Terminal Sliding Mode Controller Tuned Using Evolutionary Algorithms for Finite-Time Robust Tracking Control in a Class of Nonholonomic Systems

In order to solve the attitude synchronization control problem of an on-orbit servicing spacecraft autonomously docking to a tumbling satellite with the unknown bounded disturbances and system uncertainties, a fast terminal sliding mode control law is presented in this paper. The most important contribution of this paper is to design an attitude synchronization control law, which will be realized by the terminal sliding mode control method, for a servicing spacecraft autonomously docking to a freely tumbling satellite in space. First of all, the model of relative attitude dynamics is derived from the attitude dynamics of servicing spacecraft and tumbling satellite. Then, the relative attitude dynamic model is converted to the normal formation to apply the control method of fast terminal sliding mode. Furthermore, a fast terminal sliding mode control law for attitude synchronization is designed based on the normal formation of relative attitude dynamic model. During the design process of the control law, the measurement errors and parameter variations are also considered. Finally, several numerical simulations are conducted to verify the designed attitude synchronization control law, and the results verified the effectiveness of the designed control law. Moreover, it's robustness to the unknown bounded disturbances, system uncertainties and measurement errors has also been demonstrated.

Vehicle platoon is one of the innovations in the automated highway systems, which has the potential to reduce fuel consumption, alleviate traffic congestion and lighten the driver’s burden. How to control the vehicle effectively to ensure the stability of the queue is a challenge. Aiming to overcome the shortcomings of the platoon control method based on traditional sliding mode control, a non-singular terminal sliding mode control method optimized by the extreme learning machine is proposed in this paper. Firstly, the vehicle longitudinal dynamics are derived from the analysis of the forces acting on the vehicle in the longitudinal direction. A constant time headway policy is taken as the spacing policy. The modified non-singular terminal sliding mode control method has outstanding performance, simulation results demonstrate that the following vehicles can rapidly track the trajectory of the leading vehicle in the platoon with less spacing error and guarantee string stability. In this study, several experiments are set up to consider the disturbance and other uncertain practical factors. The performance of the proposed method is superior to the traditional sliding mode control method. Experimental results show that the proposed method can significantly reduce chattering and has good robustness under the circumstances of the disturbance.

This paper investigates the trajectory-tracking problem of an uncertain quadrotor in the presence of complex disturbances. A new fractional-order terminal sliding mode control method (FOTSMC) is designed for a quadrotor attitude, which can increase the control robustness against the external disturbances and modeling uncertainty, and decrease the chattering problem. A new fractional non-integer sliding mode control technique for a quadrotor position is designed to stabilize its state variables and attenuate wind disturbance and the effects of variation in the mass. The stability analysis is studied by the Lyapunov theory. Numerical simulation for complex flight trajectory under disturbances is given to illustrate the validity of the proposed methods.

In order to realize the trajectory tracking control of mobile robots, a global fast terminal sliding mode control method is proposed in the kinematic analysis. Based on the combination of the backstepping method and the thought of the fast terminal sliding mode control, the method is more superior than the backstepping design method on convergence time and convergence rate. The system state variables are designed based on based backstepping method, then, the controller is applied to mobile robot system by recursive structure of second order fast terminal sliding mode, the control law is designed by Lyapunov method. Finally, simulation results show the validity of the presented method.

For a hybrid mechanism for automobile electro-coating conveying which is self-developed, a dynamic model is established based on screw theory and the principle of virtual work to simplify the process of modeling. Then, to solve the chattering problem and the slow rate of convergence problem of the existing sliding mode control methods for the hybrid mechanism, a super-twisting algorithm based second-order nonsingular fast terminal sliding mode control method is proposed. The stability of the proposed control method is proved by Lyapunov stability theorem. Finally, compared with the reaching law based sliding mode control method and the super-twisting algorithm based second-order sliding mode control method, it is indicated from the simulation and experiment results that the proposed control method not only has high steady-state accuracy, better dynamic performance and strong robustness, but also reduces the chattering and improves the rate of convergence of the system. And it lays foundation for realizing the high performance control of the hybrid mechanism for automobile electro-coating conveying.

In order to cope with the changing industrial operation environment, based on the Flexible Joint Robot systems (FJR), this paper explores a control method of decoupling high-order systems by using singular perturbation theory (SPT). Considering the limitations of SPT in FJR systems, the method of introducing a saturated flexible compensator is used to change the premise that the joints need to be assumed to be weakly flexible, thereby expanding the application scope of SPT in such systems. Moreover, the improved third-order time-varying parameters extended state observer is used to observe the lumped interferences which can effectively suppress the peak problem caused by the initial value, and the adaptive continuous nonsingular fast terminal sliding film control method is combined to control the slow subsystem. Aiming at the fast subsystem, the integral flow is used to reconstruct and fast terminal sliding mode control method is combined to improve the initial oscillation problem.

