Linear Sliding Mode Control Research Articles

Aircraft pitch control tracking with sliding mode control

Sliding mode control (SMC) is one of the robust and nonlinear control methods. An aircraft flying at high angles of attack is considered nonlinear due to flow separations, which cause aerodynamic characteristics in the region to be nonlinear. This paper presents the comparative assessment for the flight control based on linear SMC and integral SMC implemented on the nonlinear longitudinal model of a fighter aircraft. The controller objective is to track the pitch angle and the pitch rate throughout the high angles of attack envelope. Numerical treatments are carried out on selected conditions and the controller performances are studied based on their transient responses. Obtained results show that both SMCs are applicable for high angles of attack.

Quadratic Integral Sliding Mode Control for Nonlinear Harmonic Gear Drive Systems with Mismatched Uncertainties

For a class of nonlinear harmonic gear drive systems with mismatched uncertainties, a novel robust control method is presented on the basis of quadratic integral sliding mode surface, and the closed-loop system has satisfying performance and strong robustness against mismatched uncertainties and nonlinear disturbances. Considering time-varying nonlinear torques and parameters variations which are caused by nonlinear frictions and backlash, a nonlinear harmonic gear drive system mathematic model is established and the effect of nonlinear parts is compensated during control system design. It is proven that the quadratic integral sliding mode surface can be reached in finite time and the closed-loop system is asymptotic stable robustly. The simulation studies are carried out in comparison with traditional linear sliding mode control and integral sliding mode control, verifying the effectiveness of the proposed method.

Adaptive-gain fast nonsingular terminal sliding mode for position control of a piezo positioning stage

This article proposed a variable gain fast terminal sliding mode controller with an estimator of the uncertainty model for a piezo positioning stage system. The designed terminal sliding mode control has some advantages over the linear sliding mode control such as fast convergence and chattering reduction while maintains its robustness to the uncertainties. Next, an indirect technique is developed to enable the elimination of the singularity problem corresponding to initial terminal sliding mode control. In addition, a cerebellar model articulation controller is carried out to estimate the nonlinear dynamics of the piezo positioning stage. To deal with unknown bounds of uncertainties and disturbances, the proposed scheme consists of using online tuning control gains that ensure the establishment of a real terminal sliding mode in a finite time. Moreover, a fuzzy logic scheme is presented to smooth out the discontinuity part of the control signal, hence improve the control performance. Stability analysis of closed loop system is provided using the Lyapunov function method. Experiment results are presented to evaluate the effectiveness of the designed control approach.

Coupled Dynamic Control of Unicycle Robot Using Integral Linear Quadratic Regulator and Sliding Mode Controller

Unicycle robot is a non-linear, unbalance system that has the less number of point contact to the ground, therefore it is a best platform for researchers to study balance control and motion. This paper focuses on the dynamic modeling and control of unicycle robot. A coupled nonlinear system dynamics is considered for the controller design. Two different controllers are proposed –integral LQR for pitch dynamics and integral sliding mode for roll dynamics. Simulations performed on MATLAB/SIMULINK platform proved the effectiveness of the proposed controllers.

Non-linear sliding mode load frequency control in multi-area power system

This paper addresses non-linear sliding mode controller (SMC) with matched and unmatched uncertainties for load frequency control (LFC) application in three-area interconnected power system. In conventional LFC scheme, as the nominal operating point varies due to system uncertainties, frequency deviations cannot be minimized. These lead to degradation in the dynamic performance or even system instability. In this paper, an effective control law is proposed against matched and unmatched uncertainties.. The proposed controller has ability to vary closed-loop system damping characteristics according to uncertainties and load disturbances present in the system. The frequency deviation converges to zero with minimum undershoot/overshoot, fast settling time, significantly reduced chattering and ensures asymptotic stability. In addition, the controller is robust in the presence of parameter uncertainties and different disturbance patterns. It also guarantees high dynamic performance in the presence of governor dead band (GDB) and generation rate constraint (GRC). Simulations are performed to compare the proposed controller with linear SMC. Using proposed control strategy, undershoot/overshoot and settling time gets reduced by approximately 30% with respect to linear SMC. The computed performance indices and qualitative results establish the superiority as well as applicability of the proposed design for the LFC problem. Further, the proposed controller scheme is validated on IEEE 39 bus large power system.

