T-S fuzzy model-based robust finite time control for uncertain nonlinear systems

This paper deals with an adaptive robust tracking control using a multilayer neural network (NN) for a class of nonlinear dynamic systems with unknown time varying state delays. Typical adaptive NN backstepping controllers for uncertain nonlinear systems with time-delay give rise to computation complexity caused by the the repeated derivatives of virtual controllers and nonlinear functions. Moreover, the combined techniques usually result in only uniformly ultimately bounded (UUB) stability caused by the inherent NN approximation error. This paper presents a control scheme that uses an integral sliding mode control as a feedback term and an adaptive neural controller as a feedforward term based on the desired compensation adaptive law (DCAL) technique. First, we develop a new DCAL formulation which avoids the explosion of complexity caused by the general NN backstepping scheme to compensate for nonlinear system uncertainties, bounded system disturbances, and unknown state time delays. Then, using a Lyapunov-Krasovskii (LK) functional, it is shown that the proposed controller renders the class of uncertain nonlinear time-delay systems asymptotically stable.

When a permanent magnet synchronous motor runs at low speed, the inverter will output discontinuous current and generate torque ripple; when the motor is runs at high speed, a large amount of stator harmonic current generates, which affects its speed following ability and torque stability. To ensure the fast and smooth switching of a permanent magnet synchronous motor in the full speed domain, this paper proposes the nonsingular terminal sliding mode control of PMSM speed control based on the improved exponential reaching law. Firstly, the improved exponential reaching law is composed of the state variables and power terms of the sliding mode surface functions. The reaching law function is designed in sections to balance the fast dynamic response of the system and chattering control. Secondly, an improved exponential reaching law based on the sliding mode control strategy of the PMSM speed loop is proposed. By designing the initial value of the integral term in the nonsingular terminal sliding mode surface function, the initial state of the system is located on the sliding mode surface. The integral sliding mode surface is used to reduce the system steady-state error, while the proposed sliding mode reaching law is used to increase the arrival speed and suppress system chattering, ultimately affecting modeling error problems, complex working conditions, and uncertainty factors. This paper proposes a sliding mode observer based on an improved exponential reaching law to compensate for the disturbances. Lyapunov stability theory can prove that this system can make the speed tracking error converge to zero in finite time. Hardware-in-the-loop experiments were used to validate the effectiveness of the proposed method.

The magnetic levitation technology has attracted blooming attention from all walks of life thanks to its superiorities such as noncontact and active control. While the intrinsic features of open-loop instability and strong nonlinearity, along with the uncertain external disturbance make the levitation control particularly significant and difficult. For speeding up the convergence and obtaining a better stability and disturbance robustness, this article proposes an ultralocal model-free adaptive supertwisting nonsingular terminal sliding mode control strategy for the magnetic levitation system. Different from the conventional model-based control, ultralocal model-free control breaks the constraint of a precise system model. Therefore, an improved second-order ultralocal model is established for the magnetic levitation system. For the benefit of finite time convergence and nonsingularity, the nonsingular terminal sliding mode surface is chosen. As a second-order algorithm, supertwisting (ST) algorithm can fundamentally suppress the chattering effect of the sliding mode control. An adaptive ST algorithm is designed for the further improvement of the system dynamic response. The stability of the proposed scheme is strictly verified based on the Lyapunov stability theory. Simulation and experimental comparisons with the existing control methods validate the exceeding performance of the proposed strategy under various operating conditions.

To reduce energy consumption in the active suspension, this paper proposes a new method for vehicle active suspension control. The energy consumption characteristics of the coupling system is analyzed. On this basis, a finite time controller based on unknown state estimation is proposed, and its global finite time convergence is proved, the upper limit of time convergence is given. Secondly, based on Analytic Hierarchy Process (AHP) and the force random walk PSO algorithm (FRWPSO), a multi-objective optimization function is constructed to determine the control parameters under different driving modes. Finally, simulation experiments show that under random road surfaces and triangular obstacles, the proposed control method can effectively improve suspension comfort and operational stability compared to nonsingular terminal sliding mode control (TSMC), The RMS values of energy consumption decreased by 55.34% and 20.55% respectively, verifying the effectiveness of the proposed control method.

Safe operation for teleoperated robotic manipulators with restricted synchronization error via non-singular terminal sliding-mode control

This article investigates the trajectory tracking problem of quadrotor formation with collision avoiding. The safety distributed control strategy is introduced for quaternion-based multiple quadrotors formation to avoid collision. Then, based on super-twisting and adaptive control method, a multiple adaptive finite time super-twisting control method (MAFTSTC) is proposed, which rarely relies on the information of the formation model. The purpose of the robust controller designed in the position loop and the attitude loop is to ensure that quadrotor formation tracks the desired trajectory and maintains formation configuration in finite time. The closed-loop system stability of the novel control method is verified through Lyapunov theory. Finally, compared with traditional finite time convergence (FTC) method and non-robustness control (NRC) method, the simulation results illustrate the effectiveness of the proposed control method.

Nonsingular Fixed-time Sliding Mode Control (NFSMC) method is one of the nonlinear control methods which is robust against uncertainties and external disturbances. This paper presents an NFSMC method to synchronize two similar Willamowski–Rossler reaction chaotic systems. The proposed control method is robust against uncertainties and external disturbances; also, it is an accurate and fast control method. The proposed control method is compared with a Nonsingular Terminal Sliding Mode Control. The comparison results show that the proposed control method provides a better control solution for this system.

