Second-order Sliding Mode Control Law Research Articles

Real-Time Voltage Control Based on a Cascaded Super Twisting Algorithm Structure for DC–DC Converters

This article proposes a second-order sliding mode control law, based on a super twisting algorithm (STA), aimed at regulating the output voltage of a dc–dc buck converter. A closed-loop system is designed consisting of two distinct nested loops organized within a cascaded STA structure. Several sliding mode control algorithms are here surveyed for the regulation of a dc–dc buck converter. The STA of second-order sliding mode is also experimented in an HIL system. The comparative evaluations include comparing the output voltage transient responses to load step changes for all developed sliding mode control algorithms and the start-up responses of the output voltage to step changes of the input voltage of the buck converter. Furthermore, theoretical considerations, numerical simulations, and experimental results from a laboratory prototype are compared, at different operating points, for all surveyed control methods. It results from the simulations and experiments that the designed STA achieves the fastest convergence, a consistent chattering reduction, the smallest settling time under loaded situations, and small steady-state error during load changes over all contrasted control methods.

Adaptive Higher-Order Sliding Mode Control of Series-Compensated DFIG-Based Wind Farm for Sub-Synchronous Control Interaction Mitigation

Sub-synchronous control interaction (SSCI) is an oscillation phenomenon caused by the interaction of converter control and series-compensated transmission line. This paper proposes a novel adaptive higher-order sliding mode (AHOSM) control strategy for damping the SSCI of a series-compensated DFIG-based wind power system. On the basis of system modeling and oscillation mechanism analysis, SSCI suppression is converted to the current tracking control problem. Firstly, an auxiliary feedback control is employed for the nonlinear series-compensated system, then integral sliding mode functions are defined to design a second-order sliding mode control law for the equivalent system. Adaptive laws for the control gains are then conceived based on the Lyapunov function considering unknown upper bounds of uncertainty derivatives. System stability is also analyzed in detail along with adaptive laws’ design. The effectiveness of the proposed control scheme is verified under different series-compensated level, different wind speed, symmetric and asymmetric short circuit fault, and internal and external disturbances. The PI control and conventional first-order sliding mode control scheme are also executed to compare the damping effect.

Tracking control of an underwater manipulator using fractional integral sliding mode and disturbance observer

In this paper, a fractional integral sliding mode control (FISMC) strategy with a disturbance observer (DO) is proposed for the trajectory tracking problem of the underwater manipulator, under lumped disturbances namely parameter uncertainties and external disturbances. The modified fractional integral sliding mode surface (FISMS) is designed to guarantee the fast convergence of system states. The DO method and the second-order sliding mode control law are used in the controller design, in which the former is introduced to compensate the effect of the lumped disturbances. Also, a saturated function is selected to replace the sign function to attenuate the chattering phenomenon. The stability of the overall closed-loop system is proved via Lyapunov’s finite-time stability theory. Numerical simulations are performed on a 6 degree of freedom (DOF) underwater manipulator. Simulation results demonstrate that the proposed control scheme can achieve better tracking performance and stronger robustness against disturbances, by comparing with the DO-based PD control and the DO-based PID-type linear sliding mode control (SMC).

Optimal Lyapunov-Based Reaching Time Bounds for the Super-Twisting Algorithm

The super-twisting algorithm is a second-order sliding mode control law commonly used for robust control and observation. One of its key properties is the finite time it takes to reach the sliding surface. Using Lyapunov theory, upper bounds for this reaching time may be found. This contribution considers the problem of finding the best bound that may be obtained using a family of quadratic Lyapunov functions. An optimization problem for finding this bound is derived, whose solution may be obtained using semidefinite programming. It is shown that the restrictions imposed on the perturbations and the conservativeness of the obtained bound are significantly reduced compared to existing results from literature.

Continuous sliding mode control of compliant robot arms: A singularly perturbed approach

Compliant actuators are essential for ensuring safety in physical human-robot interaction. A compact-sized series elastic actuator (SEA), a type of compliant actuators, was developed to guarantee high force control fidelity and low output impedance in our previous work. This study is focused on the control design of a compliant robot arm driven by the developed SEA. The control problem is formulated into a singularly perturbed form which contains a slow rigid robot dynamics and a fast SEA dynamics. To achieve high-precision tracking without serious control chattering, a second-order sliding mode control (SMC) law is proposed such that the equilibrium point of the closed-loop rigid robot dynamics has semiglobal exponential stability. A derivative-type control law is employed such that the equilibrium point of the closed-loop SEA dynamics has global exponential stability. As the SMC law developed is continuous so that the rigid robot dynamics is continuously differentiable, the singular perturbation theory is applicable to establish semiglobal practical exponential stability of the entire system. This study provides the first application of continuous SMC to robots driven by compliant actuators. Experimental results have verified a high-accuracy and high-resolution tracking performance of the robot control system.

Second-order fuzzy sliding-mode control of photovoltaic power generation systems

In order to maximize the conversion efficiency of photovoltaic systems, it is usually essential to design a maximum power point tracking controller. In this paper, a new second-order fuzzy sliding-mode controller is designed for this purpose. Since the proposed scheme is based on the second-order sliding-mode control law, it can handle nonlinear dynamics of photovoltaic systems. Compared to previously introduced controllers, the proposed control law does not depend on model parameters and thus is robust to system uncertainties. The gain of the control signal is determined using a fuzzy gain tunning algorithm. Therefore, not only the robustness of the system will be improved, but also chattering amplitude will be suppressed. The proposed scheme does not require asymptotic observers, and thus its analysis and implementation are fairly simple. The performance of the proposed control system is verified through simulation and experiment. Compared to terminal sliding mode control system, the proposed system can increase the efficiency up to 1.5%.

