Search

A new robust high-order sliding mode controller for a class of uncertain minimum-phase single-input–single-output (SISO) nonlinear systems is designed. The high-order sliding mode problem is formulated in input–output term and is viewed in uncertain linear context by considering uncertain nonlinear functions as bounded non-structured parametric uncertainties. A sliding manifold is designed in order to ensure finite-time convergence of sliding variable and its high-order time derivatives. The control law allows the establishment of an rth-order sliding mode. This result is extended to multi-input–multi-output (MIMO) systems. Copyright © 2007 John Wiley & Sons, Ltd.

This paper presents the application of two nonlinear observers in order to estimate the absolute orientation angle of a quadruped walking robot. The designed observers are based on high gain and high order sliding mode approaches. A loss of observability during the robot step appears: this problem is dealed by using two different observers structures.

This paper proposes a new second order sliding mode output feedback controller. In the continuous case for which sampling frequency is supposed infinite, this controller uses only the output information and ensures desired trajectory tracking in a finite time in spite of uncertainties and perturbations. Moreover, in case of finite sampling frequency, it is shown that the controller needs also the sign of output time derivative to ensure the finite time convergence to an origin neighborhood.

Under an existing approach, an unknown input observer is designed in deterministic context. The main purpose of this paper consists in analyzing observer performance in presence of both state/measurement noise by using a stochastic framework. This analysis allows to establish an optimal choice of observer gain, and is completed by simulations on a reduced model of an unmanned aerial vehicle for which wind gusts are unknown input. The improvement of controller performances of a light helicopter by using low-cost (noise) sensors and a wind gusts estimator is established.

In this paper, we address the problem of finite-time observation and trajectory tracking for the control of a direct wave energy converter device. We first consider a simplified model of the system on which we develop an homogeneity-based finite-time observer. Then we design a control able to make the system follow a given reference trajectory in finite-time. Simulation results finally demonstrate the applicability of the method.

International audience; In this paper, a new pose estimation solution for perspective vision system is presented and applied to a civil aircraft landing phase. Vision sensor is used to overcome the need of external technologies and runway knowledge. First-of-all, an existing structure of observation is applied to real landing scenarios; in this case, an observability analysis highlights some limitations of this solution. Therefore, a new extended observer solution is proposed which removes observability singularities. Last but not least, all simulation results have been obtained on an Airbus simulator used for certification purpose.

This paper demonstrates a discrete-time state observer for a 3DOF helicopter subject to unknown perturbations. The observer is based on a very recent second order sliding mode scheme [12], which is robust in spite of uncertainties and perturbations, ensures finite time convergence to boundary layer, reduces the chattering, increases estimation accuracy and does not require the knowledge of the bound of unknown input, not restricted to matched disturbances. Also, an unknown input estimation scheme is proposed based on the second order sliding mode observer. A practical example of perturbation estimation for a 3DOF helicopter is experimentally demonstrated.

The objective of this paper is to propose a new control strategy in the context of higher order sliding mode. In fact, the main result concerns a third order sliding mode controller which requires only the sliding variable and its first time derivative (whereas standard third order sliding mode controllers are using also the second order time derivative of the sliding variable). This reduction of the use of time derivatives is very important because it strongly reduces the noise introduced in the controller, and simplifies the controller application to real systems. The control strategy is experimentally applied to an electropneumatic system.

International audience; This paper deals with the problem of state and delay estimation for SISO LTI systems, with unknown time-varying delay in the input. Thanks to an adequate approximation of the delayed input by the Taylor’s theorem, an original approach based on observer design is proposed in order to estimate both state and delay. This new technique allows the estimation of time-varying delay. The convergence of the observer is formally proved. The efficiency of the method is widely illustrated by simulations.

Two observers based on high order sliding mode approach are proposed to determine the absolute orientation of a walking biped robot without feet. Contrary to velocities observers which have been often designed for robot control, very few works have been proposed for the orientation estimation: in this paper, the estimation of all state variables are derived from only the actuated joint variables. Then the technology problem of the absolute measurement is avoided. This latter point is an original contribution of this paper. The observers and the control law converge in finite-time and are well adapted for analysis of the cyclic walking gait. Then, a second original contribution consists in adapting an existing “simplified” Poincaré's sections-based analysis of the stability of the walking to nonlinear systems with not fully available state variables.

