Publikacyje i wystōmpiynia

The availability of two additional tunable parameters compared with Proportional Integral Derivative (PID) controllers makes it possible to incorporate fractional-order (FO) integral/derivative actions. The selection of the optimization algorithm and objective function is important for tuning the fractional-order PID controller. This paper presents the formulation of the FOPID controller design as an optimization problem and its solution using four built-in algorithms in MATLAB. Each algorithm solves the optimization by minimizing two cost functions resulting eight sets of controller parameters. To overcome the sensitivity of algorithms to the initial and boundary values of the parameters, we considered nine different initial and boundary conditions. The proposed method considers the minimum of the optimal values obtained in each case. This provides globally-optimal FOPID controllers. To validate its efficiency, the proposed method uses a Twin Rotor Aerodynamic System (TRAS) as an example. Comparison with a nonlinear approach shows that the proposed approach ensures tracking with minimal and smooth control efforts.

The purpose of an automatic control is to provide the best quality of the output signal of a controlled object. This quality is dependent on the type and tuning parameters of the used controller and on the properties of a transducer measuring the output signal. In this work, it was considered how the imperfections of the transducer propagate by the fractional-order (FO) control system. It was revealed that the assumed approximation method of FO derivation changes the trajectory of the output signal and also has an influence on the steady-state value. In turn, the measurement uncertainty estimation should take into account the analysis of the occurrence of oscillations, arising from drifts of imperfect components, that may exceed the permissible errors of the measuring transducer.

The paper deals with the problem of ion activity determination for a mixture by means of ion-selective electrodes. Mathematical model of the analysed phenomenon is described by the Nicolsky-Eisenman equation, which relates activities of ions and ion-selective electrode potentials. The equation is strongly nonlinear and, especially in the case of multi-compound assays, the calculation of ion activities becomes a complex task. Application of multilayer perceptron artificial neural networks, which are known as universal approximators, can help to solve this problem. A new proposition of such network has been presented in the paper. The main difference in comparison with the previously proposed networks consists in the input set, which includes not only electrode potentials but also electrode parameters. The good network performance obtained during training has been confirmed by additional tests using measurement results and finally compared with the original as well as the simplified analytical model.

Determination of pH using a typical glass electrode requires prior calibration in order to determine the electrode parameters. Knowledge about uncertainties of the parameters is insufficient to calculate the uncertainty of measured pH because of existing correlation. In the paper, an example illustrating the problem is presented. Two ways of proper uncertainty assessment are suggested: (1) analytical with removing the correlated variables and (2) numerical using Monte Carlo simulations. The second one seems to be much less time-consuming and allows easier investigations of the uncertainty properties.

The plot of ion-selective electrode's potential vs. ion concentration in a solution is non-linear and very complex. In the paper, a set-up is described which allows to determine the plot using multiple dilution method in an automatic way. The set-up is not expensive and the presence of experimenter in the laboratory is not necessary during the test of the electrode. Additionally, the system allows for simultaneous investigation of several electrodes.