Higher Order Sliding Mode Research Articles

Output-feedback finite-time stabilization of disturbed feedback linearizable nonlinear systems

A novel methodology for designing multivariable High-Order Sliding-Mode (HOSM) controllers for disturbed feedback linearizable nonlinear systems is introduced. It provides for the finite-time stabilization of the origin of the state-space by using output feedback. Only the additional assumptions of algebraic strong observability and smooth enough matched disturbances are required. The control problem is solved in two consecutive steps: firstly, designing an observer based on the measured output and, secondly, designing of a full-state controller computed from a new virtual output with vector relative degree. The introduced notion of algebraic strong observability allows recovering the state of the system using the measured output and its derivatives. By estimating the required derivatives through the HOSM differentiator, a finite-time convergent observer is constructed.

Robust exact uniformly convergent arbitrary order differentiator

An arbitrary order differentiator that, in the absence of noise, converges to the true derivatives of the signal after a finite time independent of the initial differentiator error is presented. The only assumption on a signal to be differentiated (n−1) times is that its n-th derivative is uniformly bounded by a known constant. The proposed differentiator switches from a newly designed uniform differentiator to the classical High-Order Sliding Mode (HOSM) differentiator. The Uniform part drives the differentiation error trajectories into a compact neighborhood of the origin in a time that is independent of the initial differentiation error. Then, the HOSM differentiator is used to bring the differentiation error to zero in finite-time.

Flight control for a flexible air-breathing hypersonic vehicle based on quasi-continuous high-order sliding mode

The focus of this paper is on control design and simulation for the longitudinal model of a flexible air-breathing hypersonic vehicle (FAHV). The model of interest includes flexibility effects and intricate couplings between the engine dynamics and flight dynamics. To overcome the analytical intractability of this model, a nominal control-oriented model is constructed for the purpose of feedback control design in the first place. Secondly, the multi-input multi-output (MIMO) quasi-continuous high-order sliding mode (HOSM) controller is proposed to track step changes in velocity and altitude, which is based on full state feedback. The simulation results are presented to verify the effectiveness of the proposed control strategy.

High order sliding mode control for hybrid vehicle stability

This paper tackles the problem of driving stability for a hybrid vehicle. A rear electric motor has been added to the vehicle driveline and the positive/negative torque generated by this motor affects the driving conditions. The vehicle stability control is addressed using high order sliding modes (HOSMs) control and observation techniques. Two cases are studied: yaw stability and traction control. The proposed controllers preserve the system’s safety under undesirable rear motor effects, at the same time, they cope with vehicle uncertainties. The feasibility of this platform was tested in a vehicle simulator.

Adaptive integral higher order sliding mode controller for uncertain systems

This paper proposes an adaptive integral higher order sliding mode (HOSM) controller for uncertain systems. Instead of a regular control input, the derivative of the control input is used in the proposed control law. The discontinuous sign function in the controller is made to act on the time derivative of the control input. The actual control signal obtained by integrating the derivative control signal is smooth and chattering free. The adaptive tuning law used in the proposed controller eliminates the need of prior knowledge about the upper bound of the system uncertainties. Stability and robustness of the proposed controller are proved by using the classical Lyapunov criterion. Simulation results demonstrate the advantages of the proposed control scheme.

Finite-time Stabilization Using Implicit Lyapunov Function Technique

The Implicit Lyapunov Function (ILF) method for finite-time stability analysis is introduced. The control algorithm for finite-time stabilization of a chain of integrators is developed. The scheme of control parameters selection is presented by a Linear Matrix Inequality (LMI). The robustness of the finite-time control algorithm with respect to system uncertainties and disturbances is studied. The new high order sliding mode (HOSM) control is derived as a particular case of the developed finite-time control algorithm. The settling time estimate is obtained using ILF method. The algorithm of practical implementation of the ILF control scheme is discussed. The theoretical results are supported by numerical simulations.

Adaptive High Order Sliding Mode Controller Design for Hypersonic Vehicle with Flexible Body Dynamics

This paper describes the design of a nonlinear robust adaptive controller for a flexible hypersonic vehicle model which is nonlinear, multivariable, and unstable, and includes uncertain parameters. Firstly, a control-oriented model is derived for controller design. Then, the model analysis is conducted for this model via input-output (I/O) linearized technique. Secondly, the sliding mode manifold is designed based on the homogeneity theory. Then, the adaptive high order sliding mode controller is designed to achieve the tracking for hypersonic vehicle where the upper bounds of the uncertainties are not known in advance. Furthermore, the stability of the system is proved via the Lyapunov theory. Finally, the Monte-Carlo simulation results on the full-order nonlinear model with aerodynamic uncertainties are provided to demonstrate the effectiveness of the proposed control strategy.

