Sliding Surface Function Research Articles

Robustness control for nonlinear systems based on homogeneous prescribed sliding mode control

This paper presents a new homogeneous control using dual sliding mode control, and robustness control using linear matrix inequality (LMI) constraints. The controller is applied for the severe disturbance. A sliding surface function, which relates to an exponential function and itself t-norm, is applied to save the energy consumption of the control system. The constraints related LMI are proposed with the matrices and vectors of the systems following the chosen matrices in control the energy for control. Solution of the constraints is also presented with new approach to save the time of calculation. In addition, the proof for the proposed controller is also presented by using the candidate Lyapunov function. In the input control function, the t-norm type is embedded to improve its performance in control disturbance. Besides of the t-norm, the modified sliding surface in the input control is also improve the energy for controlling. The combination of these robustness control elements would bring a new view for the design of control. The advantages of the controller are demonstrated via computer simulation for a seat suspension system. A magneto-rheological fluid seat suspension with its random disturbances is used. To prove the flexibility of the controller, the proposed approach is compared with an existing controller. The compared control has the same structure as shown in the proposed model. However, its design has a disadvantage in control the severe disturbance. The comparison between two controls is a clear view of distinct improvement. The results of simulations show that the controller provides better performance and stability of the system. The stability is also analyzed through the variation of the input control and power spectral density related energy consumption.

Sliding Mode Control for Markov Jump Systems With Delays via Asynchronous Approach

In this paper, the problem of sliding mode control (SMC) is considered for a class of nonlinear continuous-time Markov jump systems (MJSs) with uncertainties and time delay. A novel integral-type switching sliding surface function is designed, where the controller gain may jump asynchronously with original MJSs. Then, an SMC law is constructed to force system trajectories onto the specified switching sliding surface in a finite time. The stochastic stability and dissipative performance of sliding mode dynamics are analyzed and the delay-dependent sufficient condition for the existence of the desired switching surface is developed. Moreover, we also extend SMC to investigate the finite-time stability problem during both reaching phase and sliding motion phase in the stochastic setting. Finally, simulation results are given to illustrate the effectiveness of the proposed design techniques.

Dynamic sliding mode control for nonlinear parameter‐varying systems

AbstractThis article deals with the dynamic sliding mode control (SMC) problem for unmatched nonlinear parameter‐varying systems. The unmatched nonlinear model refers to the systems matrices of control input and nonlinearity terms having inconsistent values and structures. A linear sliding surface function is constructed, and the resulting sliding mode dynamics is formulated into a full‐order descriptor nonlinear parameter‐varying system. Then, based on a parameter‐dependent Lyapunov function, the synthesis procedure of the sliding manifold is derived, which guarantees the asymptotic stability of the sliding motion. Furthermore, a dynamic SMC law is proposed to enforce the resultant closed‐loop system towards the sliding manifold in finite time. It is noteworthy that both the sliding surface and control law are depended on both time‐varying and measurable parameters. Finally, simulation studies are provided to unfold the validity of the proposed method.

A New Switching Adaptive Fuzzy Controller with an Application to Vibration Control of a Vehicle Seat Suspension Subjected to Disturbances

This paper proposes a new switching adaptive fuzzy controller and applies it to vibration control of a vehicle seat suspension equipped with a semi-active magnetorheological (MR) damper. The proposed control system consists of three functioned filters: (1) Filter 1: a model of interval type 2 fuzzy to compensate disturbances; (2) Filter 2: a ‘switching term’ to evaluate the magnitude of disturbance; and (3) Filter 3: a group of adaptation laws to enhance the robustness of control input. These filters play a role of powerful shields to improve control performance and guarantee the stability of the applied system subjected to external disturbances. After embedding a PID (proportional-integral-derivative) model into Riccati-like equation, main control parameters are updated based on the adaptation laws. The proposed controller is then synthesized in two different cases: high disturbance and small disturbance. For the high disturbance, a special type of sliding surface function, which relates to an exponential function and its t-norm, is used to increase the energy of control system. For the small disturbance, the energy from the modified t-norm of the sliding surface is neglected to reduce the energy consumption with maintaining the desired performance. To demonstrate the effectiveness of the proposed controller, a vehicle seat suspension installed with controllable MR damper is adopted to reflect the robustness against external disturbances corresponding to road excitations. It is validated from computer simulation that the proposed controller can provide better vibration control performance than other existing robust controllers showing excellent control stability with well-reduced displacement and velocity at the position of the seat.

