A novel dynamic terminal sliding mode control of uncertain nonlinear systems

A new dynamic terminal sliding mode control （DTSMC） technique is proposed for a class of single-input and single-output （SISO） uncertain nonlinear systems. The dynamic terminal sliding mode controller is formulated based on Lyapunov theory such that the existence of the sliding phase of the closed-loop control system can be guaranteed, chattering phenomenon caused by the switching control action can be eliminated, and high precision performance is realized. Moreover, by designing terminal equation, the output tracking error converges to zero in finite time, the reaching phase of DSMC is eliminated and global robustness is obtained. The simulation results for an inverted pendulum are given to demonstrate the properties of the proposed method.

Nonlinear dynamic fractional sliding mode control to the motor of mining locomotive

The harsh operating environment and complex operating conditions of the mine electric locomotive affect the control performance of the locomotive traction motor.In order to improve the speed control performance of electric locomotive traction motors,a dynamic fractional-order sliding mode control(DFOSMC)algorithm considering uncertain factors was proposed.A load torque sliding mode observer was designed for the complex load disturbance of the traction motor,and its observations were integrated into the DFOSMC controller to overcome the influence of load disturbance.Finally,the stability of the designed controller was proved by Lyapunov's theorem.Besides,the control performance of DFOSMC controller was compared with integer-order sliding mode controller and fractional-order sliding mode controller through simulation experiments.Compared with integer-order sliding mode and fractional-order sliding mode controllers,the dynamic and static performance of the DFOSMC controller with load observation is better,and it has stronger anti-interference ability.The DFOSMC controller effectively improves the control performance of the traction motor of the mining locomotive.

Trajectory tracking control for underactuated unmanned surface vehicles with dynamic uncertainties

The trajectory tracking control problem for underactuated unmanned surface vehicles(USV) was addressed, and the control system took account of the uncertain influences induced by model perturbation, external disturbance, etc. By introducing the reference, trajectory was generated by a virtual USV, and the error equation of trajectory tracking for USV was obtained, which transformed the tracking problem of underactuated USV into the stabilization problem of the trajectory tracking error equation. A backstepping adaptive sliding mode controller was proposed based on backstepping technology and method of dynamic slide model control. By means of theoretical analysis, it is proved that the proposed controller ensures that the solutions of closed loop system have the ultimate boundedness property. Simulation results are presented to illustrate the effectiveness of the proposed controller.

Serret-Frenet frame based on path following control for underactuated unmanned surface vehicles with dynamic uncertainties

The path following problem for an underactuated unmanned surface vehicle(USV) in the Serret-Frenet frame is addressed. The control system takes account of the uncertain influence induced by model perturbation, external disturbance, etc. By introducing the Serret-Frenet frame and global coordinate transformation, the control problem of underactuated system(a nonlinear system with single-input and ternate-output) is transformed into the control problem of actuated system(a single-input and single-output nonlinear system), which simplifies the controller design. A backstepping adaptive sliding mode controller(BADSMC)is proposed based on backstepping design technique, adaptive method and theory of dynamic slide model control(DSMC). Then, it is proven that the state of closed loop system is globally stabilized to the desired configuration with the proposed controller. Simulation results are presented to illustrate the effectiveness of the proposed controller.

Carrier Landing Robust Control Based on Longitudinal Decoupling

We studied carrier landing robust control based on longitudinal decoupling.Firstly,due to the relative strong coupling between the tangential and the normal directions,the height and the velocity channels were decoupled by using the exact linearization method,so that controllers for the two channels could be designed seperately.In the height control,recursive dynamic surface was used to accelerate the convergence of the height control and eliminate″the explosion of complexity″.The radial basis function(RBF)neural network was designed by using the minimum learning parameter method to compensate the uncertainty.A kind of surface with nonsingular fast terminal sliding mode and its reaching law were developed to ensure finite time convergence and to avoid singularity.The controller for the velocity was designed by using super-twisting second-order sliding mode control.The stability of the proposed system was validated by Lyapunov method.The results showed that the Levant′s robust differential observer was improved and used for the observation of the required higher order differential of signals in the controller.The response of aircraft carrier landing under the complex disturbance is simulated and the results verified the approach.

