Sliding Mode Surface Function Research Articles

Adaptive integral sliding-mode finite-time control with integrated extended state observer for uncertain nonlinear systems

For the typical uncertain nonlinear systems subjected to controller gain variation and disturbances, an integrated adaptive robust controller, called integral sliding-mode finite-time controller with an integrated extended state observer (ISFC-IESO), is proposed. The designed controller mainly consists of an integrated ESO (IESO) unit and an integral sliding-mode control (ISMC) unit. The IESO unit is composed of improved linear and nonlinear ESOs which are designed to automatically switch each other, with the aim of enhancing disturbance estimation capability. Moreover, the ISMC unit produces an integral sliding-mode control law (SMCL) based on the newly designed integral sliding-mode surface function (SMSF) and sliding-mode reaching law (SMRL). The integral SMSF is developed based on the n-th estimated state and a designed convergence function of tracking error to suppress the influence of the disturbance estimation error. On this basis, SMRL is further presented by combining integral SMSF with a specially designed variable boundary layer thickness saturation function, for the purpose of eliminating chattering and enhancing robustness. Finally, fourteen control methods are compared to illustrate the effectiveness and superiority of the proposed ISFC-IESO.

Sliding mode variable structure control of RP manipulator based on computational torque

Study the control problem of a coupled robotic arm with moving and rotating joints, a PID control method based on calculated torque is proposed. Considering that the robot model is difficult to obtain accurately, only its estimation model can be obtained. The output feedback signal is used to define the sliding mode surface function with error signal. Sliding mode variable structure controller(SMVSC) is designed based on the computational torque control method. Taking the mathematical model of RP robot as an example, Experimental calculations have found that the control accuracy can be guaranteed, but there is a significant chattering situation. In engineering practice, it is necessary to process the symbol function.

Sliding mode control with an adaptive switching power reaching law

This paper proposes a adaptive reaching law-based sliding mode control (SMC) method for maintaining favorable velocity control performance of permanent magnet synchronous motors (PMSMs) under internal and external perturbations. An adaptive switching power reaching law (ASPRL) is designed, which contains adaptive terms and state variables of the sliding mode surface function. This augmented reaching law decreases the chatter of the control system and increases the rate at which the state variables of the system reach the sliding mode surface. Additionally, a Luenberger observer load torque (LOLT) is designed to observe the external load and provide feedback to the velocity controller, reducing the impact of load disturbances and improving the jamming performance of the controller. Simulation experiments confirm that ASPRL reduces buffeting, decreases overshoot, and shortens response time, demonstrating its advantages in PMSM control.

Coordinated Optimal Control of AFS and DYC for Four-Wheel Independent Drive Electric Vehicles Based on MAS Model.

The problem that it is difficult to balance vehicle stability and economy at the same time under the starting steering condition of a four-wheel independent drive electric vehicle (4WIDEV) is addressed. In this paper, we propose a coordinated optimal control method of AFS and DYC for a four-wheel independent drive electric vehicle based on the MAS model. Firstly, the angular velocity of the transverse pendulum at the center of mass and the lateral deflection angle of the center of mass are decoupled by vector transformation, and the two-degree-of-freedom eight-input model of the vehicle is transformed into four two-degree-of-freedom two-input models, and the reduced-dimensional system is regarded as four agents. Based on the hardware connection structure and communication topology of the four-wheel independent drive electric vehicle, the reduced-dimensional model of 4WIDEV AFS and DYC coordinated optimal control is established based on graph theory. Secondly, the deviation of the vehicle transverse swing angular velocity and mass lateral deflection angle from their ideal values is oriented by combining sliding mode variable structure control (SMC) with distributed model predictive control (DMPC). A discrete dynamic sliding mode surface function is proposed for the ith agent to improve the robustness of the system in response to parameter variations and disturbances. Considering the stability and economy of the ith agent, an active front wheel steering and drive torque optimization control method based on SMC and DMPC is proposed for engineering applications. Finally, a hardware-in-the-loop (HIL) test bench is built for experimental verification, and the results show that the steering angle is in the range of 0-5°, and the proposed method effectively weighs the system dynamic performance, computational efficiency, and the economy of the whole vehicle. Compared with the conventional centralized control method, the torque-solving speed is improved by 32.33 times, and the electrical consumption of the wheel motor is reduced by 16.6%.

