improve the positioning accuracy and anti-interference capacity of the motion platform where the end effector is mounted, the system’s dynamic model, considering wave excitation, is established. Further, the controllable workspace and cable tension optimization algorithm are studied. In addition, a fast non-singular terminal sliding-mode controller is designed. Meanwhile, the adaptive technique is used to estimate the disturbance upper bound. Then, the Lyapunov theory is applied to prove the stability of the system. Finally, the performance of the controller is verified by high-fidelity simulations in two different scenarios. The results show that the proposed controller can converge in finite time and maintain small error under multiple external disturbances. The relevant research in this article can provide theoretical guidance for the application of CDPDRs on ships.

Seaport throughput forecasting and post COVID-19 recovery policy by using effective decision-making strategy: A case study of Vietnam ports

This study deals with the dynamic interactions between seaports and decision-making strategy for seaport operations by utilizing four-dimensional fractional Lotka-Volterra competition model under frequently disrupted by time-delay factor. Nonlinear analysis methods, including equilibrium analysis, stability evaluation, and time series investigation, are intensely explored to describe the cooperation and competition dynamics in maritime logistics. The dynamical analysis indicates that the port competition system shows a complex and highly nonlinear behaviour, notably illustrating unstable equilibria and even chaotic phenomena. Besides, nonlinear dynamical interactions in seaport management have been analysed by exploiting fractional calculus (FC) and system dynamics theory. Novel multi-criteria decision-making strategies realized by the neural network prediction controller (NNC) and adaptive fractional-order super-twisting sliding mode control (AFOSTSM) have been presented for dealing with throughput dynamics under parametric perturbations and external disturbances. Particularly, the active control algorithms are implemented to ensure the recovery strategy for throughput growth of Vietnam ports in the post-coronavirus (COVID-19) pandemic era. The case study has confirmed the efficacy of the proposed strategy by using system dynamics and control theory. The simulation results show that the average growth rates of container throughput can be ensured up to 7.46% by exploiting resilience management scheme. The presented method can be also utilized for providing managerial insights and solutions on efficient port operations. In addition, the control strategies with neural network forecasting can help managers obtain timely and cost-effective decision-making policy for port sustainability against unprecedented impacts on global supply chains related to COVID-19 pandemic.

Aerodynamic Heating Ground Simulation of Hypersonic Vehicles Based on Model-Free Control Using Super Twisting Nonlinear Fractional Order Sliding Mode

In this article, a model-free control (MFC) using super twisting nonlinear fractional order sliding mode for aerodynamic heating ground simulation of hypersonic vehicles (AHGSHV) is proposed. Firstly, the mathematical model of AHGSHV is built up. To reduce order and simplify the dynamic model of AHGSHV, an ultra-local model of MFC is taken into consideration. Then, time delay estimation can be used to estimate systematic uncertainties and external unknown disturbances. On the basis of the original fractional order sliding mode surface, the nonlinear function fal is introduced to design the nonlinear fractional order sliding mode surface, which can guarantee stability, increase convergence rate, and reduce static error and saturation error. In addition, the super twisting reaching law is used to improve the control performance of the reaching phase, resulting from the existence of sign function in the integral term, and it can effectively reduce the high-frequency chattering. Moreover, the Lyapunov function is used to prove the stability of the whole system. Finally, several numerical simulations show that the designed controller has more advantages than others.

Design and implementation of finite time sliding mode controller for fuzzy overhead crane system

This paper considers the problem of fuzzy overhead crane system modelling and finite-time stability/boundedness via sliding mode control (SMC) method. Due to the strong coupling of control input, the fuzzy technique is utilized to linearize the overhead crane system and a fuzzy overhead crane model is established with appropriate membership functions. Considering the bad effect, including the swing of hook and plates, the external disturbances of the friction and air resistances, is inevitable during the transportation of copper electrode plates, the SMC method is adopted to stabilize the fuzzy system and robust to these interference signals. Furthermore, taking the time cost of actual industry into account, the finite-time stability/boundedness is introduced to achieve the state of system could be stable in a specified finite time. Moreover, the reaching law of sliding mode dynamics is analysed and the sufficient conditions for finite-time stability/boundedness of system state are formulated, respectively. Finally, the simulation results of the control strategy put forward in this article with the comparisons on some existing algorithms are provided to verify the effectiveness of the control strategy in the copper electrolytic overhead crane system.

