Sliding Mode Dynamic Surface Control Research Articles

Linear Parameter Varying Observer-Based Adaptive Dynamic Surface Sliding Mode Control for PMSM

This paper presents an adaptive dynamic surface sliding mode control technique to address the issue of system parameter changes in permanent magnet synchronous motor (PMSM) position servo systems. The proposed method involves adopting a linear parameter varying (LPV) observer-based parameter identification algorithm and adaptive control technique. Initially, a mathematical model of the PMSM is established, and the system parameters are divided into nominal and perturbation values. This allows for the reconstruction of the system model into a state space equation that incorporates the unknown perturbation parameters. To accurately estimate these unknown parameters, an LPV observer is designed based on the reconstructed model. Additionally, an adaptive dynamic surface sliding mode control technique is explored to achieve the desired tracking performance. Meanwhile, an exponential reaching law is introduced to expedite the dynamic behavior of the system and mitigate chattering. Finally, a suitable Lyapunov function is selected to ensure the overall stability of the system. The simulation results demonstrate the effectiveness of the parameter identification and control algorithm in achieving good identification and tracking control ability for PMSM systems.

Dynamic surface sliding mode control of chaos in the fourth-order power system

As a typical complex nonlinear model, the power system is influenced by the parameters and initial values, and chaotic oscillations can easily occur in the actual operation process, which seriously endangers the stability of its operation and may even lead to the collapse of the whole power system. To suppress chaotic oscillations in power systems, a method of dynamic surface sliding mode control is first proposed, which overcomes the “term explosion” problem in the traditional backstepping design process by introducing first-order low-pass filters, and reduces the design steps of dynamic surface controllers and the complexity of stability analysis by combining sliding mode control. And then, the steadiness of the closed-loop controlled system is evaluated according to Lyapunov asymptotic stability theory. Lastly, the simulation and experiment are implemented to show that the designed control method can effectively inhibit the power system's chaotic oscillations and stabilize it.

Disturbance Observer based Dynamic Surface Sliding Mode Control for Manipulator Arm with Adaptive RBF Networks

For the rotation position control of automatic loading manipulator arm with uncertain problems of load change and external disturbances, an adaptive radial basis function networks (RBF) dynamic surface sliding mode control (DSMC) strategy based on disturbance observer (DOB) is proposed. The value of the external disturbance, which is estimated by the DOB on line, is added to the output of the proposed controller for feedforward compensation. The dynamic performance of the controller is ensured by introducing the adaptive RBF networks while the stability of the controller is verified by designing the Lyapunov function. Comparison between the results of the proposed control strategy and those of the conventional sliding mode control (SMC) shows that the controller has better dynamic tracking characteristics, steady-state accuracy and strong robustness under load changes.

An Improved Dynamic Surface Sliding Mode Method for Autonomous Cooperative Formation Control of Underactuated USVS with Complex Marine Environment Disturbances

Abstract In this paper, a novel dynamic surface sliding mode control (DSSMC) method, combined with a lateral velocity tracking differentiator (LVTD), is proposed for the cooperative formation control of underactuated unmanned surface vehicles (USVs) exposed to complex marine environment disturbances. Firstly, in view of the kinematic and dynamic models of USVs and the design idea of a virtual control law in a backstepping approach, the trajectory tracking control problem of USVs’ cooperative formation is transformed into a stabilisation problem of the virtual control law of longitudinal and lateral velocities. Then, aiming at the problem of differential explosion caused by repeated derivation in the process of backstepping design, the first-order low-pass filter about the virtual longitudinal velocity and intermediate state quantity of position is constructed to replace differential calculations during the design of the control law, respectively. In order to reduce the steady-state error when stabilising the virtual lateral velocity control law, the integral term is introduced into the design of the sliding mode surface with a lateral velocity error, and then the second-order sliding mode surface with an integral is structured. In addition, due to the problem of controller oscillation and the role of the tracking differentiator (TD) in active disturbance rejection control (ADRC), the LVTD is designed to smooth the state quantity of lateral velocity. Subsequently, based on the dynamic model of USV under complex marine environment disturbances, the nonlinear disturbance observer is designed to observe the disturbances and compensate the control law. Finally, the whole cooperative formation system is proved to be uniformly and ultimately bounded, according to the Lyapunov stability theory, and the stability and validity of the method is also verified by the simulation results.