Dissipativity‐based adaptive integral sliding mode control of Takagi‐Sugeno fuzzy descriptor systems

This paper focuses on the problem of adaptive integral sliding mode control (ISMC) with dissipativity for a type of complex non-linear system represented by Takagi-Sugeno (T-S) fuzzy descriptor models. First, T-S fuzzy descriptor systems with different derivative matrices are transformed into augmented systems that have the same properties as the original systems, and an integral sliding mode surface function is designed considering the descriptor matrices. Then, based on the dissipativity theory and the non-parallel distributed compensation (non-PDC) method, ISMC strategies and dissipativity-based ISMC strategies are proposed, and the system uncertainties and external disturbances with unknown upper bounds are addressed with an adaptive controller. According to the Lyapunov theory and the dissipativity theory, a fuzzy Lyapunov function is designed, and the obtained criteria are presented in the form of strict linear matrix inequalities (LMIs); this approach guarantees that the closed-loop system is asymptotically stable and strictly ( Q , R , S ) − α $(\mathcal{Q},\mathcal{R},\mathcal{S}) - {{\alpha}}$ dissipative. Moreover, the controller gain matrices and Lyapunov matrices are decoupled by introducing the corresponding auxiliary variables and employing Finsler's lemma. Finally, two examples are provided to illustrate the effectiveness and merit of the proposed method.

Non-fragile mixed H ∞/passive-based asynchronous sliding mode control for nonlinear singular Markovian jump systems

In this paper, the problem of asynchronous sliding mode control (SMC) is addressed for discrete-time singular Markovian jump systems (DSMJSs) with external disturbances and randomly occurring nonlinearities. Moreover, the states of DSMJSs are unavailable for measurement, and the synchronisation between the controller and the system modes is not surely ensured. Our attention is mainly focused on solving the control problem by proposing an observer-based adaptive sliding mode controller for such a class of complex systems. First, a non-fragile observer is designed not only to estimate the system states but also to relax the multiplicative gain variations and to construct an appropriate mode-dependent sliding mode surface function. Then, by assuming that the bounds of nonlinear terms are unknown, an adaptive SMC control law is synthesised to drive the system trajectories onto the specified sliding surface and completely compensate for the influences of the external disturbances and fluctuations of the controller and observer gains. Sufficient conditions are established to ensure that the closed-loop system is stochastically admissible with a γ level of the mixed /passive performance, and to provide the observer and controller gain matrices. Finally, to numerically substantiate the efficacy of the proposed control scheme, two examples are given.

Nonsingular Terminal Sliding Mode Control of PMSM Based on Improved Exponential Reaching Law

When a permanent magnet synchronous motor runs at low speed, the inverter will output discontinuous current and generate torque ripple; when the motor is runs at high speed, a large amount of stator harmonic current generates, which affects its speed following ability and torque stability. To ensure the fast and smooth switching of a permanent magnet synchronous motor in the full speed domain, this paper proposes the nonsingular terminal sliding mode control of PMSM speed control based on the improved exponential reaching law. Firstly, the improved exponential reaching law is composed of the state variables and power terms of the sliding mode surface functions. The reaching law function is designed in sections to balance the fast dynamic response of the system and chattering control. Secondly, an improved exponential reaching law based on the sliding mode control strategy of the PMSM speed loop is proposed. By designing the initial value of the integral term in the nonsingular terminal sliding mode surface function, the initial state of the system is located on the sliding mode surface. The integral sliding mode surface is used to reduce the system steady-state error, while the proposed sliding mode reaching law is used to increase the arrival speed and suppress system chattering, ultimately affecting modeling error problems, complex working conditions, and uncertainty factors. This paper proposes a sliding mode observer based on an improved exponential reaching law to compensate for the disturbances. Lyapunov stability theory can prove that this system can make the speed tracking error converge to zero in finite time. Hardware-in-the-loop experiments were used to validate the effectiveness of the proposed method.

