High-order Sliding Mode Observer Research Articles

Robust output feedback control for electro-hydraulic servo system with error constraint based on high-order sliding mode observer

In this paper, a robust output feedback controller with error constraint is proposed to improve the position tracking performance of the electro-hydraulic servo system. Since only the position signal of the system is available, a high-order sliding mode observer is designed to estimate the unobtainable system states. The new state observer can not only avoid the influence of sensor measurement noise but also reduce the chattering of traditional sliding mode observer. To cope with the modeling error, parameter uncertainty, and external disturbance, a robust controller based on backstepping method is designed. In addition, barrier Lyapunov function is introduced to limit the maximum tracking error to a preset range. Finally, comparative experiments are carried out on the asymmetric hydraulic cylinder test bench. The experimental result shows that the proposed controller has a satisfied tracking performance.

Delay Estimation for Nonlinear Systems With Unknown Output Delay

In this letter, the problems of delay identifiability and delay estimation for a nonlinear systems subject to constant unknown output delay are studied. Usually, the estimation of such delay is based on a monotonic condition which is hard to satisfy in the case of nonlinear systems. To deal with this open and interesting problem, a change of coordinates is introduced in this letter to transform the nonlinear system to the triangular form. Then, a high order sliding mode observer is designed based on implicit Lyapunov function to estimate the state and delayed-input, based on these estimation, the delay estimator is proposed. The convergence of the proposed observer is proved and the effectiveness of the proposed method is illustrated through simulation results of an Electro-Hydraulic Actuator (EHA) system.

A High-Order Sliding-Mode Adaptive Observer for Uncertain Nonlinear Systems

A high-order sliding-mode adaptive observer is proposed to solve the problem of an adaptive estimation, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i.e.,</i> the simultaneous estimation of the state and parameters, for a class of uncertain nonlinear systems in the presence of external disturbances, which do not need to satisfy a relative degree condition equal to one. This approach is based on a high-order sliding-mode observer and a nonlinear parameter identification algorithm. The practical, global, and uniform asymptotic stability of the adaptive estimation error, despite the external disturbances, is guaranteed through the small-gain theorem. The convergence proofs are developed based on the Lyapunov and input-to-state stability theories. Some simulation results illustrate the performance of the proposed high-order sliding-mode adaptive observer.

Comparative Analysis of a Family of Sliding Mode Observers under Real-Time Conditions for the Monitoring in the Bioethanol Production

Online monitoring of fermentation processes is a necessary task to determine concentrations of key biochemical compounds, diagnose faults in process operations, and implement feedback controllers. However, obtaining the signals of all-important variables in a real process is a task that may be difficult and expensive due to the lack of adequate sensors, or simply because some variables cannot be directly measured. From the above, a model-based approach such as state observers may be a viable alternative to solve the estimation problem. This work shows a comparative analysis of the real-time performance of a family of sliding-mode observers for reconstructing key variables in a batch bioreactor for fermentative ethanol production. These observers were selected for their robust performance under model uncertainties and finite-time estimation convergence. The selected sliding-mode observers were the first-order sliding mode observer, the proportional sliding mode observer, and the high-order sliding mode observer. For estimation purposes, a power law kinetic model for ethanol production by Saccharomyces cerevisiae was performed. A hybrid methodology allows the kinetic parameters to be adjusted, and an approach based on inference diagrams allows the observability of the model to be determined. The experimental results reported here show that the observers under analysis were robust to modeling errors and measurement noise. Moreover, the proportional sliding-mode observer was the algorithm that exhibited the best performance.

Robust Locomotion Exploiting Multiple Balance Strategies: An Observer-Based Cascaded Model Predictive Control Approach

Robust locomotion is a challenging task for humanoid robots, especially when considering dynamic disturbances. This article proposes a disturbance observer-based cascaded model predictive control (MPC) approach for bipedal locomotion, with the capability of exploiting ankle, stepping, hip and height variation strategies. Specifically, based on the variable-height inverted pendulum model, a nonlinear MPC that is run at a low frequency is built for 3-D locomotion (i.e., with height variation) while accounting for the footstep modulation as well. Differing from previous works, the nonlinear MPC is formulated as a convex optimization problem by semidefinite relaxation. Subsequently, assuming a flywheel at the pelvis center, a linear MPC that is run at a high frequency is proposed to regulate angular momentum (e.g., through rotating the upper body), which is solved by convex quadratic programming. To run the cascaded MPC in a closed-loop manner, a high order sliding mode observer is designed to estimate system states and dynamic disturbances simultaneously. Simulation and hardware experiments demonstrate the walking robustness in real-world scenarios, including 3-D walking with varying speeds, walking across non-coplanar terrains and push recovery.