Prescribed Performance Control with Sliding-Mode Dynamic Surface for a Glue Pump Motor Based on Extended State Observers

The actuator of a particleboard glue-dosing system, the glue pump motor, is affected by external disturbances and unknown uncertainty. In order to achieve accurate glue-flow tracking, in this paper, a glue pump motor compound control method was designed. First, the prescribed performance control method is used to improve the transient behaviors, and the error of the glue flow tracking is guaranteed to converge to a preset range, as a result of the design of an appropriate performance function. Second, two extended state observers were designed to estimate the state vector and the disturbance, in order to improve the robustness of the controlled system. To further strengthen the steady-state performance of the system, the sliding-mode dynamic surface control method was introduced to compensate for uncertainties and disturbances. Finally, a Lyapunov stability analysis was conducted, in order to prove that all of the signals are bounded in a closed-loop system, and the effectiveness and feasibility of the proposed method were verified through numerical simulation.

Recursive Sliding-Mode Dynamic Surface Containment Control With Nonlinear Gains for Uncertain Nonlinear Multiagent Systems

Containment control is one of critical issues in multiagent systems (MASs). A recursive sliding-mode dynamic surface control (DSC) strategy with a nonlinear gain is addressed for the containment problem of uncertain MASs in strict-feedback form. Two factors, a recursive dynamic sliding-mode surface and a nonlinear gain function, are introduced to solve the contradiction between control accuracy and dynamic performance in the traditional DSC method. The function approximation technique, by radial basis function neural networks, is employed to compensate unknown dynamics. On the basis of the backstepping and graph theory, a full-state feedback containment control strategy is presented. Subsequently, we propose an output feedback containment control strategy via a state observer for individual followers. From the Lyapunov stability theorem, we construct an improvement Lyapunov function for the MAS, and it is proven that all followers converge to a convex hull formed by leaders for both full-state feedback and output feedback cases. Simulation examples are presented for verification of the effectiveness of the strategy.

Sliding Mode Dynamic Surface Control for Multi-Machine Power Systems with Time Delays and Dead-Zones

This paper presents a sliding mode dynamic surface control strategy for multi-machine power systems with static var compensator (SVC) to design the controller of the generator excitation system. Firstly, compared with the existing control methods, the combination of sliding mode control and dynamic surface control improves the robustness of the system and avoids the “explosion of complexity” problems. Subsequently, the fuzzy logic system is introduced to estimate the unknown continuous function in power system, and the norm of the weight vector is used to replace the estimation of the entire weight vector. In this way, computational burden will be reduced. In addition, the influences of unknown time delays and dead-zones are considered. Finite cover lemma is introduced to deal with unknown time delays, which enables arbitrarily small tracking performance. The unknown dead-zone is converted into the sum of linear dead zone and bounded nonlinear dead zone. Finally, the simulation results are provided to validate the feasibility and effectiveness of the proposed control strategy.

MLP neural network-based recursive sliding mode dynamic surface control for trajectory tracking of fully actuated surface vessel subject to unknown dynamics and input saturation

In this work, we present a MLP neural network-based recursive sliding mode dynamic surface control scheme for a fully actuated surface vessel with uncertain dynamics and external disturbances, where the control input are required to be constrained. First of all, the minimum learning parameter (MLP) neural networks (NN)-based are designed to enhance the robustness against model uncertainties. Subsequently, an adaptive law is employed to compensate neural networks approximation errors and disturbances. The recursive sliding mode control method combined with dynamic surface control (DSC) is designed to eliminate repeated derivative of virtual control laws and enhance systems robustness. A smooth hyperbolic tangent function is incorporated with the control scheme to reduce the risk of actuator saturation. At the same time, the Nussbaum function is used to compensate for the saturation function and ensure the stability of system. We show that under the proposed control method, despite the presence of system uncertainties and disturbances, the tracking errors can converge into arbitrarily small neighborhoods around zero, while the constraint requirements on the control force and torque will not be violated. By using the Lyapunov function, it is proven that the proposed control method can guarantee the uniform boundedness of all the closed loop signals. Finally, simulation results further demonstrate the effectiveness of the proposed method.

