Discrete-time Sliding Mode Control Research Articles

Sampled‐Data Based Second‐Order Discrete‐Time Sliding Mode Control via Output Feedback

ABSTRACTThis article proposes a second‐order discrete‐time sliding mode controller (DSMC) by only using sampled‐data information of the system output. On one hand, different from the continuous‐time sliding mode control, the finite‐time stability of the closed‐loop system under DSMC is usually not kept due to the limited sampling frequency. On the other hand, in the output feedback framework, the second‐order sliding mode observer cannot independently estimate the internal state of the system if there exist unknown mismatched term and unknown time‐varying coefficient of the control input. To solve the above problems, a joint design strategy of second‐order discrete‐time sliding mode observer and sliding mode controller based on the “non‐separation principle” is proposed. The stability and robustness of the closed‐loop system is analyzed based on the Lyapunov design method. Finally, simulation example verifies the correctness of the theory.

Discrete-Time Sliding Mode Control Strategies—State of the Art

Variable structure control systems are known to provide a high level of robustness to external disturbances and modeling uncertainties with comparably low computational complexity. Thanks to these features, they have found applications in various fields, such as power engineering, electronics, robotics, and aviation. In recent decades, the field of sliding mode control has developed significantly. Therefore, this study aims to discuss the basic concepts and design methodology of such strategies. Although in the 20th century, continuous-time sliding mode control has been the center of the control engineering society’s attention, it has certain major shortcomings. In particular, such control schemes result in undesirable high-frequency oscillations when applied digitally. Therefore, the more recent discrete-time approach to sliding mode control has gained recognition in the 21st century. Since the introduction of discrete-time sliding mode control strategies, the reaching law-based controller design method has been designed, within which two main paradigms may be named: the switching type and the nonswitching type quasi-sliding mode. This paper presents a broad review of the discrete-time sliding mode control strategies, starting from the definition of sliding mode through the controller design procedures and up to potential applications. The aim of this study is to provide an up-to-date state of the art and introduce readers to the newest trends and achievements in the field of sliding mode control.

Fast Terminal Sliding-Mode Predictive Speed Controller for Permanent-Magnet Synchronous Motor Drive Systems

This paper proposes a kind of discrete-time sliding-mode predictive control (SMPC) based on a nonlinear sliding function for permanent-magnet synchronous motors’ (PMSMs’) speed control to improve the convergence performance. Compared with traditional sliding-mode predictive control based on a linear sliding function, the proposed SMPC has a faster convergence rate thanks to the design of a nonlinear fast terminal sliding function. Moreover, one-step prediction is employed, which greatly simplifies the algorithm and improves the real-time performance of its operation. The sliding state will follow the expected trajectory of a predefined sliding-mode reaching law. The stability and convergence performance of the proposed method is analyzed. The results of the theoretical analysis, simulations, and experiments indicate that the proposed method has excellent convergence performance and robustness.

Discrete-time sliding mode control with inverse hyperbolic sine reaching law

Discrete-time sliding mode control (DTSMC) is a popular control strategy used in applications like drones, aerospace, and automotive due to its robustness against parameter uncertainties and external disturbances. One of the crucial components of DTSMC is the reaching law, which governs the motion of the system towards the sliding surface. In this paper, a novel reaching law based on the inverse hyperbolic sine function is proposed. Initially, we examine the unperturbed (nominal) system case, followed by a subsequent scenario involving unidentified disturbances i.e. for the perturbed system. It is observed that the proposed reaching law not only decreases the control effort but also results in a smoother control input characterized by reduced chattering within a low quasi-sliding band. The simulation results show that the proposed reaching law outperforms the existing reaching law (seminal work of Gao et al.) in terms of both lower control effort and quasi-sliding mode band. Additionally, the proposed reaching law is compared with a similar class of reaching law i.e. with the hyperbolic tangent reaching law and the inverse tangent reaching law. The comparison results demonstrate superior performance in terms of robustness, further demonstrating the effectiveness of the proposed reaching law.

Adaptive Dynamic Model-Based Path Following Controller Design for an Unmanned Surface Vessel

Abstract The effective design of a path following controller for Unmanned Surface Vessels (USVs) under uncertain influences induced by various factors such as environmental disturbances is a challenging task. In this study, we propose to ful?lling this task through taking benefits from an online parameter identi?cation technique, the discrete-time sliding mode control (DSMC) method, and the improved line of sight (LOS) algorithm. The Particle Swarm Optimization algorithm (PSO) was adopted to provide initial settings for the straightforward online identification method, i.e., the Forgetting Factor Recursive Least Square method (FFRLS). In order to handle the time-varying sideslip angle of a ship that exists in reality due to environmental disturbances, a multi-model course control scheme is proposed to improve the control performance. For this control scheme, a flexible selection mechanism in-between a heading angle or a course angle tracking controller based on the DSMC method is designed. A solution to ?xing the tracking deviation problem of the LOS guidance law is investigated for which the gradient descent method is introduced. A series of experiments are carried out at sea with a USV called Orca to verify and validate the proposed hybrid path following approach. The results showed that tracking errors mainly induced by environmental disturbances existed but the maximum magnitude among them was small enough and remaining within the acceptable range especially from the marine engineering point of view. These results, to a high degree, validated the robustness and precision of the proposed controller.

