Classical Sliding Mode Control Research Articles

Integration of PD-type Iterative Learning Control with Adaptive Sliding Mode Control

Proportional-Derivative type Iterative Learning Controller (PD-ILC) is combined with an Adaptive Sliding Mode Controller (ASMC) using a plug-in structure to a rotary pendulum. The ASMC adaptation law is used to update a switching gain of sliding surface in Sliding Mode Control (SMC) controller. The proposed hybrid controller stability and convergence are mathematically shown and then experimentally demonstrated using two-degree-of-freedom (2-DOF) Quanser© QUBETM Servo 2 Rotary Pendulum. Results illustrate that adaptation law helps the controllers to achieve higher accuracy tracking performance compared to the classic SMC controller. Based on the experimental results, the hybrid control of PD-ILC and ASMC has faster and more accurate tracking results than ILC controller indicating the combined controller has better performance than the individual controllers.

Sliding Mode Control For Heartbeat Electrocardiogram Tracking Problem

In this paper, we have exploited the first-order sliding mode control method to track the ECG data of the human heart by three different nonlinear control laws. In order to lessen the intrinsic chattering of the classic sliding mode control system, smooth function approximations of the control input, by means of the hyperbolic tangent and the saturation function, were used. The fast Fourier transform was used to evaluate the average chattering frequency of the control inputs. The synthesized control schemes namely SMC-sign, SMC-tanh, and SMC-sat, were able to track the real-world ECG signal with an average root mean square error of 0.0306 and a chattering frequency of 92.7 Hz. The findings show that the sliding mode controllers can be implemented in electronic artificial pacemakers to provide the intended results successfully. Based on today's electronics, the involved frequency range (556.4 Hz for the worst case) is quite acceptable and practical.

A study of stability and power consumption of electric vehicles using different modern control strategies

This research paper aims at applying modern control techniques to study the stability and power consumption of electric vehicles. The main purpose is to propose an artificial neural network controller to estimate the direct yaw moment required for stabilizing the dynamics of electric vehicles with four in-wheel motors. Only one state variable, that can be measured using a cheap and standard sensor, is used to define the error signal for the controller. The algorithm of equality-constrained quadratic program is used to split the estimated yaw moment onto the four in-wheel motors. The neural network controller is trained using data obtained from fuzzy logic controller. In addition, the classical sliding mode control is applied for the sake of comparison. Simulation results prove that in comparison to classical controller, the mentioned modern controller provides better stability of the electric vehicle's lateral dynamics and lower usage of electric power for the motors.

Fast Terminal Sliding-Mode Control with an Integral Filter Applied to a Longitudinal Axis of Flying Vehicles

The automatic pilot flight control system is undoubtedly one of the most important parts of the flying vehicle that provide stability and to operate appropriately in the guidance section. Considering to nonlinear, dynamic and time-varying system, structural and parametric uncertainties of the flying vehicles, in flight control, varietal control approach have to achieve stability, proper operation as well as decreasing effect of uncertainties and modeling errors. In this paper, designing of the longitudinal flying vehicles autopilot a Fast Terminal Sliding Mode Control (FTSMC). Variable structure systems because of the robustness effect on uncertainty and the effects on disturbances which a contributor to widespread efficiency. One of the methods for controlling the variable structure is a sliding mode, which is one of the nonlinear controllers that can control the system in the structured uncertainties and unstructured uncertainties. Additionally, in the method of classic sliding Mode Control is got convergence of states equilibrium point by an asymptotic curve. While proportional Integral Sliding Mode Control has the convergence of states to the equilibrium point in finite time. One of the issues is that finite time cannot determine the time of convergence when the state turn initial position to a final position. The proposed method is based on the Lyapunov stability theory and has guaranteed stability of the control system. The controller is robust to external disturbances and unmodified dynamics. Three types of controllers which are multi-input-multi-output (MIMO) system with random uncertainty are designed. Furthermore, the classic sliding mode controller, the proportional-integral sliding mode controller as well as the integral terminal sliding mode controller are reviewed. A glance at the results simulates shows an improved in the proposed method. Simulations are done using MATLAB software.