A HOSM control algorithm to stabilize the quadrotor vehicle with experimental validation

A High Order Sliding Mode control technique to stabilize the quadrotor vehicle is presented in this paper. The simplified nonlinear equations are evoked to develop the control algorithms. The closed-loop system using this sliding mode methodology is robust even in presence of unknown disturbances and uncertainties parameters in the model. The control scheme is validated in simulations and some experiments are developed to prove the experimental feasibility of the control strategy. Simulation and experimental results demonstrate the well performance of the proposed algorithms.

Observability Analysis and Improved Zero‐Speed Position Observer Design of Synchronous Motor with Experimental Results

AbstractThis paper deals with the permanent magnet synchronous motor (PMSM) observability analysis for sensorless control design. The problem of loss of observability at low frequency range is always recognized in experimental settings. Nevertheless, there are no sufficient theoretical observability analyses for the PMSM. In the literature, only the sufficient observability condition has been presented. Therefore, the current work is aimed especially towords the necessary observability condition analysis. Furthermore, improved zero‐speed observation is presented here for a surface PMSM (SPMSM) to overcome position observability problems at zero‐speed which is an unobservable state point. The proposed observer based on higher order sliding mode (HOSM) is designed in order to ensure robustness against disturbances and to avoid the chattering phenomenon which is inherent in standard first order sliding modes. The stability and finite time convergence of the developed observer are studied and discussed. Experimental results are carried out to illustrate the effectiveness and robustness of the proposed observer.

Quasi-continuous high-order sliding mode controller and observer design for flexible hypersonic vehicle

The problem of robust output feedback control and simulation for the longitudinal model of a flexible air-breathing hypersonic vehicle (FAHV) is investigated in this paper. A control-oriented uncertainty model is established for the feedback linearization design, and the multi-input and multi-output (MIMO) quasi-continuous high-order sliding mode (HOSM) controller is formulated to track the responses of the vehicle to a step change in velocity and altitude based on full state feedback. In addition, a high order sliding mode observer is designed to estimate the angle of attack and the flight path angle, which are difficult to measure in a hypersonic flight. Furthermore, the combination of the HOSM controller and observer is proposed for vehicle model with partial state measurements. The simulation results are presented to verify the effectiveness of the proposed control strategy.

Interval estimation for LPV systems applying high order sliding mode techniques

In this paper, the problem of design of interval observers for Linear Parameter-Varying (LPV) systems, containing non-detectable or non-strongly-observable parts, is addressed. Firstly, a High Order Sliding Mode (HOSM) method is applied to the strongly observable subsystem, obtained by an appropriate change of coordinates, to estimate the state and its derivative. Secondly, this information is used to decrease the level of uncertainty in the rest of the system, which leads to improvement of accuracy of the set-membership estimates generated by an interval observer. Moreover, it is shown that HOSM techniques allows us to relax the applicability conditions of standard interval observer design methods. The efficiency of the proposed approach is demonstrated through simulation examples.

A High Order Sliding Mode Control with PID Sliding Surface: Simulation on a Torpedo

Position and speed control of the torpedo present a real problem for the actuators because of the high level of the system non linearity and because of the external disturbances. The non linear systems control is based on several different approaches, among it the sliding mode control. The sliding mode control has proved its effectiveness through the different studies. The advantage that makes such an important approach is its robustness versus the disturbances and the model uncertainties. However, this approach implies a disadvantage which is the chattering phenomenon caused by the discontinuous part of this control and which can have a harmful effect on the actuators. This paper deals with the basic concepts, mathematics, and design aspects of a control for nonlinear systems that make the chattering effect lower. As solution to this problem we will adopt as a starting point the high order sliding mode approaches then the PID sliding surface. Simulation results show that this control strategy can attain excellent control performance with no chattering problem.

Optimum torque sensorless HOSM controller for IPMSM via adaptive interconnected observer

In this paper, a nonlinear high order sliding mode (HOSM) controller and an adaptive interconnected observer for sensorless interior permanent magnet synchronous motors (IPMSM) are designed. A maximum-torque-per-ampere strategy (MTPA) is used to compute direct rotor current reference. The high order sliding mode controller is designed in order to ensure finite-time convergence of sliding variables and its high order time derivatives despite parameter uncertainties and unknown load torque. The adaptive interconnected observer estimates the currents, the angular velocity, the position, the load torque and the stator resistance. By Lyapunov theory, the observer-controller stability is proved. Simulation results confirm the effectiveness of the proposed method.