Disturbance Compensation in Discrete-Time Sliding Mode Control – A Comparative Study

This work is intended to compare three methods for disturbances estimation and compensation in discrete-time variable structure systems with sliding modes. All methods detect disturbance, which appear in control channel, with time delay of one sampling period. The first method is based on nominal discrete-time plant model and can be used in any type of discrete-time control systems. The second and the third methods detect disturbance by measurement of sliding function, and it is applicable in discrete-time sliding mode control systems only. The main task of this work is to check efficiency of the given methods in the presence of unmodeled inertial dynamics in actuators and position and velocity sensors of a positional servo system. It is shown that all three methods give near identical results in the nominal case, while the second and the third methods are superior in the presence of unmodelled dynamics. The third method introduces zig-zag motion in the nominal case. Results of research are illustrated by computer simulation of an example of positional servo system.

A New Design Approach to Discrete-Time Sliding Mode Controllers With Disturbance Compensation

A new design approach to discrete time sliding-mode-based controllers with disturbance compensation is proposed in this paper. The approach is applicable for linear time invariant plants with matched disturbances. Starting from the known methods for disturbance estimation (i) using discrete time nominal plant model and (ii) using original sliding mode control design method, full integration of those two algorithms into single one is proposed. Besides, the proposed algorithm can be additionally simplified for a small sampling time. The simplified algorithm does not directly depend on the equivalent control but only on the present and previous values of the sliding variable and previous value of the control. The obtained results are compared with the corresponding system with disturbance estimator based on sliding variable measurement. It is established that both methods give identical results in the nominal case. The method is illustrated in a positional servo system design. Comparative analysis of different methods is done by computer simulation.

Trajectory Following Control of an Unmanned Vehicle for Marine Environment Sensing.

An autonomous surface vehicle is indispensable for sensing of marine environments owing to its challenging and dynamic conditions. To accomplish this task, the vehicle has to navigate through a desired trajectory. However, due to the complexity and dynamic nature of a marine environment affected by factors such as ocean currents, waves, and wind, a robust controller is of paramount importance for maintaining the vehicle along the desired trajectory by minimizing the trajectory error. To this end, in this study, we propose a robust discrete-time super-twisting second-order sliding mode controller (DSTA). Besides, this control method effectively suppresses the chattering effect. To start with, the vehicle's model is discretized using an integral approximation with nonlinear terms including environmental disturbances treated as perturbation terms. Then, the perturbation is estimated using a time delay estimator (TDE), which further enhances the robustness of the proposed method and allows us to choose smaller controller gains. Moreover, we employ a genetic algorithm (GA) to tune the controller gains based on a quadratic cost function that considers the tracking error and control energy. The stability of the proposed sliding mode controller (SMC) is rigorously demonstrated using a Lyapunov approach. The controller is implemented using the Simulink® software. Finally, a conventional discrete-time SMC based on the reaching law (DSMR) and a heuristically tuned DSTA controller are used as benchmarks to compare the tracking accuracy and chattering attenuation capability of the proposed GA based DSTA (GA-DSTA). Simulation results are presented both with or without external disturbances. The simulation results demonstrate that the proposed controller drives the vehicle along the desired trajectory successfully and outperforms the other two controllers.

Sliding mode control for gasifier reactor temperature control

This paper presents a sliding mode control (SMC) design for gasifier reactor temperature control. Temperature control is a critical aspect of biomass gasification for quality syngas production. However, accurate modeling and effective control method are the major challenges of gasifier reactor temperature control. The gasification system processes are not yet well understood to model from the first principle due to the complex and nonlinear nature of the process. Also, conventional control methods such as proportional, integral, and derivative control have not been effective in controlling gasification systems. Hence, this work has used experimental data from a 500 kVA updraft gasifier reactor to develop a data-driven mathematical model. The system identification result predicts 86.36% goodness of fit on the model data and 88.26% on the validation data. Discrete time sliding mode control has been designed from the model and implemented in Simulink to investigate the performance of the control method on the gasifier. The result of the system time response shows that the controller effectively drives the temperature monotonically from 25°C to 700 °C in finite time (11.37 minutes). It also establishes a quasi-sliding motion with an ultimate band of ±1℃ for the remainder of the simulation time. Hence, the control technique guarantees optimal temperature control for any feedstock type which will result in higher conversion efficiency, more syngas yield, and improve syngas quality and durability of the gasifier reactor among others.

