Sliding Mode Error Research Articles

Input–output linearization minimum sliding-mode error feedback control for spacecraft formation with large perturbations

To improve the control precision of nonlinear spacecraft formation flying, the input–output linearization minimum sliding-mode error feedback controller is presented based on the linear-decoupled spacecraft formation model by input–output linearization method incorporating the sliding-mode control. This paper proposes a new strategy to estimate and offset the system-control errors, which include various kinds of uncertainties and disturbances. To facilitate the analysis, the linear-decoupled spacecraft formation model is first given; on which basis, the concept of equivalent control error is introduced to define the entire model error. Based on the minimum sliding-mode covariance constraint, a cost function is formulated to estimate the equivalent control error and fed back to the conventional sliding-mode control. It is shown that the sliding mode after the input–output linearization minimum sliding-mode error feedback controller will approximate to the ideal sliding mode with high-control precision. In addition, the new methodology is applied to spacecraft formation flying. It guarantees global asymptotic convergence of the relative-tracking error in the presence of the large perturbations. More exactly, the two input–output linearization minimum sliding-mode error feedback controller laws (continuous sliding-mode control and nonsingular terminal sliding-mode control) are developed for this spacecraft formation flying system. Several fault-tolerant scenarios are considered to verify that the input–output linearization minimum sliding-mode error feedback controller is still effective in the presence of faults in spacecraft thrusters. Numerical simulations are performed to demonstrate the efficacy of the proposed methodology to maintain and reconfigure the spacecraft formation with existence of initial offsets and large perturbations effects.

Minimum sliding mode error feedback control for fault tolerant reconfigurable satellite formations with J2 perturbations

Minimum Sliding Mode Error Feedback Control (MSMEFC) is proposed to improve the control precision of spacecraft formations based on the conventional sliding mode control theory. This paper proposes a new approach to estimate and offset the system model errors, which include various kinds of uncertainties and disturbances, as well as smoothes out the effect of nonlinear switching control terms. To facilitate the analysis, the concept of equivalent control error is introduced, which is the key to the utilization of MSMEFC. A cost function is formulated on the basis of the principle of minimum sliding mode error; then the equivalent control error is estimated and fed back to the conventional sliding mode control. It is shown that the sliding mode after the MSMEFC will approximate to the ideal sliding mode, resulting in improved control performance and quality. The new methodology is applied to spacecraft formation flying. It guarantees global asymptotic convergence of the relative tracking error in the presence of J2 perturbations. In addition, some fault tolerant situations such as thruster failure for a period of time, thruster degradation and so on, are also considered to verify the effectiveness of MSMEFC. Numerical simulations are performed to demonstrate the efficacy of the proposed methodology to maintain and reconfigure the satellite formation with the existence of initial offsets and J2 perturbation effects, even in the fault-tolerant cases.

Minimum sliding mode error feedback control for fault tolerant small satellite attitude control

This paper proposes a new control strategy (which we call “minimum sliding mode error feedback control, MSMEFC”) for small satellite attitude control. As we know, the attitude control algorithm plays a significant role in the whole performance of the satellite, especially under the existence of uncertain disturbances from the space. Without loss of generality, the MSMEFC is presented based on the sliding mode theory. It is assumed that the equivalent control error is defined to offset the uncertain disturbances to improve the control performance. Hence, in order to estimate the optimal equivalent control error, a cost function is derived on the basis of the principle of minimum sliding mode error. Then, the equivalent control error wills feedback to the conventional sliding mode control to obtain the final MSMEFC. According to the theoretical analyzes, the sliding mode after the MSMEFC will approximate to the ideal sliding mode, resulting in enhancing the control performance. Moreover, an adaptive non-singular terminal sliding mode is employed to compare with the performance of MSMEFC. Several simulations are performed to verify the effectiveness of proposed MSMEFC in the presence of serious perturbations, even in some fault-tolerant scenarios.

