Dynamic Sliding Mode Control Research Articles

Byrnes-Isidori-based dynamic sliding-mode control for nonminimum phase hypersonic vehicles

This paper deals with the dynamic sliding-mode (DSM) control problem for nonminimum phase hypersonic vehicles (HSVs). When the elevator is the only control surface available for the altitude dynamics, the HSV model exhibits unstable zero dynamics, preventing the application of standard inversion-based control techniques. To solve this problem, a DSM control method based on Byrnes-Isidori (B-I) normalized form is proposed, achieving asymptotic tracking of velocity and Flight-Path-Angel (FPA) while stabilizing internal dynamics. First, for the pitch dynamics with nonminimum phase behavior, external dynamics and internal dynamics are determined by coordinate transformation to convert the longitudinal model to B-I normalized form, based on which a criterion of nonminimum phase property is given by the stability analysis of internal dynamics. Then, a DSM control method is proposed for the FPA subsystem of nonminimum phase, which transforms the output tracking problem into stabilization problem of an augmented system consisting of internal dynamics and dynamic compensator, making closed-loop pole adjustable, and thus improves the tracking performance. The principle of parameters determination is proposed, which is proved to achieve the stability of the system on the sliding surface. Besides, nonlinear disturbance observer is utilized to compensate the error caused by dynamic inversion control. The proposed method is compared with approximate backstepping control and is shown to have superior tracking accuracy as well as robustness from the simulation results. This paper may also provide a beneficial guidance for control design of other complex systems of nonminimum phase.

Robust tracking control for vehicle electronic throttle using adaptive dynamic sliding mode and extended state observer

• The mathematical modelling of automotive engine electronic throttle (EET) system is obtained by considering the nominal model and parameter uncertainty component and all the system uncertainties are detailedly analyzed, then a modified extended state observer (ESO) is adopted to estimate the lumped uncertainty online. • An adaptive dynamic sliding mode (ADSM) feedback control scheme with ESO techniques is designed to achieve a robust closed-loop tracking performance. By adopting the ESO and designing the dynamic secondary sliding surface (DSSS), the chattering phenomenon of the conventional sliding mode can be significantly alleviated. • The additional dynamics introduced in the sliding mode can improve the system stability. A detailed theoretical stability analysis for the whole closed-loop EET control system is presented by innovatively combining the observer dynamics with the feedback control system. • The real-time experimental results from the DSP-based EET experimental platform are given with performance comparisons with other controllers, and both the excellent performance and robustness of the proposed control are achieved. • The robust adaptive dynamic sliding mode control scheme for EET systems will provide the automotive engineers with a good candidate of robust EET controller in practical applications. The proposed control technique can also be applied to other automotive systems for achieving excellent control performance. This article proposes an extended state observer (ESO)-based robust adaptive dynamic sliding mode (ADSM) tracking control for an automobile engine electronic throttle (EET) system. The newly developed control scheme exhibits the following three attractive characteristics. First, a modified ESO is adopted to estimate the lumped uncertainty online. Second, an ADSM feedback control is then designed to achieve a robust closed-loop tracking performance. Third, the switching gain is adaptively updated by the adaptive law to eliminate the need of the uncertainty information. The stability proof combining the observer with the feedback control is presented in detail. High tracking precision and robustness of the proposed control are verified by extensive experimental results with comparison of existing adaptive sliding mode control and conventional robust controllers.

Dynamic Sliding Mode Control of Gyroscopic Balancing Vehicles Based on Disturbance Observer

Gyroscopic balancing vehicle is a new means of transportation with flexible structure and environmental friendliness, which has broad application prospects. However, it is also a typical system of nonlinear characteristics, static instability and parameter uncertainty, making its balance control problem difficult to dealing with. Based on the Lagrange equation of the dynamics model for single-frame CMG, a dynamic sliding mode controller with disturbance observer is designed to solve the severe chattering in conventional sliding mode method by compensating the parameter variation and external disturbance. The simulation results show that the introduced method effectively suppresses the chattering phenomenon, and the dynamic performance of the system is improved at the same time, which further enhances the robustness and application range of the gyroscopic balancing vehicle.