The space flexible netted pocket capture system provides a flexible and stable solution for capturing non-cooperative space objects. This paper investigates the control problem for the capture of non-cooperative targets undergoing motion. A dynamic model of the capturing net is established based on the absolute nodal coordinate formulation (ANCF) and equivalent plate–shell theory. A contact collision force model is developed using a spring–damper model. Subsequently, a feedforward controller is designed based on the estimated collision force from the dynamic model, aiming to compensate for the collision effects between the target and the net. By incorporating the collision estimation data, an extended state observer is designed, taking into account the collision estimation errors and the flexible uncertainties. A sliding mode feedback controller is then designed using the fast terminal sliding mode control method. Finally, simulation analysis of target capture under different motion states is conducted. The results demonstrate that the spacecraft system’s position and attitude average flutter amplitudes are less than 10−2 m and 10−2 deg. In comparison to standard sliding mode control, the designed controller reduces the attitude jitter amplitude by an order of magnitude, thus demonstrating its effectiveness and superiority.

The paper presents a method of synthesizing the Variable Structure Controller (VSC) based on the Fast Terminal Sliding Mode (FTSM) control for an optoelectronic observatory to eliminate the effects of the vibration and the change of vehicle’s direction. An improved fast terminal sliding surface and a fuzzy saturation function have been proposed to develop the improved fast terminal sliding mode variable structure controller (IFTSM-VSC). Based on the theory of Lyapunov stability, the article has proved that the IFTSM-VSC controller ensures the Line of Sight (LOS) stabilization of the observation devices and ensures the tracking errors converge to zero in finite time. The simulation uses data about the vibration and navigation of the vehicle recorded on some streets and roads. Simulation results in Matlab/Simulink show the effectiveness of the IFTSM-VSC controller.

A Global Fast Terminal Sliding Mode Controller (GFTSMC) is proposed for n-link robotic manipulators by employing the Fast Terminal Sliding Mode (FTSM) control concept in both the reaching phase and the sliding phase. Under the control, the system states will reach FTSM in desired finite time and then converge to the origin along the FTSM in specified finite time, resulting in a reduced steady tracking error in comparison with the conventional sliding mode controller. The proposed controller is continuous and therefore chattering-free. An example is presented to demonstrate its effectiveness.

This paper proposes a Disturbance-Compensated Non-Singular Fast Terminal Sliding Mode Control (DC-NFTSMC) method to address the issues of slow convergence speed and poor robustness in traditional turntable control methods. By designing an improved non-singular fast terminal sliding mode surface and reaching law, the convergence speed of the turntable system is significantly enhanced. Additionally, an Extended State Observer (ESO) is incorporated to estimate and compensate for complex disturbances and improving the robustness of the turntable system. Simulation results demonstrate that, compared with traditional methods, this control method not only effectively improves the tracking response speed of the turntable system but also ensures superior robustness in the presence of multiple superimposed disturbances.

To address the issue of energy scarcity and to use solar photovoltaic energy as a renewable source, a three-phase grid-connected photovoltaic inverter system with uncertain system model parameters is investigated, which converts DC power into AC power, feeds it into the grid, and maintains the grid-connected part’s quality. An enhanced back-stepping approach is proposed to explore the control strategy of three-phase solar grid-connected inverter, which includes adaptive control, dissipative theory, sliding mode control, and rapid terminal sliding mode control, respectively. It is verified that the system is subjected to external interference F = 5 during 0.5 s–0.8 s. As per the simulation results, the improved adaptive terminal sliding mode control method can suppress the interference to a certain extent and has strong robustness to the external interference. When compared with the adaptive sliding mode control approach, the anti-interference ability is better, and the system stability is improved. Then, to improve the above approach, a high speed terminal sliding mode control method is proposed, which can swiftly converge in finite time and the estimated value of uncertain parameters is closer to the actual value, thereby boosting the system’s robustness.

