Discrete-time Quasi-sliding Mode Control Research Articles

Discrete time quasi-sliding mode-based control of LCL grid inverters

Application of a discrete time (DT) sliding mode controller (SMC) in the control structure of the primary controller of a three-phase LCL grid inverter is presented. The design of the inverter side current control loop is performed using a DT linear model of the grid inverter with LCL filter at output terminals. The DT quasi-sliding mode control was used due to its robustness to external and parametric disturbances. Additionally, in order to improve disturbance compensation, a disturbance compensator is also implemented. Also, a specific anti-windup mechanism has been implemented in the structure of the controller to prevent large overshoots in the inverter response in case of random disturbances of grid voltages, or sudden changes in the commanded power. The control of the grid inverter is realized in the reference system synchronized with the voltage of the power grid. The development of the digitally realized control subsystem is presented in detail, starting from theoretical considerations, through computer simulations to experimental tests. The experimental results confirm good static and dynamic performance.

Extended Discrete-Time Quasi-Sliding Mode Control for VTOL UAV in the Presence of Uncertain Disturbances

Extended Discrete-Time Quasi-Sliding Mode Control for VTOL UAV in the Presence of Uncertain Disturbances

Robust cascade control of electrical drives using discrete-time chattering-free sliding mode controllers with output saturation

The paper considers electrical drives control having a hierarchical cascaded structure. This structure has an inner current control loop and outer loops for speed and position control. The design of the control is performed using a discrete-time model of electrical drive. In all the loops, the discrete-time quasi sliding mode control is used for controller design because of its robustness to external and parametric matched disturbances (inherent to electrical drives) and the capability to ensure the desired dynamics. To enhance the robustness to disturbances, a nonlinear disturbance compensator is also implemented. The chattering in sliding mode is eliminated by using a new modified discrete-time super twisting control. The current and the speed controllers are designed for linear discrete-time first-order models, while the position controller is designed for a linear second-order discrete-time model. The axis position is measured by a mechanical sensor (encoder). The speed is estimated from the position measurements using Euler derivative approximation. Alternatively, it can be obtained by an observer. The proposed design is straightforward and results in high-performance, robust control with strong disturbance rejection capability and negligible overshoots. All theoretically obtained claims are demonstrated by experiments on an induction motor drive with a rotor field-oriented control structure.

Quasi-sliding mode control for discrete-time uncertain systems with time-varying delay and stochastic disturbance

This paper investigates an effective controller design method for discrete-time linear system with parameter uncertainty, time-varying delay, input nonlinearity and process disturbance. A novel discrete-time quasi-sliding mode control (DQSMC) scheme is mainly proposed. Since the sliding mode bound is directly involved in the DQSMC law, the chattering bound can be accurately specified. By the proposed method, the dynamic of the sliding mode is unable to escape from the pre-given neighbourhood once it is attracted into the neighbourhood, in addition, the closed-loop system achieves the almost surely stable in mean square sense. Moreover, the proposed DQSMC provides a convenient method to simultaneously regulate the convergence rates of the sliding mode and the closed-loop system. Numerical example is provided to demonstrate the effectiveness of the proposed method.

Sliding Mode Control for A Class of Uncertain Discrete Switched Systems

This paper considers the discrete-time quasi-sliding mode control for a class of uncertain switched systems. Since the input matrices are different, a weighted sum approach is proposed such that a common sliding surface is designed. Moreover, by designing a sliding mode control law, the state trajectories are driven into a certain band of the sliding surface. Furthermore, to guarantee the exponential stability of the sliding mode dynamics, a sufficient condition based on the average dwell time technology is given. Finally, a simulation is given to demonstrate the efficiency of the proposed method.

Discrete time quasi-sliding mode control of nonlinear uncertain systems

The control of nonlinear uncertain systems is still an open area of research, and sliding mode control (SMC) is one of the robust and effective methods to cope with uncertain conditions. In this paper, a new sliding mode control algorithm for a class of discrete-time nonlinear uncertain systems is proposed. By using an estimator of uncertainties and external disturbances, the proposed algorithm ensures the stability of the closed loop system as well as the reference tracking. The controller designed using the above technique is completely insensitive to the parametric uncertainty and the external disturbances. Simulations are carried out on a numerical example and a bioreactor benchmark, and the results confirm the effectiveness of our proposition.

Discrete time quasi-sliding mode control of nonlinear uncertain systems

Discrete time quasi-sliding mode control of nonlinear uncertain systems

Discrete Time Quasi Sliding Mode Control For Piezo-Actuated Positioning Systems: A Prescribed Performance Control Approach

The piezoelectric actuators (PEAs) with many advantages such as sub-nanometers resolution, low power consumption, quick response, high stiffness, etc., have been widely used in micro/nano positioning systems which play a very important role in many key technologies recently. To achieve high precision in tracking applications based on PEAs, advanced control techniques are needed to cope with the nonlinearity exhibiting between the input voltage and output displacement of the PEAs. This paper proposes a new approach to get high tracking performance by combining discrete-time quasi-sliding mode control (DQSMC) and prescribed performance control (PPC) techniques. The effectiveness of the proposed method is verified by experiments on a piezo-actuated positioning system.