Introduction and realization of four fractional-order sliding mode controllers for nonlinear open-loop unstable system: a magnetic levitation study case

The concept of magnetic levitation attracts the attention of researchers and developers on the global platform for its serviceability in both industrial and research applications. Sliding mode controller is a nonlinear and robust control strategy to provide efficient control over variable structure systems. This paper is initiating with nonlinear modelling of magnetic levitation system dynamics. Various sliding mode controllers for controlling the current through electromagnetic coil to levitate the ferromagnetic ball are presented. This paper is mainly focusing on design robust and energy-efficient fractional sliding mode controller for a nonlinear system. Four novel controllers called fractional static sliding mode controller, fractional integral static sliding mode controller, fractional dynamic sliding mode controller and fractional integral dynamic sliding mode controller are proposed. Stability proof of Lyapunov criteria for the proposed controller has been done. Performance of the proposed controllers is analysed in comparison with the existing sliding mode controllers. Experimental validation is done on a benchmark Feedback 33–210 magnetic levitation system.

Dynamic Event-Triggered Sliding Mode Control: Dealing With Slow Sampling Singularly Perturbed Systems

This brief endeavors to investigate the sliding mode control (SMC) issue of the networked singularly perturbed systems (SPSs) under slow sampling. For the energy saving purpose in network communication, a dynamic event-triggered mechanism is introduced to SMC design. By considering the structure characteristics of the controlled system, a novel sliding function is constructed with taking the singular perturbed matrix $E_\varepsilon $ into account properly. With the aid of some appropriate Lyapunov functionals, the sufficient conditions are derived to ensure the asymptotic stability of the sliding mode dynamics and the reachability of the specified sliding surface. Besides, it is shown that the quasi-sliding motion is dependent on the dynamic event-triggered parameters and its bound converges to a constant. The solving algorithm for the dynamic event-triggered SMC law is formulated in a convex optimization framework. Finally, an numerical example is provided to illustrate the effectiveness of the proposed results.

Robust Dynamic Sliding Mode Control-Based PID–Super Twisting Algorithm and Disturbance Observer for Second-Order Nonlinear Systems: Application to UAVs

This paper introduces a robust dynamic sliding mode control algorithm using a nonlinear disturbance observer for system dynamics. The proposed method is applied to provide a rapid adaptation and strictly robust performance for the attitude and altitude control of unmanned aerial vehicles (UAVs). The procedure of the proposed method consists of two stages. First, a nonlinear disturbance observer is applied to estimate the exogenous perturbation. Second, a robust dynamic sliding mode controller integrated with the estimated values of disturbances is presented by a combination of a proportional–integral–derivative (PID) sliding surface and super twisting technique to compensate for the effect of these perturbations on the system. In addition, the stability of a control system is established by Lyapunov theory. A numerical simulation was performed and compared to recently alternative methods. An excellent tracking performance and superior stability of the attitude and altitude control of UAVs, exhibiting a fast response, good adaptation, and no chattering effect in the simulation results proved the robustness and effectiveness of the proposed method.

Sliding mode controller-observer pair for p53 pathway.

A significant loss of p53 protein, an anti‐tumour agent, is observed in early cancerous cells. Induction of small molecules based drug is by far the most prominent technique to revive and maintain wild‐type p53 to the desired level. In this study, a sliding mode control (SMC) based robust non‐linear technique is presented for the drug design of a control‐oriented p53 model. The control input generated by conventional SMC is discontinuous; however, depending on the physical nature of the system, drug infusion needs to be continuous. Therefore, to obtain a smooth control signal, a dynamic SMC (DSMC) is designed. Moreover, the boundedness of the zero‐dynamics is also proved. To make the model‐based control design possible, the unknown states of the system are estimated using an equivalent control based, reduced‐order sliding mode observer. The robustness of the proposed technique is assessed by introducing input disturbance and parametric uncertainty in the system. The effectiveness of the proposed control scheme is witnessed by performing in‐silico trials, revealing that the sustained level of p53 can be achieved by controlled drug administration. Moreover, a comparative quantitative analysis shows that both controllers yield similar performance. However, DSMC consumes less control energy.

