Improving control effort in output feedback sliding mode control of sampled‐data systems

This study proposes a new adaptive output feedback sliding mode control (SMC) for mismatched uncertain time-delay systems. First, sufficient conditions in terms of linear matrix inequalities are derived such that the equivalent reduced-order system in the sliding mode is asymptotically stable. Second, based on a new lemma and a novel adaptive law, an adaptive sliding mode controller is designed to guarantee the finite-time reachability of the system states using output feedback only. The proposed method is not limited by the following conditions: (1) the exogenous disturbances must be bounded by a known function of the outputs or by a known function of the state and delayed state variables, and (2) the norm of unmeasured states must be bounded by a constant value. As these conditions are required for the application of most existing SMC approaches for time-delay systems, the proposed approach can be applied to a more generalized system, making it a valuable contribution to the field.

Discrete sliding mode control for nonlinear systems using feedback linearization

In this paper, the tracking control scheme is presented using the framework of finite-time sliding mode control (SMC) law and high-gain observer for disturbed/uncertain multi-motor driving systems under the consideration multi-output systems. The convergence time of sliding mode control is estimated in connection with linear matrix inequalities (LMIs). The input state stability (ISS) of proposed controller was analyzed by Lyapunov stability theory. Finally, the extensive simulation results are given to validate the advantages of proposed control design.

In this paper, the observer-based output feedback sliding mode control (SMC) problem is investigated for discrete delayed nonlinear systems subject to packet losses under the event-triggered strategy. It is assumed that the packet losses may occur in the control channel from the sensor to the observer. A suitable compensation strategy via the Bernoulli distributed random variable is used to reduce the effects of packet losses. In order to avoid the phenomenon of network congestion during the networked transmission, an event-triggered mechanism is introduced to determine if the last released measurement needs to be updated. Based on the zero-order-hold (ZOH) measurement, an output feedback observer is designed to reconstruct the system state. This method can facilitate the design of the discrete-time sliding surface. A sufficient condition is proposed to guarantee the stochastic stability of sliding mode dynamics systems by using linear matrix inequality (LMI) method, and a novel observer-based sliding mode controller is synthesized to force the trajectories of the error systems onto the pre-designed sliding mode surface within finite time. Finally, an example is given to illustrate the validity of the proposed theoretical result.

Output feedback sliding mode control of base isolated structures

In this paper, a nonlinear robust output feedback control is proposed for a class of autonomous underwater vehicles. In specific, we consider the nonlinear mathematical model of a heavy-weight torpedo and design a sliding mode controller to achieve robust stabilization of the closed-loop system in the presence of environmental disturbances and parametric uncertainties. Lyapunovs method is used to present the closed-loop stability analysis of the system. Then, the state feedback sliding mode control law is extended to an output feedback control design using a fourth order observer. It is highlighted that the performance of the state feedback control is recovered arbitrarily fast by the proposed output feedback controller in the presence of parametric uncertainties and environmental disturbances. Finally, the performance of the proposed control design is shown using simulation.

This paper focuses on the regulation problem of a planar vertical take-off and landing (PVTOL) aircraft using output feedback sliding mode controller where a sliding mode observer is used to estimate the velocity. The observer design is independent of the feedback control design (separation principle). Considering as important the actuators response in the performance of the closed-loop systems, the dynamics of the PVTOL is augmented with the dynamics of the actuators. The performance of the closed-loop system is illustrated through simulation results.

The paper presents an algorithm for the discrete-time output feedback sliding mode control of time delayed systems with uncertainty. The proposed algorithm is capable of handling systems with both state and input delay. The major advantage of the algorithm is that it is based on system output and hence more practical. Moreover, it reduces chattering by avoiding the usage of a switching input.

Based on a kind of regular form, a Lyapunov matrix with special structure is presented to design the sliding surface matrix conveniently and then an effective algorithm is developed on it. A simple static output feedback sliding mode control law without extra dynamic equation is given, such that the predefined sliding surface is reached in finite time for the general matching uncertainties. In the reported result, this extra dynamic equation is used for evaluating the norm bound of the unmeasured state vector. Finally, some examples are studied to illustrate the proposed approach.

We consider the sliding-mode output feedback controller (SMOFC) design problem for a class of uncertain multivariable systems. We first design a stabilizing SMOFC for matched uncertain systems. Using linear matrix inequalities (LMIs), we derive a necessary and sufficient condition for the existence of a linear sliding surface depending on outputs and compensator states. Using the solution of the LMI existence condition, we characterize the gain matrices. We give the nonlinear switching feedback gain guaranteeing the reachability condition. Second, we give an LMI-based design method to combine various useful performance criteria which can be used to guarantee a desired robust performance in spite of mismatched uncertainties. The performance criteria include alpha-stability, LQ performance, H 2/H infin performance, and peak-to-peak gain bound. In particular, we show that by including H infin performance constraints, we can easily solve the SMOFC design problem for challenging system models to which the previous methods are not easily applicable. Finally, we give a numerical design example showing that our method can be successfully applied to the problem of designing reduced-order SMOFCs for uncertain time-delay systems or mismatched uncertain systems.

Traditional thrusters using chemical fuels could hardly afford long-term hovering in low Earth orbits due to the considerable fuel consumptions, which, however, could be feasible with the geomagnetic Lorentz force acting on a charged Lorentz spacecraft as auxiliary propulsion. And this kind of hovering using hybrid control inputs consisting of the net charge and thruster-generated control force of Lorentz spacecraft is termed as Lorentz-augmented spacecraft hovering. Based on the dynamical model of Lorentz-augmented spacecraft relative motion, fuel-optimal open-loop control laws are first derived by a Lagrange method. To achieve closed-loop hovering in the presence of external perturbations and system uncertainties and in the absence of velocity measurements, a neural network–based observer and an adaptive output feedback sliding mode controller are designed. Neural networks are used to approximate the unknown nonlinear dynamics, and sliding mode control method is used to ensure the system robustness. The adaptive tuning law of the neural networks is derived by a Lyapunov approach to guarantee the uniform ultimate boundedness of the overall closed-loop system. The validity and feasibility of the proposed control schemes are substantiated by numerical simulations.

For a class of linear MIMO uncertain systems, a dynamic output feedback sliding mode control algorithm that avoids the chattering problem and high gain control is proposed in this paper. Without using any differentiator, we develop a modified asymptotically stable second order sliding mode control law in which the developed controller can guarantee the finite time convergence to the sliding mode and the system states asymptotically approach to zero. Finally, a numerical example is explained for demonstrating the applicability of the proposed scheme.

Twin spool gas turbine engine which is the integral part of the avionics, is a non linear higher order multi input multi output (MIMO) system. Design of tracking controller for turbine engine with the classical techniques is a tedious task and implementation of the complex controller is also an issue. The Basic philosophy of this paper is to design a sliding mode controller with model order reduction. Implementation of this designed tracking controller on the original system is easier due to reduced controller complexity.

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.

In this article, a discrete-time design of higher-order repetitive sliding mode controller (HO-RSMC) for uncertain linear systems with time-varying periodic disturbances is presented. In the design, a higher-order repetitive control (HORC) is employed to significantly suppress the periodic exogenous disturbance with period variation. The HORC-based control system offers a slow transient response due to the multiple control delays. Moreover, since the system stability is easily affected by model uncertainties, an output-feedback sliding mode controller (SMC) is added to overcome the shortcomings of HORC. Stability analysis of the resulting closed-loop system is rigorously provided. The simulation results and comparison studies confirm the effectiveness and good performance of the proposed design.