Decoupled Dynamic Control of Unicycle Robot Using Integral Linear Quadratic Regulator and Sliding Mode Controller

Unicycle robot is a non-holonomic, non-linear, static unbalance system that has the minimal number of point contact to the ground, therefore it is a perfect platform for researchers to study motion and balance control. This paper focuses on the dynamic modeling of unicycle robot. Two concepts used for modeling unicycle robot are: reaction wheel pendulum and inverted pendulum. The pitch axis is modeled as inverted pendulum and roll axis is modeled as reaction wheel pendulum. The unicycle yaw dynamics is not considered which makes derivation of dynamics relatively simple. For the roll controller, sliding-mode controller has been adopted and optimal methods are used to minimize switching-function chattering. For pitch controller, a Linear Quadratic Regulator controller has been implemented to drive the unicycle robot to follow the desired velocity trajectory.

Adaptive backstepping-based NTSM control for unmatched uncertain nonlinear systems

An adaptive backstepping-based non-singular terminal sliding mode (NTSM) control method is proposed for a class of uncertain nonlinear systems in the parameteric-strict feedback form. The adaptive control law is combined with the first n−1 steps of the backstepping method to estimate the unknown parameters of the system. In the nth step, an NTSM control strategy is utilized to drive the last state of the system to converge in a finite time. Furthermore, the derivate estimator is used to obtain the derivates of the states of the error system; the higher-order non-singular terminal sliding mode control (HONTSMC) law is designed to eliminate the chattering and make the system robust to both matched and unmatched uncertainties. Compared to the adaptive backstepping-based linear sliding mode control method (LSMC), the proposed method improves the convergence rate and the steady-state tracking accuracy of the system, and makes the control signal smoother. Finally, the compared simulation results are presented to validate the method.

A Nonlinear Sliding Mode Controller for IPMSM Drives with an Adaptive Gain Tuning Rule

This paper presents a nonlinear sliding mode control (SMC) scheme with a variable damping ratio for interior permanent magnet synchronous motors (IPMSMs). First, a nonlinear sliding surface whose parameters change continuously with time is designed. Actually, the proposed SMC has the ability to reduce the settling time without an overshoot by giving a low damping ratio at the initial time and a high damping ratio as the output reaches the desired setpoint. At the same time, it enables a fast convergence in finite time and eliminates the singularity problem with the upper bound of an uncertain term, which cannot be measured in practice, by using a simple adaptation law. To improve the efficiency of a system in the constant torque region, the control system incorporates the maximum torque per ampere (MTPA) algorithm. The stability of the nonlinear sliding surface is guaranteed by Lyapunov stability theory. Moreover, a simple sliding mode observer is used to estimate the load torque and system uncertainties. The effectiveness of the proposed nonlinear SMC scheme is verified using comparative experimental results of the linear SMC scheme when the speed reference and load torque change under system uncertainties. From these experimental results, the proposed nonlinear SMC method reveals a faster transient response, smaller steady-state speed error, and less sensitivity to system uncertainties than the linear SMC method.

Decoupling control based on terminal sliding mode and wavelet network for the speed and tension system of reversible cold strip rolling mill

To weaken the nonlinear coupling influences among the variables in the speed and tension system of reversible cold strip rolling mill, a novel dynamic decoupling control strategy is proposed based on nonsingular fast terminal sliding mode (NFTSM) and wavelet neural network (WNN). First, nonlinear disturbance observers are developed to counteract the mismatched uncertainties, and then input/output dynamic decoupling and linearisation for the speed and tension nonlinear coupling system are realised by utilising the inverse system theory. Second, nonsingular fast terminal sliding mode controller (NFTSMC) for each pseudo linear subsystem is presented based on backstepping and two-power reaching law, so as to improve the global convergence speed and robust stability of the system. Third, adaptive WNNs are used to approximate the uncertain items of the system, so as to improve the control precision of the speed and tension of reversible cold strip rolling mill. Theoretical analyses show that the NFTSMs satisfy reachability condition, the system error variables can converge to equilibrium point in finite time, and the resulting closed-loop system is globally asymptotically stable. Finally, simulation research is carried out on the speed and tension system of a 1422 mm reversible cold strip rolling mill by using the actual data, and results show the superiority of the proposed control strategy in comparison with the strategies of cascade PI, linear sliding mode control and internal model control.

