Time-varying Sliding Mode Controls in Rigid Spacecraft Attitude Tracking

To solve the problem of attitude tracking of a rigid spacecraft with an either known or measurable desired attitude trajectory, three types of time-varying sliding mode controls are introduced under consideration of control input constraints. The sliding surfaces of the three types initially pass arbitrary initial values of the system, and then shift or rotate to reach predetermined ones. This way, the system trajectories are always on the sliding surfaces, and the system work is guaranteed to have robustness against parameter uncertainty and external disturbances all the time. The controller parameters are optimized by means of genetic algorithm to minimize the index consisting of the weighted index of squared error （ISE） of the system and the weighted penalty term of violation of control input constraint. The stability is verified with Lyapunov method. Compared with the conventional sliding mode control, simulation results show the proposed algorithm having better robustness against inertia matrix uncertainty and external disturbance torques.

Robust control of uncertain time delay system:a novel sliding mode control design via LMI

The sliding mode control problem （SMC） is studied for a class of uncertain delay system in the presence of both parameter uncertainties and external disturbances. A novel virtual feedback control method is presented. Based on Lyapunov theory, sufficient conditions for design of the robust sliding mode plane are derived. Sliding mode controller based on reaching law concept is developed, which is to ensure system trajectories from any initial conditions asymptotically convergent to sliding mode plane. The global asymptotically stability of the closed-loop system is guaranteed. A numerical example with simulation results is given to illustrate the effectiveness of the methodology.

Robust H_∞ Load Frequency Control of Multi-area Power System With Time Delay:A Sliding Mode Control Approach

This paper is devoted to investigate the robust H∞sliding mode load frequency control(SMLFC) of multi-area power system with time delay. By taking into account stochastic disturbances induced by the integration of renewable energies,a new sliding surface function is constructed to guarantee the fast response and robust performance, then the sliding mode control law is designed to guarantee the reach ability of the sliding surface in a finite-time interval. The sufficient robust frequency stabilization result for multi-area power system with time delay is presented in terms of linear matrix inequalities(LMIs). Finally,a two-area power system is provided to illustrate the usefulness and effectiveness of the obtained results.

Disturbance observer based time-varying sliding mode control for uncertain mechanical system

It is now well known that the time-varying sliding mode control （TVSMC） is characterized by its global robustness against matched model uncertainties and disturbances. The accurate tracking problem of the mechanical system in the presence of the parametric uncertainty and external disturbance is addressed in the TVSMC framework. Firstly, an exponential TVSMC algorithm is designed and the main features are analyzed. Especially, the control parameter is obtained by solving an optimal problem. Subsequently, the global chattering problem in TVSMC is considered. To reduce the static error resulting from the continuous TVSMC algorithm, a disturbance observer based time-varying sliding mode control （DOTVSMC） algorithm is presented. The detailed design principle and the stability of the closed-loop system under the composite controller are provided. Simulation results verify the effectiveness of the proposed algorithm.

Time delay control of hydraulic manipulators with continuous nonsingular terminal sliding mode

For the position tracking control of hydraulic manipulators,a novel method of time delay control(TDC) with continuous nonsingular terminal sliding mode(CNTSM) was proposed in this work.Complex dynamics of the hydraulic manipulator is approximately canceled by time delay estimation(TDE),which means the proposed method is model-free and no prior knowledge of the dynamics is required.Moreover,the CNTSM term with a fast-TSM-type reaching law ensures fast convergence and high-precision tracking control performance under heavy lumped uncertainties.Despite its considerable robustness against lumped uncertainties,the proposed control scheme is continuous and chattering-free and no pressure sensors are required in practical applications.Theoretical analysis and experimental results show that faster and higher-precision position tracking performance is achieved compared with the traditional CNTSM-based TDC method using boundary layers.

Adaptive backstepping finite-time sliding mode control of spacecraft attitude tracking

This paper investigates the finite-time attitude tracking problem for rigid spacecraft. Two backstepping finite-time slid- ing mode control laws are proposed to solve this problem in the presence of inertia uncertainties and external disturbances. The first control scheme is developed by combining sliding mode con- trol with a backstepping technique to achieve fast and accurate tracking responses. To obtain higher tracking precision and relax the requirement of the upper bounds on the uncertainties, a se- cond control law is also designed by combining the second or- der sliding mode control and an adaptive backstepping technique. This control law provides complete compensation of uncertainty and disturbances. Although it assumes that the uncertainty and disturbances are bounded, the proposed control law does not require information about the bounds on the uncertainties and disturbances. Finite-time convergence of attitude tracking errors and the stability of the closed-loop system are ensured by the Lya- punov approach. Numerical simulations on attitude tracking control of spacecraft are provided to demonstrate the performance of the proposed controllers.