Takagi–Sugeno Model-Based Reliable Sliding Mode Control of Descriptor Systems With Semi-Markov Parameters: Average Dwell Time Approach

This paper deals with the issue of reliable sliding mode control for descriptor systems with semi-Markov parameters using the Takagi-Sugeno fuzzy model, in which an average dwell time approach is utilized to tackle generic uncertain transition rates (TRs). From the analysis of the inner mechanism of switching singular system, a continuous sliding surface function is proposed. Different from continuity with probability one for stochastic systems, the absolute continuity of system solution is a key point in this paper being ensured for application of the average dwell time approach. Then, the mean-square exponential stability of the obtained sliding mode is analyzed based on two types of uncertain TRs. Moreover, a sliding mode controller is constructed to ensure the reachability condition in finite time. Lastly, the method is verified numerically by a single-link robot arm model.

Nonsingular Terminal Sliding Mode Control for Flexible Spacecraft Attitude Control

In this paper, a nonsingular terminal sliding mode control method is applied to design an attitude control law for flexible spacecraft. First, the Lagrange method is applied to establish the dynamic equation of the flexible spacecraft and the vibration equation of the flexible appendages. Then, by designing a nonlinear terminal sliding surface function, the spacecraft terminal sliding mode control law is designed. In order to solve the singular problem, a nonsingular terminal sliding mode control law is further designed. At the same time, the saturation function is introduced to replace the sign function to suppress chattering problem of flexible appendages. The Lyapunov method is used to prove that the involved nonsingular terminal sliding mode control law can realize the precise attitude control of the flexible spacecraft. Finally, a numerical simulation example verifies the effectiveness of the control law designed in this paper.

$$H_{\infty }$$ Performance-Based Sliding Mode Control Approach for Load Frequency Control of Interconnected Power System with Time Delay

This paper proposes a sliding mode control (SMC) approach to design $$H_{\infty }$$ performance-based load frequency controller for interconnected power system (IPS) with time delay. Incorporating an artificial delay, a sliding surface function is designed to enhance dynamic performance of the power system. Linear matrix inequality-based stabilization criterion is derived using Lyapunov–Krasovskii functional for multi-area power system. A novel SMC law is designed with artificial delay to drive the system trajectory into the predefined sliding surface. The applicability of the proposed controller is proved by considering a two-area time-delay IPS. Performance of the controller is verified from the simulation study of the time-delay IPS with proposed controller in MATLAB/Simulink. Then, the controller performance is verified in real time by using OPAL-RT OP4510 digital simulator.

Sliding mode control strategy with maximized existence region for DC–DC buck converters

In this article, a sliding mode control (SMC) strategy with maximized existence region (ER) is presented for DC–DC buck converters. The ERs of the sliding mode are determined from the existence condition of the SMC. It is shown that the ER can be enlarged to its maximum size by an optimum sliding coefficient whose equation is determined analytically. Also, it is pointed out that the enlargement of the ER results in a considerable improvement in the dynamic response of the output voltage. In addition, it is shown that the optimum sliding coefficient is not sensitive to the variations in the DC input voltage and load resistance. Moreover, the capacitor current that is employed in the sliding surface function to avoid the derivative operation does not lead to any steady-state error in the output voltage in case of an uncertainty in the capacitance value. The correctness of the proposed control approach is validated by computer simulations and experimental results. These results demonstrate that the proposed SMC strategy results in an excellent dynamic response without overshoot and undershoot in the output voltage and inductor current and guarantees a maximized ER for the sake of stronger closed-loop stability.

Super Twisting Sliding-Mode Control of DVR With Frequency-Adaptive Brockett Oscillator

This article presents a super twisting sliding-mode control (ST-SMC) for single-phase dynamic voltage restorers (DVRs). Unlike the conventional first-order sliding-mode controller, the proposed ST-SMC technique eliminates the need for differentiating the compensation voltage in the sliding surface function while keeping the merits of first-order SMC. As a consequence of employing ST-SMC, a continuous control signal is achieved from which the pulsewidth modulation (PWM) signals can be generated. In this case, the inverter operates at a constant switching frequency. The stability analysis of ST-SMC is also presented. The reference compensation voltage needed in ST-SMC is estimated by using Brockett oscillator-based frequency-locked loop. Theoretical considerations are verified through experimental results under ideal and distorted grid voltage conditions. The obtained results show that the ST-SMC has good dynamic performance and can maintain the load voltage at a desired level under voltage sag, swell, and harmonically distorted grid voltages.

Adaptive Fuzzy Sliding Mode Control for a Micro Gyroscope with Backstepping Controller.

This paper developed an adaptive backstepping fuzzy sliding control (ABFSC) approach for a micro gyroscope. Based on backstepping design, an adaptive fuzzy sliding mode control was proposed to adjust the fuzzy parameters with self-learning ability and reject the system nonlinearities. With the Lyapunov function analysis of error function and sliding surface function, a comprehensive controller is derived to ensure the stability of the proposed control system. The proposed fuzzy control scheme does not need to know the system model in advance and could approximate the system nonlinearities well. The adaptive fuzzy control method has self-learning ability to adjust the fuzzy parameters. Simulation studies were implemented to prove the validity of the proposed ABFSMC strategy, showing that it can adapt to the changes of external disturbance and model parameters and has a satisfactory performance in tracking and approximation.

