Discrete-time Sliding Mode Control Algorithm Research Articles

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.

Comparison of discrete-time sliding mode control algorithms for seismic control of buildings with magnetorheological fluid dampers

Semi-active control implementations for structures are gaining considerable attention in civil engineering. This paper presents a method for the design and implementation of the discrete-time sliding mode controller with a hybrid control strategy, based on Gao’s reaching law and the variable rate reaching law, for practical applications in civil structures by using magnetorheological (MR) dampers. The structure is modeled as a five-degree-of-freedom lumped mass system, controlled by an MR damper placed in between the ground and the first floor. The MR damper is experimentally tested and its behavior is represented by using modified Bouc–Wen model and artificial neural network (ANN) as forward and inverse models, respectively. The five-story building is simulated under the seismic excitation of El Centro earthquake along with the historical earthquake records, Northridge and Kobe. It is demonstrated that the hybrid control strategy yields better results regarding the energy consumption of the controller and time-averaged structural responses by eliminating the chattering, compared to Gao’s controller.

Input-decoupled discrete-time sliding mode control algorithm for servo multi-field multi-armature DC machine

The multivariable modeling of a servo actuating system consisting of multi-field multi-armature direct current (MFMADC) machine is extracted and a novel discrete time nonlinear algorithm is proposed for the corresponding system. The proposed control algorithm demonstrates robustness against modeling uncertainty and by utilizing its novel mathematical structure, decouples the dynamical interactions of the connected motors. The main contribution of this paper is the proposition of a new decoupling control algorithm that in which, the driving (commanding) voltages of the connected driving motors are extracted separately and independently using the Lyapunov principle in discrete time. In fact, the obtained coupled stabilizing convex inequalities of the controlling voltages, resulting from the evaluation of the Lyapunov functions, are analytically decoupled using elementary matrix operations. Consequently, each motor now has the capability to perform its controlling task (position control or torque control) with asymptotic stability and robustness against uncertainty. To assess the performance of the proposed controlling algorithm and its verification, a MFMADC machine is attached to a harmonic drive reducer (HDR) whose flex spline and circular spline are fabricated using viscoelastic polyesters PLA and thermoplastic PLA, respectively. A number of experiments are conducted where in the first test, the MFMADC is controlled in only-position mode while in the second test, the MFMADC is controlled in simultaneous position-torque control mode. Comparative assessments confirm that the MFMADC technology is needed when a high precision tracking of position, under high frequency disturbances, is desired.

Piezoelectric Nanopositioning Control Using Second-Order Discrete-Time Terminal Sliding-Mode Strategy

This paper presents the design of a novel second-order discrete-time terminal sliding-mode control (2-DTSMC) strategy and its application to motion tracking control of a piezoelectric nanopositioning system, which possesses a high-order plant model. The 2-DTSMC strategy is established based on the output feedback only, which eliminates the use of a state observer and facilitates an easy realization. Theoretical analysis proves that the quasi-sliding mode is reached in finite time along with high accuracy of the output tracking. The effectiveness of the proposed control scheme is validated through comparative investigations. Experimental results show that the 2-DTSMC strategy is superior to traditional discrete-time sliding-mode control (DSMC), second-order DSMC, and DTSMC algorithms in terms of motion tracking accuracy, which demonstrates the efficiency of the reported 2-DTSMC scheme with a second-order nonlinear sliding surface.

Enhanced discrete‐time sliding mode strategy with application to piezoelectric actuator control

This study presents a new discrete-time sliding mode control (DSMC) scheme with applications to precise motion control of piezoelectric actuators. Different from existing DSMC algorithms whose implementations rely on the construction of state observers for providing the state feedback, a simple yet effective DSMC strategy is developed based on a discrete-time model without using the state observer. Hence, one distinctive feature of the proposed DSMC lies in that it is very easy to implement. Only a second-order plant model is needed whereas the modelling of piezoelectric non-linearities is not required, which further simplifies the practical implementation process. The local stability of the closed-loop system is proved in theory and the effectiveness of the DSMC is demonstrated by several experimental studies. Results show that the DSMC strategy is superior to proportional-integral-derivative control in terms of transient response speed, positioning accuracy and robustness against external disturbances. The reported method can be extended for precise motion control of other second-order systems as well.

Precision Position/Force Interaction Control of a Piezoelectric Multimorph Microgripper for Microassembly

Precision position and force control is a critical issue for automated microassembly systems to handle micro-objects delicately. This paper presents two new approaches to regulating both position and contact force of a piezoelectric multimorph microgripper dedicated to microassembly tasks. One of the advantages of the proposed approaches lies in that they are capable of controlling the position and contact force of a gripper arm simultaneously. The methodology is easy to implement since neither a state observer nor a hysteresis model of the system is required. The first approach is a position-based sliding mode impedance control which converts the target impedance into a desired position trajectory to be tracked, and the second one is established on the basis of a proportional-integral type of sliding function of the impedance measure error. Their tracking performances are guaranteed by two devised discrete-time sliding mode control algorithms, whose stabilities in the presence of model uncertainties and disturbances are proved in theory. The effectiveness of both schemes are validated by experimental investigations on a glass microbead gripping task. Results show that both approaches are capable of accomplishing promising interaction control accuracy.

Discrete-Time Sliding Mode Control for Robot Manipulators

In the real-field of control cases for robot manipulators, there always exists a modeling error, which results the model has the uncertainties in its parameters and/or structure. In many modem applications, digital computers are extensively used to implement control algorithms to control such systems. The discretization of the nonlinear dynamic equations of such systems results in a complicated discrete dynamic equations. Therefore, it will be difficult to design a discrete-time controller to give good tracking performances in the presence of certain uncertainties. In this paper, a discrete-time sliding mode control algorithm for nonlinear and time varying robot manipulators with uncertainties is presented. Sufficient conditions for guaranteeing the convergence of the discrete-time SMC system are derived. As example simulations, the proposed SMC algorithm is applied to a two-link robotic manipulator with unknown dynamics. The results of the simulation indicate that the developed control scheme is effective in manipulators and electro-mechanical system control.

Improved Discrete-Time Sliding-Mode Position Control Using Euler Velocity Estimation

This paper presents a design of digitally controlled positional systems with Euler velocity estimation within the framework of the discrete-time sliding mode (DSM). The effects of quantization and simple velocity estimation on DSM quality are analyzed. It is shown that the introduced and amplified quantization noise degrades sliding motion into the quasi-sliding mode and threatens to provoke chattering. Furthermore, a new DSM control algorithm is proposed, featuring a two-scale reaching law and a supplemental integral action. This algorithm avoids chattering and provides excellent performance. The developed DSM controller has been experimentally tested in an induction motor position control.

Discrete-time sliding mode control for MR vehicle suspension system

This paper presents control performance of a full-vehicle suspension system featuring magnetorheological (MR) dampers via a discrete-time sliding mode control algorithm (DSMC). A cylindrical MR damper is designed by incorporating Bingham model of the MR fluid and the field-dependent damping characteristics of the MR damper are evaluated. A full-vehicle suspension model installed with independent four MR dampers is constructed and the governing equations which include vertical, pitch and roll motion are derived. A discrete-time control model is established with considering system uncertainties and a discrete-time sliding mode controller which has inherent robustness to model uncertainty and external disturbance is formulated. Vibration control performances under bump excitation are evaluated and presented.