High-order Sliding Mode Observer Research Articles

Continuous and discrete state reconstruction for nonlinear switched systems via high-order sliding-mode observers

A class of nonlinear switched systems is studied, and a finite-time converging state observer is proposed. The observer strategy, based on the high-order sliding-mode approach, is able to reconstruct both the continuous and discrete states of the switched system based on output measurements and on the knowledge of the set of possible system's dynamics. All the ‘operating modes’ of the switched system are required to satisfy certain observability-like and boundedness restrictions. The observer provides a finite-time converging estimate and, after a switching of the active mode, it features an arbitrarily fast transient to recover the correct (continuous and discrete) state estimate. A numerical example illustrates the performance of the proposed observer.

High-order sliding-mode observation for linear systems with unknown inputs

A high-order sliding-mode observer is designed for linear systems with unknown inputs. The concepts of strong observability and strong detectability are studied and their relation with the relative degree of a plant is established. High-order sliding-mode-based observers for linear time-invariant systems with unknown inputs satisfying the condition of strong observability or strong detectability are developed.

State observation and friction estimation in engine air path actuator using higher order sliding mode observers

AbstractThis paper presents the application of higher order Sliding Mode observers (SMO) for state observation and friction estimation of an engine air path actuator. The actuator model incorporates LuGre Friction Model for dynamic friction modeling. The study has two objectives, to observe the system dynamics and the friction dynamics, and to use the equivalent output injection to estimate the parameters of the LuGre model. Cascaded sliding mode observers have been used to observe system and friction dynamics separately. Friction force has been estimated using the Equivalent output injection of the observer, considering friction as an unknown external input. Through this estimation, identification of the LuGre model parameters becomes simplified. Simulation and experimental results show the effectiveness of the proposed observation and identification scheme.

Differential Estimators for State Observers in Vehicle Dynamics: HOSM and ALIEN

AbstractIn this paper we compare robust differentiators to design observers to estimate the system state vector (HOSMO and ALIEN). We use for validation a driving simulator developed by Oktal. Robust partial state observers are developed for estimation using High Order Sliding Mode Observers and Algebraic approach (ALIEN*).

High order sliding mode observer for linear systems with unbounded unknown inputs

A global observer is designed for strongly detectable systems with unbounded unknown inputs. The design of the observer is based on three steps. First, the system is extended taking the unknown inputs (and possibly some of their derivatives) as a new state; then, using a global high-order sliding mode differentiator, a new output of the system is generated in order to fulfil, what we will call, the Hautus condition, which finally allows decomposing the system, in new coordinates, into two subsystems; the first one being unaffected directly by the unknown inputs, and the state vector of the second subsystem is obtained directly from the original system output. Such decomposition permits designing of a Luenberger observer for the first subsystem, which satisfies the Hautus condition, i.e. all the outputs have relative degree one w.r.t. the unknown inputs. This procedure enables one to estimate the state and the unknown inputs using the least number of differentiations possible. Simulations are given in order to show the effectiveness of the proposed observer.

Finite-time converging jump observer for switched linear systems with unknown inputs

This work addresses the state observation problem for a class of switched linear systems with unknown inputs. The proposed high-order sliding-mode observer provides a finite-time converging estimate of the continuous system’s state vector in spite of the presence of unknown inputs. The design procedure, which assumes knowledge of the discrete state of the switched system, is based on the principles of disturbance decoupling and hierarchical observer output injection. In order to cope with the switching nature of the plant under observation, jumps in the observer state space are enforced intentionally. The implementation of an additional observer allows for the reconstruction of the unknown inputs, which may be important in the framework of fault detection. Numerical examples illustrate the effectiveness of the suggested technique.

HOSM Observer for a Class of Non-Minimum Phase Causal Nonlinear MIMO Systems

A higher order sliding mode observer is proposed for asymptotic identification of the full state vector and the vector of unknown inputs for MIMO nonlinear causal systems with unstable internal dynamics. The problem is addressed via consistent application of exact higher order sliding mode differentiators in conjunction with the method of stable system center. A numerical example illustrates the performance of the proposed algorithm.

Fault diagnosis for the vertical three-tank system via high-order sliding-mode observation

This paper presents an approach to the fault diagnosis and disturbance observation for the hydraulic vertical three-tank system. An observer is designed which contains a corrective term based on a second-order sliding mode control algorithm featuring global convergence properties. Thanks to the proposed global observer, the reconstruction of certain faults and/or disturbances can be performed directly from the continuous observer output injection signal, without requiring any filtration. The effectiveness of the proposed method is shown by means of a simulation example and is then validated by performing real experiments.

Synchronization in reduced-order of chaotic systems via control approaches based on high-order sliding-mode observer

The reduced-order synchronization problem of two chaotic systems (master–slave) with different dimension and relative degree is considered. A control scheme based on a high-order sliding-mode observer-identifier and a feedback state controller is proposed, where the trajectories of slave can be synchronized with a canonical projection of the master. Thus, the reduced-order synchronization is achieved in spite of master/slave mismatches. Simulation results are provided in order to illustrate the performance of the proposed synchronization scheme.

