Closed-Loop Identification with an Unstable or Non-minimum Phase Controller

In many practical cases, the identification of a system is done in closed loop with some controller. In this paper, we show that the internal stability of the resulting model, in closed loop with the same controller, is not always guaranteed if this controller is unstable and/or nonminimum phase, and that the classical closed-loop prediction-error identification methods present different properties regarding this stability issue. With some of these methods, closed-loop instability of the identified model is actually guaranteed. This is a serious drawback if this model is to be used for the design of a new controller. We give guidelines to avoid the emergence of this instability problem; these guidelines concern both the experiment design and the choice of the identification method

Closed-loop Identification with an Unstable or Nonminimum Phase Controller

In many practical cases, the identification of a system is done in closed loop with some controller. In this paper, we show that the internal stability of the resulting model, in closed loop with the same controller, is not always guaranteed if this controller is unstable and/or nonminimum phase, and that the classical closed-loop prediction-error identification methods present different properties regarding this stability issue. With some of these methods, closed-loop instability of the identified model is actually guaranteed. This is a serious drawback if this model is to be used for the design of a new controller. We give guidelines to avoid the emergence of this instability problem; these guidelines concern both the experiment design and the choice of the identification method

Model Validation for Control and Controller Validation in a Prediction error Identification Framework - Part I

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

Model Validation for Control and Controller Validation in a Prediction error Identification Framework - Part II: illustrations

The results on model validation for control and controller validation in a prediction error identification framework are illustrated. The results are illustrated with two realistic identification and control design applications. The first is the control of a flexible mechanical system with a tracking objective and the second is the control of a ferrosilicon production process with a disturbance rejection objective