Remote tele‐operation using model reference discrete‐time sliding mode control

AbstractIn this article, a dissipativity based discrete time sliding mode controller is proposed for bilateral tele‐operation in presence of communication delays and packet losses. The controllers for both master and slave arm are designed to follow a predefined impedance dynamics with dissipative characteristics. The slave arm controller is designed as a two layered structure. The first layer uses the tracking error between master and slave to create a target velocity profile based on the user defined impedance dynamics. The second layer uses this target velocity profile, slave motion and the contact forces to design a reaching law based discrete time sliding mode controller. A model following reaching law approach is used to design the sliding mode control which alleviates the chattering in the input by removing the impact of the accumulated effects of the past disturbance from the system. Moreover, an adaptive tuning method is used for the switching gain of the sliding mode control so that the controller can be designed even when exact information on the uncertainty bounds are unknown. Numerical simulations are presented for Phantom Omni arm to show the efficacy of the proposed method.

Neural tracking trajectory of discrete-time nonlinear systems based on an exponential sliding mode algorithm

For a class of discrete-time nonlinear systems, this paper proposes a discrete-time sliding mode control algorithm with an exponential term that acts as a variable gain to improve the convergence to a bounded region around the origin for the state variable. To compensate for unknown, but bounded disturbances, it has been employed a discontinuous function through a discrete-time integral action. A discrete-time neural network has also been employed to identify such nonlinear system with a block controllable structure. Finally, the proposed controller and the neural network algorithms are applied to a discretised direct current (DC) motor to follow a desired admissible trajectory. Numerical simulations show the effectiveness of the proposed control law.

Difference Equation With Minima-Based Discrete-Time Sliding Mode Control

This note proposes a reaching law based on a difference equation with minima, for discrete-time sliding mode control, providing a solution that has properties of modified Gao’s reaching law when far away from the origin and Utkin’s equivalent control law when close to the origin. On one hand, the proposed approach eliminates chattering and makes the system states stay on the sliding hyperplane perfectly, while on the other hand, it restricts the rate of change of the sliding variable by tuning a design parameter. As a result, the control law derived from this reaching law is not as aggressive as it is for Gao’s reaching law, for very large initial conditions. The proposed reaching law based discrete-time sliding mode control is designed for both unperturbed and perturbed systems. For the unperturbed system, the sliding variable is made zero in finite time, and for the perturbed system, the sliding variable remains in the neighborhood of the sliding hyperplane. An example is simulated to show the effectiveness of the proposed reaching law.

Robust discrete-time super twisting formation protocol for a 6-DOF Quadcopter swarm

This paper contains a discrete-time higher-order sliding mode control for achieving the formation of a 6-Degrees of Freedom (DOF) Quadcopter swarm using the concept of a discrete Multi-agent system (DMAS). A graph theory is used to represent the communication between the Quadcopters and a leader-follower approach of DMAS is used to design the discrete super-twisting (DST) protocol for the formation of a 6-DOF Quadcopter swarm. The DST protocol not only ensures robustness but also reduces the convergence time and the chattering during the formation process of Quadcopters in a swarm. The stability condition of the formation is also derived using the Lyapunov function. The protocol is validated for the formation of 5 Quadcopters in the given pattern. The simulation results show that the formation is achieved in a finite time. Further to show the efficacy of the DST formation protocol, the results are compared with the first-order discrete-time sliding mode controllers designed by switching type reaching law and non-switching type of reaching law. As the first-order discrete-time sliding mode controllers have a significant amount of quasi-sliding mode band (QSMB) in the sliding surface during the operations, the DST protocol of higher-order discrete-time sliding mode control is preferred. From the comparative analysis, it is inferred that the DST protocol performs better for the formation of a 6-DOF Quadcopter swarm.