Robust non-aggressive three-axis attitude control of spacecraft:dynamic sliding mode approach

Conventional sliding mode control(SMC)has been extensively applied in controlling spacecrafts because of its appealing characteristics such as robustness and a simple design procedure.Several methods such as second-order sliding modes and discontinuous controllers are applied for the SMC implementation.However,the main problems of these methods are convergence and error tracking in a finite amount of time.This paper combines an improved dynamic sliding mode controller and model predictive controller for spacecrafts to solve the chattering phenomenon in traditional sliding mode control.To this aim,this paper develops dynamic sliding mode control for spacecraft’s applications to omit the chattering issue.The proposed approach shows robust attitude tracking by a set of reaction wheels and stabilizes the spacecraft subject to disturbances and uncertainties.The proposed method improves the performance of the SMC for spacecraft by avoiding chattering.A set of simulation results are provided that show the advantages and improvements of this approach(in some sense)compared to SMC approaches.

A New Sliding Function for Discrete Predictive Sliding Mode Control of Time Delay Systems

The control of time delay systems is still an open area for research. This paper proposes an enhanced model predictive discrete-time sliding mode control with a new sliding function for a linear system with state delay. Firstly, a new sliding function including a present value and a past value of the state, called dynamic surface, is designed by means of linear matrix inequalities （LMIs）. Then, using this dynamic function and the rolling optimization method in the predictive control strategy, a discrete predictive sliding mode controller is synthesized. This new strategy is proposed to eliminate the undesirable effect of the delay term in the closed loop system. Also, the designed control strategy is more robust, and has a chattering reduction property and a faster convergence of the system s state. Finally, a numerical example is given to illustrate the effectiveness of the proposed control.

Robust Optimal Higher-order-observer-based Dynamic Sliding Mode Control for VTOL Unmanned Aerial Vehicles

This paper investigates the precise trajectory tracking of unmanned aerial vehicles(UAV) capable of vertical take-off and landing(VTOL) subjected to external disturbances. For this reason, a robust higher-order-observer-based dynamic sliding mode controller(HOB-DSMC) is developed and optimized using the fractional-order firefly algorithm(FOFA). In the proposed scheme, the sliding surface is defined as a function of output variables, and the higher-order observer is utilized to estimate the unmeasured variables,which effectively alleviate the undesirable effects of the chattering phenomenon. A neighboring point close to the sliding surface is considered, and as the tracking error approaches this point, the second control is activated to reduce the control input. The stability analysis of the closed-loop system is studied based on Lyapunov stability theorem. For a better study of the proposed scheme, various trajectory tracking tests are provided, where accurate tracking and strong robustness can be simultaneously ensured. Comparative simulation results validate the proposed control strategy′s effectiveness and its superiorities over conventional sliding mode controller(SMC) and integral SMC approaches.

An integrated approach for dynamic traffic routing and ramp metering using sliding mode control

The problem of designing integrated traffic control strategies for highway networks with the use of route guidance, ramp metering is considered. The highway network is simulated using a first order macroscopic model called LWR model which is a mathematical traffic flow model that formulates the relationships among traffic flow characteristics in terms of density, flow, and mean speed of the traffic stream. An integrated control algorithm is designed to solve the proposed problem, based on the inverse control technique and variable structure control（super twisting sliding mode）. Three case studies have been tested in the presence of an on-ramp at each alternate route and where there is a capacity constraint in the network. In the first case study, there is no capacity constraint at either upstream or downstream of the alternate routes and the function of the proposed algorithm is only to balance the traffic flow on the alternate routes. In the second case study, there is capacity constraint at downstream of alternate routes. The proposed algorithm aims to avoid congestion on the main road and balance the traffic flow on the alternate routes. In the last case study, there is capacity constraint at upstream of alternate routes. The objective of proposed algorithm is to avoid congestion on the main road and to balance the traffic flow on the alternate routes. The obtained results show that the proposed algorithms can establish user equilibrium between two alternate routes even when the on-ramps, located at alternate routes, have different traffic demands.

