Sliding Mode Function Research Articles

Sensorless Control for PMLSM Based on Fuzzy Sliding Mode Observer

In this paper, a new sensorless control method is proposed for a permanent magnet linear synchronous motor based on Fuzzy sliding mode observer, which combines the advantages of sliding mode observer and Fuzzy controller respectively. The difference between the current estimated value and the actual current value is regarded as sliding mode function; sliding mode function (current error) and variation of the error are used as the input of fuzzy controller, and the width of the boundary layer as the output, adjusting the width of the boundary layer dynamically in real time. The simulation results show that Fuzzy sliding mode observer is able to find a balance between soft chattering and steady-state error, keep the system robustness and control precision.

Sliding mode control based guidance law with impact angle constraint

The terminal guidance problem for an unpowered lifting reentry vehicle against a stationary target is considered. In addition to attacking the target with high accuracy, the vehicle is also expected to achieve a desired impact angle. In this paper, a sliding mode control (SMC)-based guidance law is developed to satisfy the terminal angle constraint. Firstly, a specific sliding mode function is designed, and the terminal requirements can be achieved by enforcing both the sliding mode function and its derivative to zero at the end of the flight. Then, a backstepping approach is used to ensure the finite-time reaching phase of the sliding mode and the analytic expression of the control effort can be obtained. The trajectories generated by this method only depend on the initial and terminal conditions of the terminal phase and the instantaneous states of the vehicle. In order to test the performance of the proposed guidance law in practical application, numerical simulations are carried out by taking all the aerodynamic parameters into consideration. The effectiveness of the proposed guidance law is verified by the simulation results in various scenarios.

Global Robust Sliding Mode Tracking Control for Helicopter with Input Time Delay

In this paper, a global sliding mode control scheme is proposed for a helicopter with input time delay and disturbance. We proposed a new method for integral sliding surface. By the design of dynamic nonlinear sliding mode function, the controller has the advantage of eliminating the reaching movement of traditional sliding mode control, overcoming the effect of the disturbance and time delay. The system state variables reached the sliding surface at the very beginning by means of designing a dynamic nonlinear sliding mode function, and moved to the expected state under the control of control law. The efficiency of the proposed method is demonstrated by simulation results.

The active disturbance rejection and sliding mode control approach to the stabilization of the Euler–Bernoulli beam equation with boundary input disturbance

In this paper, we are concerned with the boundary feedback stabilization of a one-dimensional Euler–Bernoulli beam equation with the external disturbance flowing to the control end. The active disturbance rejection control (ADRC) and sliding mode control (SMC) are adopted in investigation. By the ADRC approach, the disturbance is estimated through an extended state observer and canceled online by the approximated one in the closed-loop. It is shown that the external disturbance can be attenuated in the sense that the resulting closed-loop system under the extended state feedback tends to any arbitrary given vicinity of zero as the time goes to infinity. In the second part, we use the SMC to reject the disturbance by removing the condition in ADRC that the derivative of the disturbance is supposed to be bounded. The existence and uniqueness of the solution for the closed-loop via SMC are proved, and the monotonicity of the “reaching condition” is presented without the differentiation of the sliding mode function, for which it may not always exist for the weak solution of the closed-loop system. The numerical simulations validate the effectiveness of both methods.

A novel grasping force control strategy for multi-fingered prosthetic hand

A grasping force control strategy is proposed in order to complete various fine manipulations by using anthropomorphic prosthetic hand. The position-based impedance control and force-tracking impedance control are used in free and constraint spaces, respectively. The fuzzy observer is adopted in transition in order to switch control mode. Two control modes use one position-based impedance controller. In order to achieve grasping force track, reference force is added to the impedance controller in the constraint space. Trajectory tracking in free space and torque tracking in constrained space are realized, and reliability of mode switch and stability of system are achieved. An adaptive sliding mode friction compensation method is proposed. This method makes use of terminal sliding mode idea to design sliding mode function, which makes the tracking error converge to zero in finite time and avoids the problem of conventional sliding surface that tracking error cannot converge to zero. Based on the characteristic of the exponential form friction, the sliding mode control law including the estimation of friction parameter is obtained through terminal sliding mode idea, and the online parameter update laws are obtained based on Lyapunov stability theorem. The experiments on the HIT Prosthetic Hand IV are carried out to evaluate the grasping force control strategy, and the experiment results verify the effectiveness of this control strategy.

Variable Structure Control of the Brushless DC Motor

In order to increase the degree of the angular velocity tracking precision of the brushless DC motors control system, the controller is designed using the variable structure control with sliding mode. The mathematical model of the brushless DC motors is built. The sliding mode function includes tracking error and the differential coefficient of the tracking error. In order to alleviate the chattering, the saturation function replaces the sign function. The simulation result show the tracking precision is high and the controller output has not obvious chattering. The controller meets the tracking precision of he brushless DC motors control system.