This paper deals with the problem of disturbance reconstruction acting on an autonomous helicopter. The disturbance consists in wind gusts, the objective, which is original in this context, being to estimate it by using differentiation of the measurements, in order to compensate these disturbances and to improve the performances of the control. Two differentiation variable structure based strategies are used and compared in term of control performances.

This paper presents an adaptive third order sliding mode controller based on integral sliding mode concept. This new controller is designed for the position control of an electropneumatic actuator, on which bounded external perturbations with unknown magnitude are applied. The efficiency of the controller is experimentally evaluated.

International audience; In this note, we present an implementation of the twisting controller on an electropneumatic plant for a tracking control problem. Implicit and explicit discrete-time twisting controllers are considered, and some implementation details are provided. Experimental results are provided and analyzed. They sustain the theoretical superiority of the implicitly discretized version, as shown in previous work. The main advantages of the implicit method are better tracking and drastic reduction in the input and output chattering. This is achieved without modifying the controller structure compared to its continuous-time version.

This article deals with the well known problem of robust visual servoing (VS), which is formulated by the use of the general task function approach. Robustness is provided with respect to calibration parametric errors not only in terms of stability, but also in terms of tracking errors boundness. As a result, the proposed approach allows the user to choose a bound on the tracking error so as to guarantee the visibility of the target during the task execution. Most importantly, the error boundness is obtained while avoiding the use of large gains. Rather, one uses bounded gains, together with the modulation of the desired velocity along the desired path. An application of this general approach is developed and experimentally validated.

An observer-based controller is proposed for the walking of a biped without feet, i.e. an underactuated system in single support phase. The originality is both: first, the observer is based on second-order sliding mode approach and is original in biped robot context. Secondly, an existing “simplified” Poincare's sections-based analysis of the stability of the walking is adapted to nonlinear system with not fully available state variables.

The aim of this paper is to present a new high-order sliding mode controller for uncertain SISO minimum-phase nonlinear systems. The main properties of this controller are that the convergence time is finite and the uncertainties robustness is ensured. The controller design combines standard equivalent sliding mode control with linear quadratic (LQ) one over a finite time interval with a fixed final state (Lewis. 1986). The advantages of the algorithm are that no exact differentiation is necessary if the value of sliding mode order is equal to the relative degree ρ and the discontinuous gain is minimized via a preliminary nonlinear feedback. Furthermore, the upper bound of the convergence time is chosen a priori and the control law can be adjusted via two weighting matrices.

A higher order sliding mode control scheme for uncertain nonlinear systems is presented in this paper. It is shown that the problem is equivalent to the finite time stabilization of r th -order input output dynamics with bounded uncertainties (r ∊ IN). The controller uses integral sliding mode concept and contains two parts. The first part rejects bounded uncertainties throughout the entire response of the system. The second part achieves finite time stabilization of the r th -order input-output dynamics without uncertainties. As a result, r th order sliding mode is established. The advantages of the method are that its implementation is simple, the time convergence is stated a priori and the robustness is ensured. An illustrative example on a car control shows the applicability of the method.

The primary goal of this paper is to demonstrate a means to prove asymptotically stable walking in an underactuated, planar, five-link biped robot model. The analysis assumes a rigid contact model when the swing leg impacts the ground and an instantaneous double support phase. The specific robot model analyzed corresponds to a prototype under development by the Centre National de la Recherche Scientifique (CNRS), Paris, France. A secondary goal of the paper is to establish the viability of the theoretically motivated control law. This is explored in a number of ways. First, it is shown how known time trajectories, such as those determined on the basis of walking with minimal energy consumption, can be incorporated into the proposed controller structure. Secondly, various perturbations to the walking motion are introduced to verify disturbance rejection capability. Finally, the controller is demonstrated on a detailed simulator for the prototype which includes torque limits and a compliant model of the walking surface, and thus a noninstantaneous double support phase.