Passivity-based asynchronous fault-tolerant control for nonlinear discrete-time singular markovian jump systems: A sliding-mode approach

This paper deals with the problem of passivity-based asynchronous fault-tolerant control for a class of non-linear discrete-time singular Markovian jump systems (DSMJSs) subjected to matched uncertainties, external disturbance, and actuator faulty signals. The system’s states are generally unavailable for measurement, and the asynchronous phenomenon between the system and controller modes may occur in practice. Our particular concern is to design an asynchronous observer-based sliding mode control (SMC) law for the considered complex system. Firstly, an observer is established for the estimation of the unmeasured states of the system. Secondly, based on the estimated states, a mode-dependent sliding mode surface function is designed. Moreover, an asynchronous adaptive observer-based SMC is synthesized to drive the system trajectories onto the specified sliding surface and completely compensate for the effects of actuator faults and parameter uncertainties of the DSMJSs. Sufficient conditions are developed to identify the sliding function parameters and to guarantee that the closed-loop system is stochastically admissible with a γ level of passivity performance. Finally, the feasibility and effectiveness of the proposed control scheme are verified by two examples.

Research and Design of Marine Underwater LED Illumination System Based on Sliding Mode Variable Structure

Pan, P., 2019. Research and design of marine underwater LED illumination system based on sliding mode variable structure. In: Li, L.; Wan, X., and Huang, X. (eds.), Recent Developments in Practices and Research on Coastal Regions: Transportation, Environment and Economy. Journal of Coastal Research, Special Issue No. 98, pp. 239–242. Coconut Creek (Florida), ISSN 0749-0208.This paper introduces the working characteristics of an underwater LED illumination system and analyzes the driving power supply of the LED illumination system and the application of its control mode. In addition, the sliding mode variable structure control (SMVSC) method of constant-current power supply for an underwater LED illumination system is studied and designed in this paper. By choosing appropriate sliding mode surface function and control parameters, the constant-current control of the LED load is realized. Finally, to verify the effectiveness and superiority of the SMVSC method design for the LED illumination system, the SMVSC method is modeled and simulated using MATLAB software and compared with the conventional PI control method, which proves the validity of the design.

Finite-time asynchronous sliding mode control for Markovian jump systems

In this research article, the finite-time asynchronous sliding mode control (SMC) scheme for Markovian jump systems (MJSs) subject to sensor and actuator faulty signals, is investigated based on the average dwell time approach. Firstly, an asynchronous stochastic hybrid model is proposed in the light of the existing non-synchronization phenomenon of unmeasurable state and indirect access to jump information of original systems. The average dwell time technique, which has the ability to compensate the effects of arbitrary switching by generating a sequence of signals to regulate/choose an appropriate feedback Markov switching signal among the Markov chains, is developed during the reaching phase and sliding motion phase of the sliding mode dynamics. Secondly, based on the asynchronous stochastic hybrid model, a mode-dependent sliding mode surface function is designed. Moreover, the SMC law is synthesized such that the system state trajectories can be driven onto the specified sliding surface in a prescribed limited time. Thirdly, the finite-time analysis method combining with a mode-dependent Lyapunov function, which can reduce drastically the design conservatism, is adopted to guarantee the finite-time boundedness of the sliding mode dynamics both in the reaching phase and sliding motion phase. Fourthly, sufficient conditions are interpreted for the solutions of asynchronous controller gain matrices and an algorithm is provided to assist computing the SMC gain as an auxiliary tool. Finally, a numerical example is given to illustrate the effectiveness of the proposed new design techniques.

Observer‐based mode‐independent integral sliding mode controller design for phase‐type semi‐Markov jump singular systems

SummaryThis paper considers the observer‐based integral sliding mode controller design problem of semi‐Markovian jumping singular systems with time‐varying delays. Firstly, by using a plant transformation and supplementary variable technique in the work of Hou et al, the discussed phase‐type semi‐Markov jump singular system is equivalently transformed into its associated Markov jump singular system. Secondly, an observer‐based sliding mode controller design problem is investigated for the associated singular Markov jump systems. The highlight of this paper is that we construct an observer‐based mode‐independent integral sliding mode surface function, which is different from the mode‐dependant sliding mode surface function in the previous literatures. Based on this, an observer‐based sliding mode controller is designed to guarantee that the associated singular Markov jump system meets the reachable condition. Finally, a practical example is presented to demonstrate the efficiency and effectiveness of our obtained results.