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In most electro-mechanical systems, robust controller design is an important issue to deal with various uncertainties including external disturbances. The sliding mode control is widely known as a robust control technique for many practical control applications. In applying classical sliding mode techniques, however, the chattering phenomenon caused by switching operation is a main factor that deteriorates the control performance. To achieve the desired control performance with a relatively low switching function gain, this paper presents a robust position controller for a class of mechanical systems under parameter uncertainties and an external disturbance by using an integral sliding mode controller combined with a sliding mode disturbance observer. The sliding mode controller is adopted to reduce the steady state error. The sliding mode disturbance observer is designed to estimate the relatively slowly varying part in an equivalent disturbance. The control objective can be achieved with a relatively low switching function gain by compensating the disturbance through the proposed sliding mode disturbance observer that constructed without using the switching control input. To verify the performance of the proposed controller, comparative computer simulations are carried out with classical sliding mode controllers for a position control system. The control performance of the proposed controller is confirmed through analysis of the simulation results.

Robust adaptive backstepping fast terminal sliding mode controller for uncertain quadrotor UAV

The problem of controlling the quadrotor orientation and position is considered in the presence of parametric uncertainties and external disturbances. Previous works generally assume that the flight controller parameters are constants. In reality, these parameters depend on the desired trajectory. In this article, a complete mathematical model of a quadrotor UAV is presented based on the Euler-Newton formulation. A robust nonlinear fast control structured for the quadrotor position and attitude trajectory tracking is designed. The position loop generates the actual thrust to control the altitude of the quadrotor and provides the desired pitch and roll angles to the attitude loop, which allow the control of the quadrotor center of gravity in the horizontal plane. The attitude loop generates the rolling, pitching and yawing torques that easily allow the insurance of the quadrotors stability. The outer loop (position loop) uses the robust adaptive backstepping (AB) control to get the desired Euler-angles and the control laws. The inner loop (attitude loop) employs a new controller based on a combination of backstepping technique and fast terminal sliding mode control (AB-ABFTSMC) to command the yaw angle and the tilting angles. In order to estimate the proposed controller parameters of the position and the upper bounds of the uncertainties and disturbances of the attitude, online adaptive rules are proposed. Furthermore, the Lyapunov analysis is used to warranty the stability of the quadrotor UAV system and to ensure the robustness of the controllers against variation. Finally, different simulations were performed in the MATLAB environment to show the efficiency of the suggested controller. The sovereignty of the proposed controller is highlighted by comparing its performance with various approaches such as classical sliding mode control, integral backstepping and second order sliding mode controls.

Fuzzy sliding mode control design based on stability margins

Fuzzy Sliding Mode Control (FSMC) algorithms have been widely studied and implemented to combine the robustness of the classical sliding mode control with lower chattering levels, but industrial implementation requires a robustness measurement such as the stability margins. Due to the significance of stability margins in control systems, the computation of the phase Margin (PM) and gain margin (GM) in FSMC has already been proposed with the self-sustained oscillations considered as an unstable behavior. However, a procedure to obtain the desired PM and GM from the FSMC design itself has not been developed yet. Hence, in this study, a method to design FSMC algorithms with desired PM and GM is presented. The describing function (DF) and harmonic balance (HB) techniques were used to identify the limit cycles; then, a step-by-step process to tune the FSMC parameters was provided. Examples and simulations are presented to validate the proposed method.

Application of Sliding Switching Functions in Backstepping Based Speed Observer of Induction Machine

This paper presents an analysis of the speed observer, which is based on the backstepping and sliding mode approach. The speed observer structure is based on the extended mathematical model of an induction machine. The observer structure is based on the measured phase stator currents and transformed to (αβ) coordinate system. The stator voltage vector components are treated as known values. Additionally, such an observer structure is extended to the integrators. The observer stabilizing functions contain the appropriate sliding surfaces, which result from Lyapunov function. The rotor angular speed is obtained from nonadaptive dependence. Stability analysis of the observer structure based on Lyapunov theory is presented in order to guarantee the estimation errors decay to zero. In the sensorless control system, the classical sliding-mode controllers are applied with the multiscalar variables transformation. The theoretical derivations are verified in experimental waveforms.