Estimation of precursor concentration in a research reactor by using second order sliding mode observer

The paper pertains to novel higher order sliding mode observer (SMO) design for estimating precursor concentration of a nuclear research reactor. The linear and nonlinear models of Pakistan Research Reactor-1 (PARR-1) have been tuned and validated with experimental data. These models are subsequently used for higher order sliding mode observer design and performance evaluation. In thermal reactors, precursor concentration is a very important reactor variable because it is responsible for delayed neutron production and finally for reactor control. Linear observers have been used in the past to estimate precursor concentration, but the bandwidth is much limited and performance degraded as the operating point is changed. The nonlinear observer can cater for this problem in a much efficient manner. In this paper a robust nonlinear observer for estimating precursor concentration has been developed by using second order sliding mode technique. The higher order sliding mode observer is efficient and has the main advantage of reduced chattering. The observer estimates the precursor concentration with the measurement of neutron flux only and the estimated value is in close agreement with the theoretically calculated value.

High-order sliding modes observer for linear systems with unbounded unknown inputs

In this article is provided a high order sliding mode observer for linear systems with unbounded unknown inputs. Linear time-invariant systems satisfying conditions of strong observability are studied and an observer basing on high-order sliding-modes di erentiator is designed.

Experimental Validation of Unknown Inputs Estimation Via High Order Sliding Mode Observer

In this work, A new method is developed to estimate the unknown inputs of heavy vehicle. These inputs represent road profile which is very interesting since is used to estimate the vertical forces acting on the wheels. We reconstruct these unknown inputs by using higher order sliding mode observer. First, we estimate speeds and accelerations of heavy vehicle in finite time. Validation process is done using an instrumented heavy vehicle and measured road profile by LPA instrument.

Vehicle Parameter Estimation and Stability Enhancement

In this paper, high order sliding mode observers are used to estimate tires longitudinal forces, vehicle side slip angle and velocities. Two types of high order sliding mode observers are used. A third order one is used to estimate the longitudinal forces, while for the estimation of the vehicle side slip and velocities, an observer based on the super twisting algorithm is proposed. Validations with the simulator ve-dyna pointed out the good performance and the robustness of the proposed observers. Controller design for the braking is accomplished using a reduced state space model representing the movement of the vehicle center of gravity in the (X, Y ) plane. Driver's reactions are taken into account. The performance of the closed loop system is carried out by means of simulation tests.

HOSM observer for a class of non-minimum phase causal nonlinear MIMO systems

Abstract A higher order sliding mode observer is proposed for asymptotic identification of the full state vector and the vector of unknown inputs for MIMO nonlinear causal systems with unstable internal dynamics. The problem is addressed via consistent application of exact higher order sliding mode (HOSM) differentiators in conjunction with the method of stable system center (SSC). A numerical example illustrates the performance of the proposed algorithm.

Vehicle parameter estimation and stability enhancement using sliding modes techniques

In this paper, tyres longitudinal forces, vehicle side slip angle and velocity are identified and estimated using sliding modes observers. Longitudinal forces are identified using higher order sliding mode observers. In the estimation of the vehicle side slip angle and vehicle velocity, an observer based on the broken super-twisting algorithm is proposed. Validations with the simulator VE-DYNA pointed out the good performance and the robustness of the proposed observers. After validating these observers, controller design for the braking is accomplished using a reduced state space model representing the movement of the vehicle centre of gravity in the (X, Y) plane. Driver's reactions are taken into account. The performance of the closed loop system is carried out by means of simulation tests.

Super twisting algorithm-based step-by-step sliding mode observers for nonlinear systems with unknown inputs

This article highlights the interest of step-by-step higher order sliding mode observers for Multi-Input Multi-Output (MIMO) nonlinear systems with unknown inputs. A structural matching condition, commenting on the possibility to design such observers and to reconstruct the unknown inputs, is derived. A finite time sliding mode observer, based on the hierarchical use of the super twisting algorithm, is developed. Then, it is shown that this observer is of interest in the field of hybrid systems and systems with observability singularities. Lastly, it is shown through an example how to relax the usual matching condition by the means of this type of finite time sliding mode observer.

Observation of linear systems with unknown inputs via high-order sliding-modes

A high-order sliding-mode observer is designed for linear time invariant systems with single output and unknown bounded single input. It provides for the global observation of the state and the output under sufficient and necessary conditions of strong observability or strong detectability. The observation is finite-time-convergent and exact in the strong observability case. The accuracy of the proposed observation and identification schemes is estimated via the sampling step or magnitude of deterministic noises. The results are extended to the multi-input multi-output case.

On-line Monitoring in an Aerobic Batch Bioreactor Employing a Robust Soft Sensor

The main objective of this work is to design a soft sensor with finite convergence time for a class of batch reacting systems. Considering the necessity to fast response for monitoring and control issues for batch processes a finite time high order sliding-mode observer is considered.Theoretical analysis is developed to demonstrate the convergence properties of the proposed observer and the finite time of convergence is calculated from the analysis. A simple model for a batch wastewater bioreactor corrobored experimentally is proposed as application example and numerical experiments show the adequate observer performance compared to a standard nonlinear Luenberger observer.