Second-order Sliding Mode Control Design Research Articles

Practical Event-Triggered Finite-Time Second-Order Sliding Mode Controller Design.

This article proposes a novel event-triggered second-order sliding mode (SOSM) control algorithm using the small-gain theorems. The developed algorithm has global event property in aspects of the triggering time intervals. First, an SOSM controller is designed related to the sampling error of states, and it is proved that the closed-loop system is finite-time input-to-state stable (FTISS) with the sampling error via utilizing the small-gain theorems. Second, combined with the constructed SOSM controller, a new triggering mechanism is proposed depending on the sampling error by designing the appropriate FTISS gain condition. Third, the practical finite-time stability of the closed-loop system is verified. It is shown that the minimum triggering time interval is always a positive value in the whole state space. Finally, the simulation results demonstrate the effectiveness of the developed control method.

First-and Second-Order Sliding Mode Control Design for Networked 2-D Systems Under Round-Robin Protocol.

This article investigates the sliding mode control (SMC) problem for a class of uncertain 2-D systems described by the Roesser models with a bounded disturbance. In order to reduce the communication usage between the controller and the actuators, it is supposed that only one actuator node can gain the access to the network at each sampling time along horizontal or vertical direction, where a proper 2-D round-robin protocol is designed to periodically regulate the access token and a set of zero-order holders (ZOHs) is employed to keep the other actuator nodes unchanged until the next renewed signal arrives. Based on a novel 2-D common sliding function, a token-dependent 2-D SMC scheme with first-order sliding mode is appropriately constructed to cope with the impacts from the periodic scheduling signal and the ZOHs. Furthermore, a novel super-twisting-like 2-D SMC scheme with second-order sliding mode is designed to improve the robustness against the bounded disturbance. By resorting to token-dependent Lyapunov-like function, sufficient conditions are obtained to guarantee the ultimate boundedness of the horizontal and vertical states as well as the 2-D common sliding function. For acquiring the optimized gain matrices, two searching algorithms are formulated to solve two optimization problems arising from finding optimized control performance. Finally, two comparative examples are exploited to demonstrate the effectiveness and the advantageous of the proposed first-and second-order 2-D SMC design schemes under round-robin scheduling mechanism.

Event-Triggered Second-Order Sliding Mode Controller Design and Implementation

The paper presents an event-triggered higher-order sliding mode controller design. The event-triggering technique is the alternative approach to real-time controller execution, unlike the classic time-triggering technique, which is not time-dependable and is governed by the triggering policy. The technique is suitable for system resource relaxation in case of computation burden or network usage mitigation. The paper describes the stability analysis of the super-twisted sliding mode controller based on input-to-state stability notation. The stability analysis introduces a triggering policy related directly to the ultimate boundness of the system states and preselected sliding variables. The controller time execution with the selected triggering condition prevents the exhibition of the Zeno phenomena, where the minimal inter-event time of the controller has a positive non-zero lower bound. The minimal value of the inter-event time is related directly to the controller parameters and triggering bound, the selection of which is given with the derived stability conditions regarding the designer’s objective. Preventing the fast nonlinear controller execution, especially close to the sliding manifold, also alleviates the chattering phenomena effectively, which is a primal drawback, and limits the usage of the controller on various systems. The method’s efficiency is verified with the hardware-in-the-loop system, where the dynamic and robustness of the triggering approach are compared to the standard time-triggered execution technique.

Prescribed-Time Second-Order Sliding Mode Controller Design Subject to Mismatched Term

This paper investigates the second-order sliding mode (SOSM) control for uncertain nonlinear systems subject to unknown mismatched terms. A new prescribed-time SOSM controller is developed by applying a time-varying coordinate transformation. The proposed controller can allow to prescribe the convergence time a priori and irrespective of initial conditions even in the presence of mismatched terms. Moreover, all the upper bounds of matched and mismatched uncertainties are not required to be exactly known. Finally, a simulation example with different initial conditions is given to show the effectiveness of the proposed controller.

Global Prescribed-Time Second-Order Sliding Mode Controller Design Subject to Asymmetric Output Constraint

Global Prescribed-Time Second-Order Sliding Mode Controller Design Subject to Asymmetric Output Constraint

Second-order sliding mode controller design of buck converter with constant power load

Multi-converter systems used in DC microgrid feed supply constant power loads (CPL) as well as classical electrical loads. CPL has a non-linear load nature because of the negative impedance effect. This impact causes instability in converter systems within the micro-grid. This paper proposes a super twisting-based second-order sliding mode control (SOSMC) for regulating the output voltage of a DC/DC buck converter feeding CPL. The goal of this method is to suppress the chattering effect and maintaining the robustness under load variations and parametric uncertainties. With the experimental studies constructed in the laboratory and simulations executed in Matlab environment, the proposed SOSMC was compared with classical first-order SMC for the response of the buck converter feeding CPL under various conditions. The simulation and experimental results show the proposed controller has higher tracking precision and stronger robustness during any disturbance in input voltage or CPL power, as well as reducing the chattering effect.