Efficient Control of a Non-Linear System Using a Modified Sliding Mode Control

Trajectory tracking is an essential requirement in robot manipulator movement and localization applications. It is a current research topic of interest, and several researchers have proposed different schemes to achieve the task accurately. This research proposes efficient control of a hydraulic non-linear robot manipulator using a modified sliding mode control, named proportional derivative sliding mode control with sliding perturbation observer (PDSMCSPO), to overcome parameter uncertainties and non-linearity. The proposed new control strategy achieves higher accuracy and better time convergence than the previous one. A positive derivative gain, which has a value less than one, is multiplied with the velocity error term of the sliding surface. The proposed control (PDSMCSPO) also achieves robustness. Results show that by introducing the derivative gain, the chattering from the system has been reduced more than classical sliding mode control (SMC). The reason is that during reaching phase this small gain multiplies with the perturbation and minimizes the effect of perturbation on the system. A smaller value of switching gain K is required as compared to SMC, and the transfer function between sliding surface and perturbation in proportional derivative sliding mode control (PDSMC)has low pass filter characteristics. The proposed PDSMCSPO has a faster response than previous sliding mode control with sliding perturbation observer (SMCSPO), and the output and sliding surface convergence to the desired value is much quicker than conventional logic. Some other characteristics such as error in the output are small because of more attenuation of the perturbation signal. Simulation and experimental results are presented for a link between the hydraulic robot manipulator and the mass damper system.

Sliding mode controller based on type-2 fuzzy logic PID for a variable speed wind turbine

In this paper, an optimal type-2 fuzzy logic proportional integral derivative controller based on sliding mode controller (IT2FL-PID-SMC) is designed for a wind turbine with variable speed. The major aim of this work is to overcome the deficiencies of the classical sliding mode controller. In this study, the sliding mode controller presented is modified; the sliding surface is replaced by the type-2 fuzzy proportional integral derivative controller. The type-2 fuzzy system is used to improve the classical sliding mode control efficiency and the robustness. The proposed (IT2FL-PID-SMC) can be used to reach strong stability as well as increase the variable speed wind turbine performance. The reliability and consistency of the proposed approach is assessed by completing simulations and analyzing comparisons with the classical SMC. The simulation results are clearly indicated the effectiveness and the validity of the proposed method, in terms of precision and time of convergence.

Design of higher-order sliding mode controller based on genetic algorithm for a cooperative robotic system

This paper proposes a new control framework for a cooperative robotic system which consists of two manipulators to grasp and handle an object with known geometry. Based on passive decomposition approach, the dynamics of the cooperative system are decomposed into the shape and locked systems, considering uncertainty in the dynamics of the robots. Two higher-order sliding mode controllers are designed for them and are tuned by genetic algorithm in the form of an optimization problem. Using the passivity property of passive decomposition approach, the proposed new higher-order sliding mode controllers ensure passivity of the closed loop system. Stability and convergence of the tracking errors are proved by defining a Lyapunov function and using Barbalat’s lemma. Eventually, the comparative simulation results confirmed that the proposed control scheme works well and as expected, works better than the classical sliding mode controllers.

Tuning and Feasibility Analysis of Classical First-Order MIMO Non-Linear Sliding Mode Control Design for Industrial Applications

Model-based control techniques have been gaining more and more interest these days. These complex control systems are mostly based on theories, such as feedback linearization, model predictive control, adaptive and robust control. In this paper the latter approach is investigated, in particular, sliding mode (SM) control is analyzed. While several works on the description and application of SM control on single-input single-output systems can easily be found, its application on multi-input multi-output systems is not examined in depth at the same level. Hence, this work aims at formalizing some theoretical complements about the necessary conditions for the feasibility of the SM control for multi-input-multi-output systems. Furthermore, in order to obtain the desired performance from the control system, a method for parameter tuning is proposed in the particular case in which the relative degree of the controlled channels is equal to one. Finally, a simple control problem example is shown with the aim of stressing the benefits derived from the application of the theoretical complements described here.

