Discrete-time Sliding Mode Control Research Articles

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.

Extended observer‐based hybrid tracking control strategy for networked system with FDI attacks

AbstractThis paper studies the speed tracking control of networked control systems (NCSs) with external disturbance and false data injection (FDI) attacks. First, the system model with external disturbances and FDI attacks is built. Then, an extended observer based on discrete time sliding function and neural network (NN) is proposed to observe the extended states and suppress the effect of external disturbance and FDI attacks. Furthermore, a novel hybrid discrete‐time sliding mode control (HDSMC) strategy combining discrete time sliding mode control with super‐twisting control is designed to perform closed‐loop control of the system, in which the exponential term and nonlinear term are constructed to restrain the jitters. The convergence and reachability of the sliding motion are proofed. Finally, the validity and feasibility of the proposed methods are proved by simulations and experiments.

Discrete-time Sliding Mode Control with Adaptive Reaching Law via Implicit Euler Method

Discrete-time Sliding Mode Control with Adaptive Reaching Law via Implicit Euler Method

Design of Sliding Mode Controllers using Reduced-order Koopman Mode Representations

The Koopman operator framework allows for a linear, but infinite-dimensional, representation of the dynamics of a non-linear system. The Koopman modes, or observables, and the resulting linear dynamics are derived purely using a data-driven framework, where the data are system outputs measured at discrete samples; improving accuracy of the Koopman representation requires a large number of such modes to be considered. Recent results consider the system input as well, in the derivation of the discrete linear dynamics, thus enabling the design of controllers. Sliding mode controllers (SMCs), including the discrete-time versions, can handle parameter uncertainties and variations and also ensure that the control objective is satisfied in finite time. In this paper, a discrete-time SMC is designed for the output control of a dynamic system approximated by fewer Koopman modes; the SMC is expected to handle uncertainties introduced by the ignored modes. Conditions are identified for the closed-loop system to be stable, with the occurrence of sliding mode.

Sliding mode control and its application in switched systems: A survey

According to the development and research of sliding mode variable structure control (SMVSC) in recent years. This paper mainly reviews the development and applications of some popular sliding mode control (SMC), such as adaptive SMC, discrete-time system SMC, fuzzy SMC, and neural network SMC. With the research and development of switched system (SS), the research scholars can deal with the complex and changeable system more effectively by combining the SMC with the SS, so as to improve the efficiency and stability of the system. The theoretical research and applications of SMC combined with fuzzy SS, predictive SS and uncertainty SS are also becoming more and more attractive. The purpose of this paper is to analyze and organize the current research status of the popular directions of SMC, and provide the readers with the latest research results on the application directions and new trends in the field of SMC. By considering these theoretical studies and numerous applications, the research and development of intelligent control techniques and switching systems based on sliding mode control are reviewed. Finally, some prospects for related research are presented.

Advanced discrete-time sliding mode control with fast output sampling and its application to buck converter

In this paper, a relative degree two (RD2) sliding variable based discrete time sliding mode control (DTSMC) is designed for a linear time invariant system when output sampling is done faster than control input computation. The RD2 framework has been established for better performance and improved robustness of the discrete time sliding mode control system. The paradigm of fast output sampling (FOS) is utilized since it allows control computation using only the sampled output information, which is important from the implementation perspective making the design practical. A formal analysis is presented to establish the range of the controller parameters for this novel combination of DTSMC with RD2 sliding variable in the FOS framework. Also, a quantitative analysis of robustness in terms of ultimate band for the RD2 approach is done and compared with that of the RD1 approach. The theory is validated in a test bench application of a buck converter for tracking voltage references utilizing the FOS paradigm. The FOS paradigm had previously not been tested in any practical system with DTSMC, and this is the first time it is presented for the dc–dc buck converter system.

Feedback control of actuation‐constrained moving structure carrying Timoshenko beam

AbstractThis article deals with tracking control and active vibration suppression of a hybrid rigid‐elastic vibrational mobile system with a nonlinear elastic foundation in the presence of actuator bandwidth limitation and control input saturation. The system consists of a rigid rectilinearly mobile frame on an elastic foundation, and a flexible Timoshenko beam clamped to it with a heavy attached concentrated mass. The hybrid partial differential equation (PDE)‐ordinary differential equation (ODE) system of the plant is obtained using Hamilton's principle and then is converted to a system of ODEs using the assumed mode method (AMM). Next, the model will be discretized in the time domain using the two‐step Adams‐Bashforth technique. Considering the first‐order dynamics to cover the bandwidth limitation of the actuator, a discrete‐time sliding mode controller (DSMC) is designed based on a positive definite Lyapunov functional. Following that, an innovative optimal predictive algorithm is proposed to compensate for the effects of input saturation. The proposed algorithm is based on a positive definite cost function and using an intelligent regime of optimizations and decisions, minimizes the cost function in a predefined prediction horizon. The vibratory behavior of the system also is included in the mentioned cost function. Consequently, the overall control scheme called optimal rigid‐elastic interaction control (OREIC) will be able to follow the desired tracking trajectory, suppress the beam vibrations, and compensate for the effect of bandwidth limitation as well as the effect of input saturation. The performance of the OREIC algorithm is compared with a saturated DSMC controller and the simulation results demonstrate the efficiency of the method in vibration control of mobile rigid‐elastic systems subjected to actuator bandwidth frequency and saturation limitations.

Sensor fault-tolerant control for a doubly fed induction generator in a smart grid

This study proposes a sensor fault-tolerant controller for a doubly fed induction generator connected to a smart grid. Mathematical models are the main tools for the synthesis of modern control systems; however, an accurate model for complex systems is not always available. Therefore, in this study, a recurrent high-order neural network trained with an extended Kalman filter is proposed to develop a mathematical model for a wind turbine with a doubly fed induction generator connected to a smart grid. The neural model is combined with a modified discrete-time sliding mode controller, which compensates for the presence of sensor faults on each of the state variables on both sides of the back-to-back converter. Real-time results are included to illustrate the effectiveness of the proposed scheme under five sensor faults.