Disturbance-observer-based fixed-time second-order sliding mode control of an air-breathing hypersonic vehicle with actuator faults

This paper presents a disturbance-observer-based fixed-time second-order sliding mode approach for fault-tolerant control of an air-breathing hypersonic vehicle, where both partial loss of effectiveness faults and bias faults in actuators are considered. Firstly, a fixed-time second-order sliding mode control law is designed to guarantee the reaching time, independent of initial conditions. Then, by using a robust uniformly convergent differentiator technique, a fixed-time convergent disturbance observer is established to quickly estimate the lumped uncertainty, which consists of actuator faults and system uncertainties. Therefore, any information of actuator faults is not required by this design. Finally, simulation results of a generic air-breathing hypersonic vehicle are presented to demonstrate the effectiveness of the proposed controller.

Adaptive robust control of Mecanum-wheeled mobile robot with uncertainties

This paper presents a novel implementation of an adaptive robust second-order sliding mode control (ARSSMC) on a mobile robot with four Mecanum wheels. Each wheel of the mobile robot is actuated by separate motors. It is the first time that higher-order sliding mode control method is implemented for the trajectory tracking control of Mecanum-wheeled mobile robot. Kinematic and dynamic modeling of the robot is done to derive an equation of motion in the presence of friction, external force disturbance, and uncertainties. In order to make the system robust, second-order sliding mode control law is derived. Further, adaptive laws are defined for adaptive estimation of switching gains. To check the tracking performance of the proposed controller, simulations are performed and comparisons of the obtained results are made with adaptive robust sliding mode control (ARSMC) and PID controller. In addition, a new and low-cost experimental approach is proposed to implement the proposed control law on a real robot. Experimental results prove that without compromising on the dynamics of the robot real-time implementation is possible in less computational time. The simulation and experimental results obtained confirms the superiority of ARSSMC over ARSMC and PID controller in terms of integral square error (ISE), integral absolute error (IAE), and integral time-weighted absolute error (ITAE), control energy and total variance (TV).

Decentralized multi-machine power system excitation control using continuous higher-order sliding mode technique

A new decentralized continuous higher-order sliding mode (HOSM) excitation control scheme is proposed to enhance transient stability and robustness of multi-machine power system. Power angle deviations are chosen as sliding variables. The HOSM control for uncertain nonlinear multi-machine power system is equivalently transformed into finite time stability problem of uncertain integrator chains. The alleged continuous HOSM excitation controller is composed of geometric homogeneous continuous control and super-twisting second-order sliding mode control law to achieve finite time convergence and overcome power system uncertainties. An adaptive gain, constructed for the super-twisting control item, enables reducing the switching control amplitude of excitation voltage to the minimum possible value along with a finite time convergence. The first-order and second-order time derivatives of power angles are estimated by the exact robust differentiators. Finite time stability of closed-loop power system is strictly proved. Simulation results for a three-machine system and 10-machine 39-bus New England power system demonstrate the effectiveness of the proposed decentralized continuous HOSM excitation control approach.

Adaptive smooth second-order sliding mode control method with application to missile guidance

This paper proposes an adaptive smooth second-order sliding mode control law for a class of uncertain non-linear systems. The key point of this control law is ensuring a smooth control signal considering parametric uncertainty and disturbances with unknown bounds. The proposed control method is obtained by introducing a continuous function under the integral and using adaptive gains. The switching function and its derivative are forced to zero in finite time. This is achieved using a smooth control command and without the prior knowledge of upper bound parameters of uncertainties. The finite-time stability is proved based on a quadratic Lyapunov approach and the reaching time is estimated. This structure is used to create a homing guidance law and the efficiency is evaluated via simulations.

Dynamic sliding mode controller design for reducing chattering

A dynamic sliding mode control algorithm that can successfully avoid the chattering problem and does not provide high gain control is proposed in this paper. Without using any differentiator, a modified asymptotically stable second-order sliding mode control law is developed in which the proposed controller can guarantee finite time convergence to the sliding mode, and the system states asymptotically approach zero. Simulation results demonstrate the effectiveness of the proposed dynamic sliding mode controller and provide alleviation of chattering.

Impact Time and Angle Guidance With Sliding Mode Control

A novel sliding mode-based impact time and angle guidance law for engaging a modern warfare ship is presented in this paper. In order to satisfy the impact time and angle constraints, a line-of-sight rate shaping process is introduced. This shaping process results in a tuning parameter that can be used to create a line-of-sight rate profile to satisfy the final time and heading angle requirements and to yield acceptable normal acceleration values. In order to track the desired line-of-sight rate profile in the presence of uncertainties, a novel robust second-order sliding mode control law is developed using a backstepping concept. Due to the robustness of the control law, it can be applied to many realistic engagement scenarios which include uncertainties such as target motion. Numerical simulations with different warship engagements are presented to illustrate the potential of the developed method.

On Chattering-Free Dynamic Sliding Mode Controller Design

For a class of linear MIMO uncertain systems, a dynamic sliding mode control algorithm that avoids the chattering problem is proposed in this paper. Without using any differentiator, we develop a modified asymptotically stable second-order sliding mode control law in which the proposed controller can guarantee the finite time convergence to the sliding mode and can show that the system states asymptotically approach to zero. Finally, a numerical example is explained for demonstrating the applicability of the proposed scheme.