Hybrid Petri network super twisting sliding mode control of wind turbine for maximum power point tracking

This paper deals with a hybrid sliding mode control and super twisting algorithm second order sliding mode control with Petri network (HSMC-STA) applied to reach the maximum power point tracking (MPPT) of a variable speed wind energy conversion system. It is aimed to solve the main and major undesired phenomenon faced by conventional sliding mode control, the high frequency oscillations (chattering), and to reduce the transient response (rise time) of super twisting algorithm second order sliding mode control systems. The design of a hybrid controller based on switching Petri network sliding mode control (PNSMC) is proposed, wherein a Petri network is used to supervise and switch between the classical sliding mode control law and the super twisting control law. The new hybrid controller is tested in a Simulink/MATLAB environment. Simulation results of the proposed control scheme present good dynamic and steady-state performance compared to the classical SMC and high order sliding mode with respect to the reduction of the chattering phenomenon and transient response.

Hybrid Petri network super twisting sliding mode control of wind turbine for maximum power point tracking

This paper deals with a hybrid sliding mode control and super twisting algorithm second order sliding mode control with Petri network (HSMC-STA) applied to reach the maximum power point tracking (MPPT) of a variable speed wind energy conversion system. It is aimed to solve the main and major undesired phenomenon faced by conventional sliding mode control, the high frequency oscillations (chattering), and to reduce the transient response (rise time) of super twisting algorithm second order sliding mode control systems. The design of a hybrid controller based on switching Petri network sliding mode control (PNSMC) is proposed, wherein a Petri network is used to supervise and switch between the classical sliding mode control law and the super twisting control law. The new hybrid controller is tested in a Simulink/MATLAB environment. Simulation results of the proposed control scheme present good dynamic and steady-state performance compared to the classical SMC and high order sliding mode with respect to the reduction of the chattering phenomenon and transient response.

Robust Control Design of Nonlinear System by Using Back-Stepping-GSA and Sliding Mode Technique

This work presents the integration of two robust controllers such as back-stepping and sliding mode controller, which is designed for nonlinear system with external disturbance injected to its actuator. Gravitational Search Algorithm (GSA) is applied to the designed controller to optimize the control and reaching law parameters for the system. The dynamics of the system is developed by consider the external force as system’s nonlinearities. The tracking output and tracking error produced by combination of these two controllers is compared with the performance of classical sliding mode controller. Based on the results obtained, integration of these two controllers generates better performance than classical sliding mode controller based on its output and error.

Neural network adaptive sliding mode control for omnidirectional vehicle with uncertainties

This paper presents a novel neural network adaptive sliding mode control (NNASMC) method to design the dynamic control system for an omnidirectional vehicle. The omnidirectional vehicle is equipped with four Mecanum wheels that are actuated by separate motors, and thus has the omnidirectional mobility and excellent athletic ability in a narrow space. Considering various uncertainties and unknown external disturbances, kinematic and dynamic models of the omnidirectional vehicle are established. The inner-loop controller is designed based the sliding mode control (SMC) method, while the out-loop controller uses the proportion integral derivative (PID) method. In order to achieve the stable and robust performance, the artificial neural network (ANN) based adaptive law is introduced to model and estimated the various uncertainties disturbances. Stability and robustness of the proposed control method are analyzed using the Lyapunov theory. The performance of the proposed NNASMC method is verified and compared with the classical PID controller and SMC controller through both the computer simulation and the platform experiment. Results validate the effectiveness and robustness of the NNASMC method in presence of uncertainties and unknown external disturbances.