Quasi-Sliding Mode Control With Orthogonal Endocrine Neural Network-Based Estimator Applied in Anti-Lock Braking System

This paper presents a new control method for nonlinear discrete-time systems, described by an input–output model which is based on a combination of quasi-sliding mode and neural networks. First, an input–output discrete-time quasi-sliding mode control with inserted digital integrator, which additionally reduces chattering, is described. Due to the presence of various nonlinearities and uncertainties, the model of the controlled object cannot be described adequately enough. These imperfections in modeling cause a modeling error, resulting in rather poor system performances. In order to increase the steady-state accuracy, an estimated value of the modeling error in the next sampling period is implemented into the control law. For this purpose, we propose two improved structures of the neural networks by implementing the generalized quasi-orthogonal functions of Legendre type. These functions have already been proven as an effective tool for the signal approximation, as well as for modeling, identification, analysis, synthesis, and simulation of dynamical systems. Finally, the proposed method is verified through digital simulations and real-time experiments on an anti-lock braking system as a representative of the considered class of mechatronic systems, in a laboratory environment. A detailed analysis of the obtained results confirms the effectiveness of the proposed approach in terms of better steady-state performances.

Decentralized discrete-time quasi-sliding mode control of uncertain linear interconnected systems

In this paper, a new global decentralized discrete-time quasi-sliding mode control of linear interconnected systems is presented. The proposed controller is free of chattering problem and can be applied to a broader class of large-scale systems. Additionally, it is capable to deal with both known and unknown interconnections among the subsystems. Stability of the reduced-order interconnected systems is analyzed using Lyapunov approach. The proposed decentralized controller guarantees the reachability of the connective sliding manifold. The resultant dynamics are proved to be globally asymptotically stable. Furthermore, the controller is made robust to external disturbances by employing a disturbance estimation scheme. The simulations are performed on model of a two-area power generation system and the results show the efficacy of the proposed scheme.

Non-switching reaching law based discrete time quasi-sliding mode control with application to warehouse management problem

In this paper a new non-switching type reaching law for sliding mode control of discrete time systems is introduced and applied to the problem of periodic review inventory management. The considered inventory is refilled by multiple suppliers through delivery channels subject to non-negligible commodity losses. The reaching law proposed in this paper is inspired by the earlier work of Gao, Wang and Homaifa, however, in this paper the original formulation is essentially modified in order to avoid undesirable switching, and to ensure good dynamic performance with limited commodity orders. These improvements are obtained by the application of a modified definition of the quasi-sliding mode, and also by the introduction of an adjustable, state dependent sliding variable decrease rate factor. The sliding mode inventory management strategy proposed in this paper ensures full customer demand satisfaction and enables the designer to specify upper limit of the on-hand stock level.

Output feedback discrete-time sliding mode control for time delay systems

Several algorithms for discrete-time quasi-sliding mode control of time-delay systems with different delay and disturbance structures are proposed. Four different delay structures are considered. All the algorithms are based on multirate output feedback. Hence, they are more practical than state feedback and are less complex compared with observer-based control strategies.

Discrete-time quasi-sliding mode control of an autonomous underwater vehicle

This paper presents a discrete-time quasi-sliding mode controller for an autonomous underwater vehicle (AUV) in the presence of parameter uncertainties and a long sampling interval. The AUV, named VORAM, is used as a model for the verification of the proposed control algorithm. Simulations of depth control and contouring control are performed for a numerical model of the AUV with full nonlinear equations of motion to verify the effectiveness of the proposed control schemes when the vehicle has a long sampling interval. By using the discrete-time quasi-sliding mode control law, experiments on depth control of the AUV are performed in a towing tank. The controller makes the system stable in the presence of system uncertainties and even external disturbances without any observer nor any predictor producing high rate estimates of vehicle states. As the sampling interval becomes large, the effectiveness of the proposed control law is more prominent when compared with the conventional sliding mode controller.

Adaptive quasi-sliding mode control for discrete-time multivariable systems

In this paper, the discrete-time adaptive quasi-sliding mode control for multivariable systems with perturbations and partial model uncertainties is studied. Even though no a priori knowledge of the perturbations is required, the dead-zone function is constructed based on the on-line estimates of the upper bound of the perturbations. By applying the adaptation algorithm with dead-zone, the unknown model parameters are estimated. Then, a discrete quasi-sliding mode adaptive controller with no chattering is synthesized to guarantee the global stability of the closed-loop systems in the sense that all signals remain bounded. If some information of the perturbations is known, the controller can be modified to improve the performance of the controlled systems. Examples and simulation results are presented to illustrate the proposed algorithms.

Discrete-time quasi-sliding mode tracking control of uncertain systems with long sampling interval

This paper presents a discrete-time quasi-sliding mode controller of SIMO systems with parameter uncertainty and long sampling interval. The discrete quasi-sliding mode control system is designed to track the desired path on the basis of a Lyapunov function, and sufficient conditions of the switching gain are given to make the discrete system stable. Each component of the switching gain can be determined separately. The switching region is variable according to the product of the bounds of uncertainty and the amplitude of the trajectory. The controller is robust to the uncertainties, and the reaching condition of the control system is satisfied for any initial condition. This control law is a generalized form of the discrete quasi-sliding mode control and reduces the chattering problem considerably. Simulation results for motion control of an autonomous underwater vehicle which acquires position information with a discrete interval show the effectiveness of the proposed technique.