Observer-based adaptive sliding mode backstepping output-feedback DSC for spin-stabilized canard-controlled projectiles

This article presents a complete nonlinear controller design for a class of spin-stabilized canard-controlled projectiles.Uniformly ultimate boundedness and tracking are achieved,exploiting a heavily coupled,bounded uncertain and highly nonlinear model of longitudinal and lateral dynamics.In order to estimate unmeasurable states,an observer is proposed for an augmented multiple-input-multiple-output（MIMO） nonlinear system with an adaptive sliding mode term against the disturbances.Under the frame of a backstepping design,an adaptive sliding mode output-feedback dynamic surface control（DSC） approach is derived recursively by virtue of the estimated states.The DSC technique is adopted to overcome the problem of ‘‘explosion of complexity＂ and relieve the stress of the guidance loop.It is proven that all signals of the MIMO closed-loop system,including the observer and controller,are uniformly ultimately bounded,and the tracking errors converge to an arbitrarily small neighborhood of the origin.Simulation results for the observer and controller are provided to illustrate the feasibility and effectiveness of the proposed approach.

Predefined-time bipartite tracking consensus for second-order multi-agent systems with cooperative and antagonistic networks

This paper addresses the predefined-time bipartite tracking problem for second-order Multi-Agent Systems(MASs)with undirected signed topologies.A group of observers,which can estimate the state tracking errors for each follower in a pre-specified time,is proposed based on the time-varying function.In order to deal with the uncertainties caused by the unknown disturbances and the unknown input signal of the leader,we propose a predefined-time distributed control protocol based on the sliding mode control method.In addition,an auxiliary dynamic sliding variable is designed to reduce system chattering.Wetheoretically prove that the two control protocols can drive the state trajectories of each follower to reach the corresponding sliding surface within a specified time,and finally ensure that the prescribed-time bipartite tracking consensus is achieved for the MASs.Simulations are provided to verify the proposed schemes,and the simulation results further confirm the superiority of the adaptive control protocol.

Diffusion of a Ring Threaded on a Linear Chain

A mesoscopic simulation is applied to investigate the effects of hydrodynamic interactions and axial chains on the dynamics of threaded rings.The hydrodynamic interactions significantly speed up the diffusion and relaxation of both free and threaded rings.The decoupled diffusion and relaxation dynamics indicate the broken of the Einstein-Stokes relationship.The diffusion of a ring threaded on a flexible chain exhibits a synergism effect compared to that on an axial rod,which originates from the self-diffusion of the ring and the reptation-like motion of the axial chain.Meanwhile,hydrodynamic interactions significantly improve the synergism effect,leading to an enhanced sliding motion of the threaded ring.The faster sliding of threaded rings suggests that the entropic barrier is negligible,which agrees well with the basic assumption of barrier-less confining tube at equilibrium in tube theory.Our results provide a new perspective on analysis of the effects of topology constraints on polymer dynamics.

Investigation of the unstable flow phenomenon in a pump turbine

Instability of pump turbine with S-shaped curve is characterized by large fluctuations of rotational speed during the transient processes.For investigating this phenomenon,a numerical model based on the dynamic sliding mesh method(DSSM)is presented and used to numerically solve the 3D transient flow which is characterized by the variable rotation speed of runner.The method is validated by comparison with measured data for a load rejection process in a prototype pump turbine.The results show that the calculated rotation speed agrees well with the experimental data.Based on the validated model,simulations were performed for the runaway process using an artificially assumed operating condition under which the unstable rotation speed is expected to appear.The results confirm that the instability of runner rotational speed can be effectively captured with the proposed method.Presented results include the time history profiles of unit flow rate and unit rotating speed.The internal flow characteristics in a typical unstable period are discussed in detail and the mechanism of the unstable hydraulic phenomenon is explained.Overall,the results suggest that the method presented here can be a viable alternative to predict the dynamic characteristics of pump turbines during transient processes.

Super twisting controller for on-orbit servicing to non-cooperative target

A relative position and attitude coupled controller is proposed for rendezvous and docking between two docking ports located in different spacecraft. It is concerned with servicing to a tumbling non-cooperative target spacecraft in arbitrary orbit subjected to external disturbances.By considering both kinematic and dynamical coupled effects of relative rotation on relative translation, a coupled dynamic model is established to represent the relative motion of docking port on target spacecraft with respect to another on the service spacecraft. The spacecraft control is based on the second order sliding mode algorithm of super twisting（ST）. It is schemed to manipulate the relative position and attitude synchronously. A formal proof of the finite time convergence property of the closed-loop system is derived theoretically by the second method of Lyapunov. Numerical simulations with the designed ST controller are presented to validate the analytic analysis by contrast with the twisting control algorithm. Simulation results demonstrate that the proposed relative position and attitude integrated controller is characterized by high precision, strong robustness and high reliability.