Active damping of sound transmission through an electrorheological fluid-actuated sandwich cylindrical shell

An exact model is proposed for sound transmission through a sandwich cylindrical shell of infinite extent that includes a tunable electrorheological fluid core, and is obliquely insonified by a plane progressive acoustic wave. The basic formulation utilizes Hamilton’s variational principle, the classical and first order shear deformation shell theories, the Kelvin–Voigt viscoelastic damping model (for the electrorheological fluid-core layer), and the wave equations for internal/external acoustic domains coupled by the proper fluid/structure compatibility relations. The Fourier–Bessel series expansions are used to arrange the governing (coupled) system equations in state-space form. The classical Sliding Mode Control law is then applied to semi-actively reduce sound transmission through the composite cylinder by smart variation of stiffness and damping characteristics of the electrorheological fluid-core actuator layer according to the control command. Numerical results present both the uncontrolled and controlled sound transmission loss spectra of the sandwich cylindrical shell at three angles of incidence for three distinct sets of material input parameters that represent the electric-field dependency of the complex shear modulus of the electrorheological fluid-core layer. The superior soundproof performance of electrorheological fluid-based sliding mode control system in avoiding the highly detrimental sound transmission loss dips occurring throughout the critical resonance and coincidence regions is demonstrated. Likewise, remarkable enhancements in the sound insulation characteristics of the electrorheological fluid-actuated structure utilizing the first or second electrorheological fluid material model are achieved within the stiffness-controlled region, especially at lower frequencies in near-grazing incidence situation. A number of limiting cases are introduced and validity of the formulation is confirmed by comparison with the available data.

Design of Second Order Sliding Mode for Glucose Regulation Systems with Disturbance

In this work, Design of second order sliding mode control has been developed to control the diabetic glucose concentration level under disturbing meal has been controlled using three sliding mode controllers. A comparative study of three sliding mode controllers is made in terms of robustness characteristics due to meal feeding. The first is the classical sliding mode controller, the second is integral sliding mode controller and the third is the second order sliding mode controller. Due to their characteristic features of disturbance rejection, all the three sliding mode controllers are presented here for comparison. The Bergman minimal mathematical model is used to describe the dynamic behavior of blood glucose concentration due to insulin regulator injection. Simulations, based on MATLAB/Simulink, were performed to verify the performance of each controller. It has been shown that integral and second order sliding mode controllers are the best of all in terms of disturbance rejection capability.

Adaptive sliding mode control with moving surface: Experimental validation for electropneumatic system

Abstract In this work, an Adaptive Sliding Mode Control (ASMC) is proposed for a class of nonlinear MIMO system with external disturbances. Although the Sliding Mode Control (SMC) is known for its precision and robustness against disturbance and uncertainties, it suffers from a chattering phenomenon and the choice of sliding surface parameters. To solve such problems, the SMC discontinuous term was replaced by a proportional derivative term and a moving sliding surface was used. The adaptive parameters were obtained by Lyapunov stability analysis to guarantee the stability of the closed loop system. In order to illustrate the efficiency of the proposed controller, experimental results on electropneumatic system were presented and compared to a classic sliding mode controller.

Performance Comparison of Different Advanced Control Schemes for Glucose Level Control under Disturbing Meal

Abstract
 In this work, diabetic glucose concentration level control under disturbing meal has been controlled using two set of advanced controllers. The first set is sliding mode controllers (classical and integral) and the second set is represented by optimal LQR controllers (classical and Min-, ax). Due to their characteristic features of disturbance rejection, both integral sliding mode controller and LQR Minmax controller are dedicated here for comparison. The Bergman minimal mathematical model was used to represent the dynamic behavior of a diabetic patient’s blood glucose concentration to the insulin injection. Simulations based on Matlab/Simulink, were performed to verify the performance of each controller. In spite that Min-max optimal controller gave better disturbance rejection capability than classical optimal controller, classical sliding mode controller could outperform Min-max controller. However, it has been shown that integral sliding mode controller is the best of all in terms of disturbance rejection capability.
 
 Key words: Optimal LQR control, Optimalminimax control, Sliding mode control, Integral sliding mode control.