The design of nonsingular terminal sliding-mode feedback controller based on minimum sliding-mode error

To eliminate the effect of the uncertain disturbances and improve the control accuracy of spacecraft Attitude Control System, a nonlinear control algorithm named nonsingular terminal sliding-mode feedback controller is proposed in this work, which is mainly made up of nonsingular terminal sliding-mode controller and sliding-mode feedback controller. In the first place, nonsingular terminal sliding-mode controller is designed, which guarantees global asymptotic convergence of the attitude in the presence of the uncertain perturbations from the space. Despite that, it is the influence of the uncertain disturbances that hinder the control accuracy. Then, in order to promote the control accuracy, the sliding-mode feedback controller based on the principle of minimum sliding-mode error is proposed, which is used to compensate the control errors of the nonsingular terminal sliding-mode controller caused by the uncertainties. Hence, the determination principle of the weighting matrix in sliding-mode feedback controller is discussed, and the algorithm structure of the sliding-mode feedback controller is also analyzed, which provides the theoretical basis for the sliding-mode feedback controller. By contrast, an adaptive fuzzy algorithm is designed and introduced into the nonsingular terminal sliding-mode controller to improve the control accuracy, which named the nonsingular terminal fuzzy sliding-mode controller. Last but not the least, several numerical examples are presented to demonstrate the efficacy of the proposed nonsingular terminal sliding-mode feedback controller. Simulation results confirm that the control accuracy of the nonsingular terminal sliding-mode feedback controller is higher than the nonsingular terminal sliding-mode controller and the same as nonsingular terminal fuzzy sliding-mode controller. Not only is the calculation of the nonsingular terminal fuzzy sliding-mode feedback controller smaller than nonsingular terminal fuzzy sliding-mode controller, the adjusted parameters are also fewer than nonsingular terminal fuzzy sliding-mode controller obviously. The numerical results clearly indicate that the proposed nonsingular terminal sliding-mode feedback controller based on the principle of minimum sliding-mode error can compensate control errors accurately and quickly; therefore, it can reduce the effect of the uncertainties from the space indirectly.

Sliding mode iterative learning control for non-linear systems with uncertainties

A new sliding mode-based iterative learning control algorithm is proposed and its stability is proved. An important characteristic of the algorithm is that the entire control signal is comprised of the sliding mode part and the iterative learning part, while the current signal of the iterative part is computed by its previous value and the sliding mode error. As a result, repeatable disturbances are cancelled out by the iterative learning part, while non-repeatable uncertainties are dealt with by the sliding mode part. The effectiveness is illustrated by simulations.

Slide-mode control scheme with dynamic modifying errors for boost converter

A novel control scheme is presented by using sliding-mode control for boost converter operating in continuous conduction mode (CCM). Although the non-ideal switching condition and physical constraint of the control are considered on the base of equivalent control, the scheme is still simple. By modifying the sliding-mode errors in each switching period, the steady-state errors and chattering can be substantially reduced. Simulation results confirm the theoretical analysis and show the improvement of the converter’s start-up behavior and low sensitivity to external perturbation.

Finite-time Tracking for Robot Manipulators with Continuous Control

Terminal attractors are introduced in dynamic sliding mode error coordinates in order to obtain two control schemes for robot manipulators that guarantee finite-time convergence of tracking errors. The simple passivity-based design yields continuous controllers with singularity-free closed-loop dynamics. Robustness to a class of bounded disturbance and complex friction models are discussed. Simulation data show the performance of the controllers.

A passivity-based adaptive sliding mode position-force control for robot manipulators

Based on a novel orthogonalized sliding mode error co-ordinate system, a passivity-based adaptive sliding mode control that yields the global exponential convergence of position and force tracking errors is proposed. The holonomic constraint is efficiently manipulated to derive two orthogonal transformations at the velocity level. These transformations are used to propose a convenient representation of error modelling such that simple proofs of passivity and stability are established. Sliding modes arise on the tangential and normal subspaces at the contact point. The parametric uncertainty is compensated via an adaptive control loop and the sliding modes allow one to conclude the exponential convergence. Computer simulation data show a robust performance.