Finite-time robust control of uncertain fractional-order Hopfield neural networks via sliding mode control

The finite-time control of uncertain fractional-order Hopfield neural networks is investigated in this paper. A switched terminal sliding surface is proposed for a class of uncertain fractional-order Hopfield neural networks. Then a robust control law is designed to ensure the occurrence of the sliding motion for stabilization of the fractional-order Hopfield neural networks. Besides, for the unknown parameters of the fractional-order Hopfield neural networks, some estimations are made. Based on the fractional-order Lyapunov theory, the finite-time stability of the sliding surface to origin is proved well. Finally, a typical example of three-dimensional uncertain fractional-order Hopfield neural networks is employed to demonstrate the validity of the proposed method.

Finite time convergent control using terminal sliding mode

A method for terminal sliding mode control design is discussed. As we know, one of the strong points of terminal sliding mode control is its finite-time convergence to a given equilibrium of the system under consideration, which may be useful in specific applications. The proposed method, different from many existing terminal sliding model control desin methods, is studied, and then feedback laws are designed for a class of nonlinear systems, along with illustrative examples.

Uniformed model of networked control systems with long time delay

Feedback control systems wherein the control loops are closed through a real-time network are called networked control systems （NCS）. The defining feature of an NCS is that information is exchanged using a network among control system components. Two new concepts including long time delay and short time delay are proposed. The sensor is almost always clock driven. The controller or the actuator is either clock driven or event driven. Four possible driving modes of networked control systems are presented. The open loop mathematic models of networked control systems with long time delay are developed when the system is driven by anyone of the four different modes. The uniformed modeling method of networked control systems with long time delay is proposed. The simulation results are given in the end.

Finite-time adaptive sliding mode control for heavyweight airdrop operations

This paper investigates the problem of designing a fast convergent sliding mode flight controller of a transport aircraft for heavyweight airdrop operations in the presence of bounded uncertainties without the prior knowledge of the bounds. On the basis of feedback linearization of the aircraft-cargo motion system, a novel integral sliding mode flight control law with gains adaptation is proposed. It contains a nominal control law used to achieve finite-time stabilization performance and a compensated control law used to reject the uncertainties. The switching gains of the compensated control law are tuned using adaptation algorithms, and the knowledge of the bounds of the uncertainties is not required to be known in advance. Meanwhile, the severe chattering of the sliding mode control that caused by high switching gains is effectively reduced. The controller and its performance are evaluated on a transport aircraft performing a maximum load airdrop task in a number of simulation scenarios.

Characteristic Model-based Discrete-time Sliding Mode Control for Spacecraft with Variable Tilt of Flexible Structures

In this paper, the finite-time attitude tracking control problem for the spacecrafts with variable tilt of flexible appendages in the conditions of exogenous disturbances and inertia uncertainties is addressed. First the characteristic modeling method is applied to the problem of the spacecraft modeling. Second, a novel adaptive sliding mode surface is designed based on the characteristic model. Furthermore, a discrete-time sliding mode control (DTSMC) law, which makes the tracking error converge into a predefined bound in finite time, is proposed by employing the parameters of characteristic model associated with the sliding mode surface to provide better performances, robustness, faster response, and higher control precision. The designed DTSMC includes the adaptive control architecture and is chattering-free. Finally, digital simulations of a sun synchronous orbit satellite (SSOS) are presented to illustrate effectiveness of the control strategies as well as to verify the practical feasibility of the rapid maneuver mission. © 2014 Chinese Association of Automation.

Finite-time Sliding Mode Control Design for a Class of Uncertain Conic Nonlinear Systems

This paper studies the sliding mode controller design problems for a class of nonlinear system. The nonlinear function is considered to satisfy conic-type constraint condition. A novel finite-time boundedness(FTB) based sliding mode controller design theory is proposed. And then a sufficient condition is obtained in terms of linear matrix inequalities(LMIs), which guarantees the resulted sliding mode dynamics to be FTB wrt some predefined scalars. Thereafter, a FTB-based sliding mode control(SMC) law is synthesized to ensure the state of the controlled system is driven into a novel desired switching surface s(t) = c(c is a constant) in a finite time. Simulation results illustrate the validity of the proposed FTB-based SMC design theory.

Sliding mode control and Lyapunov based guidance law with impact time constraints

This paper analyses the issue of impact time control of super-cavitation weapons impact fixed targets which mainly refer to the ships or submarines who lost power, but still have combat capability. Control over impact time constraints of guidance law(ITCG) is derived by using sliding mode control(SMC) and Lyapunov stability theorem. The expected impact time is realized by using the notion of attack process and estimated time-to-go to design sliding mode surface(SMS). ITCG contains equivalent and discontinuous guidance laws, once state variables arrive at SMS,the equivalent guidance law keeps the state variables on SMS,then the discontinuous guidance law enforces state variables to move and reach SMS. The singularity problem of ITCG is also analyzed. Theoretical analysis and numerical simulation results are given to test the effectiveness of ITCG designed in this paper.