Adaptive fuzzy dynamic surface sliding mode control of large-scale power systems with prescribe output tracking performance

This paper focuses on an adaptive fuzzy based dynamic surface sliding mode control (ADSSMC) strategy for multi-machine power systems with SVC. The main characteristics of the proposed ADSSMC strategy are: (1) System robustness and the convergency speed of all surface error are enhanced by combining dynamic surface control with sliding mode, leading to the structural complexity of the controller in backstepping control scheme is eliminated; (2) By introducing an error performance conversion function, the errors of desired trajectory and system output are always within a predetermined range; (3) In the adaptive regulation laws, the number of estimated parameters of the control system is significantly reduced due to the utilization of the estimations of weight vector norm instead of the weight vectors itself. The stability analysis proves that the proposed ADSSMC control strategy can guarantee the boundaries of all signals in the closed-loop control system. Experimental results verify the effectiveness of the proposed ADSSMC scheme.

Integrated Guidance and Control of Multiple Interceptor Missiles Based on Improved Distributed Cooperative Control Strategy

In this study, an improved cooperative integrated guidance and control (IGC) design method is proposed based on distributed networks to address the guidance and control problem of multiple interceptor missiles. An IGC model for a leading interceptor is constructed based on the relative kinematic relations between missiles and a target and the kinematic equations of the missiles in a pitch channel. The unknown disturbances of the model are estimated using a finite-time disturbance observer (FTDO). Then, the control algorithm for the leading interceptor is designed according to the disturbance estimation and nonsingular fast dynamic surface sliding mode control (SMC). To enhance the rate of convergence of the cooperative control commands for the interceptors, an improved cooperative control strategy is proposed based on the leader-follower distributed network. Consequently, the two velocity components of the interceptor in the pitch channel can be obtained, which are subsequently converted to the total velocity and flight path angle commands of the interceptor using kinematic relations. The control algorithm for the following interceptor is similarly designed using an FTDO and dynamic surface SMC. The effectiveness of the improved distributed cooperative control strategy for multiple interceptors is validated through simulations.

High-Gain Observer-Based Sliding-Mode Dynamic Surface Control for Particleboard Glue Mixing and Dosing System

In the process of particleboard glue mixing and dosing control under the working condition of intermediate frequency, a sliding-mode dynamic surface control strategy based on high-gain observer is proposed in this paper to deal with the problem of glue flow stability caused by strong nonlinearity. The high-gain observer (HGO) is aimed at estimating the derivative of the immeasurable system input signal for feedback, and the robustness of the system is improved by the dynamic surface control (DSC) method. Furthermore, the sliding-mode control (SMC) method is used to deal with disturbances caused by the uncertainties as well as external disturbances. It is proven that the system is exponential asymptotic stable by constructing a suitable Lyapunov function. Simulation results show that the proposed control methods can make the system track the expected flow value quickly and accurately. Finally, numerical simulation results are exhibited to authenticate and validate the effectiveness of the proposed control scheme.