A non-singular terminal sliding mode control based on finite time observer is designed to achieve speed direct control for the permanent magnet synchronous motor (PMSM) drive system. Speed and current are regulated in one loop under the non-cascade structure, taking place of the cascade structure control method in the vector control of PMSM. Based on the second-order speed function of the PMSM, the disturbance and parameters uncertainties are estimated by the designed finite time observer (FTO), and compensate to the drive system. The estimated value of the finite time observer will converge to the actual disturbance value in a finite time. A second-order non-singular terminal sliding mode controller is proposed to realize the speed and current single-loop, which can track the reference speed and reference current in a finite time. Rigorous stability analysis is established. Comparative results verified that the proposed method has faster speed tracking performance and disturbance rejection property.

This paper presents a new dynamic motion control method using a fast nonsingular finite time control approach based on an adaptive disturbance observer to solve the trajectory tracking problem of nonholonomic autonomous mobile robots (AMR) with uncertain disturbances. The proposed method combines fast nonsingular terminal sliding mode control (FNTSMC) with an adaptive sliding mode observer (ASMO), referred to as FNTSMC+ASMO. The ASMO estimates disturbances in finite time, and its output is used by FNTSMC to enhance system robustness and ensure fixed‐time convergence of tracking errors under practically bounded initial conditions via Lyapunov stability theory. Additionally, an artificial potential field (APF) technique is incorporated to achieve effective obstacle avoidance, further improving its practical applicability. The validity and superiority of the proposed method are well exemplified through extensive simulations and experiments, demonstrating superior tracking accuracy and excellent disturbance rejection compared to other sliding‐mode control methods.

The article presents a novel control strategy for cable-driven aerial manipulators (UAMs) aimed at enhancing impedance control during contact operations in complex environments. A fractional-order nonsingular terminal sliding mode control (FONTSMC) integrated with a disturbance observer (DOB) is proposed to improve the robustness and precision of the UAM under lumped disturbances. This developed approach utilizes the flexibility of fractional calculus, the finite-time stability of nonsingular terminal sliding mode, and the real-time disturbance estimation capabilities of the DOB to ensure smooth and compliant contact interactions. The effectiveness of the proposed control strategy is validated through comprehensive simulation studies, which demonstrate significant improvements in control performance, stability, and disturbance rejection when compared to traditional methods. The results indicate that the FONTSMC-DOB framework is highly suitable for complex aerial manipulation tasks, offering both theoretical and practical insights into the design of advanced control systems for UAMs.

Barrier function-based adaptive nonsingular terminal sliding mode control technique for a class of disturbed nonlinear systems

This article investigates the sliding mode control problem of uncertain nonlinear systems and its application in tracking periodic motion. Traditional sliding mode control fulfils perfect tracking at the cost of chattering, especially in the case of high-frequency scenarios. To address the limitations of this method, this article introduces the internal model of the reference signal in building the sliding manifold, which fully takes the advantages of two fundamental methodologies. Specifically, the internal model of the reference signal is involved in the closed-loop system dynamics after the sliding manifold is reached. Thence, all terms related to the reference signal in the tracking error can be eliminated and high-precision tracking can be achieved while reducing chattering phenomenon. Remarkably, the detailed expressions of the derivatives of the reference signal are unnecessarily required, which simplifies the controller design and implementation. It is rigorously proved mathematically that the closed-loop system is asymptotically stable. Finally, the proposed control algorithm is applied for solving the position tracking control problem for permanent magnet synchronous motor servo systems, and experimental results verify the effectiveness and superiority.

This paper develops a novel non-singular terminal sliding mode control scheme for trajectory tracking of robot manipulators in the presence of external disturbances and uncertainties. Firstly, with the introduction of two nonlinear terms, a newly terminal sliding surface is designed. Then utilizing this sliding surface, a novel non-singular terminal sliding mode controller is proposed to eliminate the reaching interval, singularity issue and subsequently with this controller, the finite time error convergence is also assured. In the proposed controller, radial basis function neural network is employed to approximate highly uncertain nonlinear dynamics of robot manipulators using update laws derived with Lyapunov approach. Meanwhile, the effects of approximation errors are attenuated with $$H_\infty $$ performance criterion by introducing a robust term into the controller. As a result of proposed approach, asymptotic convergence of tracking errors is achieved within finite time and the approximation errors are attenuated to desired levels. The numerical simulation result shows the effectiveness of proposed controller for the case of microbot type robot manipulator.

This paper investigates the finite time trajectory tracking problem for the nonlinear dynamics of ship heading system in the presence of external disturbances and model uncertainties. In fact, based on the second order nonsingular terminal sliding mode control, two novel classes of robust nonlinear controllers (rudder angles) are designed to precisely reach the ship course to the desired trajectory in the specified finite times. Moreover, two new formulas (in the form of two nonlinear inequalities) are derived to estimate these convergence finite times. Furthermore, two theorems and their proofs are presented to demonstrate the global finite time stability of the uncertain closed-loop ship heading system forced by each class of proposed controllers. Finally, two computer based numerical simulations are provided to depict the applicability and the good performance of two suggested controllers.

This paper presents the problem of observer-based fuzzy H/sup /spl infin// control for a class of uncertain nonlinear systems with time-varying delayed systems on the basis of Takagi-Sugeno fuzzy model. First, we design a fuzzy observer such that destination error system is globally, exponentially stable. Next, we design a fuzzy H/sup /spl infin// controller such that the closed loop system is globally, exponentially stable and achieves L/sub 2/ gain performance. The fuzzy control systems utilize the concept of the so-called parallel distributed compensation. A sufficient condition for the existence of robust fuzzy H/sup /spl infin// controllers and observers are given in terms of linear matrix inequalities (LMIs). The control gains can also be directly obtained from the LMI solutions.