Giorgio Bartolini

Chattering avoidance by second-order sliding mode control

Relying on the possibility of generating a second-order sliding motion by using, as control, the first derivative of the control signal instead of the actual control, a new solution to the problem of chattering elimination in variable structure control (VSC) is presented. Such a solution, inspired by the classical bang-bang optimal control strategy, is first depicted and expressed in terms of a control algorithm by introducing a suitable auxiliary problem involving a second-order uncertain system with unavailable velocity. Then, the applicability of the algorithm is extended, via suitable modifications, to the case of nonlinear systems with uncertainties of more general types. The proposed algorithm does not require the use of observers and differential inequalities and can be applied in practice by exploiting such commercial components as peak detectors or other approximated methods to evaluate the change of the sign of the derivative of the quantity accounting for the distance to the sliding manifold.

A survey of applications of second-order sliding mode control to mechanical systems

The effective application of sliding mode control to mechanical systems is not straightforward because of the sensitivity of these systems to chattering. Higher-order sliding modes can counteract this phenomenon by confining the switching control to the higher derivatives of the mechanical control variable, so that the latter results are continuous. Generally, this approach requires the availability of a number of time derivatives of the sliding variable, and, in the presence of noise, this requirement could be a practical limitation. A class of second-order sliding mode controllers, guaranteeing finite-time convergence for systems with relative degree two between the sliding variable and the switching control, could be helpful both in reducing the number of differentiator stages in the controller and in dealing with unmodelled actuator dynamics. In this paper different second-order sliding mode controllers, previously presented in the literature, are shown to belong to the above cited class, and some challenging control problems involving mechanical systems are addressed and solved. Simulations and experimental results are provided throughout the paper.

On multi-input chattering-free second-order sliding mode control

A solution to the problem of eliminating the chattering effect, which is always associated with practical implementations of variable structure control, is presented with reference to a class of uncertain multi-input nonlinear systems. The solution procedure relies on the application of an original control approach capable of enforcing a second-order sliding mode (i.e., a sliding regime on a surface s[x(t)]=0 in the system state space, with s/spl dot/[x(t)] identically equal to zero, a regime enforced by a control signal depending on s[x(t)], but directly acting only on s/spl uml/[x(t)]). Such an approach, in its original formulation, only applies to single-input nonlinear systems with particular types of uncertainties. In the present paper, its validity is extended to multi-input nonlinear systems characterized by uncertainties of more general nature, covering a wide class of real processes.

Adaptive sliding mode control in discrete-time systems

Abstract Discrete-time sliding mode control is considered. The case of known parameters is first analyzed, leading to a new definition of the so-called ‘equivalent control’ as the piecewise-constant control that reduces to zero, in finite time, the distance of the system state from the sliding manifold. In the presence of bounded parametric uncertainties, an adaptive control scheme that guarantees the asymptotic satisfaction of the same control objective is presented. The main feature of this approach is the reduction of the order of the relevant error equation, and the possibility of dealing with the nonmatched uncertainties introduced by the sampling process.

Output tracking control of uncertain nonlinear second-order systems

Abstract The solution of a tracking problem for a secondorder nonlinear system with uncertain dynamics and incomplete state measurement is obtained by means of a procedure directly inspired by the solution of the classical minimum-time optimal control problem. Two different types of uncertainty are considered in the paper: in the first case a constant bound on the uncertain dynamics is assumed to be known; in the second case, the bound is a function of both the measurable and the unmeasurable state variable of the system. In both cases, the possibility of applying the proposed control algorithms is proved to be determined by a proper choice of the control signal features. The resulting system is characterized by a suitable feedback switching logic and the convergence of the system trajectory to the desired one (or to a δ-vicinity of this latter) is proved also in the uncertain case.

Second-order sliding-mode control of container cranes

Moving a suspended load along a pre-speci0ed path is not an easy task when strict speci0cations on the swing angle and on the transfer time need to be satis0ed. Intuitively, minimizing the cycle time and the load swing are con5icting requirements, and their satisfaction requires proper control actions, especially if some uncertainties in the system dynamics are present. In this paper we propose a simple control scheme, based on second-order sliding modes, which guarantees a fast and precise load transfer and the swing suppression during the load movement, despite of model uncertainties and unmodeled dynamic actuators. Such controller has been tested on a laboratory-size model of the crane, and some experimental results are reported. ? 2002 Elsevier Science Ltd. All rights reserved.

