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1

Application-oriented experiment design for model predictive control

Jakowluk W., Świercz M.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2020

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Vol. 68, nr 4

883--891

EN

The model predictive control (MPC) technique has been widely applied in a large number of industrial plants. Optimal input design should guarantee acceptable model parameter estimates while still providing for low experimental effort. The goal of this work is to investigate an application-oriented identification experiment that satisfies the performance objectives of the implementation of the model. A- and D-optimal input signal design methods for a non-linear liquid two-tank model are presented in this paper. The excitation signal is obtained using a finite impulse response filter (FIR) with respect to the accepted application degradation and the power constraint. The MPC controller is then used to control the liquid levels of the double tank system subject to the reference trajectory. The MPC scheme is built based on the linearized and discretized model of the system to predict the system’s succeeding outputs with reference to the future input signal. The novelty of this model-based method consists in including the experiment cost in input design through the objective function. The proposed framework is illustrated by means of numerical examples, and simulation results are discussed.

2

Optimal input signal design for fractional-order system identification

Jakowluk W.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2019

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Vol. 67, nr 1

37--44

EN

The optimal design of excitation signal is a procedure of generating an informative input signal to extract the model parameters with maximum pertinence during the identification process. The fractional calculus provides many new possibilities for system modeling based on the definition of a derivative of noninteger-order. A novel optimal input design methodology for fractional-order systems identification is presented in the paper. The Oustaloup recursive approximation (ORA) method is used to obtain the fractional-order differentiation in an integer order state-space representation. Then, the presented methodology is utilized to solve optimal input design problem for fractional-order system identification. The fundamental objective of this approach is to design an input signal that yields maximum information on the value of the fractional-order model parameters to be estimated. The method described in this paper was verified using a numerical example, and the computational results were discussed.

3

Power spectrum optimization in the design of multisine manoeuvre for identification purposes

Lichota P., Szulczyk J., Noreña D. A., Vallejo Monsalve F. A.

Journal of Theoretical and Applied Mechanics

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2017

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Vol. 55 nr 4

1193--1203

EN

In this paper, two sets of multisine signals are designed for system identification purposes. The first one is obtained without any information about system dynamics. In the second case, the a priori information is given in terms of dimensional stability and control derivatives. Magnitude Bode plots are obtained to design the multisine power spectrum that is optimized afterwards. A genetic algorithm with linear ranking, uniform crossover and mutation operator has been employed for that purpose. Both designed manoeuvres are used to excite the aircraft model, and then system identification is performed. The estimated parameters are obtained by applying two methods: Equation Error and Output Error. The comparison of both investigated cases in terms of accuracy and manoeuvre time is presented afterwards.

4

On infinite horizon active fault diagnosis for a class of non-linear non-Gaussian systems

Punčochář I., Šimandl M.

International Journal of Applied Mathematics and Computer Science

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2014

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Vol. 24, no. 4

795--807

EN

The paper considers the problem of active fault diagnosis for discrete-time stochastic systems over an infinite time horizon. It is assumed that the switching between a fault-free and finitely many faulty conditions can be modelled by a finite-state Markov chain and the continuous dynamics of the observed system can be described for the fault-free and each faulty condition by non-linear non-Gaussian models with a fully observed continuous state. The design of an optimal active fault detector that generates decisions and inputs improving the quality of detection is formulated as a dynamic optimization problem. As the optimal solution obtained by dynamic programming requires solving the Bellman functional equation, approximate techniques are employed to obtain a suboptimal active fault detector.

5

Optymalizacja pobudzeń dla celów identyfikacji parametrów modeli zmiennych stanu

Kalicka R., Pietrenko-Dąbrowska A., Lipiński S.

Pomiary Automatyka Kontrola

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2008

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R. 54, nr 3

114-117

PL

W pracy omówiono zagadnienie optymalizacji pobudzeń dla celów identyfikacji parametrów modeli kompartmentowych systemów farmakokinetycznych opisanych w kategoriach zmiennych stanu. Przedstawiono pobudzenia optymalne zaprojektowane według kryterium A-optymalności. Zaprojektowane pobudzenia optymalne, w obrębie klasy pobudzeń o ograniczonej energii, zapewniają maksymalną osiągalną dokładność estymat parametrów. W farmakokinetyce nałożenie ograniczenia na energię pobudzenia konieczne jest w przypadku leków, których szybkie podawanie powoduje występowanie skutków ubocznych.

EN

Optimal input design for parameter estimation of compartmental state-space models of pharmacokinetic systems is presented in the paper. The results presented were obtained for two-compartmental model of procainamide pharmacokinetics. In the paper A-optimality criterion was utilised. A-optimal inputs presented, in the equienergy class of optimal inputs, ensure the best achievable accuracy of parameter estimates. The optimisation procedure delivered optimal inputs of non-positive values presented in Fig. 2. In order to ensure the applicability of the optimal inputs in drug delivery the additional constraint, lower bound was imposed on the optimal inputs. The applicable optimal inputs presented in Fig. 3 were used for parameter estimation. In the Tab. 2 the parameter estimates as well as their accuracies are presented.

6

Optimal inputs in pharmacokinetics model's identification

Pietrenko-Dąbrowska A., Kalicka R.

Biocybernetics and Biomedical Engineering

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2006

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Vol. 26, no. 3

3-14

EN

The paper presents optimal input design for parametric identification of the SISO state space compartmental models of pharmacokinetic systems. The adopted objective function is the trace of the Fisher information matrix (the sensitivity criterion). The class of equienergy admissible inputs is concemed, as rate-dependent side effects occur for many medicines. The optimal input design problem is a nonlinear programming problem with constraint. The problem is solved using Kuhn-Tucker necessary conditions. SeveraI compartmental models were examined. The optimal inputs of different shapes were obtained and compared.

7

An optimal input design using the sensitivity criterion for parametric identification of pharmacokinetic models

Kalicka R., Pietrenko-Dąbrowska A.

Biocybernetics and Biomedical Engineering

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2005

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Vol. 25, no. 2

3-18

EN

The parametric approach to the identification of the SISO state space compartmental models of pharmacokinetic systems is presented. The model structure is formulated basing on the a priori knowledge. The initial parameter estimates are calculated on the base of the output measurements collected during the intuitive experiment. They are used for designing the optimal input, which ensures the best accuracy of the parameter estimates. The sensitivity criterion is adopted and presented in terms of nonlinear programming problem with constraints. Two classes of optimal inputs are considered: equidose and equienergy inputs. The results obtained with optimal and standard inputs are presented and compared.