This paper focuses on the design of robust vision based control of a 2-DOF planar manipulator. The controller is expressed in the image space, where the system can be modeled as a pure integrator with a nonlinear matrix gain. It involves a simple proportional controller with a feedforward velocity input. Robustness is provided by the guarantee of a bounded tracking error, thanks to the online computation on the desired velocity along the trajectory. The approach is both formally proven and experimentally validated on a lab apparatus.

International audience; This paper presents a set of experimental results concerning the sliding mode control of an electro-pneumatic system. Two discrete-time control strategies are considered for the implementation of the discontinuous part of the sliding mode controller: explicit and implicit discretizations. While the explicit implementation is known to generate numerical chattering [6], [7], [12], [13], the implicit one is expected to significantly reduce chattering while keeping the accuracy. The experimental results reported in this work remarkably confirm that the implicit discrete-time sliding mode supersedes the explicit ones, with several important features: chattering in the control input is almost eliminated (while the explicit and saturated controllers behave like high-frequency bang-bang inputs), the input magnitude depends only on the perturbation size and is largely independent of the controller gain and sampling time.

A perturbed nonlinear system of relative degree two controlled by output feedbacks discontinuous-hybrid-impulsive control is studied. The output hybrid-impulsive terms serve to drive instantaneously the system's trajectory to the origin or to its small vicinity. The output feedback impulsive action combined with the output relay feedback control guarantees a uniform exact convergence with zero convergence time of system's trajectory to a real 2-SMC in the presence of bounded perturbations. The stability of the considered hybrid-impulsive system is studied using Lyapunov approach. © 2014 IEEE.

This paper presents an adaptive higher order sliding mode controller based on first adaptive sliding mode control and an integral sliding variable. The idea is based on the definition of a nominal control which can stabilize a pure chain of integrators to zero in finite time. The novelty of the proposed approach is that uncertainties/perturbations effects are rejected by a first order sliding mode control tuned without any information about the bounds of the uncertainties. The efficiency of this controller is evaluated on an academic example with two kinds of nominal controls.

International audience; This paper addresses the problem of linear adaptive controller for a class of un- certain continuous-time single-input single-output (SISO) nonaffine nonlinear dy- namic systems. Firstly, using the implicit function theory, the existence of an ideal controller which can achieve control objectives will be demonstrated. Nevertheless, this ideal controller can not be known and computed even if the system model is well known. The aim of our work is to construct this unknown ideal controller us- ing a simple linear controller with the gains updated online by a stable adaptation mechanism designed to minimize the error between the unknown ideal controller and the used linear controller. Since the mathematical model of the system is assumed unknown in this work, the proposed control scheme can be regarded as a simple model free controller for the studied nonaffine class of systems. We prove that the closed-loop system controlled is stable and all the signals are bounded. An application of the proposed linear adaptive controller for a nonaffine system is illustrated through the simulation results to demonstrate the effectiveness of the proposed control scheme.

The problem addressed is the linearization of multi-input multi-output (MIMO) nonlinear systems by a generalized state coordinates transformation and generalized input–output injection, in order to design an observer. This observer will have linear error dynamics. The goal is to bring together two observers design approaches: a structural one and a numerical one. Necessary and sufficient conditions for the existence of a linearizing generalized state transformation are obtained by an algebraic way and without computing the input–output differential equations. The main result tests integrability conditions of differential one-forms derived from the state space representation and is applicable to a large subclass of nonlinear systems. Copyright © 2001 John Wiley & Sons, Ltd.

Biped robots form a subclass of legged or walking robots. The study of mechanical legged motion has been motivated by its potential use as a means of locomotion in rough terrain, as well as its potential benefits to prothesis development and testing. The paper concentrates on issues related to the automatic control of biped robots. More precisely, its primary goal is to contribute a means to prove asymptotically-stable walking in planar, underactuated biped robot models. Since normal walking can be viewed as a periodic solution of the robot model, the method of Poincare sections is the natural means to study asymptotic stability of a walking cycle. However, due to the complexity of the associated dynamic models, this approach has had limited success. The principal contribution of the present work is to show that the control strategy can be designed in a way that greatly simplifies the application of the method of Poincare to a class of biped models, and, in fact, to reduce the stability assessment problem to the calculation of a continuous map from a subinterval of R to itself. The mapping in question is directly computable from a simulation model. The stability analysis is based on a careful formulation of the robot model as a system with impulse effects and the extension of the method of Poincare sections to this class of models.