Robust adaptive fractional-order nonsingular terminal sliding mode stabilization of three-axis gimbal platforms

This paper proposes an adaptive fractional-order nonsingular terminal sliding mode (AFNTSMC) control scheme combined with the independent joint control approach for trajectory tracking of three-axis gimbal platforms (GPs) mounted on a moving vehicle subjected to external disturbances. To achieve accurate images taken by the camera mounted on the GP, the motions and vibrations of the vehicle must be isolated from the camera. Thus, precise mathematical modeling of a three-axis GP with considering the external disturbances is studied, such that the GP tracks the target accurately and holds the line of sight stationary. Various tests with different vehicle conditions are performed to collect the movement data to be considered as the desired input for the GP. Thanks to the utilization of AFNTSMC, fast convergence together with simultaneous accurate trajectory tracking and strong robustness can be ensured. Corresponding comparative simulation results validate the effectiveness of the theoretical design results and superiorities of the proposed method over the existing methods.

Adaptive robust controller using intelligent uncertainty observer for mechanical systems under non-holonomic reference trajectories

Non-holonomic reference trajectories and uncertainties are typically encountered in a class of mechanical systems. For such systems, this paper investigates the development of a novel explicit adaptive robust controller. By employing the structure of the Udwadia controller, the designed controller can deal with holonomic and non-holonomic reference trajectories in a unified manner. To avoid degradation of performance due to uncertainties, an observer is proposed to identify the uncertainties; the observer is designed using a fuzzy cerebellar model articulation controller neural network. A robust term is designed to restrain the initial deviations and to enhance the robustness of systems. Moreover, a compensatory term is designed to compensate for the residual errors resulted from the uncertainty observer. Rigorous theoretical analysis of the proposed controller is verified via the Lyapunov stability method, and an illustrative example is presented to demonstrate the effectiveness of the designed controller.

Trajectory tracking control for electro-optical tracking system based on fractional-order sliding mode controller with super-twisting extended state observer

This paper investigates a trajectory tracking control scheme for electro-optical tracking systems subject to friction and other nonlinear disturbances. The proposed approach is based on a super-twisting extended state observer (ESO) and a fractional-order nonsingular terminal sliding mode (FONTSM) with a switching-type reaching law. The novel hybrid control scheme exhibits the following advantageous characteristics. First, the extended state observer injected with a super-twisting algorithm is capable of simultaneously estimating the friction and other nonlinear disturbances without detailed knowledge of the precise friction and disturbance models. Second, the FONTSM surface enhances the control accuracy and robustness, and provides a more flexible controller structure than its integer counterpart. Third, a novel switching-type reaching law is utilized to achieve fast response, constraining chattering in the system. Additionally, the finite-time convergence of the adopted ESO and the finite-time stability of the control system are demonstrated based on the rigorous Lyapunov criteria. Finally, the effectiveness of the proposed hybrid control scheme is demonstrated for an electro-optical tracking system via trajectory tracking experiments.

Model-free adaptive sliding mode control with adjustable funnel boundary for robot manipulators with uncertainties

Considering that the nominal dynamics model or numerous parameters of robotics are usually unsuitable for real applications, a model-free adaptive sliding mode control with an adjustable funnel boundary is proposed for robot manipulators with uncertainties. First, time delay estimation (TDE) technique is utilized to estimate the unknown dynamics of the control system, which ensures an attractive model-free advantage. Furthermore, a modified funnel function is introduced to transform the trajectory tracking error fall within an adjustable funnel boundary strictly. Then, based on the transformed error variable, a novel funnel nonsingular fast terminal sliding mode control scheme is developed to enhance the transient and steady-state tracking performance of the closed-loop control system. To cope with the TDE error, an adaptive update method is designed with only one adaptive parameter, which is adaptively tuned according to the sliding surface. Finally, the simulation and experimental results are presented to illustrate the superiority and high-precision tracking performance of the proposed approach.