A Novel Fuzzy Output Feedback Dynamic Sliding Mode Controller Design for Two-Dimensional Nonlinear Systems

The system information of 2-D systems is usually in propagation along two independent directions. This article focuses on the issue of output feedback sliding mode control (SMC) for 2-D nonlinear systems through T-S fuzzy affine models. Associated with the sliding surface function, a singular system is established to describe the sliding mode dynamics. Based on piecewise quadratic Lyapunov functions, some new stability analysis results on the sliding mode dynamical system are attained, and the analysis conservatism can be further reduced. A robust output feedback dynamic SMC synthesis scheme is developed to guarantee the finite-time reachability of the sliding surface. It is also worthy of mentioning that the proposed dynamic SMC synthesis method can handle the mismatched disturbances, and the control input channels are permitted to have parameter uncertainties. Simulation studies are given to illustrate the validity of the developed scheme.

Observer-based passive control for polynomial fuzzy singular systems with time-delay via sliding mode control

This paper is concerned with the problem of sliding mode observer design and observer-based sliding mode controller synthesis for polynomial fuzzy singular systems with time-delay. The polynomial fuzzy model is constructed for singular nonlinear system to eliminate the upper and lower bounds restriction of states in the system and reduce the calculation quantity. An integral-type sliding surface function, which has a stabilizing effect on the sliding variable, is proposed for the observer system. In terms of sum-of-squares approach, observer-based sliding mode passive controller is designed for the system with unknown membership functions, which drives the system trajectories onto the predefined sliding surface in a finite time, meanwhile, the stability and robust passivity of the closed-loop system are guaranteed. The information of membership functions is included in the stability conditions, which can reduce the conservatism. Finally, an example is performed to verify the merits of the method proposed.

Robust [formula omitted] sliding mode control for nonlinear stochastic T-S fuzzy singular Markovian jump systems with time-varying delays

In this paper, the robust H∞ stabilization problem for stochastic T-S fuzzy singular Markovian jump systems with time delays is investigated by using integral sliding mode control. A novel fuzzy integral-type sliding surface function is designed by fully taking the singular derivative matrix into account. By the utilization of linear matrix inequality technique, a delay-dependent criterion is derived, which guarantees the sliding mode dynamics to be stochastically admissible with a prescribed H∞ performance. Moreover, a suitable sliding mode law is synthesized to ensure the stochastic admissibility of the resulting closed-loop system, and the proposed sliding mode control law can steer the trajectories of the controlled system to the specified sliding surface in finite time. Finally, three examples are provided to illustrate the effectiveness of the proposed method.

Robust adaptive sliding mode control for discrete singular systems with randomly occurring mixed time-delays under uncertain occurrence probabilities

This paper is concerned with the problem of robust adaptive sliding mode control (RASMC) for discrete singular systems subject to randomly occurring mixed time-delays (ROMTDs) under uncertain occurrence probabilities. The mixed time delays are considered, which are comprised of both the discrete interval delays and infinite distributed delays. Meantime, two random variables obeying the Bernoulli distribution are utilised to depict the phenomena of randomly occurring discrete time-varying delay and distributed time-delay, in which the uncertain occurrence probabilities are modelled by the known scalars. An appropriate sliding surface function is firstly presented. Furthermore, some sufficient criteria via the free weighting matrices idea are obtained to ensure the admissibility of the resultant sliding motion by introducing new Lyapunov-Krasovskii functional. Subsequently, an RASMC law is synthesised to ensure the reachability criterion of pre-designed sliding surface, where an adaptive mechanism is introduced to estimate the related unknown bounds. Finally, the feasibility of the new RASMC strategy is illustrated by a numerical simulation.

Passivity analysis for singular systems with randomly occurring uncertainties via the event-based sliding mode control

This paper studies the passivity of the T–S fuzzy singular system with randomly occurring uncertainties via the event-based sliding mode control. The sliding surface function is designed such that the resulting sliding mode dynamics can be expressed by the considered system. Some sufficient conditions are proposed to guarantee the sliding mode dynamics is generalized admissible and robustly passive. Under the aperiodic sampled-data environment, the sliding mode control law is proposed via the event-triggered method. It guarantees that the state trajectory of the system can be driven onto the predefined sliding surface in a finite time and keep it forever. Finally, three examples are given to demonstrate the feasibility and superiority of the design method.