Robust temperature tracking and estimation for resistive heater circuit board with implementation

SummaryResistive heating is an efficient method for temperature control in many applications that need robust control designs. Very few attempts have been reported in this direction to deal robustness issues like parametric variations, disturbances and uncertainties. Moreover, there are hardly any laboratory scaled setups available, that are of low cost and provide ease of implementation for such applications to test various algorithms. To that end, lately a resistive heater circuit board (RHCB) setup has become a benchmark setup for testing. For which, available control schemes largely use PID based schemes so far that are not robust. Besides, they employ numerical derivatives of measurements, resulting in the added noise. To circumvent these issues and to address the mentioned literature gap, this paper reports new experimental and simulation studies by developing new robust control and estimation designs for temperature tracking. We design via sliding mode algorithms, a sliding mode observer (SMO) and discrete‐time sliding mode controller (DTSMC) for an uncertain system of RHCB. The proposed controller outperforms the existing PID schemes and tracks the temperature reference accurately, despite the uncertainties. Moreover, SMO robustly estimates the temperature measurements and provide accurate signal for the control purpose. In addition, this study also reports a first of its kind application of such DTSMC and SMO, for which the idea of using different temporal designs for each of them is employed and integrated together for the ease of implementation on RHCB. Thus, the novelty also lies in how to judicially stitch these approaches and showcase their efficacy through simulation and experimental validations.

Adaptive fuzzy sliding mode control of an actuator powered by two opposing pneumatic artificial muscles

Pneumatic artificial muscle (PAM) is a potential actuator in human–robot interaction systems, especially rehabilitation systems. However, PAM is a nonlinear actuator with uncertainty and a considerable delay in characteristics, making control challenging. This study presents a discrete-time sliding mode control approach combined with the adaptive fuzzy algorithm (AFSMC) to deal with the unknown disturbance of the PAM-based actuator. The developed fuzzy logic system has parameter vectors of the component rules that are automatically updated by an adaptive law. Consequently, the developed fuzzy logic system can reasonably approximate the system disturbance. When operating the PAM-based system in multi-scenario studies, experimental results confirm the efficiency of the proposed strategy.

Experimental Verifications of Electric Power Steering Controller Based on Discrete-Time Sliding Mode Control with Disturbance Observer

Experimental Verifications of Electric Power Steering Controller Based on Discrete-Time Sliding Mode Control with Disturbance Observer

Fast Terminal Discrete-time Sliding Mode Control with Fuzzy-based Impedance Modulation for Toe Foot Bipedal Robot Going Upstairs

Fast Terminal Discrete-time Sliding Mode Control with Fuzzy-based Impedance Modulation for Toe Foot Bipedal Robot Going Upstairs

Nonsmooth funnel transformation function-based discrete-time sliding-mode control with deterministic performance margin for servo systems

This paper proposes a nonsmooth funnel transformation function-based discrete-time sliding-mode control strategy for the discrete-time servo systems with unknown frictions and disturbances. For obtaining a more accurate discrete-time system model, a filter-based adaptive identification algorithm (FAIA) is introduced, where the unknown measurement noises are considered. Based on the identified system model and a novel discrete-time nonsmooth funnel transformation function (improving the tracking performances), a discrete-time sliding-mode surface is designed to confine the tracking error to a smaller funnel region compared with the predefined one, which has a deterministic performance margin related to the upper bound of the lumped disturbance. Furthermore, selections of steady-state funnel boundary and sliding-mode surface parameter can be guided theoretically according to the upper bound of the lumped disturbance. Experimental results show that the tracking error is guaranteed in the predefined funnel with a deterministic performance margin by using the proposed control strategy.

SMC for Discrete-Time Networked Semi-Markovian Switching Systems With Random DoS Attacks and Applications

This article concentrates on the discrete-time sliding mode control (DTSMC) problem for uncertain networked semi-Markovian switching systems (S-MSSs) under random denial-of-service (DoS) attacks. The semi-Markovian kernel (SMK) approach is utilized such that the switching among different modes is mutually governed by the transition probability and the sojourn-time distribution function. Considering randomly occurring DoS attacks, a sliding mode function related to the attack probability is constructed to analyze the impact of malicious attacks. Then, sufficient conditions under the equivalent DTSMC law are derived in view of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\sigma $ </tex-math></inline-formula> -error mean square stability criterion. Furthermore, the synthesis problem of the proposed DTSMC law ensures that the resulting closed-loop system dynamics can be driven onto the prespecified sliding region within a limited time. Finally, an electronic throttle control system is shown to validate the proposed algorithm.

SMC for Discrete-Time Nonlinear Semi-Markovian Switching Systems With Partly Unknown Semi-Markov Kernel

This article is devoted to the discrete-time sliding mode control (DSMC) for nonlinear semi-Markovian switching systems (S-MSSs). Motivated by the fact that the complete information of the semi-Markov Kernel is difficult to be obtained in practical applications, it is recognized to be partly unknown as the most common mean. By utilizing the prior information of the sojourn-time upper bound for each switching mode, sufficient conditions under the equivalent DSMC law are proposed for the mean square stability. Moreover, the designed DSMC law realizes the finite-time reachability of the sliding region, and makes the sliding dynamics converge to the predesignated sliding region in a finite time. In the end, a numerical example and an electronic throttle model are given to validate the proposed control strategy.