Wyniki wyszukiwania - BazTech

1

Identification of parametric models with a priori knowledge of process properties

Janiszowski K. B., Wnuk P.

International Journal of Applied Mathematics and Computer Science

|

2016

|

Vol. 26, no. 4

767--776

EN

An approach to estimation of a parametric discrete-time model of a process in the case of some a priori knowledge of the investigated process properties is presented. The knowledge of plant properties is introduced in the form of linear bounds, which can be determined for the coefficient vector of the parametric model studied. The approach yields special biased estimation of model coefficients that preserves demanded properties. A formula for estimation of the model coefficients is derived and combined with a recursive scheme determined for minimization of the sum of absolute model errors. The estimation problem of a model with known static gains of inputs is discussed and proper formulas are derived. This approach can overcome the non-identifiability problem which has been observed during estimation based on measurements recorded in industrial closed-loop control systems. The application of the proposed approach to estimation of a model for an industrial plant (a water injector into the steam flow in a power plant) is presented and discussed.

2

Approximation of a linear dynamic process model using the frequency approach and a non-quadratic measure of the model error

Janiszowski K. B.

International Journal of Applied Mathematics and Computer Science

|

2014

|

Vol. 24, no. 1

99--109

EN

The paper presents a novel approach to approximation of a linear transfer function model, based on dynamic properties represented by a frequency response, e.g., determined as a result of discrete-time identification. The approximation is derived for minimization of a non-quadratic performance index. This index can be determined as an exponent or absolute norm of an error. Two algorithms for determination of the approximation coefficients are considered, a batch processing one and a recursive scheme, based on the well-known on-line identification algorithm. The proposed approach is not sensitive to local outliers present in the original frequency response. Application of the approach and its features are presented on examples of two simple dynamic systems.

3

Control error dynamic modification as an efficient tool for reduction of effects introduced by actuator constraints

Janiszowski K. B.

International Journal of Applied Mathematics and Computer Science

|

2009

|

Vol. 19, no 2

271-279

EN

A modification of digital controller algorithms, based on the introduction of a virtual reference value, which never exceeds active constraints in the actuator output is presented and investigated for some algorithms used in single-loop control systems. This idea, derived from virtual modification of a control error, can be used in digital control systems subjected to both magnitude and rate constraints. The modification is introduced in the form of on-line adaptation to the control task. Hence the design of optimal (in a specified sense) digital controller parameters can be separated from actuator constraints. The adaptation of the control algorithm (to actuator constraints) is performed by the transformation of the control error and is equivalent to the introduction of a new, virtual reference value for the control system. An application of this approach is presented through examples of three digital control algorithms: the PID algorithm, the dead-beat controller and the state space controller. In all cases, clear advantages of transients are observed, which yields some general conclusions to the problem of processing actuator constraints in control.

4

Inversion of Square Matrices in Processors With Limited Calculation Abillities

Janiszowski K. B.

International Journal of Applied Mathematics and Computer Science

|

2003

|

Vol. 13, no 2

199-204

EN

An iterative inversion algorithm for a class of square matrices is derived and tested. The inverted matrix can be defined over both real and complex fields. This algorithm is based only on the operations of addition and multiplication. The numerics of the algorithm can cope with a short number representation and therefore can be very useful in the case of processors with limited possibilities, like different neuro-computers and accelerator cards. The quality of inversion can be traced and tested. The algorithm can be used in the case of singular matrices, and then it automatically produces a result that contains the inverse of this part of the processed matrix which can be inverted. An example of the inversion of a six-order square matrix is presented and discussed.

5

Least-squares estimation for a long-horizon performance index

Janiszowski K. B.

International Journal of Applied Mathematics and Computer Science

|

2000

|

Vol. 10, no 3

559-573

EN

Estimation of a parametric, discrete-time model for a SISO dynamic plant, derived for minimisation of a performance index determined as a sum of squared prediction errors within some time horizon is considered. A formula for a Long-Horizon Least-Squares (LHLS) off-line solution as well as a theorem for an LHLS recursive on-line scheme are derived. The LHLS scheme reveals some features of Least-Squares (LS) estimation and Instrumental-Variable (IV) estimation. An algorithm for the on-line LHLS scheme is presented and compared with LS and IV estimation schemes for a linear, second-order system. The fast convergence of the derived LHLS on-line scheme is demonstrated in the case of detecting changes in parameters of a non-stationary system.

6

Identification of coefficients of a low order continuous time transfer function from discrete-time recorded measurements

Janiszowski K. B.

Archives of Control Sciences

|

2000

|

Vol. 10, no. 1/2

31-46

EN

The paper deals with a problem of identification of parameters of a continuous time (CT) transfer function for low order linear systems with discrete-time (DT) recorded data. Algorithms for a direct estimation of the CT-coefficients are developed from rules for transformation of a CT-transfer function controlled via a zero-order sampling unit into DT-representation. Two schemes are derived and tested: one based on the Goodwin transformation and the second derived from the modified Tustin transformation. Both approaches have resulted in similar relations, which can be used for direct estimation of the CT-coefficients of the model of an investigated system. The numerical schemes contain some expressions, that are like DT-differences and in effect they can magnify impacts of different disturbances. Therefore the paper presents results of extended testing of both schemes including different type disturbances; measurement noises, slow varying drifts, measurement resolution errors together with changes of the sampling time. A model is used of a third order linear servomechanism system with oscillating and integration actions. A comparison with results determined by the LS-recursive scheme is presented.

7

Identification of Low-Order Continuous-Time Models Via Discrete-Time Trends of Measurements

Janiszowski K. B.

International Journal of Applied Mathematics and Computer Science

|

1999

|

Vol. 9, no 4

839-853

EN

The paper deals with the problem of continuous-time (CT) identification of parameters in transfer functions for low-order linear systems, based on recorded discrete-time (DT) data. Algorithms for direct estimation of CT parameters are developed from rules for transformation of a CT transferfunction controlled via a zero-order sampling-and-hold unit into a DT representation.Two schemes are derived and tested: the first is based on the Goodwin transformation and the other is derived from the modified Tustin transformation. Both the approaches result in relations which can be used for direct estimationof CT parameters in a model of the investigated system. The numerical schemes contain some expressions that are reminiscent of DT differences and consequently they may magnify disturbances. Therefore the results of extensively testing both the schemes including different types of disturbances, measurement noise, slow varying drifts, measurement resolution errors together with changes in the sampling time are presented. A model of a pneumatic servomechanism system was used as a test plant.