Alexandre Sanfelice Bazanella

Identification and the Information Matrix: How to Get Just Sufficiently Rich?

In prediction error identification, the information matrix plays a central role. Specifically, when the system is in the model set, the covariance matrix of the parameter estimates converges asymptotically, up to a scaling factor, to the inverse of the information matrix. The existence of a finite covariance matrix thus depends on the positive definiteness of the information matrix, and the rate of convergence of the parameter estimate depends on its ¿size¿. The information matrix is also the key tool in the solution of optimal experiment design procedures, which have become a focus of recent attention. Introducing a geometric framework, we provide a complete analysis, for arbitrary model structures, of the minimum degree of richness required to guarantee the nonsingularity of the information matrix. We then particularize these results to all commonly used model structures, both in open loop and in closed loop. In a closed-loop setup, our results provide an unexpected and precisely quantifiable trade-off between controller degree and required degree of external excitation.

Brief paper: Virtual Reference Feedback Tuning for non-minimum phase plants

Model Reference control design methods fail when the plant has one or more non minimum phase zeros that are not included in the reference model, leading possibly to an unstable closed loop. This is a very serious problem for data-based control design methods where the plant is typically unknown. For Iterative Feedback Tuning a procedure was proposed in [1] to overcome this difficulty. In this paper we extend this idea to Virtual Reference Feedback Tuning, another data-based control design method. We present a simple two-step procedure that can cope with the situation where the unknown plant may or may not have non minimum phase zeros.

Iterative minimization of H2 control performance criteria

a b s t r a c t Data-based control design methods most often consist of iterative adjustment of the controllers parameters towards the parameter values which minimize an H2 performance criterion. Typically, batches of input-output data collected from the system are used to feed directly a gradient descent optimization — no process model is used. A limiting factor in the application of these methods is the lack of useful conditions guaranteeing convergence to the global minimum; several adaptive control algorithmssufferfromthesamelimitation.InthispapertheH2 performancecriterionisanalyzedinorder to characterize and enlarge the set of initial parameter values from which a gradient descent algorithm can converge to its global minimum.

Brief Robust tuning of the speed loop in indirect field oriented control of induction motors

In this paper, we analyze the occurrence of Hopf bifurcations in indirect field-oriented control of induction motors and derive guidelines for setting the PI speed controller in order to keep the bifurcations far enough from the operating conditions in the parameter space.

Closed-Loop Identification of MIMO Systems: A New Look at Identifiability and Experiment Design

This paper addresses a question raised by a leading expert in the identification of multivariable systems: “Is it necessary to excite all reference signals for the identification of a multivariable system operating in closed loop with a linear time-invariant controller?” On the basis of earlier results on identifiability of closed-loop systems, he conjectured that this was necessary. We show that it is not, on the basis of a careful re-examination of the notions of identifiability and informative experiments for closed-loop systems.

Informative data: How to get just sufficiently rich?

Prediction error identification requires that data be informative with respect to the chosen model structure. Whereas sufficient conditions for informative experiments have been available for a long time, there were surprisingly no results of necessary and sufficient nature. With the recent surge of interest in optimal experiment design, it is of interest to know the minimal richness required of the externally applied signal to make the experiment informative. We provide necessary and sufficient conditions on the degree of richness of the applied signal to generate an informative experiment, both in open loop and in closed loop. In a closed-loop setup, where identification can be achieved with no external excitation if the controller is of sufficient degree, our results provide a precisely quantifiable trade-off between controller degree and required degree of external excitation.

Necessary and sufficient conditions for uniqueness of the minimum in Prediction Error Identification

The contribution of this paper is to establish computable necessary and sufficient conditions on the model structure and on the experiment under which the Prediction Error Identification (PEI) criterion has a unique global minimum. We consider a broad class of rational model structures whose numerator and denominator are affine in the unknown parameter vector; this class encompasses all classical model structures used in system identification. The main results in this paper rely on the standard assumption that the system is in the model set, while some intermediate results are valid even when this assumption does not hold (in particular Theorem 4.2 and Lemma 6.1). This is achieved by first establishing necessary and sufficient conditions on the model structure and on the experiment under which a global minimum is isolated; these conditions must hold locally, at the global minimum. A second contribution is to show that these conditions are equivalent to the nonsingularity of the information matrix at that minimum. For open loop identification and, with some additional constraints also for closed loop identification, the nonsingularity of the information matrix is then also equivalent to the uniqueness of the global minimum.

Robustness margins for indirect field-oriented control of induction motors

The influence of the rotor time constant mismatch on the stability of induction motors under indirect field oriented control is analyzed. The results of De Wit et al. (1996) are generalized. A Lyapunov function which provides a global stability test and allows to compute robustness margins is given. Different mechanisms for the loss of stability are detected by means of bifurcation analysis. Robustness margins and design guidelines are derived from these results.

Tuning Rules for Proportional Resonant Controllers

In this brief, we propose a particular structure for resonant controllers and a tuning method of the Ziegler–Nichols type for their tuning. Performance criteria for resonant controllers are also defined. The effectiveness of the tuning rules is illustrated by their application and corresponding performance assessment in a test batch consisting of four representative classes of processes. The control performance is analyzed in detail for one particular example, shedding light on the virtues and limitations of the control structure and of the tuning method.

Connecting informative experiments, the information matrix and the minima of a Prediction Error Identification criterion

This paper establishes, in a Prediction Error Identification (PEI) context, the connections that exist between the identifiability of the model structure, the informativity of the data, the information matrix and the existence of a unique global minimum of the PEI criterion. By introducing the concept of informative data at a particular parameter value, we are able to establish a number of equivalences and connections between these four ingredients of the identification problem, for both open-loop and closed-loop identification.