Observer-based second-order sliding mode control for grid-connected VSI with LCL-type filter under weak grid

LCL-type grid-connected voltage source inverters (VSI) have been widely used in distributed generation systems. However, due to the inherent LCL resonance, it brings a stability challenge to the control system. To address this issue, a sliding mode observer-based second-order sliding mode control method is proposed to achieve arbitrary poles placement, which can ensure desired resonance damping and dynamic performance even under weak grid operation. With the help of sliding mode observer (SMO), only the grid current and grid voltage are sensed to realize system stable operation and grid synchronization, which reduces the cost of system. To improve the robustness and dynamic response of LCL-filtered grid-connected inverters under weak grid operation, a super-twisting algorithm (STA) second order sliding mode control (SOSMC) is proposed. Due to the existence of grid impedance in weak grid, the sliding surface would drift, which increases the track error of grid current. To solve this problem, an integral term is added to the sliding surface function. The systematic design approach of SOSMC is presented, and the stability of system under the grid impedance uncertainties as well as external disturbances is proved by Lyapunov theory. Simulation results are finally presented to validate the effectiveness of the proposed control strategy.

Non‐fragile sliding mode control of discrete switched singular systems with time‐varying delays

This study tends to solve the H ∞ finite-time boundedness (FTB) problems for discrete switched singular systems with time-varying delays via a non-fragile sliding mode approach. The remarkable feature of the provided method is that a new sliding surface function is constructed such that a full-order dynamic system is acquired. Thus, a non-fragile sliding mode controller can be proposed to guarantee the FTB of the dynamic system. Therein, by employing the multiple Lyapunov-like functions and dwell time (DT) method, sufficient conditions and the DT of switching signal are given to ensure the FTB of the sliding mode dynamics. These results are then applied to the H ∞ FTB issue, being expressed as a solvable optimisation problem. Furthermore, by employing a discrete reaching condition, the proposed sliding mode controller can guarantee the reachability of the quasi-sliding mode. The validity of the proposed theorems is verified through a numerical example.

Robust control for a class of uncertain neutral‐type systems with time‐varying delays

AbstractThis paper investigates the problem of robust asymptotic stabilization for a class of uncertain neutral‐type systems with time‐varying delays. A sufficient condition is obtained to ensure the considered system is robust asymptotic stabilization with disturbance attenuation level , which is based on the sliding mode observer framework. Meanwhile, a novel integral sliding surface function with the compensator is proposed to make sure the considered system can be stabilized. And the gain matrix is obtained by solving a strict linear matrix inequality. Finally, two numerical examples are provided to demonstrate the validity and potential of the proposed method.

Design and Implementation of Observer-Based Sliding Mode for Underactuated Rendezvous System

This article addresses the design and implementation of observer-based sliding mode controller with H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance for underactuated rendezvous system under the constraints of fault signals, maximum input, and disturbances. The nonlinear constrained model considered in this article is an underactuated system since the number of control input variables is less than that of state variables, besides, owing to the full state information is unavailable or not so accurate for the controller design, an observer is first constructed to estimate the full state of system, and then the state of observer is adopted to synthesize the integral-type sliding surface function. Considering three fault signals, input constraint, and disturbances, the stability criteria with H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance are derived based on Lyapunov method and the ellipsoidal approximation algorithm. Furthermore, the sliding mode control law is formulated to guarantee the sliding mode dynamic could be driven onto the sliding surface and remain there for subsequent time. Finally, the simulation experiments are implemented to verify the effectiveness of the proposed scheme for the underactuated rendezvous system.

Modeling and Fuzzy Decoupling Control of an Underwater Vehicle-Manipulator System

This paper presents the detailed modeling and simulation of the dynamic coupling between an autonomous underwater vehicle (AUV) and a manipulator. The modeling processes are described with the incorporation of the most dominating hydrodynamic effects such as added mass, lift and drag forces. The hydrodynamic coefficients are derived using strip theory and are adjusted according to dynamical similarity. A fuzzy decoupling controller (FDC) is proposed for an autonomous underwater vehicle-manipulator system (UVMS) which consists of two subsystems, an underwater vehicle and a manipulator. The proposed controller uses a fuzzy algorithm (FA) to adaptively tune the gain matrix of the error function (EF). The EF is described by the integral sliding surface function. This technique allows the off-diagonal elements developed for decoupling the system to be incorporated in the gain matrix. Tracing the FA and EF back to the principle of feedback linearization, one further obtains evidence about the decoupling and stability of the system. Moreover, a desired trajectory with the consideration of the dynamic coupling of the AUV is designed to reduce the thruster forces and manipulator's torques. This technique provides high performance in terms of tracking error norms and expended energy norms. A major contribution of this study is that it adopts the off-diagonal elements to exploit the dynamic coupling between the degrees of freedom of the subsystem and the dynamic coupling between the two subsystems. Simulation results demonstrate the effectiveness and robustness of the proposed technique in the presence of parameter uncertainties and external disturbances.