Neural dynamic sliding mode control of nonlinear systems with both matched and mismatched uncertainties

Mismatched uncertainty and chattering appear as two challenges in sliding mode control. To overcome the problem of mismatched uncertainty, multiple sliding surfaces with virtual inputs are proposed. Accordingly, we have proposed two new methods based on designed neural observer: sliding mode control (SMC) and dynamic sliding mode control (DSMC) methods. Although, the proposed SMC can significantly cope with the mismatched uncertainties, but it suffers from chattering phenomenon. The chattering problem can be removed in DSMC, because an integrator is placed before the system. This results in increased number of the system states. This new state can be identified with the proposed neural observer. Note that in both proposed approaches, the robust performance (invariance property) of system is reserved, even in the presence of mismatch uncertainties. Then, to have a valid comparison the proposed DSMC is also designed using loop transfer recovery observer (LTRO). This comparison shows the good performance of the DSMC based neural networks. Moreover, the upper bound of uncertainties is not used in SMC and DSMC controllers and also in the neural observer and LTRO, which is important in practical implementation. Finally, comparing the equations, one can see the simplicity of DSMC in concept and also in realization.

Dexterous robotic manipulation via a dynamic sliding mode force/position control with bounded inputs

Grasping and manipulation are common robotic tasks which require to properly control the interaction forces and position of multiple robots end-effectors. In this study, the authors focus on the problem of dexterous manipulation of rigid objects by means of a cooperative robotic system. Unlike several works, they consider the more complex case when the manipulated object is not mechanically attached to the robots' end-effectors. In addition, they address the control problem of designing a control law with continuous and bounded input torques for cooperative robots in constrained motion. To guarantee a stable grasp and a fine manipulation a centralised control algorithm based on the Orthogonalisation principle and a dynamic sliding mode control is proposed. The control algorithm does not require the knowledge of the dynamic model of the robot manipulators and manipulated object for implementation. Experimental results are presented to show the good performance of the proposed controller. In addition, the stability analysis of the closed-loop dynamics is developed.

Reduction of matched and unmatched uncertainties for a class of nonlinear perturbed systems via robust control

SummaryThe aim of this paper is to design a robust control for stabilization of a class of nonlinear perturbed system subject to matched and unmatched disturbances. Here, the concept of dynamic sliding mode control and the attractive ellipsoid method advantages are used to design a robust nonlinear control algorithm, which reduces considerably the perturbation effects. Hence, in finite time, the dynamic sliding mode control brings the system trajectory to a specific configuration. After this time, the controller reduces the perturbation effects by using the high‐gain control obtained in the attractive ellipsoid method. Thus, based on the solution of a specific matrix inequality, the feedback control of the system guarantees that the trajectory will be stabilized in the ultimate uniform bounded sense. To illustrate the theoretical results, a numerical example with a comparative study is introduced. Finally, the performance of the controller designed in this paper is tested on an electromechanical real‐time system.

Fractional Order Fuzzy Dynamic Backstepping Sliding Mode Controller Design for Triaxial MEMS Gyroscope Based on High-gain and Disturbance Observers

In this paper, a dynamic backstepping sliding mode controller with a fractional order sliding surface, which has a fuzzy boundary layer, is designed based on high-gain and disturbance observers for controlling the performance of a micro-electro-mechanical triaxial gyroscope. To compensate uncertainties of a system, a combination of sliding mode and robust nonlinear backstepping controller is used. In this design, in order to increase the degree of freedom of the controller, the sliding surface is selected to be of fractional order. in this paper, in order to significantly reduce the chattering phenomenon in the control signal, a new dynamic sliding surface in addition to the initial sliding surface and also fuzzy control theory to controllig the boundary layer are used. In addition, a high-gain observer and a disturbance observer are used to estimate the system states and incoming disturbances to the system. The asymptotic stability of the closed-loop system is proven by Lyapunov stability theorem. In order to evaluate the performance of the designed controller, this controller is compared with other sliding mode controllers. Simulation results show that the proposed controller has much less chattering phenomenon in control signal, increasing system stability, reducing the rise time and better tracking.