Angular position estimation error extraction for speed and angular position estimation of IPMSM using a parameter-free adaptive observer

In this paper, an alternative approach for extracting the angular position estimation error for an Interior Permanent Magnet Synchronous Machine (IPMSM) is introduced.The originality of this work consists on obtaining the angular position estimation error by the measurable currents, in the αβ stationary reference frame, without considering the high frequency signal injection. Then, using the obtained angular position estimation error, an Adaptive High Order Sliding Mode Observer (AHOSMO) is proposed for estimating the position, speed and acceleration of the IPMSM. The observer is used for a parameter-free virtual dynamical system to avoid impact of the parameter variations on the estimation. The convergence analysis of the proposed observer is established using a Lyapunov stability theory. Furthermore, simulation and experimental results are presented to illustrate the efficiency of the proposed approach against disturbances and noises. The proposed approach is compared with high frequency (HF) and back electromotive force (BEMF) approaches.

Exact uncertainty compensation of linear systems by continuous fixed-time output-feedback controller

This paper studies the fixed-time output-feedback control for a class of linear systems subject to matched uncertainties. To estimate the uncertainties and system states, we design a composite observer which consists of a high-order sliding mode observer and a Luenberger observer. Then, a robust output-feedback controller with fixed-time convergence guarantee is constructed. Rigorous theoretical proof shows that with the proposed controller, the system states can converge to zero in fixed-time free of the initial conditions. Finally, simulation comparison with existing algorithms is given. Simulation results verify the effectiveness of the proposed controller in terms of its fixed-time convergence and perfect disturbance rejection.

High-order sliding mode-based synchronisation of fractional-order chaotic systems subject to output delay and unknown disturbance

This work deals with chaos synchronisation. One of the commonly used methods is the master-slave configuration, where the response of the chaotic receiver (slave) system must converge to the chaotic trajectory of the transmitter (master). The major problem with this configuration is the delay that occurs during the transmission of the drive signal from the master to the slave, which can degrade the synchronisation. The objective of this paper is to propose a solution to the synchronisation problem of nonlinear fractional-order chaotic systems in the presence of a transmission delay at the output and unknown disturbance. The proposed approach consists of combining a fractional high-order sliding mode observer (FHOSMO) and a predictor arranged in a cascade to compensate for the delayed transmission signal from the transmitter to the receiver. The observer permits to estimate the delayed states and the delayed total disturbance (uncertainties and external disturbances) in finite time. These estimates are injected into the predictor to obtain the estimated states at the current time. The finite time convergence of the proposed method is established. The numerical simulations illustrate the theoretical results and the performance of the proposed method. The proposed synchronisation method is compared with other synchronisation methods using the chattering free sliding mode approach such as the fractional first-order sliding mode observer using the continuous function instead of the discontinuous sign function and the fractional second-order sliding mode observer. In addition, a conventional first-order sliding mode observer with the sign function is also considered.

A Robust Dynamic Control Strategy for Standalone PV System under Variable Load and Environmental Conditions

Dual-stage standalone photovoltaic (PV) systems suffer from stability, reliability issues, and their efficiency to deliver maximum power is greatly affected by changing environmental conditions. A hybrid back-stepping control (BSC) is a good candidate for maximum power point tracking (MPPT) however, there are eminent steady-state oscillations in the PV output due to BSC’s recursive nature. The issue can be addressed by proposing a hybrid integral back-stepping control (IBSC) algorithm where the proposed integral action significantly reduces the steady-state oscillations in the PV array output under varying temperature and solar irradiance level. Simultaneously, at the AC stage, the primary challenge is to reduce both the steady-state tracking error and total harmonic distortion (THD) at the output of VSI, resulting from the load parameter variations. Although the conventional sliding mode control (SMC) is robust to parameter variations, however, it is discontinuous in nature and inherit over-conservative gain design. In order to address this issue, a dynamic disturbance rejection strategy based on super twisting control (STC) has been proposed where a higher order sliding mode observer is designed to estimate the effect of load disturbances as a lumped parameter which is then rejected by the newly designed control law to achieve the desired VSI tracking performance. The proposed control strategy has been validated via MATLAB Simulink where the system reaches the steady-state in 0.005 s and gives a DC–DC conversion efficiency of 99.85% at the peak solar irradiation level. The AC stage steady-state error is minimized to 0 V whereas, THD is limited to 0.07% and 0.11% for linear and non-linear loads, respectively.