Discrete-Time Terminal Sliding Mode Control Systems Based on Euler's Discretization

In this technical note, the dynamical behaviors of discrete-time terminal sliding mode control systems based on Euler's discretization is investigated. Based on a recursive analysis, the boundedness for the steady states of the system is established. Theoretical analysis shows that the discrete-time terminal sliding mode control method can offer a higher output tracking precision than the discrete-time linear sliding mode control method. Simulations are given to verify the theoretical results.

Evaluation Performance of IC Engine: Linear Tunable Gain Computed Torque Controller vs. Sliding Mode Controller

Design a nonlinear controller for second order nonlinear uncertain dynamical systems (e.g., internal combustion engine) is one of the most important challenging works. This paper focuses on the comparative study between two important nonlinear controllers namely; computed torque controller (CTC) and sliding mode controller (SMC) and applied to internal combustion (IC) engine in presence of uncertainties. In order to provide high performance nonlinear methodology, sliding mode controller and computed torque controller are selected. Pure SMC and CTC can be used to control of partly known nonlinear dynamic parameters of IC engine. Pure sliding mode controller and computed torque controller have difficulty in handling unstructured model uncertainties. To solve this problem applied linear error-based tuning method to sliding mode controller and computed torque controller for adjusting the sliding surface gain ( ) and linear inner loop gain ( ). Since the sliding surface gain ( ) and linear inner loop gain ( ) are adjusted by linear error-based tuning method. In this research new and new are obtained by the previous and multiple gains updating factor . The results demonstrate that the error-based linear SMC and CTC are model-based controllers which works well in certain and uncertain system. These controllers have acceptable performance in presence of uncertainty.

Discrete‐time based sliding‐mode control of robot manipulators

PurposeThe purpose of this paper is to develop sliding mode control with linear and nonlinear manifolds in discrete‐time domain for robot manipulators.Design/methodology/approachFirst, a discrete linear sliding mode controller is designed to an n‐link robot based on Gao's reaching law. In the second step, a discrete terminal sliding mode controller is developed to design a finite time and high precision controller. The stability analysis of both controllers is presented in the presence of model uncertainties and external disturbances. Finally, sampling time effects on the continuous‐time system outputs and sliding surfaces are discussed.FindingsComputer simulations on a three‐link SCARA robot show that the proposed controllers are robust against model uncertainties and external disturbance. It was also shown that the sampling time has important effects on the closed loop system stability and convergence.Practical implicationsThe proposed controllers are low cost and easily implemented in practice in comparison with continuous‐time ones.Originality/valueThe novelty associated with this paper is the development of an approach to finite time and robust control of n‐link robot manipulators in discrete‐time domain. Also, obtaining an upper bound for the sampling time is another contribution of this work.

Comparison between Direct Control Method and Indirect Control Method of Non Linear Sliding Mode Controller for DC-DC Buck Converter

Comparison between Direct Control Method and Indirect Control Method of Non Linear Sliding Mode Controller for DC-DC Buck Converter

Dual-quaternion-based finite-time control for spacecraft tracking in six degrees of freedom

This article investigates the tracking control problem for the six-degree-of-freedom motion of a follower spacecraft relative to a leader spacecraft. Employing dual quaternion representation, the model of the six-degree-of-freedom relative motion between the two spacecraft is derived. Taking into account the model uncertainties and external disturbances, two robust fast sliding mode control laws are proposed to guarantee the finite-time convergence of the tracking errors, where the second control law can solve the dual-equilibrium problem that exists in the first one. In order to alleviate chattering phenomenon, continuous saturation function is introduced into the controller and a softening control strategy is developed. It is worth pointing out that the convergence rate of the proposed fast sliding mode control is faster than that of the linear sliding mode control and terminal sliding mode control. Finally, numerical simulations are performed to demonstrate the effectiveness of the proposed approaches.