Research on Integrated Guidance and Control of Distributed Cooperation of Multi-Interceptor with State Coupling

With the aim of achieving cooperative target interception by using multi-interceptor, a distributed cooperative control algorithm of the multi-interceptor with state coupling is proposed based on the IGC (integrated guidance and control) method. Considering the coupling relationship between the pitch and ya w channels, a state coupling “leader” IGC model is established, an FTDO (finite-time disturbance observer) is designed for estimating the unknown interference of the model, and the “leader” controller is designed according to the adaptive dynamic surface sliding-mode control law. Secondly, the cooperative control strategy of the multi-interceptor is designed with the “leader-follower” distributed network mode to obtain the speed in the three directions of the interceptor in air and transform them to the general flight speed, trajectory inclination angle, and trajectory deflection instruction by using the transformational relation of kinematics. Finally, the “follower” controller is designed with the FTDO and dynamic surface sliding-mode control. The designed multi-interceptor distributed cooperative IGC algorithm with state coupling has good stability according to the simulation results of two different communication topologies.

Three-dimensional integrated guidance and control for terminal angle constrained attack against ground maneuvering target

A neuro-adaptive fast terminal sliding-mode dynamic surface control method based on a finite-time stable nonlinear extended state observer is applied to integrated guidance and control design for skid-to-turn missile attacking a ground maneuvering target with terminal angle constraints. A three-dimensional integrated guidance and control design model against a maneuvering target for skid-to-turn missile is established without the assumption that the missile velocity vector and the line of sight coincide with each other. The non-singular fast terminal sliding surface is applied to construct the first error surface of dynamic surface control and the first virtual control law is designed to guarantee hitting accuracy with desired terminal angles. The finite-time stable nonlinear extended state observer is designed separately to estimate uncertainties in the system. And the neuro-adaptive technique is applied to compensate estimation errors of nonlinear extended state observer by training a three-layer feedforward neural network online. Synthesizing all of above, a neuro-adaptive fast terminal sliding-mode dynamic surface control based on nonlinear extended state observer is derived on Lyapunov stability theory, which guarantees stability of the system. Finally, the numerical simulations are conducted to demonstrate the effectiveness of the proposed three-dimensional integrated guidance and control scheme.

Global sliding-mode dynamic surface control for MDF continuous hot-pressing slab thickness via LESO

In this paper, a robust slab thickness tracking control problem is investigated for medium density fiberboard continuous hot-pressing using an electro-hydraulic servo system in the presence of interior parameter perturbations and external load disturbances. By utilizing a linear extended state observer (LESO) and combining dynamic surface control method with a global sliding mode control (GSMC) technique, a robust controller is designed. Firstly, the LESO is constructed to estimate the total number of disturbances for system model compensation. Subsequently, a global sliding-mode dynamic surface controller is designed. Using first order low-pass filters to calculate the derivatives of synthetic control inputs, the controller form is simplified in the procedure. Introducing the GSMC into the third subsystem, the control precision and response speed are further improved. Moreover, an appropriate Lyapunov function is chosen to demonstrate that all signals from the closed-loop system are semi-globally uniformly ultimately bounded and the tracking error converges to zero asymptotically. Finally, numerical simulation results are used to authenticate and validate the benefits of the proposed control scheme.

Application of sliding mode dynamic surface control in fast steering mirror

A sliding mode dynamic surface control(SMDSC)strategy was proposed in order to solve the uncertain interference problem which may influence the tracking precision and the response time of the fast steering mirror (FSM)system, due to the external environment and the mechanical inertia and electromagnetic inertia of the voice coil actuator in the course of acquisition, tracking and pointing in FSM system. The controller introduces the tracking differentiator (TD) to instead the first-order filter in the traditional dynamic surface control, which improves the problem of unsatisfactory convergence speed and control precision of the first-order inertial link. Besides, the controller which combines sliding mode control with dynamic surface control further improves the anti-interference ability and tracking accuracy of the system. A large number of simulation studies show that, compared with the traditional dynamic surface control and classical proportional-integral-derivative (PID) control, the designed SMDSC increases by 62.5%, 75% respectively in the response time, 72%, 88% respectively in the adjustment time, and 75%, 96% respectively the tracking accuracy.