State tracking control of nonlinear systems using neural adaptive dynamic sliding mode

This paper describes control issues of a general-class, single-input, unknown, nonlinear, non-affine system using dynamic sliding-mode control (DSMC). Chattering can be removed in DSMC with an integrator as a low-pass filter, placed before the input control signal of the plant. As a result, the augmented system (which contains the integrator) in DSMC has one more dimension than the actual system. Then the plant model must be completely known. To overcome this problem and to identify the plant model, an adaptive radial basis-function neural network has been employed and a robust procedure developed to train the parameters of a neural network based on Lyapunov theory. A smooth controller has been developed and some numerical simulations have been performed to verify the validity of the proposed approach. Two nonlinear systems were used for simulation: a Duffing–Holmes chaotic system and a switch reluctance motor. The advantage of the presented approach is that the system model can be considered unknown and can be in non-affine form.

Dynamic Sliding-Mode Control for T-S Fuzzy Singular Time-Delay Systems With ${H}_{\infty}$ Performance

In this paper, we propose a novel sliding-mode control for Takagi-Sugeno (T-S) fuzzy singular system with time-delay and mismatched uncertainties and disturbances. In the majority of T-S fuzzy sliding-mode control ways, a restrictive assumption is required, that is every subsystem's input matrix is identical. In order to eliminate the restrictive assumption, we put forward a dynamic sliding-mode control method for T-S fuzzy singular time-delay systems. Additionally, the dynamic sliding-mode control law is designed to guarantee the reachability of the sliding surface in finite time interval. Stability of sliding motion is analyzed and the dynamic sliding-mode controller is parameterized in terms of the solutions of a set of linear matrix inequalities which facilitates design. In the end, three examples are shown to verify the merit and effectiveness of the proposed approaches are provided.

Dynamic Sliding Mode Control of Active Power Filter With Integral Switching Gain

Owing to the fact that the active power filter with conventional sliding mode controller has a chattering problem, an improved dynamic sliding mode controller is proposed in this paper to increase the performance of the APF. A dynamic sliding mode controller with integral switching gain is developed. The first-order dynamic sliding surface has the characteristic of transferring the discontinuity in traditional sliding mode control to the first derivative of the controller. Therefore, a continuously dynamic sliding controller can be obtained, so that it can effectively weaken the chattering. In the meantime, the appropriate selection of switching gain can also reduce chattering. The simulation results show that the proposed control strategy possesses good performance to suppress the harmonics. Moreover, the hardware in the loop experiment proves the practicability of the proposed algorithm.

Control of Z-Axis MEMS Gyroscope Using Adaptive Fractional Order Dynamic Sliding Mode Approach

This paper proposes a states feedback control method for Z-axis MEMS gyroscopes using fractional calculus and adaptive dynamic sliding mode control method. A new sliding mode control method is proposed to achieve trajectory tracking by adding a fractional order term in the conventional sliding manifold. The new proposed sliding surface contains integer order terms as well as fractional order terms and thus can provide an extra degree of freedom. Besides, in the presence of unknown system parameters, some adaptive laws containing the new designed sliding manifold are proposed to online tune controller parameters. All adaptive laws are derived in the stability framework and the stability of the control system is also guaranteed according to the Lyapunov stability theory and. Simulations results on a Z-axis vibrating gyroscope are provided to illustrate the effectiveness of the control method.

Modelling and robust position and orientation control of a non-affine nonlinear dielectrophoresis-based micromanipulation system

Conventional dielectrophoresis and electrorotation have attracted widespread attention in the field of individual micro-object manipulation in recent years. The improvement of current dielectrophoresis-based micromanipulation systems’ flexibility, accuracy and level of automation are essential requirements of dielectrophoresis-based micromanipulation techniques. For the purpose of high-precision automatic positioning and orientation control of a micro-object, we have developed approximate analytical expressions to describe the conventional dielectrophoretic force and electrorotation torque generated by quadrupole polynomial electrodes on a spherical micro-particle. Numerical simulations based on the finite element method are used to demonstrate the effectiveness of the proposed modelling method. In addition, the non-affine nonlinear dynamic models of the dielectrophoresis-based micromanipulation subsystems are established. Furthermore, an uncertainty and disturbance estimator based dynamic sliding mode controller is proposed and applied to achieve a robust sequential position and orientation control system. The stability of the closed-loop system is established. The performance of the proposed control is demonstrated through simulation studies.

