Antonella Ferrara

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.

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.

Vehicle Yaw Control via Second-Order Sliding-Mode Technique

The problem of vehicle yaw control is addressed in this paper using an active differential and yaw rate feedback. A reference generator, designed to improve vehicle handling, provides the desired yaw rate value to be achieved by the closed loop controller. The latter is designed using the second-order sliding mode (SOSM) methodology to guarantee robust stability in front of disturbances and model uncertainties, which are typical of the automotive context. A feedforward control contribution is also employed to enhance the transient system response. The control derivative is constructed as a discontinuous signal, attaining an SOSM on a suitably selected sliding manifold. Thus, the actual control input results in being continuous, as it is needed in the considered context. Simulations performed using a realistic nonlinear model of the considered vehicle show the effectiveness of the proposed approach.

Higher Order Sliding Mode Controllers With Optimal Reaching

Higher order sliding mode (HOSM) control design is considered for systems with a known permanent relative degree. In this paper, we introduce the robust Fullers problem that is a robust generalization of the Fullers problem, a standard optimal control problem for a chain of integrators with bounded control. By solving the robust Fullers problem it is possible to obtain feedback laws that are HOSM algorithms of generic order and, in addition, provide optimal finite-time reaching of the sliding manifold. A common difficulty in the use of existing HOSM algorithms is the tuning of design parameters: our methodology proves useful for the tuning of HOSM controller parameters in order to assure desired performances and prevent instabilities. The convergence and stability properties of the proposed family of controllers are theoretically analyzed. Simulation evidence demonstrates their effectiveness.

Integral Sliding Mode Control for Nonlinear Systems With Matched and Unmatched Perturbations

We consider the problem of designing an integral sliding mode controller to reduce the disturbance terms that act on nonlinear systems with state-dependent drift and input matrix. The general case of both, matched and unmatched disturbances affecting the system is addressed. It is proved that the definition of a suitable sliding manifold and the generation of sliding modes upon it guarantees the minimization of the effect of the disturbance terms, which takes place when the matched disturbances are completely rejected and the unmatched ones are not amplified. A simulation of the proposed technique, applied to a dynamically feedback linearized unicycle, illustrates its effectiveness, even in presence of nonholonomic constraints.

Trajectory Planning and Second-Order Sliding Mode Motion/Interaction Control for Robot Manipulators in Unknown Environments

The problem of determining an interaction control strategy, allowing a manipulator to reach a goal point even in the presence of unknown obstacles, is faced in this paper. To this end, on the basis of position/orientation and force measurements, first, a path planning strategy is proposed. The path planning is based on an a priori trajectory, which is determined without the prior knowledge of the obstacle presence in the workspace, and on a real-time approach to generate auxiliary temporary trajectories on the basis of the properties of the obstacle surface in a vicinity of the contact point, estimated through force measurements. To determine the input laws of the manipulator, a robust hybrid position/force control scheme is adopted. First- and second-order sliding mode controllers are considered to generate the robot input laws, and the obtained performances are experimentally compared with those of classical PD control. Experiments are made on a COMAU SMART3-S2 anthropomorphic industrial manipulator.

Fault Detection for Robot Manipulators via Second-Order Sliding Modes

This paper presents a model-based fault detection (FD) and isolation scheme for rigid manipulators. A single fault acting on a specific actuator or on a specific sensor of the manipulator is detected (and, if possible, the exact location of the fault), and an estimation of the fault signal is performed. Input-signal estimator and output observers are considered in order to make the FD procedure possible. By using the suboptimal second-order sliding-mode (SOSM) algorithm to design the input laws of the observers, satisfactory stability properties of the observation error are established. The proposed algorithm is verified in simulation and experimentally on a COMAU SMART3-S2 robot manipulator.

Wheel Slip Control via Second-Order Sliding-Mode Generation

During skid braking and spin acceleration, the driving force exerted by the tires is reduced considerably, and the vehicle cannot speed up or brake as desired. It may become very difficult to control the vehicle under these conditions. To solve this problem, a second-order sliding-mode traction controller is presented in this paper. The controller design is coupled with the design of a suitable sliding-mode observer to estimate the tire-road adhesion coefficient. The traction control is achieved by maintaining the wheel slip at a desired value. In particular, by controlling the wheel slip at the optimal value, the proposed traction control enables antiskid braking and antispin acceleration, thus improving safety in difficult weather conditions, as well as stability during high-performance driving. The choice of second-order sliding-mode control methodology is motivated by its robustness feature with respect to parameter uncertainties and disturbances, which are typical of the automotive context. Moreover, the proposed second-order sliding-mode controller, in contrast to conventional sliding-mode controllers, generates continuous control actions, thus being particularly suitable for application to automotive systems.

Optimal control of freeways via speed signalling and ramp metering

Abstract Freeway traffic control by means of speed signalling and ramp-metering has been addressed, by following a suboptimal approach. Starting from the estimation of the traffic flow, standard parametrized closed-loop regulators for speed signalling and ramp-metering have been tuned using an optimization procedure based on Powell’s method. Optimization is carried out by minimizing (or maximizing) an empirical mean cost function according to the Montecarlo paradigm. The regulators perform using an estimate of a macroscopic model-based state vector given by an extended Kalman filter.