Unknown input observer design for linear time-invariant multivariable systems based on a new observer normal form

In various applications in the field of control engineering, the estimation of the state variables of dynamic systems in the presence of unknown inputs plays an important role. Existing methods require the so-called observer matching condition to be satisfied, rely on the boundedness e variables or exhibit an increased observer order of at least twice the plant order. In this article, a novel observer normal form for strongly observable linear time-invariant multivariable systems is proposed. In contrast to classical normal forms, the proposed approach also takes the unknown inputs into account. The proposed observer normal form allows for the straightforward construction of a higher-order sliding mode observer, which ensures global convergence of the estimation error within finite time even in the presence of unknown bounded inputs. Its application is not restricted to systems which satisfy the aforementioned limitations of already existing unknown input observers. The proposed approach can be exploited for the reconstruction of unknown inputs with bounded derivative and robust state-feedback control, which is shown by means of a tutorial example. Numerical simulations confirm the effectiveness of the presented work.

A Novel Robust Super-Twisting Nonsingular Terminal Sliding Mode Controller for Permanent Magnet Linear Synchronous Motors

For accurate position tracking and robust control of permanent magnet linear synchronous motor (PMLSM) servo systems against various uncertainties, such as parameter change, load disturbance, friction force, and so on, this article proposes a novel super-twisting nonsingular terminal sliding mode control method based on a high-order sliding mode observer. First, a dynamic model of PMLSM with uncertainties is established. A novel nonsingular terminal sliding mode function combined with the super-twisting algorithm is then proposed to design a robust super-twisting nonsingular terminal sliding mode controller, which ensures the system convergence to the equilibrium state within a finite time, effectively eliminating the chattering phenomenon and improving the system robustness. To further improve the system tracking performance and anti-interference ability, a high-order sliding mode observer is used to estimate the system uncertainties. The effective tracking performance and robustness of the proposed control method are validated by the experimental results.

Fast-Exponential Sliding Mode Control of Robotic Manipulator With Super-Twisting Method

This brief addresses the trajectory tracking problem for robotic manipulators without angular velocity measurements in the presence of parameter perturbation and torque disturbance. A novel fast terminal sliding mode surface is developed to ensure global strong robustness and fast error convergence. Then, a high-order sliding mode observer (HOSMO) is constructed to estimate unknown joints’ angular velocities and the system lumped disturbance in a finite time. Chattering avoidance can be realized via the continuous control strategy based on super-twisting method. The finite-time arrival of sliding mode surface and fast-exponential convergence of the tracking error are strictly proved based on the Lyapunov stability theory. Finally, an example of a two-link robotic manipulator is provided. From the comparison with other control strategies, the advantages of proposed method are fully demonstrated.

Continuous Sliding-Mode Output-Feedback Control for Stabilization of a Class of Underactuated Systems

This article presents a robust output-feedback control scheme for the stabilization of a class of nonlinear underactuated mechanical systems in the presence of coupled disturbances. The scheme is based on the so-called coupled sliding-mode control, i.e., no transformation into the normal form is required. The proposed output approach is composed of a super-twisting controller and a high-order sliding-mode observer that robustly stabilize the origin of the system asymptotically. All of the results are proven by Lyapunov approaches. The proposed approach is validated by means of simulations and experimental results on a four-degree-of-freedom underactuated crane.

State-Feedback-Critical Super Twisting Sliding Mode Control for a Half-Car Suspension System

A good suspension system is of paramount importance to the operating performance of a vehicle and, consequently, to the safety and driving comfort of the passengers. Nevertheless, suspension systems are commonly susceptible to nonlinearity, parameter uncertainty, and exogenous perturbation, which can easily impair their effectiveness. This study first employs a full state feedback super twisting control (FS-STC) to stabilize both vertical displacement and pitch angle of a half-car suspension system in the presence of disturbances. FS-STC inherits the robust property of sliding mode control (SMC) while effectively attenuating the chattering phenomenon as one of its attractive features. However, FS-STC strictly requires both direct displacement and velocity state feedback, which implies additional sensors have to be installed, thus increasing the complexity of the physical structure and being prone to measurement noises. Therefore, a higher order sliding mode observer (HOSMO) based STC (HOSMO-STC) and an unscented Kalman filter (UKF) based STC (UKF-STC) are subsequently proposed to tackle this state availability problem. HOSMO estimates velocity states, thus reducing the dependence on state feedback for STC design. Meanwhile, UKF implementation takes further actions by utilizing more common and easily accessible relative displacements such as suspension strokes to estimate all concerned system states. Comparative simulation results demonstrate that UKF-STC offers better performance in terms of both convergence accuracy and chattering alleviation compared to FS-STC and HOSMO-STC while requiring the least information of state feedback.

