Sliding-mode System Research Articles

Continuous, saturation, and discontinuous tokamak plasma vertical position control systems

This paper is devoted to the design and comparison of unstable plasma vertical position control systems in the T-15 tokamak with the application of two types of actuators: a multiphase thyristor rectifier and a transistor voltage inverter. An unstable dynamic element obtained by the identification of plasma-physical DINA code was used as the plasma model. The simplest static feedback state space control law was synthesized as a linear combination of signals accessible to physical measurements, namely the plasma vertical displacement, the current, and the voltage in a horizontal field coil, to solve the pole placement problem for a closed-loop system. Only one system distinctive parameter was used to optimize the performance of the feedback system, viz., a multiple real pole. A first-order inertial unit was used as the rectifier model in the feedback. A system with a complete rectifier model was investigated as well. A system with the voltage inverter model and static linear controller was brought into a sliding mode. As this takes place, real time delays were taken into account in the discontinuous voltage inverter model. The comparison of the linear and sliding mode systems showed that the linear system enjoyed an essentially wider range of the plant model parameters where the feedback system was stable.

Adaptive Sliding Mode Control of a Spherical Wrist for Restraining Disturbance in Uncertain Environment

To overcome some shortcomings of existing wrists,such as complex structure,low integration,kinematic coupling and poor ability to resist uncertain disturbance,a 3-DOF decoupling spherical wrist with independent kinematic chain and adaptive sliding mode control is proposed. The decoupling structure of double hemispheres and double universal joints is employed to guarantee compactness and flexibility of the spherical wrist. To analyze the transitive relation of the wrist,the forward and inverse kinematics and dynamics are derived. The system control model and motion transitive relation between the working space and the joint space are established,the experimental platform of the 3-DOF decoupled spherical wrist is established. A nonlinear terminal sliding surface controller and RBF neural network are employed to increase convergent speed of the system. The Lyapunov function is used to prove the stability of the control system. Simulation and experiment demonstrate that the proposed control method is insensitive to uncertain disturbance,the chattering of sliding mode system is reduced,trajectory tracking control ability is good,and higher positional accuracy is realized.

Robust fault diagnosis of an electro-hydrostatic actuator using the Novel dynamic second-order SVSF and IMM strategy

This paper introduces a new robust fault detection and identification (FDI) structure applied to an electro-hydrostatic actuator (EHA) experimental setup. This FDI structure consists of the dynamic second-order smooth variable structure filter (Dynamic second-SVSF) and the interacting multiple model (IMM) strategy. The dynamic second-order smooth variable structure filter (SVSF) is a new robust-state estimation method that benefits from the robustness and chattering suppression properties of second-order sliding mode systems. It produces robust-state estimation by preserving the first and second-order sliding conditions such that the measurement error and its first difference are pushed towards zero. Moreover, the EHA prototype works under two different operational regimes that are the normal EHA mode and the faulty EHA mode. The faulty EHA setup contains two types of faults, namely friction and internal leakage. The FDI structure contains a bank of dynamic second-order SVSFs estimating state variables ba...

Sliding Mode Control Based on Novel Nonlinear Sliding Surface for a Class of Time-Varying Delay Systems

The sliding mode control (SMC) design is discussed for a class of time-varying delay systems which is delay-range-dependent and rate-range-dependent. A novel time-varying nonlinear sliding surface is employed. The choice of nonlinear sliding surface is to change the state matrix of sliding mode system, which can combine the advantages of different conventional linear sliding surfaces. Thus the better transient qualities of system states, i.e., quicker response and smaller overshoot, can be achieved. The sufficient conditions ensuring the asymptotic stability of sliding mode are derived in terms of linear matrix inequalities. The algorithms deciding unknown parameters of the nonlinear sliding surface and the corresponding sliding mode controller are also presented. Finally, A numerical example is given to illustrate the effectiveness of the result here.

Guided Rocket Control System Design Based on Discrete-Time Adaptive Sliding Mode

The discrete-time adaptive sliding mode controller for spinning rockets in presence of parameter error is proposed. Considering the nonlinear characteristics for the system, input-output feedback linearization is utilized to transform the system model into two standard form subsystems. Then a discrete-time controller for guided rockets is designed based on discrete-time sliding mode control principle. In order to diminish the switch width of the discrete-time sliding mode system corresponding to parameter error, a dead-zone parameter adaptive law is designed. The stability of the uncertain closed-loop system is proved by Lyapunov theory, which make the controller have high robustness. Simulation result indicates that the proposed controller is robust with respect to large aerodynamic parametric uncertainty, and has excellent dynamic tracking performance.