Model-Free Control Using Improved Smoothing Extended State Observer and Super-Twisting Nonlinear Sliding Mode Control for PMSM Drives

This paper proposes a novel model-free super-twisting nonlinear sliding mode control (MFSTNLSMC) strategy with an improved smoothing extended state observer (SESO) for permanent magnet synchronous motor (PMSM) drives. First of all, the improved SESO is introduced to estimate the unknown term of the PMSM ultra-local model. Secondly, a novel nonlinear sliding mode surface (NLSMS) is designed, which can effectively overcome the disadvantages of simple and rough signal processing of the conventional linear sliding mode surface. At the same time, a super-twisting (ST) structure is chosen to suppress the chattering phenomenon and improve system robustness. Then, the Lyapunov stability theorem is used to prove the stability of the proposed control algorithm. Finally, both comparative simulations and experimental demonstrations verify the excellent speed tracking performance and robustness of the proposed control strategy.

A light cable-driven manipulator developed for aerial robots: Structure design and control research

To effectively reduce the mass and simplify the structure of traditional aerial manipulators, we propose novel light cable-driven manipulator for the aerial robots in this article. The drive motors and corresponding reducers are removed from the joints to the base; meanwhile, force and motion are transmitted remotely through cables. Thanks to this design, the moving mass has been greatly reduced. In the meantime, the application of cable-driven technology also brings about extra difficulties for high-precise control of cable-driven manipulators. Hence, we design a nonsingular terminal sliding mode controller using time-delay estimation. The time-delay estimation is applied to obtain lumped system dynamics and found an attractive model-free scheme, while the nonsingular terminal sliding mode controller is utilized to enhance the control performance. Stability is analyzed based on Lyapunov theory. Finally, the designed light cable-driven manipulator and presented time-delay estimation-based nonsingular terminal sliding mode controller are analyzed. Corresponding results show that (1) our proposed cable-driven manipulator has high load to mass ratio of 0.8 if we only consider the moving mass and (2) our proposed time-delay estimation-based nonsingular terminal sliding mode is model-free and can provide higher accuracy than the widely used time-delay estimation-based proportional–derivative (PD) controller.

A Novel Fast Terminal Sliding Mode Tracking Control Methodology for Robot Manipulators

This paper comes up with a novel Fast Terminal Sliding Mode Control (FTSMC) for robot manipulators. First, to enhance the response, fast convergence time, against uncertainties, and accuracy of the tracking position, the novel Fast Terminal Sliding Mode Manifold (FTSMM) is developed. Then, a Supper-Twisting Control Law (STCL) is applied to combat the unknown nonlinear functions in the control system. By using this technique, the exterior disturbances and uncertain dynamics are compensated more rapidly and more correctly with the smooth control torque. Finally, the proposed controller is launched from the proposed sliding mode manifold and the STCL to provide the desired performance. Consequently, the stabilization and robustness criteria are guaranteed in the designed system with high-performance and limited chattering. The proposed controller runs without a precise dynamic model, even in the presence of uncertain components. The numerical examples are simulated to evaluate the effectiveness of the proposed control method for trajectory tracking control of a 3-Degrees of Freedom (DOF) robotic manipulator.

Model-free continuous nonsingular fast terminal sliding mode control for cable-driven manipulators

This work proposes a model-free robust control for cable-driven manipulators with disturbance. To achieve accurate, singularity-free and fast dynamical control performance, we design a new NFTSM surface utilizing a new continuous TSM-type switch element. By replacing the integral power with fractional one for the error dynamics, the designed TSM-type switch element can effectively enhance the dynamical performance of the NFTSM surface. Time-delay estimation (TDE) technique is applied to cancel out complicated nonlinear dynamics guaranteeing an excellent model-free scheme. Thanks to the designed NFTSM surface, adopted reaching law and TDE, our control can provide good comprehensive control performance effectively. Stability and comparisons of control precision and convergence speed have been theoretically analyzed. Finally, comparative experiments were conducted to prove the superiorities of our control.