Robust dynamic surface sliding mode control for attitude tracking of flexible spacecraft with an extended state observer

The nonlinear attitude motion equations of flexible spacecraft described by the Euler angles are expressed in the vector form. Based on dynamic surface control, a new robust dynamic surface sliding mode controller is proposed for the attitude tracking and active vibration suppression of flexible spacecraft in the presence of parameter uncertainty and external disturbances. Then, a novel robust dynamic surface finite time sliding mode controller is proposed with an extended state observer such that the uncertainties can be estimated. Lyapunov stability analyses show that the two controllers can guarantee the asymptotical stability of the attitude control system. The undesirable vibration of flexible spacecraft is also actively suppressed by the modal velocity feedback approach. Finally, simulation results verified the effectiveness of the presented control algorithms.

Adaptive neural dynamic surface sliding mode control for uncertain nonlinear systems with unknown input saturation

In this article, an adaptive neural dynamic surface sliding mode control scheme is proposed for uncertain nonlinear systems with unknown input saturation. The non-smooth input saturation nonlinearity is firstly approximated by a smooth non-affine function, which can be further transformed into an affine form according to the mean value theorem. Then, one simple sigmoid neural network is employed to approximate the uncertain nonlinearity including the input saturation, and the approximation error is estimated using an adaptive learning law. Virtual controls are designed in each step by combing the dynamic surface control and integral sliding mode technique, and thus the problem of complexity explosion inherent in the conventional backstepping method is avoided. With the proposed control scheme, no prior knowledge is required on the bound of input saturation, and comparative simulations are given to illustrate the effectiveness and superior performance.

Nonlinear Gains Recursive Sliding Mode Dynamic Surface Control with Integral Action

AbstractIn this paper, by introducing a function with nonlinear gains and developing sliding surfaces with integral action in the dynamic surface control (DSC) recursive procedure, a novel DSC strategy is proposed. The drawbacks of conventional DSC methods, such as being sensitive to the design constant of the first order low‐pass filter and being unable to achieve zero steady‐state error for step reference signal, are overcome. Moreover, improvement of transient performance and reduction of control effort can be obtained. The stability analysis shows that the proposed new approach can guarantee semi‐global uniform ultimate boundedness (SGUUB) of all closed‐loop signals and that the ultimate tracking error bound in regulation can be made arbitrarily small.

Precise Positioning of Nonsmooth Dynamic Systems Using Fuzzy Wavelet Echo State Networks and Dynamic Surface Sliding Mode Control

This paper presents a precise positioning robust hybrid intelligent control scheme based on the effective compensation of nonsmooth nonlinearities, such as friction, deadzone, and uncertainty in a dynamic system. A new adaptive fuzzy wavelet echo state network algorithm is proposed to improve performance in terms of approximating unknown uncertainties in conventional neural network algorithms. A strict feedback controller and adaptive laws for estimating the unknown friction and deadzone parameters were developed using the recursive steps of dynamic surface control and a sliding mode control based on Lyapunov stability theory. Lyapunov stability analysis confirmed the boundedness and convergence of the closed-loop system. The performance of the proposed control scheme was validated experimentally by applying it to the precise positional control of a robot manipulator.

Adaptive Fuzzy Dynamic Surface Sliding Mode Position Control for a Robot Manipulator with Friction and Deadzone

Precise tracking positioning performance in the presence of both the deadzone and friction of a robot manipulator actuator is difficult to achieve by traditional control methodology without proper nonlinear compensation schemes. In this paper, we present a dynamic surface sliding mode control scheme combined with an adaptive fuzzy system, state observer, and parameter estimator to estimate the uncertainty, friction, and deadzone nonlinearities of a robot manipulator system. We design a dynamic surface sliding mode basic controller by systematic recursive design steps that yields several adaptive laws for the compensation of nonlinear friction, deadzone, and other unknown nonlinear dynamics. The boundedness and convergence of this closed-loop system are guaranteed by the Lyapunov stability theorem. Experiments on the Scorbot robot manipulator demonstrate the validity and effectiveness of the proposed control scheme.