This paper presents a stable linear adaptive control scheme for the position control of a pneumatic actuator system. The proposed controller does not require the experimental identification of the mass flow rate, which is really a novelty in the field of such applications. The controller synthesis is based on an uncertain non-affine nonlinear model of the pneumatic system. Firstly, the existence of an ideal controller which can achieve position control objectives is demonstrated using the implicit function theory. Nevertheless, even if the actuator model is well-known, this ideal controller cannot be known and computed. The aim of the proposed approach is to construct this unknown ideal controller using a simple linear controller with a stable adaptation mechanism. The stability of the closed-loop system is studied by using a Lyapunov approach. Finally, simulation results are provided to show the capabilities of the presented control method.

International audience; The rolling resistance and the effective radius of a vehicle's tyre are two important characteristics that affect its dynamics, performances and comfort. Thanks to their dependence on tyre inflation pressure, the online estimation of such parameters could be used to monitor tyre pressures using an indirect approach. By considering rotational and longitudinal dynamics models, this paper proposes to apply observers for this online estimation using measurements of wheel angular velocities and engine torque. These latter signals being available on major vehicle Controller Area Networks (CAN), the proposed solutions do not require additional sensors. These nonlinear observers are based, first, on high gain approach, and then on high order sliding mode approach allowing robustness and finite time convergence. The originality of the presented results consists in providing a joint estimation of both variables, wheel effective radius and rolling resistance force. The observers offer the very-first solution for dynamical estimation of rolling resistance in standard driving conditions, the rolling resistance being very difficult to estimate by an online procedure. Simulations and experimental results allow to discuss the effect of tyre pressure on these parameters and to illustrate the applicability of the proposed approach.

International audience; This paper proposes a novel adaptive-gain second order sliding mode controller. The proposed controller is based on discontinous-impulsive action and only uses information of the output, no differentiation is needed. A practical second order sliding mode is ensured in spite of bounded perturbations with unknown bound. The gain adaptation is based on particular con- ditions attainable on sliding mode which can be verified with the only information of the output. Both, the convergence conditions and adaptation proposal are tested through simulations.

International audience; Adaptive sliding mode strategies of first and second sliding orders are developed for single-input single- output systems of the first and second relative degrees respectively. Since the only concrete known uncertainty bounds are assumed to be the upper bounds of logarithmic derivatives, no standard sliding- mode technique can solve the problem

The problem under interest is the linearization of nonlinear systems by generalized input-output injection in order to built observers with linear error dynamics. The method is based on the study of the structure of the input-output differential equations; thus, the problem is solved as a realization one. A necessary and sufficient condition and an algorithm give the generalized state coordinates transformation, if it exists, and the generalized input-output injections which linearize multi-input multi-output nonlinear systems. This condition uses exterior differentiation and is fully constructive.

The goal of this paper is twofold. It unifies and generalizes existing results on input-output injection linearization of nonlinear systems. The problem is solved as a realization problem since it is based on the analysis of the structure of the input-output differential equation. The necessary and sufficient conditions are derived from a simplified and constructive procedure. For clarity, the paper is limited to the case of single output systems. Exterior differential systems are extensively used throughout the paper, giving constructive conditions.

This paper proposes a discontinuous-impulsive output feedback which is a sampled based second order sliding mode controller. First, constructive convergence conditions are established for the controller, in the unperturbed and perturbed case. An adaptation mechanism is based on the aforementioned convergence conditions and allows to reduce gain magnitude.