Neural-Network-Based Terminal Sliding-Mode Control of Robotic Manipulators Including Actuator Dynamics

A neural-network-based terminal sliding-mode control (SMC) scheme is proposed for robotic manipulators including actuator dynamics. The proposed terminal SMC (TSMC) alleviates some main drawbacks (such as contradiction between control efforts in the transient and tracking errors in the steady state) in the linear SMC while maintains its robustness to the uncertainties. Moreover, an indirect method is developed to avoid the singularity problem in the initial TSMC. In the proposed control scheme, a radial basis function neural network (NN) is adopted to approximate the nonlinear dynamics of the robotic manipulator. Meanwhile, a robust control term is added to suppress the modeling error and estimate the error of the NN. Finite time convergence and stability of the closed loop system can be guaranteed by Lyapunov theory. Finally, the proposed control scheme is applied to a robotic manipulator. Experimental results confirm the validity of the proposed control scheme by comparing it with other control strategies.

A Two-Level Approach to Fault-Tolerant Control of Distributed Systems based on the Sliding Mode

A new approach to Fault-Tolerant Control (FTC) of distributed and interconnected systems is proposed based on applying sliding mode control (SMC) to the subsystems of a level de-centralised and hierarchical scheme. The SMC approach involves a new optimal control strategy for the design of local sliding functions for the subsystem controllers, replacing the conventional approach based on constrained locally linear LQ receding horizon control. The linear SMC gains handle the reachability for the sliding surfaces and the interaction effects from subsystem interconnections as well as small fault effects (i.e. giving passive fault-tolerance), whilst the non-linear (discontinuous) SMC gains facilitate a powerful way of accounting for larger but bounded system non-linearities and faults and can fulfill the role of an active FTC scheme. The local and global performance constraints are retained and implemented under autonomous learning supervision via the interaction-prediction principle. The scheme for an Autonomous Control and Supervision System (ACSS) is described that is capable of learning its coordination function and carrying out fault-tolerant balancing of the distributed system. The paper describes how the two-level learning strategy offers advantages over single-level FTC distributed SMC. The design concepts are illustrated using a non-linear 3-tank liquid level and heating control system with component faults

DESIGN AND IMPLEMENTATION OF ROBUST CONTROL CONCEPTS μ-SYNTHESIS AND SLIDING MODE CONTROL

This paper presents the investigation results and a controller implementation example of modern robust control concepts: non linear sliding mode control and linear model-based μ-synthesis control. The performed steps for successful controller implementation on a real milling machine control unit are described. Experimental results are presented and compared with state of the art technologies.

Terminal sliding mode control for rigid robots

This paper presents a new design of terminal sliding mode control for n-link rigid robot manipulators. By exploring thoroughly some properties of robot manipulators, the proposed scheme simplifies significantly the controller designs given in Venkataraman and Gulati (1989) and Man et al. (1994). Compared to the linear sliding mode control, the main features of this terminal sliding mode control are the reduced tracking error in the steady state and reduced control efforts in the transient state. Experiment results are included to show the performance of the proposed controller.

A robust MIMO terminal sliding mode control scheme for rigid robotic manipulators

In this paper, a robust multi-input/multi-output (MIMO) terminal sliding mode control technique is developed for n-link rigid robotic manipulators. It is shown that an MIMO terminal switching plane variable vector is first defined, and the relationship between the terminal switching plane variable vector and system error dynamics is established. By using the MIMO terminal sliding mode technique and a few structural properties of rigid robotic manipulators, a robust controller can then be designed so that the output tracking error can converge to zero in a finite time, and strong robustness with respect to large uncertain dynamics can be guaranteed. It is also shown that the high gain of the terminal sliding mode controllers can be significantly reduced with respect to the one of the linear sliding mode controller where the sampling interval is nonzero. >