Unified approach to the sliding-mode control and state estimation – application to the induction motor drive

Abstract In this paper a generalized design procedure of the sliding mode systems is described. A unified approach is applied to control and state variables estimation algorithms. Selected solutions are then applied in the induction motor drive system. An identical design procedure is used to design the speed control and MRAS-type speed estimator. Presented algorithms are verified using experimental tests performed on the 3 kW laboratory setup.

On exponential stabilization for a class of neutral-type systems with parameter uncertainties: An integral sliding mode approach

This paper is focused on integral sliding mode control (ISMC) for a class of parameter uncertain neutral-type systems with time-varying delays (NTSTD). An integral sliding surface functional is firstly constructed for the NTSTD. Then, a delay-dependent robust stability criterion is established for all admissible uncertainties, which can guarantee the sliding mode dynamic system to be robustly exponentially stable under a certain decay rate. In addition, by solving the generalized eigenvalue problem (GEVP) presented in the subsequent work, the global maximal value of the decay rate as well as the condition of exponential stability for the sliding mode system are derived. Furthermore, a sliding mode control (SMC) law is then synthesised to ensure the stability of the closed-loop system, and the proposed SMC law can drive the state of controlled dynamic system into the predefined sliding surface in finite time. Finally, a numerical example is provided to demonstrate the effectiveness of the obtained results.

Robustness of finite-time stability property for sliding modes

The paper is devoted to analysis of robustness of the finite-time stability property for discontinuous systems using the homogeneity framework. A short introduction into sliding-mode systems, homogeneity and finite-time stability is given. The main result connects the homogeneity degree of a discontinuous system and its type of robust stability. For robustness analysis the input-to-state stability method is used. The proposed theory is applied to a series of well known sliding-mode control algorithms.

Stability Analysis of a Class of Second Order Sliding Mode Control Including Delay in Input

This paper deals with a class of second order sliding mode systems. Based on the derivative of the sliding surface, sufficient conditions are given for stability. However, the discontinuous control signal depend neither on the derivative of sliding surface nor on its estimate. Time delay in control input is also an important issue in sliding mode control for engineering applications. Therefore, also sufficient conditions are given for the time delay size on the discontinuous input signal, so that this class of second order sliding mode systems might have amplitude bounded oscillations. Moreover, amplitude of such oscillations may be estimated. Some numerical examples are given to validate the results. At the end, some conclusions are given on the possibilities of the results as well as their limitations.

VSI sliding mode control with regular multidimensional switching

The novel VSI control is offered. It is characterized by a switching normalization of the discontinued control components in a sliding mode due to a special choice of switching surfaces. The suggested design approach allows providing high dynamics and accuracy indexes of the sliding mode system in a combination with the respect of requirements on electromagnetic compatibility. The possible hardware implementation is presented. The simulation results confirm a regular structure of VSI phase serial switching.

Velocity and Acceleration Estimation by a Nonlinear Filter Based on Sliding Mode and Application to Control System

Proportional-integral-derivative (PID) control commonly used to operate mechanical systems has limited performance accuracy due to the influence of gravity, friction, and joint interaction caused by modeling error. Digital acceleration control is robust against modeling errors and superior to PID control, but the need for positioning, velocity, and acceleration knowledge constrains the development of digital acceleration control. To overcome this limitation, this report introduces the system which estimates the smoothed and differential values using sliding mode system (ESDS). Using ESDS enables digital acceleration control without increasing the number of sensors over that used in PID control. This paper focuses on the influence of gravity because digital acceleration control can, in principle, cancel its influence. This controls mechanical systems appropriately under attitude variations. Results of proposed control are demonstrated using 1- and 2-link manipulators.

Fuzzy boundary layer tuning for sliding mode systems as applied to the control of a direct drive robot

Chattering in the control signal is a significant problem in sliding mode control (SMC). The boundary layer approach is one of the many modifications proposed in the literature to avoid the chattering. In this approach, instead of the discontinuous SMC, a continuous feedback control law is employed in a boundary layer around the sliding surface. The thickness of the boundary layer is an important design parameter. This paper proposes a fuzzy online tuning method to adjust the boundary layer thickness for the best system performance without chattering. The method features the measurement of the chattering in the control signal. The paper validates the performance of the algorithm by experiments on a direct drive robot with a range of different payloads.

Piecewise-Smooth Dynamical Systems: Theory and Applications (M. di Bernardo, C.J. Budd, A.R. Champneys and P. Kowalczyk; 2008) [Book Review

This book deals with the analysis of bifurcation and chaos in nonsmooth (called piecewise smooth by the authors) dynamical systems. Some of the topics covered include: a very detailed study of discontinuity-induced bifurcations (DIBs) in nonsmooth maps and nonsmooth systems; limit-cycle bifurcations in vibro-impact systems; grazing bifurcations for periodic trajectories; the derivation of Poincare maps; the influence of chattering; and sliding mode systems. This book is a strong contribution to the field of bifurcation and chaos analysis and more generally to the field of nonsmooth dynamical systems analysis and will serve as a reference to specialists in the field.

