F. De Bruyne

Minimal positive realizations of transfer functions with positive real poles

A standard result of linear-system theory states that a SISO rational nth-order transfer function always has an nth-order realization. In some applications, one is interested in having a realization with nonnegative entries (i.e., a positive system) and it is known that a positive system may not be minimal in the usual sense. In this paper, we give an explicit necessary and sufficient condition for a third-order transfer function with distinct real positive poles to have a third-order positive realization. The proof is constructive so that it is straightforward to obtain a minimal positive realization.

Iterative feedback tuning for internal model controllers

Abstract In this paper, the applicability of iterative feedback tuning (IFT) to internal model controllers (IMCs) and smith predictors is examined. IFT is a model-free gradient descent controller tuning tool; refer to Hjalmarsson et al. (IEEE Control Systems Mag. 18 (1998) 26) and Hjalmarsson et al. (Proceedings of the Conference on Decision and Control, Orlando, FL, 1994, pp. 1735) for further details. It is shown that the IFT algorithm can be modified to tune IMCs and, more in particular, Smith predictors. The main difference with the original algorithm is that the cost gradient is obtained by doing four experiments (two recycling experiments) instead of three (one recycling experiment) for conventional controllers.

Identification for control: closing the loop gives more accurate controllers

We compare open loop versus closed loop identification when the identified model is used for control design, and when the system itself belongs to the model class, so that only variance errors are relevant. For three different control design criteria (minimum variance, LQG and model reference control) we show that, under those conditions, a better performance is achieved by closing the loop during the identification. The measure of performance is the variance of the error between the output of the ideal closed loop system (with the ideal controller) and that of the actual closed loop system (with the controller computed from the identified model).<<ETX>>

Iterative controller optimization for nonlinear systems

A data-driven model-free control design method has been proposed in Hjalmarsson et al. (1994). It is based on the minimization of a control criterion with respect to the controller parameters using an iterative gradient technique. In this paper, we extend this method to the case where both the plant and the controller can be nonlinear. It is shown that an estimate of the gradient can be constructed using only signal based information. It is also shown that by using open loop identification techniques, one can obtain a good approximation of the gradient of the control criterion while performing fewer experiments on the actual system.

Iterative feedback tuning with guaranteed stability

Presents an identification-based mechanism for introducing guaranteed stability when using a data-driven model-free iterative control design method known as iterative feedback tuning. Also, the use of unbiased estimates of the Hessian is shown to significantly improve the user control over the tuning procedure.

Closed-loop output error identification algorithms for nonlinear plants

A family of algorithms for the identification of continuous time nonlinear plants operating in closed-loop is presented. An adjustable output error type predictor is parametrized in terms of the existing controller and the estimated plant model. The algorithms are derived from stability considerations in the absence of noise and assuming that the plant model is in the model set. Subsequently the algorithms are analyzed in the presence of noise and when the plant model is not in the model set.

The Vinnicombe metric for nonlinear operators

Describes an extension of the Vinnicombe metric on linear operators to a pseudometric on nonlinear operators. A metric for finite-dimensional time-varying operators is shown to be capable of guaranteeing stability and performance robustness and reduces to the standard Vinnicombe metric for the time-invariant operator case, which is known to be less conservative than the gap metric. The analysis exploits the time-varying operator equivalents of unstable poles and normalized coprime fractional descriptions. In addition, a time-varying operator equivalent of the winding number is defined.

On state-estimation of a two-state hidden Markov model with quantization

We consider quantization from the perspective of minimizing filtering error when quantized instead of continuous measurements are used as inputs to a nonlinear filter, specializing to discrete-time two-state hidden Markov models (HMMs) with continuous-range output. An explicit expression for the filtering error when continuous measurements are used is presented. We also propose a quantization scheme based on maximizing the mutual information between quantized observations and the hidden states of the HMM.

Model validation in closed loop

In Ljung (1998), a model validation method was proposed that is based on the estimation of an unbiased model of the model error which relates the inputs to the simulation errors. In this paper, we extend this methodology to closed-loop validation, i.e. the validation of an open-loop model on the basis of closed-loop validation data. We show that, perhaps surprisingly, the same model may fail to be validated with open-loop data, while it is validated by data collected in closed loop. In addition, we show that the uncertainty sets generated by models validated in closed loop are better tuned towards control design, i.e. the controllers that stabilize all members of such a set are less conservative than those that stabilize all members of a set validated in open loop. The comparison between both methods is illustrated by means of a numerical example.

Closed loop identification of nonlinear systems

Several new methods for the identification of approximate models of an open loop plant on the basis of closed loop data have been presented. In this paper, we extend two of these methods to the nonlinear case: we consider that both the plant and the controller can be nonlinear. The first method is a two-step procedure. The sensitivity function of the closed loop system is identified through a high order nonlinear model and it is used in the second step to simulate a noise free input signal for an open loop like identification of the plant. The second method identifies the right coprime factors of the plant through an open loop like identification of the filtered sensitivity and complementary sensitivity functions. For both methods, we assume that the measurement noise enters the system under a high S/N ratio assumption.