The Lyapunov stability of a double integrator controlled by a discontinuous-impulsive feedback with adaptation is developed. Following previous results of the authors the gain of the impulsive control is adapted to minimize the time convergence to zero of the double integrator dynamics when the impulsive control is applied. The impulsive-sliding mode adaptive controller applied to the second order system is considered as an hybrid system. The stability of this hybrid system is studied using special Lyapunov functions.

New insight is given on the linearization by input-output injection. Necessary and sufficient conditions of the existence of (generalized or not) state and output coordinates transformations are given. The approach is based on an algebraic analysis of the input-ouput differential equation. Exterior differentiation and product are extensively used throughout the paper.

This paper presents a novel autopilot for a 3D helicopter. From desired trajectories defined by the user for elevation and travel angles, the autopilot is computing the desired trajectory of the pitch angle. Furthermore, the autopilot allows to decouple the system and to define “virtual” inputs in order to separately design controllers for each attitude angle. Travel and elevation controllers are based on adaptive version of super-twisting algorithm: this class of controllers keeps the robustness feature of sliding mode while reducing the well-known drawback of such control approach, the chattering, thanks to the online adaptation of the controller gain.

This paper presents an application of adaptive 2nd order sliding mode control. This control is based on twisting algorithm and ensures a finite time convergence to the sliding manifold σ = σ = 0, σ being the sliding variable and defined from the control objectives. The control solution required a limited information about the uncertainties and the disturbances acting on the system. This control strategy is applied to an electropneumatic set-up. This bench consists of two rod coupled pneumatic cylinders: one cylinder is controlled on position and perturbed by the second cylinder which is force-controlled. The efficacy of this strategy is evaluated through some simulations.Copyright © 2012 by ASME

International audience; This paper presents a novel autopilot for a 3D helicopter. From desired trajectories defined by the user for elevation and travel angles, the autopilot is computing the desired trajectory of the pitch angle. Furthermore, the autopilot allows to decouple the system and to define "virtual" inputs in order to separately design controllers for each attitude angle. Travel and elevation controllers are based on adaptive version of sliding mode control: this class of controllers keeps the robustness feature of sliding mode while reducing the well- known drawback of such control approach, the chattering, thanks to the online adaptation of the controller gain. The proposed autopilot is evaluated on an experimental set-up.

The rolling resistance and the effective radius of a tyre are two important characteristics that are very useful for vehicle diagnosis and wheel monitoring systems. This paper proposes to consider the physical model of rotational and longitudinal dynamics of the wheel and to apply a variable structure observer for an on-line estimation of these quantities using measurement of wheel angular velocity, vehicle speed and engine torque. These latter signals being available on major modern vehicle controller area networks (CAN), the proposed solution do not require any additional sensor. Experimental results are given in order to illustrate the relevance of this approach.

The problem under investigation is the computation of an observer for a single flexible joint robot. Several control laws need the measurements of velocities of the link and the motor axis. Since these measured data are often noisy, the use of an observer is necessary. The technique used here to built this observer is based on the linearization of a nonlinear system, via a state diffeomorphism and output injection. In opposition to the geometric approach which is difficult to apply because of the use of Frobenius theorem, we give an purely algebraic necessary and sufficient condition for the existence of a linearizing state diffeomorphism and output injection.

This paper proposes an application of a variable structure observer for wheel effective radius and velocity of automotive vehicles. This observer is based on high order sliding approach allowing robustness and finite time convergence. Its originality consists in assuming a nonlinear relation between the slip ratio and the friction coefficient and providing an estimation of both variables, wheel radius and vehicle velocity, from measurement of wheel angular velocity and torque. These signals being available on major modern vehicle CAN (Controller Area Network) buses, this system does not require additional sensors. A simulation example is given to illustrate the relevance of this approach.

The objective of this chapter is to present advanced control methodologies of uncertain nonlinear systems. Firstly, adaptive sliding mode controller that retains the system's robustness in the presence of the bounded uncertainties/perturbations with unknown bounds is proposed. Due to the on-line adaptation, the proposed approach allows reducing control chattering. Secondly, a high order sliding mode control strategy that features a priory knowledge of the convergence time is presented. Finally, the output feedback second order sliding mode controller is presented and discussed. The control algorithms are applied to experimental set-up equipped by electrical or electropneumatic actuators.