光电跟踪系统快速捕获时间最优滑模控制技术

Atime optimal sliding model controlwas proposed based on the fast acquisitionprocess of photoelectric tracking system. The sliding mode surface function of the control wasoptimal motion trail of time optimal control, which guaranteed that the system state variables slide along the optimal tracks; relevant exponential reaching lawwas designed to make the variables closer to sliding mode surface quickly and stably. Simulation and experiment research were carried out based on the capture targets of step signals of 180, 90 and 60. The experiment result shows that time optimal sliding model control and accommodation time decreases about 43.66% and 59.67% respectively compared with time optimal control and sliding model control. Besides, its overshoot and steady fluctuationare both 0, andsteady state errorsare decreased 44.94% and 62.34% approximately, whichare identical with the simulation result. The result indicates that the advantages of the method, such as short accommodation time, small overshoot, stable steady state value, little steady state error and strong robust, are applicable to quickly capture thephotoelectric tracking system and of significant research and application value. 2017, Science Press. All right reserved.

Guaranteed cost sliding mode control for discrete-time looper systems in hot strip finishing mills

A guaranteed cost sliding mode control (SMC) algorithm is investigated to further improve the control accuracy of looper-tension systems in hot strip finishing mills. First, a global sliding mode surface function is designed by linear matrix inequalities and guaranteed cost technique, which can force the system states into switching region initially, and can guarantee the system robustness with a good performance during the whole control process. Then, a novel reaching law is designed, which can satisfy the sliding mode reaching conditions. Simulation results demonstrate that the proposed control scheme has good stability and robustness comparing with traditional SMC. The designed controller can regulate the strip tension and looper angle to ensure better performance, which is very suitable for complex looper systems.

Dynamic surface adaptive integral-terminal sliding mode control for theodolite rotating systems

To improve the robustness and precision of theodolite rotation servo system, this study proposes a dynamic surface adaptive integral terminal sliding mode control (DSAITSMC). A nonlinear uncertain mathematic model of theodolite rotating system is established firstly. Integral terminal sliding mode surface function is then designed, which provides system convergence with finite time and avoids the steady state error from external disturbances. Further reason for using such design prototype is that the dynamic surface control can simplify the controller designing procedure. The adaptive algorithm is applied to estimate the uncertainty parameters and reduce sliding mode chattering. The control law and adaptive law are presented on the basis of Lyapunov theory, and the stability of the system is proved. The simulation results show, compared to PID controller and conventional sliding mode controller, this control method has better robustness, more accurate position and enhanced velocity tracking capacity.

Guaranteed cost sliding mode control for looper–tension multivariable uncertain systems

In order to further improve the control accuracy of looper–tension uncertain systems in hot strip finishing mills, an innovation-guaranteed cost sliding mode control method is researched. First, a sliding mode surface function is obtained by linear matrix inequalities and guaranteed cost technique. The function can guarantee the system robustness with a good performance during the whole control process. Then, a novel sliding mode control law is designed to satisfy the sliding mode reaching conditions, and it gives the theoretical proof. As a result, the control method can reduce external disturbances and make the strip tension to reach a stable equilibrium state quickly. Simulation results show the effectiveness of the proposed sliding mode control scheme compared with the traditional ones.

Global Robust Terminal Sliding Mode Control for PMLSM Servo System

Permanent Magnet Linear Synchronous Motor (P MLSM was hard to control with traditional control strategy for parameters variation and external load disturbance, a global robust terminal sliding mode control (GRTSMC) was designed for PMLSM servo system, the sliding mode surface function was designed, the robust sliding mode control law was deduced and the stability was proved by Lyapunov theory. With the mathematical models of PMLSM, the simulation was taken with traditional PID control, SMC control and GRTSMC control proposed in this paper, the robust performance be found with GRTSMC control when motor parameters and external load changed, the efficiency and advantages of this robust control strategy was successfully demonstrated.