Adaptive Cooperative Tracking Control of Multiple Trains With Uncertain Dynamics and External Disturbances Based on Adjacent Information

Automatic train operation is an important part of the train control system. As train operating intervals continue to shorten and train speeds continue to increase, multiple train cooperative control is currently an important technology to further improve the efficiency of train operation and line passing capacity. However, considering various factors such as the nonlinearity and uncertainty of the train dynamics model and the complexity of the line conditions, this creates even greater demands on the design of the controller. In this study, we propose an adaptive cooperative tracking control method for multiple trains using adjacent information. For the multiple-train coordinated tracking control in the presence of model uncertainties, unknown parameters, and external disturbances, a distributed cooperative control scheme for multiple trains is designed using the displacement, velocity, and acceleration information of adjacent trains, combined with radial basis function neural networks and adaptive methods. A fast high-order sliding mode observer is used to estimate the train velocity and acceleration information. Stability and convergence are proved for single and multiple trains utilizing Lyapunov stability analysis. Simulation examples demonstrate the effectiveness of the proposed controller.

Z(TN) Observability Concept Analysis for Power Flying Capacitors of Multicells Converters

—In this paper, a new Z(TN) observability concept is proposed for power flying capacitors of multicell converter based on ordering of sequences. The aim is to solve the problem of capacitor’s voltages estimation by tacking account the hybrid behavior appearing in the power multicell converters and the ordering of the sequences. Furthermore, an analysis of obervability is introduced. Some illustrative results of a3-cell-converter with two legs are given in order to show the efficiency of the proposed approach by using high order sliding mode observer. The applicability of the designed observers are emphasized by the robustness test with resistance load variation. Finally, experimental results are presented in order to illustrate the performance of the proposed approach.

Novel adaptive backstepping control for uncertain manipulator robots using state and output feedback

AbstractIn this paper, a new adaptive control strategy, based on the Modified Function Approximation Technique, is proposed for a manipulator robot with unknown dynamics. This novel strategy benefits from the backstepping control approach and the use of state and output feedback. Unlike the conventional Function Approximation Technique approach, the use of basis functions to approximate the dynamic parameters is completely eliminated in the proposed scheme. Another improvement is eliminating the need to measure velocity by means of integrating a high-order sliding mode observer. Furthermore, utilizing the Lyapunov function theory, it is demonstrated that all controller signals are uniformly ultimately bounded in the closed-loop form. Lastly, simulation and comparative studies are carried out to validate the effectiveness of the proposed control approach.

An Improved Super-Twisting High-Order Sliding Mode Observer for Sensorless Control of Permanent Magnet Synchronous Motor

This article presents an improved super-twisting high-order sliding mode observer for permanent magnet synchronous motors to achieve high-performance sensorless control. The proposed observer is able to simultaneously estimate rotor position and speed, as well as track parameter disturbances online. Then, according to the back-EMF model, the sensorless observer is further constructed to improve the estimation effect. The estimated rotor position and speed are used to replace the actual values detected by the sensor, and the estimated parameter disturbances are considered as feedback values to compensate the command voltage. In this way, not only is the estimation accuracy improved, but the robustness against uncertainties is also enhanced. Simulation and experimental results show that the proposed observer can effectively track the rotor position and speed and obtain good dynamic and steady-state performance.

Observer-based control of vertical penetration rate in rotary drilling systems

An algorithm for regulation of the vertical penetration rate in rotary drilling systems is developed under the assumption that parameters of the rock-bit interaction as well as those of the translational dynamics are unknown. The control design utilizes a multi-step approach, where the vertical penetration velocity is regulated through an appropriate assignment of a reference rotational velocity signal, while the tracking of the latter is achieved using tracking with disturbance rejection scheme. In contrast with the existing results, the algorithm does not require real-time measurement and communication to the ground level of the downhole variables, such as angular position, rotational velocity, and torque-on-bit. This is achieved through the use of high-order sliding mode observers which estimate the required downhole variables based on measurements performed at the ground level. Simulation results are presented which confirm efficiency of the proposed control method.

Fast initial alignment for inertial navigation system based on high order sliding mode observer and Kalman filter

The inertial navigation system is a dead reckoning system, thus initial alignment for an inertial navigation system plays an important role in the accuracy of it. In this paper, a novel approach for initial alignment in an inertial navigation system with increased speed and accuracy is proposed. This method has two stages, which integrates the Kalman filter and a high order sliding mode observer. In the inertial navigation system, leveling misalignment angles reach the steady-state faster than the azimuth misalignment angle does, which means the azimuth alignment takes a considerable time for initial alignment. Therefore, in this paper at the first stage estimations of state variables of the system are obtained using the Kalman filter and whenever all variables (except azimuth alignment) reach steady-state, the second stage begins. In the second stage, the estimation which is obtained by the Kalman filter is used as the input to design an equivalent system with unknown inputs for inertial navigation system. A high-order sliding mode observer is then used to estimate the states of a system with an unknown input for estimating the azimuth alignment angle. This method not only increases the speed of estimation but also has comparable accuracy.