Fixed time integral sliding mode controller and its application to the suppression of chaotic oscillation in power system

Chattering phenomenon and singularity are still the main problems that hinder the practical application of sliding mode control. In this paper, a fixed time integral sliding mode controller is designed based on fixed time stability theory, which ensures precise convergence of the state variables of controlled system, and overcomes the drawback of convergence time growing unboundedly as the initial value increases in finite time controller. It makes the controlled system converge to the control objective within a fixed time bounded by a constant as the initial value grows, and convergence time can be changed by adjusting parameters of controllers properly. Compared with other fixed time controllers, the fixed time integral sliding mode controller proposed in this paper achieves chattering-free control, and integral expression is used to avoid singularity generated by derivation. Finally, the controller is used to stabilize four-order chaotic power system. The results demonstrate that the controller realizes the non-singular chattering-free control of chaotic oscillation in the power system and guarantees the fixed time convergence of state variables, which shows its higher superiority than other finite time controllers.

Integral sliding mode control of time-delay systems with mismatching uncertainties

A linear matrix inequality （LMI）-based sliding surface design method for integral sliding mode control of uncertain time- delay systems with mismatching uncertainties is proposed. The uncertain time-delay system under consideration may have mis- matching norm bounded uncertainties in the state matrix as well as the input matrix, A sufficient condition for the existence of a sliding surface is given to guarantee asymptotic stability of the full order slJdJng mode dynamics. An LMI characterization of the slid- ing surface is given, together with an integral sliding mode control law guaranteeing the existence of a sliding mode from the initial time. Finally, a simulation is given to show the effectiveness of the proposed method.

Robust pre-specified time synchronization of chaotic systems by employing time-varying switching surfaces in the sliding mode control scheme

In the conventional chaos synchronization methods, the time at which two chaotic systems are synchronized, is usually unknown and depends on initial conditions. In this work based on Lyapunov stability theory a sliding mode controller with time-varying switching surfaces is proposed to achieve chaos synchronization at a pre-specified time for the first time. The proposed controller is able to synchronize chaotic systems precisely at any time when we want. Moreover, by choosing the time-varying switching surfaces in a way that the reaching phase is eliminated, the synchronization becomes robust to uncertainties and exogenous disturbances. Simulation results are presented to show the effectiveness of the proposed method of stabilizing and synchronizing chaotic systems with complete robustness to uncertainty and disturbances exactly at a pre-specified time.

Variable structure control with sliding mode prediction for discrete-time nonlinear systems

A new variable structure control algorithm based on sliding mode prediction for a class of discrete-time nonlinear systems is presented. By employing a special model to predict future sliding mode value, and combining feedback correction and receding horizon optimization methods which are extensively applied on predictive control strategy, a discrete-time variable structure control law is constructed. The closed-loop systems are proved to have robustness to uncertainties with unspecified boundaries. Numerical simulation and pendulum experiment results illustrate that the closed-loop systems possess desired performance, such as strong robustness, fast convergence and chattering elimination.

Robust integral sliding mode control for uncertain systems with multiple time delays

This paper proposes a robust integral sliding mode (RISM) manifold and the corresponding stabilization control law for uncertain systems with multiple time-varying time delays based on the techniques of linear matrix inequalities (LMI). The sufficient condition for the existence of the RISM manifold is given in terms of LMI, and then, the sliding mode control (SMC) law that can keep the system state on the RISM manifold from the initial time moment is developed. The efficiency and feasibility of the results are illustrated by a numerical example.

Embedding-Based Sliding Mode Control for Linear Time Varying Systems

In this paper, a novel strategy using embedding process and sliding surface is proposed. In this method, a state trajectory starting from a given initial point reaches a definite point on a sliding surface in the minimum time, and then tends to the origin along the sliding surface (SS). In the first, a SS is designed, then using an appropriate measure, an embedding is constructed to solve a time optimal control problem such that the system trajectory reaches the SS in minimum time, after that a control is designed such that the system trajectory tends to the origin along the SS. It is well-known that the main disadvantage of the use of sliding mode controls (SMCs) is a phenomenon, the so-called chattering. The proposed SMC here is piecewise continuous and chattering free. Some numerical examples is presented to illustrate the effectiveness and reliability of the proposed method.

Robust controller design for compound control missile with fixed bounded convergence time

A robust controller for bank to turn(BTT) missiles with aerodynamic fins and reaction jet control system(RCS) is developed based on nonlinear control dynamic models comprising couplings and aerodynamic uncertainties. The fixed time convergence theory is incorporated with the sliding mode control technique to ensure that the system tracks the desired command within uniform bounded time under different initial conditions. Unlike previous terminal sliding mode approaches, the bound of settling time is independent of the initial state, which means performance metrics like convergence rate can be predicted beforehand. To reduce the burden of control design in terms of robustness, extended state observer(ESO) is introduced for uncertainty estimation with the output substituted into the controller as feedforward compensation. Cascade control structure is employed with the proposed control law and therein the compound control signal is obtained.Afterwards, control inputs for two kinds of actuators are allocated on the basis of their inherent characteristics. Finally, a number of simulations are carried out and demonstrate the effectiveness of the designed controller.