Time-Varying Sliding Mode Control for Discrete-Time Nonlinear Uncertain Coupled Systems via Sliding Mode Prediction

In this paper, a novel time-varying sliding mode control (SMC) algorithm based on sliding mode prediction for a class of discrete-time nonlinear uncertain coupled systems is presented. After giving a kind of time-varying sliding mode function, a sliding mode prediction model is used to predict the future information of sliding mode. By employing feedback correction and receding horizon optimization approaches which are extensively applied in predictive control strategy, the desired discrete-time variable structure control law is obtained. Under the influence of uncertainties whose boundaries are unknown, the closed-loop systems are proofed to be robustly stable. Numerical simulation results illustrate that compared with conventional SMC method, under the algorithm proposed in this paper, chattering is eliminated, the control signals have smaller peak values, and the closed-loop system possesses stronger robustness.

Hybrid Terminal Sliding-Mode Observer Design Method for a Permanent-Magnet Synchronous Motor Control System

This paper proposes a hybrid terminal sliding-mode observer based on the nonsingular terminal sliding-mode (NTSM) and the high-order sliding-mode (HOSM) for the rotor position and speed estimation in the permanent-magnet synchronous motor control system. An NTSM manifold is utilized to realize both fast convergence and better tracking precision. In addition, a derivative estimator is used to obtain the derivative of the sliding-mode function. Meanwhile, an HOSM control law is designed to guarantee the stability of the observer and eliminate the chattering, so that smooth back-electromotive-force (EMF) signals can be obtained without a low-pass filter. According to the back-EMF equations, the rotor position and speed of the motor can be calculated. Simulation and experimental results are presented to validate the proposed method.

ZOH Discretization Effect on Higher-Order Sliding-Mode Control Systems

In this paper, the zeroth-order-hold (ZOH) discretization of higher-order sliding-mode control (SMC) systems is studied. The equivalent control-based SMC systems with a relative degree higher than one are first formulated into a canonical form which is easy for control design. Theoretical results for the ZOH-discretized SMC systems with a relative degree higher than one are given, including estimates of the bounds of steady states and higher-order sliding-mode functions, as well as periodic properties of the trajectories. Simulation results of a vehicle suspension system are presented to show the effectiveness of the analysis and theoretical results.

On ZOH Discretization of Higher-Order Sliding Mode Control Systems

In this paper, the zero-order-hold (ZOH) discretization of higher-order sliding mode control (SMC) systems is studied. The equivalent control based SMC systems with relative degree higher than one is first formulated into a canonical form which is easy for control design. Theoretical results for the ZOH-discretized SMC systems with relative degree higher than one are given, including accurate estimates of the bounds of steady states and higher order sliding mode functions. Simulation results are presented to show the effectiveness of the analysis.

SLIDING MODE PREDICTION TRACKING CONTROL DESIGN FOR UNCERTAIN SYSTEMS

ABSTRACTIn this paper, a tracking control algorithm based on sliding mode prediction for a class of discrete‐time uncertain systems is presented. By creating a special model to predict the future sliding mode function value and by combining feedback correction and receding horizon optimization approaches, which are extensively applied in predictive control strategy, a discrete‐time sliding mode control law for tracking problem is constructed. With the designed control law, closed‐loop systems have strong robustness to matched or unmatched uncertainties as they eliminate chattering. Besides, in the robustness analysis, the boundary condition for uncertainties, which is a universal presupposition in sliding mode control method, is not required. Numerical simulation and cart‐pendulum experiment results illustrate the validity of the proposed algorithm.

Second-order terminal sliding mode control of uncertain multivariable systems

A second-order terminal sliding mode controller for uncertain multivariable systems is proposed in this paper. The controller adopts the hierarchical control structure. The paper derives the state transform matrices which are used to transform a multivariable linear system to the block controllable form consisting of two subsystems, an input–output subsystem and a stable internal dynamic subsystem. The proposed controller utilizes a non-singular terminal sliding mode manifold for the input–output subsystem to realize fast convergence and better tracking precision. Meanwhile, a chattering-free second-order terminal sliding mode control law is presented. The stability of uncertain multivariable systems can be realized using the proposed controller. A derivative estimator is utilized in the paper to estimate the derivatives of the sliding mode functions for the controller. The simulation results are presented to validate the design method.

Internal Model and Saturating Actuation in Human Operation From View of Human-Adaptive Mechatronics

Human-adaptive mechatronics (HAM) is the area of mechatronics which adapts to the operator skill and assists its improvement. The analysis of human control action is one of the fundamental problems in the study of HAM. A special feature of human control action is the action being saturated with respect to the amplitude and velocity. At the same time, the human does not pay attention continuously to the response but intermittently scans and gets the information. In this paper, the continuous control action based on the scanned information is studied, and the desired trajectory of the human control action is considered to be generated by the closed-loop system including the internal model in the feedback path. Since the visual information is scanned intermittently, the closed-loop reference generator is considered as a sampled-hold system. The feedforward function of the cerebellum can be interpreted as the reference generator with a long scanning interval for the skilled operation. The saturating control action causing the pilot-induced oscillation is studied by taking the swing-up control of a single pendulum from the pendant to the upright position as an example. The two swing-up control laws are studied for reachability of the unstable nonlinear pendulum. One is the linear combination of sine function of the position and angular velocity, and the other is the variable-structure control for the sliding-mode function similar to the linear combination control law. The reachability is analyzed successfully by the color map.