Robust dynamic sliding mode control of robot manipulators using the Fourier series expansion

This paper presents a robust dynamic sliding mode control for electrically driven robot manipulators. The control law computes the motor voltages based on the voltage control strategy. Uncertainties are estimated using the Fourier series expansion and the truncation error is compensated. The Fourier coefficients are tuned based on the stability analysis. The contribution of this paper is designing a robust controller using a novel adaptive Fourier series expansion. In comparison with previous related works based on the Fourier series expansion, the superiority of this paper is presenting an adaptation law for the fundamental frequency of the Fourier series expansion and, consequently, relaxing the need for trial and error procedure in its tuning. The case study is a SCARA (Selective Compliant Articulated Robot for Assembly) robot manipulator actuated by permanent magnet DC electrical motors. The influence of uncertainty estimation based on the Fourier series expansion instead of using sign function is studied. Simulation results verify robust and satisfactory performance of the proposed controller.

Two-Degree-Of-Freedom Dynamic Model-Based Terminal Sliding Mode Control with Observer for Dual-Driving Feed Stage

The position synchronous control of multi-axis gantry-type feed stage is crucial in precision machine tools. Industrial position control which aims to widen the bandwidth and improve disturbance rejection of single axis is not enough to achieve precise synchronization in a dual-driving feed stage. The characteristics diversity, transmission-mechanism deformation, and mechanical coupling effect between dual axes will degrade the control accuracy. Hence, the novel two-degree-of-freedom (2-DOF) dynamic model-based terminal sliding mode control (TSMC) with disturbance and state observer is proposed in this paper for the synchronous control of a 2-DOF dual-driving feed stage. The 2-DOF dynamic model, based on Lagrange equation, is established along with the parameters identification method. The predictive natural frequencies and vibration modes frequencies by the proposed dynamic model are compared by a modal experiment. Then, the 2-DOF dynamic model-based TSMC is provided to satisfy the tracking and synchronization control. In order to reduce the chattering and to increase the robustness against the mechanical coupling, the disturbance and state observer is designed. Moreover, Lyapunov stability criterion is used to analyze the stability of the proposed control scheme. Finally, an industrial application of 2-DOF dual-driving feed stage is utilized to validate the effectiveness of the proposed control scheme. The proposed 2-DOF dynamic model-based TSMC with observer has been effectively demonstrated to improve synchronous performance and tracking accuracy.

Dynamic sliding mode position control of induction motors based load torque compensation using adaptive state observer

PurposeThe purpose of this paper is position control scheme for a servo induction motor (SIM) with uncertainty has been designed using a new observer issue and a dynamic sliding mode control (DSMC).Design/methodology/approachIn DSMC, the chattering is removed due to the integrator (or a low-pass filter) which is placed before the input control of the plant. However, in DSMC, the augmented system has one dimension bigger than the actual system (if integrator is used) and then, the plant model should be completely known. To solve this problem in SIM, the use of a new adaptive state observer (ASO) is proposed.FindingsThe advantage of the proposed approach is to maintain the system controlled under the external load torque variations. Then, the load variations do not affect the motor positioning. Moreover, it is demonstrated that the observer error converges to zero based on the Lyapunov stability theory.Originality/valueThe knowledge of the upper bound for the system uncertainty is not necessary in an adaptive state observer, which is important in practical implementation. Simulation results are presented to demonstrate the performance of the proposed approach.

Dynamic sliding mode controller design for networked control systems with random packet loss and event driven quantisation

This study addresses the sliding mode controller design for a networked control system with quantisation and random packet loss. A logarithmic quantiser is adopted in order to guarantee the coarsest density and decrease the possibility of unsuccessful transmission. The quantisation process is designed as an event driven to reduce the amount of data to be transmitted over the channel. A sliding mode controller is adopted to suppress the measurement noise and error caused by the features of a wireless communication channel. The existence of quasi-sliding mode in the sense of mean-square and closed loop stability in the sense of mean square are claimed. Simulations are carried out to support the algorithms proposed.