Fractional Sliding Mode Nonlinear Procedure for Robust Control of an Eutrophying Microalgae Photobioreactor

This paper proposes a fractional-order sliding mode controller (FOSMC) for the robust control of a nonlinear process subjected to unknown parametric disturbances. The controller aims to ensure optimal growth in photobioreactors of native microalgae involved in eutrophication of the Sinaloa rivers in Mexico. The controller design is based on the Caputo fractional integral-order derivative and on the convergence properties of a sliding surface. For nonlinear systems, the proposed FOSMC guarantees convergence to the sliding surface even in the presence of model disturbances. The proposed controller is compared to an Internal Model Control (IMC) through numerical simulations.

An adaptive iterative learning control approach based on disturbance estimation for manipulator system

An adaptive iterative learning control approach based on disturbance estimation has been developed for trajectory tracking of manipulators with uncertain parameters and external disturbances. The external disturbances are estimated by the feedback iterative learning method, whereas the uncertain parameters are compensated by adaptive control. This approach which is based on the disturbance estimation technique provides a rapid convergence of trajectory tracking errors. According to the Lyapunov theory, the sufficient condition of the asymptotic stability has been developed for the 2-degrees of freedom (DOFs) manipulator system. The numerical results show that the adaptive iterative learning control approach based on disturbance estimation is feasible and effective for the 2-DOFs manipulator. A comparison of the adaptive iterative learning control method and the iterative learning control method is completed, which shows that the adaptive iterative learning control method performs a faster convergence of the disturbance to the steady state.

Dynamic angular velocity turning for extremum seeking control of a two-dimensional mobile robot with external disturbances

In this article, the extremum seeking control of a two-dimensional mobile robot with external disturbances is discussed by applying dynamic angular velocity turning method. First, the extremum seeking scheme is proposed to describe the trajectory of the two-dimensional robot and to achieve extreme value optimization through dynamic feedback. Secondly, the method of finite-time control and dynamic feedback is proposed to ensure that the dynamic angular velocity converges to the virtual controller within a finite time. Thirdly, the sliding mode disturbance observer is designed to guarantee that the observer converges to an unknown disturbance in finite time. Furthermore, we allow the averaging method and the results are applied in stability analysis. Finally, our control scheme is feasible by a series of simulations.

Design and Kinematic Control of the Cable-Driven Hyper-Redundant Manipulator for Potential Underwater Applications

Underwater manipulators are important robotic tools in the exploration of the ocean environment. Up to now, most existing underwater manipulators are rigid and with fixed 5 or 7 degrees of freedom (DOF), which may not be very suitable for some complicated underwater scenarios (e.g., pipe networks, narrow deep cavities, etc.). The biomimetic concept of muscles and tendons is also considered as continuum manipulators, but load capacity and operation accuracy are their essential drawbacks and thus limit their practical applications. Recently, the cable-driven technique has been developed for manipulators, which can include numerous joints and hyper-redundant DOF to execute tasks with dexterity and adaptability and thus they have strong potential for these complex underwater applications. In this paper, the design of a novel cable-driven hyper-redundant manipulator (CDHRM) is introduced, which is driven by multiple cables passing through the tubular structure from the base to the end-effector, and the joint numbers can be extended and decided by the specific underwater task requirements. The kinematic analysis of the proposed CDHRM is given which includes two parts: the cable-joint kinematics and the joint-end kinematics. The geometric relationship between the cable length and the joint angles are derived via the established geometric model for the cable-joint kinematics, and the projection relationship between the joint angles and end-effector’s pose is established via the spatial coordinate transformation matrix for the joint-end kinematics. Thus, the complex mapping relationships among the cables, joints and end-effectors are clearly achieved. To implement precise control, the kinematic control scheme is developed for the CDHRM with series-parallel connections and hyper-redundancy to achieve good tracking performance. The experiment on a real CDHRM system with five joints is carried out and the results verify the accuracy of kinematics solution, and the effectiveness of the proposed control design. Particularly, three experiments are tested in the underwater environment, which verifies its good tracking performance, load carrying and grasping capacity.