In the declining stage of soft landing on asteroid, there are many problems in control system of probe such as low convergence speed, long convergence time and severe chattering. A terminal sliding mode control method based on double power reaching law is proposed in this paper. On the basis of conventional reaching law analysis, combined with nonlinear, weak gravitational field characteristics, control schemes in this paper proposes double power reaching law and adopts the terminal sliding mode control method. The controller can weaken the chattering, improve system stability and convergence rate, so that the system can make status tracking error converges fast to zero in the limited time. It has a fast speed either away from or approach to the sliding surface. Simulation results show that the proposed control method achieve fast convergence of the system state in a finite time and strong robustness to disturbances, and eliminates the presence of control chattering. Also, the proposed control law can ensure a smooth landing to the specified descent height, and ultimately secure a soft landing.

In this paper, the attitude control of rigid-liquid-flexible multi-body coupling spacecraft with unknown external disturbances and uncertain inertia parameters is studied, and an attitude maneuver control method based on disturbance observer and fuzzy terminal sliding mode control is proposed. The sloshing of liquid fuel in the spacecraft is equivalent to a spherical pendulum model, and the flexible appendages are assumed to be an Euler-Bernoulli beam. The coupled dynamic equation of the liquid-filled flexible spacecraft is derived by using the Lagrange method. First of all, the interference from space, the parameter uncertainty of the moment of inertia of the spacecraft, the coupling interference caused by the liquid sloshing and the vibration of flexible accessories are summed up as lumped interference. Design disturbance observer to compensate and estimate the lumped disturbance of the system. Then, based on the designed disturbance observer, a fuzzy terminal sliding mode control law is presented, and it is proved that the state of the closed-loop system is finite-time stable under the control law, and converges to the specified terminal sliding mode surface. The fuzzy terminal sliding mode control law uses fuzzy control to improve the switching gain based on the traditional terminal sliding mode control to achieve the purpose of suppressing system jitter. This optimization method can not only reduce the complexity of terminal sliding mode control method, but also reduce the difficulty of debugging parameters because it does not introduce new functions. The numerical simulation results show that the designed fuzzy terminal sliding mode control law can not only achieve the finite-time stability of the closed-loop attitude control system of the liquid-filled flexible spacecraft, but also effectively suppress the liquid sloshing and the vibration of the flexible appendages. At the same time, it has good robustness to disturbances caused by external disturbances and parameter uncertainties, and has better control performance.

This work proposes a non-singular fast terminal sliding mode control (NFTSMC) strategy based on the Twin Delayed Deep Deterministic Policy Gradient (TD3) algorithm and a nonlinear disturbance observer (NDO) to address the issues of modeling errors, motion disturbances, and transmission friction in robotic manipulators. Firstly, a novel modular serial 5-DOF robotic manipulator configuration is designed, and its kinematic and dynamic models are established. Secondly, a nonlinear disturbance observer is employed to estimate the total disturbance of the system and apply feedforward compensation. Based on boundary layer technology, an improved NFTSMC method is proposed to accelerate the convergence of tracking errors, reduce chattering, and avoid singularity issues inherent in traditional terminal sliding mode control. The stability of the designed control system is proved using Lyapunov stability theory. Subsequently, a deep reinforcement learning (DRL) agent based on the TD3 algorithm is trained to adaptively adjust the control gains of the non-singular fast terminal sliding mode controller. The dynamic information of the robotic manipulator is used as the input to the TD3 agent, which searches for optimal controller parameters within a continuous action space. A composite reward function is designed to ensure the stable and efficient learning of the TD3 agent. Finally, the motion characteristics of three joints for the designed 5-DOF robotic manipulator are analyzed. The results show that compared to the non-singular fast terminal sliding mode control algorithm based on a nonlinear disturbance observer (NDONFT), the non-singular fast terminal sliding mode control algorithm integrating a nonlinear disturbance observer and the Twin Delayed Deep Deterministic Policy Gradient algorithm (TD3NDONFT) reduces the mean absolute error of position tracking for the three joints by 7.14%, 19.94%, and 6.14%, respectively, and reduces the mean absolute error of velocity tracking by 1.78%, 9.10%, and 2.11%, respectively. These results verify the effectiveness of the proposed algorithm in enhancing the trajectory tracking accuracy of the robotic manipulator under unknown time-varying disturbances and demonstrate its strong robustness against sudden disturbances.

This paper presents a terminal sliding mode control in reaching dynamics as well as in sliding dynamics. Generally the control effort increases to make a system fast. But there exists a maximum input value of control input due to an actuator capacity. Proposed terminal sliding mode control makes a system fast and stable from reaching phase to sliding phase with input limit. Through the comparison study among a original sliding mode control, a conventional terminal sliding mode control and a modified terminal sliding mode control we can see a fast conversing property of a modified one. Simulation results are presented to validate the analysis.