International audience; This paper deals with a planar biped. The aim is the estimation, during the imbalance phases of a walking cyclic gait, of its absolute orientation by only using the measurement of the actuated joint variables. The main contribution is the experimental evaluation of an original finite-time convergent posture observer.

This paper treats the atmospheric orbit transfert of a spacecraft. The main problem developed is the atmospheric flight. The guidance law is obtained by using two classical non linear guidance methods: the trajectory tracking, and the sliding mode control technique. A model reduction by singular perturbations is also considered. The point is that the system is required to track a pre-defined reference trajectory, such that the vehicle flies, from given initial conditions, to defined exit conditions. To test the performances of the guidance law, a robustness study is done for the atmosperic density variations

International audience; A novel super-twisting adaptive sliding mode controller is proposed. A drift uncertain term is assumed to be bounded with unknown boundary. The proposed approach consists in using dynamically adapted control gains that ensure the establishment, in a finite time, of a second order sliding mode. Finite convergence time is estimated. A numerical example confirms the efficacy of the proposed adaptive super- twisting control.

This paper presents a novel control strategy based on adaptive sliding mode control. The proposed adaptation law allows adjusting the control gain by taking into account the effects of bounded uncertainties and perturbations with unknown bounds. The main advantage of the proposed adaptive sliding mode control algorithm is in adjusting the control gain without its overestimation in the presence of the bounded perturbations with the unknown bounds. This yields the reduction of chattering. The control law is applied for position-pressure control of electropneumatic actuator experimental setup.

International audience; In this paper a new neuromusculoskeletal simulation strategy is proposed. It is based on a cascade control approach with an inner muscular-force control loop and an outer joint-position control loop. The originality of the work is located in the optimization criterion used to distribute forces between synergistic and antagonistic muscles. The cost function and the inequality constraints depend on an estimation of the muscle fiber length and its time derivative. The advantages of a such criterion are exposed by theoretical analysis and numerical tests. The simulation model used in the numerical tests consists in an anthropomorphic arm model composed by two joints and six muscles. Each muscle is modeled as a second order dynamical system including activation and contraction dynamics. Contraction dynamics is represented using a classical Hill's model.

International audience; This paper proposes new methodologies for the design of adaptive sliding mode control. The goal is to obtain a robust sliding mode adaptive gain control law with respect to uncertainties and perturbations without the knowledge of uncertainties/perturbations bound (only the boundness feature is known). The proposed approaches consist in having a dynamical adaptive control gain that establishes a sliding mode in finite time.. Gain dynamics ensures also that there is no over-estimation of the gain with respect to the real a priori unknown value of uncertainties. The efficacy of both proposed algorithms is confirmed on a tutorial example and while controlling an electropneumatic actuator.

International audience; This paper proposes a new second order sliding mode output feedback controller. This latter is developped in the case of finite sampling frequency and is using only output information in order to ensure desired trajectory tracking with high accuracy in a finite time in spite of uncertainties and perturbations. This new strategy is evaluated in simulations on an academic example.

International audience; In this paper, a robust sensorless speed observer- controller scheme for a permanent magnet synchronous motor (PMSM) is proposed. To estimate both position and speed, without any mechanical sensors and only from the electrical measurements, a back-EMF-based sliding mode is designed. The convergence of this observer is proved. Then a high order sliding mode controller is developed. By using this technique, the drawback of the sliding mode technique called "chattering phenomenon" is strongly attenuated. After that, the convergence of the overall system is analyzed. Moreover, the robustness of this method with respect to the parameters uncertainties is verified by significant simulation results in the framework of an industrial benchmark.

This paper is a first attempt for a new second order sliding mode output feedback controller. This last one is developped in the case of finite sampling frequency and is using only output information in order to ensure desired trajectory tracking with high accuracy in a finite time in spite of uncertainties and perturbations. This controller ensures the establishment of a “real” second order sliding mode behaviour and its feasability is evaluated on an academic example.