Elimination of the Stator Resistance Sensitivity and Voltage Sensor Requirement Problems for DFO Control of an Induction Machine

This paper focuses on a method for achieving robust direct field orientation control of an induction machine using a closed-loop voltage model flux observer that is insensitive to stator resistance variation and does not require voltage signal information, thereby eliminating the need for a voltage sensor. In contrast, the conventional voltage model observer topology requires voltage sensors and is highly sensitive to stator resistance variation, especially at low speed. The closed-loop sliding-mode voltage model flux observer presented here is based on current estimation error including a sliding-mode function which is a derivative of the stator flux. The newly designed sliding-mode function will not only drive the estimated current to the measured one, it will also directly give the estimation results for the terms (stator flux) replaced by the sliding-mode function. The constructed observer and chosen sliding-mode function also do not require information about parameters contained in the terms replaced by the sliding-mode function, i.e., voltage signal and stator resistance. The observer stability is verified in the paper. Simulation and experimental results are also used to illustrate features of the proposed observer.

A new current model flux observer for wide speed range sensorless control of an induction machine

A new closed loop current model flux observer is designed to estimate the rotor flux, position and velocity of an induction machine. The current observer includes carefully designed sliding mode functions which are derivative of the fluxes along the /spl alpha/ and /spl beta/ axes. Therefore, when the estimated current converges to the measured one, the flux estimation is a mere integration of the sliding mode function. The rotor speed can then be derived from the sliding mode functions and the estimated flux. In the current and flux observers all of the terms that contain the rotor time constant and the rotor speed have been replaced by the sliding mode functions, thus making the proposed current and flux estimations completely insensitive to the rotor time constant variation and any error in the estimated speed. Simulations and experiments are performed under a variety of conditions to validate the effectiveness of the proposed algorithm.

Chattering-free sliding modes in robotic manipulators control

SummaryIn this paper sliding mode motion design is considered for nonlinear plants which are linear with respect to control input. The dynamics of the robotic manipulators is treated with and without those of the actuators. When the dynamics of the actuators is included a design of the sliding modes for the systems with discontinuous control is performed. If actuators' dynamics is negelected the control is assumed to be continuous quantity. By combining the variable structure systems and Lyapunov designs a new algorithm is developed which has all the good properties of the sliding mode systems while avoiding unnecessary discontinuity of the control thus eliminating chattering. Neither the explicit calculation of the equivalent control, nor high gain inside the boundary layer are used. The parameters of the control depend on the plant's gain matrix, and the gradients of the sliding mode manifold. This control method is then applied to develop a unified control strategy for the motion control systems including the path tracking control, the impedance control and the force control of a robotic manipulator. It is shown that all these tasks can be formulated in the same mathematical form in which selected so-called sliding mode functions must track their references. In this way the systems state is forced to remain on the selected manifold in the state space after reaching it. The solution is interpreted in both the Joint space and the Work space for n -degrees of freedom robotic manipulators.

An Algorithm for Robust Tracking Control of Robots

SUMMARYBased on the Lyapunov theory, a new principle was developed for synthesizing robot tracking control in the presence of model uncertainties. First, a general Lyapunov-like robust tracking concept is presented. It is then used as a basis for the control algorithm derived via a quadratic Lyapunov function constructed using a sliding mode function (based on the output error). Control synthesis is made in task-space, without any need for solving the inverse kinematics problem, i.e. one does not need to inver the Jacobian matrix. It is also shown that the tracking error becomes close to zero in a settling time which is less than a prescribed finite time. Simulation results are incorporated.

Robust Tracking Control for Robots Using the Sliding Mode. A Task-Space Approach

Based on the Lyapunov theory, a new principle of synthesizing robot tracking control in the presence of model uncertainties has been developed. We propose a control algorithm which assures desired tracking performances in a presence of model uncertainties. Uncertainties can be in a structure or/and in parameters of a model of a robot. We have defined a sliding surface based on the output error and a quadratic Lyapunov function has been constructed using a sliding mode function. Then the tracking problem is changed to that of staying in the neighborhood of the sliding surface (or keeping Lyapunov function close to zero). Control synthesis has been made in task-space, without meeting the inverse kinematics problem (no need to invert the Jacobian matrix). It is guaranteed that the tracking error becomes close to zero in a settling time which is less than a prescribed finite time. Simulation results are incorporated.