Second-order sliding mode controller design with mismatched term and time-varying output constraint

The current work develops a new approach to handle the second-order sliding mode (SOSM) controller design with mismatched term and time-varying output constraint. A novel time-varying Barrier Lyapunov Function (BLF) is firstly constructed to deal with the time-varying output constraint. A new SOSM dynamics subject to mismatched terms is established for the purpose of uncertainty reduction in control input channels. Meanwhile, by incorporating the time-varying BLF into the adding a power integrator (API) technique, a new finite-time SOSM controller, which can ensure that the system output variable will not violate the boundary of the constrained region, is explicitly constructed. Finally, a simulation example is given to illustrate the feasibility of the proposed SOSM algorithm.

Adaptive Integral Second-Order Sliding Mode Control Design for Load Frequency Control of Large-Scale Power System with Communication Delays

Nowadays, the power systems are getting more and more complicated because of the delays introduced by the communication networks. The existence of the delays usually leads to the degradation and/or instability of power system performance. On account of this point, the traditional load frequency control (LFC) approach for power system sketches a destabilizing impact and an unacceptable system performance. Therefore, this paper proposes a new LFC based on adaptive integral second-order sliding mode control (AISOSMC) approach for the large-scale power system with communication delays (LSPSwCD). First, a new linear matrix inequality is derived to ensure the stability of whole power systems using Lyapunov stability theory. Second, an AISOSMC law is designed to ensure the finite time reachability of the system states. To the best of our knowledge, this is the first time the AISOSMC is designed for LFC of the LSPSwCD. In addition, the report of testing results presents that the suggested LFC based on AISOSMC can not only decrease effectively the frequency variation but also make successfully less in mount of power oscillation/fluctuation in tie-line exchange.

Second-Order Sliding Mode Controller Design Subject to an Upper-Triangular Structure

The second-order sliding mode (SOSM) controller design problem for a class of sliding mode dynamics subject to an upper-triangular structure has been discussed in this paper. The proposed SOSM controller design involves two steps. First, a Lyapunov-based SOSM controller is developed by using the adding a power integrator technique to locally finite-time stabilize the sliding variables. Second, by combining the local SOSM controller with a saturation function, a novel SOSM controller with a saturation level is constructed. The feature of the new SOSM controller lies in that the saturation level can be tuned not only to guarantee the global convergence but also to improve the dynamic performance. Lyapunov analysis has been utilized to test the finite-time stability of the closed-loop sliding mode dynamics. The proposed method is eventually demonstrated by simulation results.

New Second-Order Sliding Mode Control Design for Load Frequency Control of a Power System

The implementation of the sliding mode control (SMC) for load frequency control of power networks becomes difficult due to the chattering phenomenon of high-frequency switching. This chattering problem in SMC is extremely dangerous for actuators used in power systems. In this paper, a continuous control strategy by combining a second-order mode and integral siding surface is proposed as a possible solution to this problem. The proposed second-order integral sliding mode control (SOISMC) law not only rejects chattering phenomenon in control input, but also guarantees the robustness of the multi-area power network, which has an effect on parametric uncertainties such as the load variations and the matched or mismatched parameter uncertainties. Moreover, the reporting of the simulation indicates that the proposed controller upholds the quality requirement by controlling with operating conditions in the larger range, rejects disturbance, reduces the transient response of frequency, eliminates the overshoot problem, and can better address load uncertainties compared to several previous control methods. The simulation results also show that the proposed SOISMC can be used for practical multi-area power network to lessen high parameter uncertainties and load disturbances.

Second-Order Sliding Mode Control Design Subject to an Asymmetric Output Constraint

In this brief, a novel second-order sliding mode (SOSM) control method is developed to solve the asymmetric output constraint problem by using a power integrator and barrier Lyapunov function (BLF). The new BLF is first constructed based on the asymmetric constraint condition. A novel SOSM algorithm is then constructed for the nonlinear systems with an asymmetric output constraint. Under the proposed SOSM algorithm, the output of the resulting closed-loop system will never escape from the asymmetric constraint. Finally, a pendulum system is adopted to verify the validity of the theoretical results.