Robust adaptive sliding mode control for a class of uncertain hybrid linear systems with Markovian jump parameters

Abstract The robust sliding mode control problem of a class of uncertain hybrid linear systems with Markovian jump parameters is considered. Under the assumption of unknown upper bounds matched system uncertainties, the sufficient conditions are proposed to guarantee exponentially stable in mean square of reduced-order sliding mode system. Under the conditions of unknown upper bounds of system uncertainties, adaptive robust sliding mode control law is proposed. The control methods guarantees that the trajectory of system arrives at the sliding surface in finite time interval and is kept here thereafter. It has been shown that the sliding mode control problem for the Markovian jump systems is solvable if a set of linear matrix inequalities(LMIs) have solution. Latsly a simulation is given to illustrate the effectiveness of the proposed approach.

Analysis of Closed-Loop Performance and Frequency-Domain Design of Compensating Filters for Sliding Mode Control Systems

For a sliding mode (SM) system containing parasitic dynamics, a model of chattering and a model of the averaged motions of the order equal to the original order of the system are obtained via the use of the locus of a perturbed relay system (LPRS) method. The latter model proves that the averaged motions in an SM system differ from those in the reduced-order model. In particular, such phenomena as the nonideal disturbance rejection and the nonideal input tracking are observed. It is shown that the non-reduced-order model transforms into the reduced one when the parasitic dynamics are removed. Yet, the chattering and the averaged motion - being the two components of the motion in the SM system - belong to two different frequency ranges (spectra). As a result, a frequency characteristic shaping aimed at achieving the desired frequency of chattering and enhancing the closed-loop performance becomes possible. This opportunity is explored in this paper. Examples that illustrate the proposed approach are provided.

Output-feedback second-order sliding-mode control of uncertain linear systems with relative degree 2

A new output-feedback sliding-mode control scheme is proposed to deal with a class of relative-degree-2 uncertain linear systems. The controller is composed of linear filters and a single relay, without any real-time differentiators employed. Based on a specific characteristic of singularly perturbed sliding-mode systems, robust stabilisation, disturbance attenuation and asymptotic output tracking are also realised. Simulations show the simplicity and efficiency of this method.

Modular design and testing for anti-lock brake actuation and control using a scaled vehicle system

A unique decoupling feature in frictional disk brake mechanisms, derived through kinematic analysis, enables modularised design of an Anti-lock Braking System (ABS) into a sliding mode system that specifies reference brake torque and a tracking brake actuator controller. Modelling of brake actuation, vehicle dynamics, and control design are described for a scaled vehicle system. The overall control scheme is evaluated by hardware-in-the loop testing of the electromechanical brake system, and experimental results for two braking scenarios illustrate the benefits of the modular control design scheme and its impact on practical hardware-in-the-loop implementation.

Author's reply [to comments on 'Research on estimating smoothed value and differential value by using sliding mode system'

The basic theoretical tool for a nonlinear filter estimating the smoothed value and the differential value from the data corrupted by impulsive noise at the ultrasonic sensors in our paper (Emaru and T. Tsuchiya, "Research on estimating smoothed value and differential value by using sliding mode system," IEEE Trans. Robot. Autom., vol. 19, no. 3, pp. 391-402, Jun. 2003) is the same as the theory proposed in the earlier paper by J. Q. Han and W. Wang (J. Q. Han and W. Wang, "Nonlinear tracking-differentiator" (in Chinese), J. Syst. Sci. Math. Sci., vol. 14, no. 2, pp. 177-183, 1994). Until now, we had not known the Journal of System Science and Mathematical Science (in Chinese), and had not read the paper listed in their comments. We should have cited their paper in our paper. We correct our failure of not citing their paper, and we sincerely apologize for our mistake.

Comments on "Research on estimating smoothed value and differential value by using sliding mode system"

This note shows that the basic theoretical tool used for smoothing data in the above paper is almost indistinguishable from the method presented in an earlier paper.

Analysis of Second-Order Sliding-Mode Algorithms in the Frequency Domain

A frequency domain analysis of the second-order sliding-mode algorithms, particularly of the twisting algorithm is carried out in the frequency domain with the use of the describing function method and Tsypkin's approach. It is shown that in the presence of an actuator, the transient process may converge to a periodic motion. Parameters of this periodic motion are analyzed. A comparison of the periodic solutions in the systems with higher order sliding-mode controllers and the oscillations that occur in classical sliding-mode systems with actuators is done.