Magnus Mossberg

Iterative feedback tuning of PID parameters: comparison with classical tuning rules

We apply the Iterative Feedback Tuning (IFT) method to the tuning of PID parameters in applications where the objective is to achieve a fast response to set point changes. We compare the performance of these IFT-tuned PID controllers with the performance achieved by four classical PID tuning schemes that are widely used in industry. Our simulations show that IFT always achieves a performance that is at least as good as that of the classical PID tuning schemes, and often dramatically better: faster settling time and less overshoot. In addition, IFT is also optimal with respect to the presence of noise, whereas the other schemes are designed for noise-free conditions. The IFT method used here is a variant of the initial IFT scheme, in which no weighting is applied to the control error during a time window that corresponds to the transient response, and where the length of this window is progressively reduced. This method was initially proposed in Lequin (CD-ROM of European Control Conference, Paper TH-A-H6, Brussels, Belgium, 1997) and elaborated on in Lequin et al. (Proceedings of the 14th IFAC World Congress, Paper I-3b-08-3, Beijing, Peoples Republic of China, 1999, pp. 433-437)

Exploiting temperature dependency in the detection of NQR signals

Nuclear quadrupole resonance (NQR) offers an unequivocal method of detecting and identifying land mines. Unfortunately, the practical use of NQR is restricted by the low signal-to-noise ratio (SNR), and the means to improve the SNR are vital to enable a rapid, reliable, and convenient system. In this paper, an approximate maximum-likelihood detector (AML) is developed, exploiting the temperature dependency of the NQR frequencies as a way to enhance the SNR. Numerical evaluation using both simulated and real NQR data indicate a significant gain in probability of accurate detection as compared with the current state-of-the-art approach.

Estimation of continuous-time AR process parameters from discrete-time data

The problem of estimating continuous-time autoregressive process parameters from discrete-time data is considered. The basic approach used here is based on replacing the derivatives in the model by discrete-time differences, forming a linear regression, and using the least squares method. Such a procedure is simple to apply, computationally flexible and efficient, and may have good numerical properties. It is known, however, that all standard approximations of the highest order derivative, such as repeated use of the delta operator, gives a biased least squares estimate, even as the sampling interval tends to zero. Some of our previous approaches to overcome this problem are reviewed. Then. two new methods, which avoid the shift in our previous results, are presented. One of them, which is termed bias compensation, is computationally very efficient. Finally, the relationship of the above least squares approaches with an instrumental variable method is investigated. Comparative simulation results are also presented.

Brief Performance evaluation of methods for identifying continuous-time autoregressive processes

Identification of continuous-time autoregressive processes from discrete-time data by replacing the differentiation operator by an approximation is considered. A linear regression model can then be formulated. The least-squares method and the instrumental variables method must be used with some care to get parameter estimates of good quality. The bias is studied explicitly in the paper together with the asymptotic distribution, and expressions are presented for the covariance matrix of the estimated parameters. It turns out that there are small differences in the dominating bias term for the different methods, whereas the statistical properties are comparable. Overall, the performance is similar to that of a prediction error method for short sampling intervals.

Non-parametric identification of viscoelastic materials from wave propagation experiments

We investigate how the frequency-dependent wave propagation coefficient and complex modulus for a linearly viscoelastic material can be estimated from wave propagation experiments. The strains at different sections of a bar specimen are measured as functions of time. The time series are transformed into the frequency domain, where a non-parametric identification is made. A thorough analysis of the quality of the non-parametric estimate is made, in which approximate expressions for the covariance matrices of the wave propagation coefficient and the complex modulus are derived. The validity of these expressions are confirmed by numerical studies and real experiments.

Frequency-selective detection of nuclear quadrupole resonance signals

Nuclear quadrupole resonance (NQR) offers an unequivocal method of detecting and identifying both hidden explosives, such as land mines, and a variety of narcotics. Unfortunately, the practical use of NQR is restricted by a low signal-to-noise ratio (SNR), and means to improve the SNR are vital to enable a rapid, reliable, and convenient system. In this paper, we introduce a frequency-selective approximate maximum-likelihood (FSAML) detector, operating on a subset of the available frequencies, making it robust to the typically present narrow-band interference. The method exploits the inherent temperature dependency of the NQR frequencies as a way to enhance the SNR. Numerical evaluations, using both simulated and real NQR data, indicate a significant gain in probability of accurate detection as compared to a current state-of-the-art approach.

A covariance matching approach for identifying errors-in-variables systems

The errors-in-variables identification problem concerns dynamic systems whose input and output variables are affected by additive noise. Several estimation methods have been proposed for identifying dynamic errors-in-variables models. In this paper a covariance matching approach is proposed to solve the identification problem. It applies for general types of input signals. The method utilizes a small set of covariances of the measured input-output data. This property applies also for some other methods, such as the Frisch scheme and the bias-eliminating least squares method. Algorithmic details for the proposed method are provided. User choices, for example specification of which input-output covariances to utilize, are discussed in some detail. The method is evaluated by using numerical examples, and is shown to have competitive properties as compared to alternative methods.

Identification of Continuous-Time ARX Models From Irregularly Sampled Data

The problem of estimating the parameters in a continuous-time ARX process from unevenly sampled data is studied. A solution where the differentiation operator is replaced by a difference operator is suggested. In the paper, results are given for how the difference operator should be chosen in order to obtain consistent parameter estimates. The proposed method is considerably faster than conventional methods, such as the maximum likelihood method. The Crameacuter-Rao bound for estimation of the parameters is computed. In the derivation, the Slepian-Bangs formula is used together with a state-space framework, resulting in a closed form expression for the Crameacuter-Rao bound. Numerical studies indicate that the Crameacuter-Rao bound is reached by the proposed method

Extended accuracy analysis of a covariance matching approach for identifying errors-in-variables systems

A system identification method for errors-in-variables problems based on covariance matching was recently proposed. In the first step, a small amount of covariances of noisy input-output data are computed, and then a parametric model is fitted to these covariances. In this paper, the method is further analyzed and the asymptotic accuracy of the parameter estimates is derived. An explicit algorithm for computing the asymptotic covariance matrix of the parameter estimates is given, and the identification method is shown to be asymptotically statistically efficient assuming that the given information is the computed covariances. As an important byproduct, an efficient algorithm is presented for computing the covariance matrix of the computed input-output covariances.

On the use of flexural wave propagation experiments for identification of complex modulus

In this paper, we investigate the nonparametric estimation of the frequency dependent complex modulus of a viscoelastic material. The strains due to flexural wave propagation in a bar specimen are registered at different cross sections. The time domain data is transformed into frequency domain using discrete Fourier transform and a nonlinear least squares algorithm is then employed to estimate the complex modulus at each frequency. Inherent numerical problems due to associated ill-conditioned matrices are treated with special care. An analysis of the quality of the nonlinear least squares estimate is also carried out. The validity of the theoretical results are confirmed by numerical studies and experimental tests.