Leonid Fridman

Second-order sliding-mode observer for mechanical systems

The super-twisting second-order sliding-mode algorithm is modified in order to design a velocity observer for uncertain mechanical systems. The finite time convergence of the observer is proved. Thus, the observer can be designed independently of the controller. A discrete version of the observer is considered and the corresponding accuracy is estimated.

Sliding Mode Control and Observation

The sliding mode control methodology has proven effective in dealing with complex dynamical systems affected by disturbances, uncertainties and unmodeled dynamics. Robust control technology based on this methodology has been applied to many real-world problems, especially in the areas of aerospace control, electric power systems, electromechanical systems, and robotics. Sliding Mode Control and Observation represents the first textbook that starts with classical sliding mode control techniques and progresses toward newly developed higher-order sliding mode control and observation algorithms and their applications.The present volume addresses a range of sliding mode control issues, including:*Conventional sliding mode controller and observer design*Second-order sliding mode controllers and differentiators*Frequency domain analysis of conventional and second-order sliding mode controllers*Higher-order sliding mode controllers and differentiators*Higher-order sliding mode observers *Sliding mode disturbance observer based control *Numerous applications, including reusable launch vehicle and satellite formation control, blood glucose regulation, and car steering control are used as case studiesSliding Mode Control and Observation is aimed at graduate students with a basic knowledge of classical control theory and some knowledge of state-space methods and nonlinear systems, while being of interest to a wider audience of graduate students in electrical/mechanical/aerospace engineering and applied mathematics, as well as researchers in electrical, computer, chemical, civil, mechanical, aeronautical, and industrial engineering, applied mathematicians, control engineers, and physicists. Sliding Mode Control and Observation provides the necessary tools for graduate students, researchers and engineers to robustly control complex and uncertain nonlinear dynamical systems. Exercises provided at the end of each chapter make this an ideal text for an advanced coursetaught in control theory.

Analysis and design of integral sliding manifolds for systems with unmatched perturbations

The robustness properties of integral sliding-mode controllers are studied. This note shows how to select the projection matrix in such a way that the euclidean norm of the resulting perturbation is minimal. It is also shown that when the minimum is attained, the resulting perturbation is not amplified. This selection is particularly useful if integral sliding-mode control is to be combined with other methods to further robustify against unmatched perturbations. H/sub /spl infin// is taken as a special case. Simulations support the general analysis and show the effectiveness of this particular combination.

Analysis of Chattering in Systems With Second-Order Sliding Modes

A systematic approach to the chattering analysis in systems with second-order sliding modes is developed. The neglected actuator dynamics is considered to be the main cause of chattering in real systems. The magnitude of oscillations in nonlinear systems with unmodeled fast nonlinear actuators driven by second-order sliding-mode control generalized suboptimal (2-SMC G-SO) algorithms is evaluated. Sufficient conditions for the existence of orbitally stable periodic motions are found in terms of the properties of corresponding Poincare maps. For linear systems driven by 2-SMC G-SO algorithms, analysis tools based on the frequency-domain methods are developed. The first of these techniques is based on the describing function method and provides for a simple approximate approach to evaluate the frequency and the amplitude of possible periodic motions. The second technique represents a modified Tsypkins method and provides for a relatively simple, theoretically exact, approach to evaluate the periodic motion parameters. Examples of analysis and simulation results are given throughout this paper.

Analysis of chattering in continuous sliding-mode controllers

An analysis of two most popular continuous sliding-mode algorithms: The power-fractional sliding-mode algorithm and a second-order sliding-mode algorithm known as the super-twisting is carried out in the frequency domain with the use of the describing function method. It is shown that in the presence of an actuator, the transient process converges to a periodic motion. Parameters of this periodic motion are analyzed. A few examples are considered to illustrate the obtained results.

Observation and identification of mechanical systems via second order sliding modes

A second-order sliding-mode observer based on the modified super-twisting algorithm providing finite time observation is applied for system identification. The value of the equivalent output injection is used to identify perturbations directly. Continuous time versions of least square and forgetting factor methods are proposed to identify unknown time-invariant and time-variant parameters respectively

Uniform Robust Exact Differentiator

The differentiators based on the Super-Twisting Algorithm (STA) yield finite-time and theoretically exact convergence to the derivative of the input signal, whenever this derivative is Lipschitz. However, the convergence time grows unboundedly when the initial conditions of the differentiation error grow. In this technical note a Uniform Robust Exact Differentiator (URED) is introduced. The URED is based on a STA modification and includes high-degree terms providing finite-time, and exact convergence to the derivative of the input signal, with a convergence time that is bounded by some constant independent of the initial conditions of the differentiation error. Strong Lyapunov functions are used to prove the convergence of the URED.

An averaging approach to chattering

The singularly perturbed relay control systems (SPRCS) as mathematical models of chattering in the small neighborhood of the switching surface in sliding mode systems are examined. Sufficient conditions for existence and stability of fast periodic solutions to the SPRCS are found. It is shown that the slow motions in such SPRCS are approximately described by equations derived from equations for the slow variables of SPRCS by averaging along fast periodic motions. It is shown that In the general case, when the equations of a plant contain relay control nonlinearly, the averaged equations do not coincide with the equivalent control equations or with the Filippovs definition (1988) for the sliding motions in the reduced system; however, in the linear case, they coincide.

Variable structure systems: from principles to implementation

* Part I: Sliding mode control theory * Chapter 1: Sliding mode control * Chapter 2: Sliding mode regulator design * Chapter 3: Deterministic output noise effects in sliding mode observation * Chapter 4: Stochastic output noise effects in sliding mode observation * Part II: New trends in sliding mode control * Chapter 5: Discrete-time VSS * Chapter 6: Robustness issues of 2-sliding mode control * Chapter 7: Sliding modes, delta-modulation and output feedback control of dynamic systems * Chapter 8: Analysis of sliding modes in the frequency domain * Chapter 9: Output tracking in causal nonminimum-phase systems using sliding modes * Part III: Applications of sliding mode control * Chapter 10: Sliding mode control and chaos * Chapter 11: Sliding modes in fuzzy and neural network systems * Chapter 12: SMC applications in power electronics * Chapter 13: Sliding modes in motion control systems * Chapter 14: Sliding mode control for automobile applications * Chapter 15: The application of sliding mode control algorithms to a diesel generator set * Chapter 16: Motion control of underwater objects by using second order sliding mode techniques * Chapter 17: Semiglobal stabilisation of linear uncertain system via delayed relay control

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.