Gérard Scorletti

Model validation for control and controller validation in a prediction error identification framework-Part I: theory

We propose a model validation procedure that consists of a prediction error identification experiment with a full order model. It delivers a parametric uncertainty ellipsoid and a corresponding set of parameterized transfer functions, which we call prediction error (PE) uncertainty set. Such uncertainty set differs from the classical uncertainty descriptions used in robust control analysis and design. We develop a robust control analysis theory for such uncertainty sets, which covers two distinct aspects: (1) Controller validation. We present necessary and sufficient conditions for a specific controller to stabilize-or to achieve a given level of performance with-all systems in such PE uncertainty set. (2) Model validation for robust control. We present a measure for the size of such PE uncertainty set that is directly connected to the size of a set controllers that stabilize all systems in the model uncertainty set. This allows us to establish that one uncertainty set is better tuned for robust control design than another, leading to control-oriented validation objectives.

Brief Robustness analysis tools for an uncertainty set obtained by prediction error identification

This paper presents a robust stability and performance analysis for an uncertainty set delivered by classical prediction error identification. This nonstandard uncertainty set, which is a set of parametrized transfer functions with a parameter vector in an ellipsoid, contains the true system at a certain probability level. Our robust stability result is a necessary and sufficient condition for the stabilization, by a given controller, of all systems in such uncertainty set. The main new technical contribution of this paper is our robust performance result: we show that the worst case performance achieved over all systems in such an uncertainty region is the solution of a convex optimization problem involving linear matrix inequality constraints. Note that we only consider single input-single output systems.

Cheapest open-loop identification for control

This paper presents a new method of identification experiment design for control. Our objective is to design the open-loop identification experiment with minimal excitation such that the controller designed with the identified model stabilizes and achieves a prescribed level of H/sub /spl infin// performance with the unknown true system G/sub 0/.

Robustness analysis with time-delays

In this paper, we consider the stability analysis of uncertain linear time invariant systems with several time-delays. The delays are assumed unknown but constant. Working on quadratic constraints within a topological separation framework, we propose an extension of the /spl mu/ analysis to address the analysis of systems with nonrational uncertainties in a connected set. We obtain (NP hard) necessary and sufficient conditions. Convex sufficient conditions, involving linear matrix inequalities, are then derived. These conditions are an extension of the /spl mu/ upper bound. Using a conventional /spl mu/ analysis approach, the obtained conditions would be delay independent or, at least, more conservative than the proposed criterion. We finally evaluate the interest of our conditions on a numerical example.

A measure of robust stability for an identified set of parametrized transfer functions

Defines a measure of robustness for a set of parameterized transfer functions as delivered by classical prediction error identification and that contains the true system at a prescribed probability level. This measure of robustness is the worst case Vinnicombe distance between the model and the plants in the uncertainty region. We show how it can be computed exactly using LMI-based optimization. In addition, we show that this measure is directly connected to the size of the set of controllers that are guaranteed to stabilize all plants in the uncertainty region, i.e., the smaller the worst case Vinnicombe distance for an uncertainty region, the larger the set of model-based controllers that are guaranteed to stabilize all systems in this uncertainty region.

Phase and gain control policies for robust active vibration control of flexible structures

The interest of this paper is to develop a general and systematic robust control methodology for active vibration control of flexible structures. For this purpose, first phase and gain control policies are proposed to impose qualitative frequency-dependent requirements on the controller to consider a complete set of control objectives. Then the proposed control methodology is developed by employing phase and gain control policies in the dynamic output feedback H??control: according to the set of control objectives, phase and gain control policies incorporate necessary weighting functions and determine them in a rational and systematic way; on the other hand, with the appropriate weighting functions efficient H??control algorithms can automatically realize phase and gain control policies and generate a satisfactory H??controller. The proposed control methodology can be used for both SISO and MIMO systems with collocated or non-collocated sensors and actuators. In this paper, it is validated on a non-collocated piezoelectric cantilever beam. Both numerical simulations and experimental results demonstrate the effectiveness of the proposed control methodology.

Open-loop versus closed-loop identification of Box-Jenkins models: a new variance analysis

We present formulae for the analysis of variance of estimated transfer functions, which are valid for Box-Jenkins (BJ) and Output Error (OE) model structures of finite order, identified in either open-loop or closed-loop, using Prediction Error (PE) Identification. The formulae are based on the asymptotic (in number of data) expression of the parameter covariance. They do not require special assumptions on the generation of the external signals. One of the results of our analysis is to show that, under reasonable assumptions on the signal powers, the variance of the estimated input-output model is smaller with closed-loop than with open-loop identification.

A Waveform Design Method for a Piezo Inkjet Printhead Based on Robust Feedforward Control

The printing quality delivered by a Drop-on-Demand (DoD) piezo inkjet printhead is limited mainly due to the residual oscillations in the ink channel. The maximal jetting frequency of a DoD inkjet printhead can be increased by quickly damping the residual oscillations and thus bringing an ink channel to rest after jetting an ink drop. In this paper, we propose a robust optimization-based method to design the input actuation waveform for the piezo actuator in order to improve the damping of the residual oscillations in the presence of parametric uncertainties in the ink-channel model. The proposed method obtains a robust actuation pulse by minimizing the tracking error under the parametric uncertainty. Experimental results with a small-droplet DoD inkjet printhead are presented to show the efficacy of the proposed method and the significant improvement in the ink drop consistency.

All-digital PLL array provides reliable distributed clock for SOCs

This brief addresses the problem of clock generation and distribution in globally synchronous locally synchronous chips. A novel architecture of clock generation based on network of coupled all-digital PLLs is proposed. Solutions are proposed to overcome the issues of stability and undesirable synchronized modes (modelocks) of high-order bidirectional PLL networks. The VLSI implementation of the network is discussed in CMOS65 nm technology and the simulation results prove the reliability of the global synchronization by the proposed method.

A clock network of distributed ADPLLs using an asymmetric comparison strategy

In this paper, we describe an architecture of a distributed ADPLL (All Digitall Phase Lock Loop) network based on bang-bang phase detectors that are interconnected asymmetrically. It allows an automatic selection between two operating modes (uni- and bidirectional) to avoid mode-locking phenomenon, to accelerate the network convergence and to improve the robustness to possible network failures in comparison to simple unidirectional mode.