Application of Interval Observers and HOSM Differentiators for Fault Detection

This work is devoted to the design of interval observers for a class of Linear-Parameter-Varying (LPV) systems. Applying High Order Sliding Mode (HOSM) techniques it is possible to decrease the initial level of uncertainty in the system, which leads to improvement of set-membership estimates generated by an interval observer and enlarges the class of the estimated systems. Next, this approach is applied to fault detection by verifying the consistency between the output trajectory and its estimated domain. The efficiency of the proposed approach is demonstrated through computer simulations of an electromechanical system.

A New DYC Control Strategy Based on Feedforward Control in the Linear Region

This paper discussed a new direct yaw moment control(DYC) method which was coupled with feedforward control by utilizing the estimated cornering stiffness coeficients. Comparing two simultaneously running single track models in the linear region,the feedforward control output was produced. Higher-order sliding modes(HOSM) was used to ensure the robustness of the control system in the limit region. A weight gain was used to combined feedforward control and feedback control. The simulation results in VeDYNA show that this new DYC control method based on the knowledge of cornering stiffness significantly improve the vehicle desired trajectory over that of feedback control alone.

State Estimation for Linear Switched Systems with Unknown Inputs

The continuous and discrete state estimation problem in linear switched systems with unknown inputs and unstable internal dynamics is addressed. A robust observer based on High-Order Sliding-Mode is proposed to solve the problem under mild structural conditions. Simulation results support the proposed estimation approach.

Fault Detection and Isolation for Nonlinear Systems via HOSM Multiple-Observer

The fault detection and isolation problem is studied for a class of nonlinear systems. Under structural conditions, a bank of High-Order Sliding-Mode observers is proposed. The value of the equivalent output injection is used for detecting and isolating particular faults in the system. The proposed method provides finite-time isolation of actuator and plant faults. Simulation results support the proposed approach.

Launch vehicle attitude control using sliding mode control and observation techniques

In determining flight controls for launch vehicle systems, several uncertain factors must be taken into account, including a variety of payloads, a wide range of flight conditions and different mission profiles, wind disturbances and plant uncertainties. Crewed vehicles must adhere to human rating requirements, which limit the angular rates. Sliding mode control algorithms that are inherently robust to external disturbances and plant uncertainties are very good candidates for improving the robustness and accuracy of the flight control systems. Recently emerging Higher Order Sliding Mode (HOSM) control is even more powerful than the classical Sliding Mode Controls (SMC), including the capability to handle systems with arbitrary relative degree. This paper proposes sliding mode launch vehicle flight controls using classical SMC driven by the sliding mode disturbance observer (SMDO) and higher-order multiple and single loop designs. A case study on the SLV-X Launch Vehicle studied under a joint DARPA/Air Force program called the Force Application and Launch from CONtinental United States (FALCON) program is shown. The intensive simulations demonstrate efficacy of the proposed HOSM and SMC-SMDO control algorithms for launch vehicle attitude control.

Integrated guidance and autopilot design for a chasing UAV via high-order sliding modes

Integrated guidance and control (IGC) approaches exploit the synergy between guidance and control designs. This study focuses on the integrated guidance and control (autopilot) design for a chasing Uninhabited Aerial Vehicle (UAV) against a target aircraft. A second-order sliding structure with a second-order sliding mode (SOSM) including a high-order sliding mode (HOSM) observer for the estimation of the uncertain sliding surfaces is selected to develop an integrated guidance and autopilot scheme. In order to make the design synthesis easier, intermediate control variables for partial derivatives of a sliding surface are carefully selected. The resulting sliding surface structure is simple and sufficient to relate the actuator input to the sliding surface. The potential of the proposed method is demonstrated through an aircraft application by comparing its simulation performance, number of tuning parameters used, and information needed for its implementation with an approach where the guidance law and the controller are designed separately.

Lunar spacecraft powered descent control using higher-order sliding mode techniques

Robust performance of a flight control system in the presence of parametric uncertainty and external disturbances is of paramount importance to a successful planetary exploration program. The present research is concerned with the design of an autopilot that uses high-order sliding mode (HOSM) control principles so as to enhance the robustness properties of a lunar landing vehicle during the approach phase of powered descent. The design technique is applied to a high-fidelity simulation of the Apollo Lunar Module (LM). The design efficiently utilizes both the reaction control system (RCS) actuators and the severely rate-limited gimbal drive actuator (GDA) to effect smooth detection and compensation of sensed angular acceleration disturbances about the vehicle's control axes. The integration of a HOSM control law for the RCS effectors with a HOSM disturbance observer is shown to provide performance comparable to that of the heritage autopilot and may also avoid some difficulties encountered in the Apollo flights. Performance is maintained with the controller implemented in discrete time in the presence of a realistic vehicle and sensor model, demonstrating a unique application of sliding mode control to a complex aerospace system.