Sergio Galeani

A Tutorial on Modern Anti-Windup Design

In this paper, several constructive linear and nonlinear anti-windup techniques are presented and explained. Two approaches, namely direct linear anti-windup (DLAW) and model recovery anti-windup (MRAW), are described in an algorithmic way, in order to illustrate their main features. Hereafter, theoretical conditions ensuring stability and performance, their applicability, their accompanying guarantees, and their merits and deficiencies are given. The possible extensions to less standard problem settings are also briefly discussed.

Active vibration control of an elastic plate using multiple piezoelectric sensors and actuators

Abstract This paper is addressed to the vibration control of an elastic plate, clamped along one side and excited by an impulsive transversal force acting in correspondence of a free corner. The plate is equipped with three couples of piezoelectric patches, used as sensors and actuators. A modal model of the coupled electromechanical structure, obtained by employing a suitable finite-element formulation together with a modal reduction, is used in the controller design. Different H2 control laws have been designed and compared by simulation, in order to evaluate the performance obtained using different combinations of sensors and actuators together with models taking into account an increasing number of structural eigenmodes.

Event-triggered transmission for linear control over communication channels

We consider an exponentially stable closed loop interconnection between a continuous-time linear plant and a continuous-time linear controller, and we study the problem of interconnecting the plant output to the controller input through a digital channel. We propose an event-triggered transmission policy whose goal is to transmit the measured plant output information as little as possible while preserving closed-loop stability. Global asymptotic stability is guaranteed when the plant state is available or when an estimate of the state is available (provided by a classical continuous-time linear observer). Under further assumptions, the transmission policy guarantees global exponential stability of the origin.

A magnitude and rate saturation model and its use in the solution of a static anti-windup problem

In this paper we address the anti-windup design problem for linear control systems with strictly proper controllers in the presence of input magnitude and rate saturation. Using generalized sector condition, we provide an LMI-based procedure for the construction of a linear anti-windup gain acting on the controller state equation such that regional closed-loop stability is guaranteed and suitable performance measures are optimized. The approach is successfully illustrated on a simulation example.

Robust Trajectory Tracking for a Class of Hybrid Systems: An Internal Model Principle Approach

This paper deals with the asymptotic tracking of periodic trajectories for hybrid systems having linear dynamics in each operating mode and isolated discrete switching events (switching systems). Parametric uncertainties are considered and the dimension of the state vector is allowed to vary among modes. To deal with the hybrid nature of the system, and the possible discontinuities of its solutions at switching times, a properly amended tracking control problem is defined and a feedback control law based on a discontinuous version of the classical internal model principle is proposed. The innovative design of the discrete-time dynamics of the compensator guarantees the robust existence of a steady-state response giving zero tracking error in the controlled output, and local convergence to it.

Trajectory tracking for a particle in elliptical billiards

An infinitely rigid unitary mass (particle) is considered, moving on a planar region delimited by a rigid elliptical barrier (elliptical billiards) under the action of proper control forces. A class of periodic trajectories, involving an infinite sequence of non-smooth impacts between the mass and the barrier at fixed times, is found by using an LMIs based procedure. The jumps in the velocities at the impact times render difficult (if not impossible) to obtain the classical stability and attractivity properties for the dynamic system describing the tracking error behaviour. Hence, the tracking control problem is properly stated using notions similar to the quasi stability concept in V. Lakshmikantham, D.D. Bainov and P.S. Simeonov, Theory of Impulsive Differential Equations, 6, World Scientific, 1989. A controller (whose state is subject to discontinuities) based on the internal model principle is shown to solve the proposed tracking problem, giving rise to control forces that are piecewise continuous function of time, with discontinuities at the desired impact times and at the impact times of the particle with the barrier.

Output regulation for a class of linear hybrid systems. Part 1: trajectory generation

In this paper the problem of generating zero error steady-state responses is addressed for a class of hybrid linear systems whose jumps are determined by time only. The procedure for the design of an automatic device generating the steady-state response and input is described. Once such device and a compensator ensuring incremental stability (see the companion paper) are available, the classical output regulation problem for the same class of hybrid linear systems can be immediately solved. Compared with previously available results, no assumption is needed on the plant about minimum phaseness, relative degree or squareness (same number of inputs and outputs). The key role of the zero dynamics and of the additional inputs (when the plant is fat) is highlighted.

Output regulation for a class of linear hybrid systems. Part 2: stabilization

This paper reports some stabilization results for a class of hybrid linear systems whose jumps are determined by time only. Linearity of the resulting closed-loop system implies that global asymptotic and incremental stability are achieved at the same time. In turn, incremental stability allows for the solution of a recently considered output regulation problem by coupling a suitable steady state generator (described in a companion paper) and the stabilizer from this paper. It is remarked that stabilization and regulation are achieved for general MIMO plants without relying on minimum phase, relative degree or squareness assumptions.

Necessary and sufficient conditions for output regulation in a class of hybrid linear systems

In this paper, the problem of output regulation for a class of hybrid linear systems is considered. Necessary and sufficient conditions for its solution are provided, both in the full information and error feedback case, under the additional constraint that the regulator is a hybrid linear time invariant system from the same class. A stronger version of the internal model principle is also shown, requiring that the regulator must contain a copy of the zero dynamics of the plant in addition to the usual copy of the exosystem dynamics.

Brief paper: Nonlinear dynamic allocator for optimal input/output performance trade-off: Application to the JET tokamak shape controller

In this paper, we revisit the dynamic allocation scheme for input redundant plants proposed in Zaccarian (2009). within a set-point regulation setting and propose generalizations that apply to cases where the plant under consideration is not input redundant but the control specifications allow us to modify the set-point regulation within certain bounds. In this case, the input allocator is extended to the nonredundant case by allowing it to improve the input allocation selection at the price of some output regulation error. We also establish here desirable convergence properties of the allocator, which were only addressed for the linear case in Zaccarian (2009). In particular, we design the allocator dynamics as the gradient of a cost function and establish its convergence to the minimum of the cost function under some mild conditions. The allocation scheme is applied to the JET tokamak shape controller by illustrating its capabilities to enforce coil currents selections that tend to move away from the saturation limits within the allowable degrees of freedom.