Fuzzy Second-Order Sliding Mode Control Design for a Two-Cell DC-DC Converter

This paper presents a fuzzy second-order sliding mode controller for a two-cell DC-DC converter. For this aim, a second-order sliding mode controller and a type-2 fuzzy system are combined to achieve an adequate control. For this reason, backgrounds on the type-2 fuzzy sets and on the second-order sliding mode control applied to discrete systems have been presented briefly. A proposed control algorithm is then presented combining these two robust approaches. The asymptotic stability of the overall controlled system has been ensured using the Lyapunov theory. The efficiency and the robustness of the proposed controller have been tested by simulations.

Second-Order Sliding Mode Controller Design with a Larger Domain of Attraction

In this paper, by combining a second-order sliding mode (SOSM) algorithm with the saturation technique, a novel SOSM control scheme has been presented. The feature of the proposed SOSM controller lies that there is a saturation function imposed on the sliding variable, which could significantly enlarge the domain of attraction for the closed-loop system. The geometric method has been utilized to prove that all the sliding variables will be steered to the origin in a finite time. Meanwhile, the relation between the control parameters and the shape of the phase trajectory has also been discussed. Finally, the proposed method has been applied to the tracking control problem for a robotic manipulator.

Second-order sliding mode controller design with output constraint

The output constraints widely exist in the physical systems and severely affect the performance of the closed-loop system. This paper considers the second-order sliding mode controller design subject to an output constraint. By constructing a new barrier Lyapunov function and applying the technique of adding a power integrator, a novel second-order sliding mode control algorithm, which can be used to deal with the output constraint problem, has been developed. The proposed sliding mode algorithm enables the output variable not to violate the boundary of the constraint region. Meanwhile, it has been shown that under the output constraint the sliding variable can still be stabilized to zero in a finite time. Finally, an academic example is given to verify the feasibility of the proposed second-order sliding mode algorithm.

A Novel Mixed Cascade Finite-Time Switching Control Design for Induction Motor

This paper presents a novel cascade proportional-integral (PI) continuous second-order sliding mode control (SMC) for induction motor in the presence of operational constraints. The inner-loop SMC is designed to control the current dynamics of the motor, while the outer-loop control is the PI control of speed. The main advantage of the proposed method is that the PI control provides reference to the inner-loop SMC with constraints according to the system requirements in terms of maximum current and speed limits. Moreover, because the inner-loop dynamics of the motor are nonlinear, SMC design has more importance in terms of robustness and disturbance rejection capability. The proposed control is a continuous-time design strategy with fixed-time convergence, while its discretization is performed at the implementation stage. The performance of the developed controller is validated by carrying out real-time experimental studies on an industrial size induction machine. Experimental results demonstrate remarkable robust tracking performance of the controller in terms of transient speed response and steady-state accuracy.

Second-order sliding mode controller design subject to mismatched term

This communique proposes a novel second-order sliding mode (SOSM) control method to handle sliding mode dynamics with mismatched term, so as to reduce the terms in the control channel. Meanwhile, it is shown that the proposed control approach can be used to design SOSM controllers under disturbances bounded by positive functions rather than conventional constant upper bounds. The finite-time stability of the sliding variables has been shown by using finite-time Lyapunov theory. The validity of the proposed approach is verified by controlling a Buck converter.

Adaptive Second-Order Sliding Mode Control Design for a Class of Nonlinear Systems with Unknown Input

An adaptive second-order sliding mode controller is proposed for a class of nonlinear systems with unknown input. The proposed controller continuously drives the sliding variable and its time derivative to zero in the presence of disturbances withunknownboundaries. A Lyapunov approach is used to show finite time stability for the system in the presence of a class of uncertainty. An illustrative simulation example is presented to demonstrate the performance and robustness of the proposed controller.

A Second-Order Sliding Mode Controller Design for Spacecraft Tracking Control

For spacecraft attitude tracking system, there exists the chattering phenomenon. In this paper, the spacecraft motion is decomposed into three-channel subsystems, and a second-order sliding mode control is proposed. This method has been proved to have good convergence and robustness. Combined with the proposed sliding surface, the three-channel controllers are designed. The control performance is confirmed by the simulation results, the approaching process is improved effectively, and a smooth transition is achieved without overshoot and buffeting.

Dynamic second-order sliding mode control of the hovercraft vessel

A suitable combination of the differential flatness property and the second-order sliding mode controller design technique is proposed for the specification of a robust dynamic feedback multivariable controller accomplishing prescribed trajectory tracking tasks for the earth coordinate position variables of a hovercraft vessel model.