Modern sliding mode control theory : new perspectives and applications

Part I Basic Theory.- Regularization of Second Order Sliding Mode Control Systems.- A comprehensive Analysis of Chattering in Second Order Sliding Mode Control Systems.- Analysis of Closed-Loop Performance and Frequency-Domain Design of Compensating Filters for Sliding Mode Control Systems.- Discontinuous Homogeneous Control.- Second-order Sliding Sector for Variable Structure Control.- On Eulers Discretization of Sliding Mode Control Systems with Relative Degree Restriction.- Part II Design Methods.- Circumventing the relative degree condition in sliding mode design.- HOSM driven output tracking in the nonminimum-phase causal nonlinear systems.- High Order Sliding Mode Neurocontrol for Uncertain Nonlinear SISO Systems: Theory and Applications.- A Generalized PI Sliding Mode and PWM Control of Switched Fractional Systems.- Stabilization of nonholonomic uncertain systems via adaptive second order sliding mode control.- Output Tracking with Discrete-Time Integral Sliding Mode Control.- Flatness, Backstepping and Sliding Mode Controllers for Nonlinear Systems.- Part III Observers and Fault Detection.- Observation and identification via high-order sliding modes.- High Order Sliding Mode Observers and Differentiators-Application to Fault Diagnosis Problem.- Vehicle Parameter and States Estimation via Sliding Mode Observers.- An alternative to the measurement of five-links biped robot absolute orientation: estimation based on high order sliding mode.- Part IV Applications.- Robust Orbital Stabilization of Pendubot: Algorithm Synthesis, Experimental Verification, and Application to Swing up and Balancing Control.- Higher Order SM Block-Control of Nonlinear Systems with Unmodeled Actuators. Application to electric power systems and electrohydraulic servo-drives.- Blood Glucose Regulation Via Double Loop Higher Order Sliding Mode Control and Multiple Sampling Rate.- Contact force regulation in wire-actuated pantographs.

Properties of a combined adaptive/second-order sliding mode control algorithm for some classes of uncertain nonlinear systems

In this paper, a combined adaptive/variable structure control approach is presented that exploits the good properties of the backstepping procedure and of a second-order sliding-mode control algorithm. This algorithm enables one to attain the conditions S=0, S/spl dot/=0 (second-order sliding mode) in a finite time, S=0 being a predefined sliding manifold. The combined approach retains the stability and convergence features of the original adaptive strategy. In addition, it allows one to deal with systems with uncertainties of more general types, ensuring robustness, as well as a reduction in the computational load.

Simplex methods for nonlinear uncertain sliding-mode control

We develop a new analysis of the behavior of simplex control methods applied to multiple-input-multiple-output nonlinear control systems under uncertainties. According to such sliding-mode control methods the control vector is constrained to belong to a finite set of (fixed or varying) vectors, with an appropriate switching logic to guarantee the specified sliding condition. Bounded uncertainties acting on the nominal system are allowed. The proposed sliding control methodology relies on the knowledge of the nominal system only. We prove rigorously the convergence of these methods to the sliding manifold in a finite time under explicit quantitative conditions on the system parameters and the available bounds of the uncertainty. Application to a robotic problem is discussed and a nonlinear example is presented.

Brief Digital second-order sliding mode control for uncertain nonlinear systems

In this note, we analyze the discrete-time implementation of a second-order sliding mode control (2-SMC) scheme. The treatment is detailed for a simple class of feedback-linearizable nonlinear systems expressed in the Brunowsky normal form. First, it is shown that the direct discretization of a continuous-time 2-SMC scheme guarantees the finite-time attainment of a motion in an O(T^2) boundary layer of the sliding manifold (T being the sampling period). Then, a suitable iterative learning procedure, that leads to the asymptotic reduction of the boundary layer to O(T^3) is proposed. Simulation results are reported at the end of the paper.