Three direct methods for the identification of a linear continuous-time system from the samples of input and output observations are considered. These are based on obtaining approximate expressions for the signals fro...
Three direct methods for the identification of a linear continuous-time system from the samples of input and output observations are considered. These are based on obtaining approximate expressions for the signals from their samples. The methods are (i) block-pulse functions, (ii) trapezoidal pulse functions, and (iii) cubic spline functions. In each case, the differential equations are integrated using these approximations and the results are used for estimating the parameters of a model of given order and structure which will provide the best fit in the least squares sense. Results of simulation are included which compare the relative performance of the three methods both in the absence and the presence of measurement noise.
A practical fault detection scheme based on a model discrimination approach is proposed for dynamical systems with various failure modes which can not he explicitly described by mathematical representations. Using ARX...
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A practical fault detection scheme based on a model discrimination approach is proposed for dynamical systems with various failure modes which can not he explicitly described by mathematical representations. Using ARX modelling, the Kullback Discrimination Information (KDI) is adopted as a model distortion measure to detect dynamics failures. In order to calculate the KDI for finite but large data sets with-out dealing with very large matrices, we derive an iterative algorithm of low dimension based on Baye' rule. The KDI is used as a detection index in a thresholding approach. This detection scheme can be combined with identification to diagnose the system operating mode. The effectiveness of the method has been confirmed through a simulation study of a second order servo system.
The Kullback discrimination index can be used to test whether two models obtained from different data sets are equal or not. Such an index can be used for model validation, which then is carried out as a crossvalidati...
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The Kullback discrimination index can be used to test whether two models obtained from different data sets are equal or not. Such an index can be used for model validation, which then is carried out as a crossvalidation. However, the form of the index and its implementation differ from traditional crossvalidation. Some simple validation criteria are developed from this index, and also numerically illustrated.
The recently obtained evidence of the need for a positive real element in an adaptive system leaves us with a disturbing gap in adaptive control theory. It is a fact that in some applications adaptive controllers are ...
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The recently obtained evidence of the need for a positive real element in an adaptive system leaves us with a disturbing gap in adaptive control theory. It is a fact that in some applications adaptive controllers are performing well in practice. How can these systems behave well in practical situations which must contain modeling error? This paper introduces a preliminary result which indicates that it may be possible to maintain the needed positive real system in the presence of modeling error. The result shows that if a continuous-time system with large high frequency uncertainty is treated appropriately with antialiasing filters and sampled slowly enough, the resulting discrete-time system may contain very little uncertainty. With small enough uncertainty in the plant, a positive real system in the adaptive loop is possible.
In this paper, two theorems are quoted which, when applied together, provide much information about the robustness of adaptive control schemes. From these two theorems, another theorem is developed which can explain w...
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In this paper, two theorems are quoted which, when applied together, provide much information about the robustness of adaptive control schemes. From these two theorems, another theorem is developed which can explain why adaptive controllers can perform robustly in certain practical situations, while possibly failing in other situations. In particular, if the bandwidth constraints on a control systems are lenient enough to allow the use of a sampling frequency which is smaller than the frequency at which unstructured uncertainty becomes significant, an adaptive controller can behave robustly. Many, if not all, of the applications of adaptive control which have been successful employ relatively slow sampling of the process. Thus, the results of this paper provide a theoretical explanation of how certain adaptive controllers are performing robustly in practice. In addition, the final theorem is of a form which provides insight into what a priori knowledge is required to achieve robust adaptive control and how this knowledge say be used.
The optimal stochastic approximation procedure (OSAP) is applied to the parameter identification problem of distributed parameter system (DPS) driven by random disturbances and observed through noisy measurements. Thi...
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The optimal stochastic approximation procedure (OSAP) is applied to the parameter identification problem of distributed parameter system (DPS) driven by random disturbances and observed through noisy measurements. This procedure is a stochastic approximation procedure (SAP) with an optimal gain sequence and an optimal transformation on the gradient of the objective function: these optimal values accelerate the convergence rate by minimizing the mean squared parameter estimation error, under the assumption that the density functions of the system and observation noises are known, or can be easily estimated. An example of parameter identification of a stochastic parabolic DPS is simulated on the digital computer. A comparison is made among the results of the optimal, the modified, the nominal first-order, and the nominal second-order SAP. It is shown that the OSAP gives higher accuracy and faster rate of convergence as compared to the nominal SAP
The paper deals with the design problem of control algorithms in fuzzy systems described by means of fuzzy relational equations, which can be implemented in the framework of fuzzy controllers applied to control of ill...
Several methods for the identification of linear multivariable continuous-time systems from the samples of input-output data are discussed. These include three new methods proposed by the authors. The suitability of t...
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Several methods for the identification of linear multivariable continuous-time systems from the samples of input-output data are discussed. These include three new methods proposed by the authors. The suitability of these methods for estimating the parameters of the system using recursive least-squares algorithm is compared using a simulated example. The results indicate that the best results are obtained using the block pulse function method as proposed by the authors.
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