scholarly journals Generalized cascade orthogonal filters based on symmetric bilinear transformation with application to modeling of dynamic systems

Filomat ◽  
2018 ◽  
Vol 32 (12) ◽  
pp. 4275-4284
Author(s):  
Nikola Dankovic ◽  
Dragan Antic ◽  
Sasa Nikolic ◽  
Stanisa Peric ◽  
Miodrag Spasic
Keyword(s):  
Dynamic Systems ◽  
Transfer Functions ◽  
Industrial Process ◽  
Inner Product ◽  
Reciprocal Transformation ◽  
Bilinear Transformation ◽  
Continuous Time Systems ◽  
Generalized Orthogonal ◽  
Time Systems ◽  
Orthogonal Filters

This paper presents generalized orthogonal cascade filters based on bilinear transformation for mapping poles to zeroes and zeroes to poles in transfer functions. The filters are orthogonal with respect to a new generalized inner product. Actually, they represent a generalization of several classes of existing traditional filters: the ones obtained by using linear transformation of poles to zeroes, and the ones obtained by reciprocal transformation of poles to zeroes. Generalized filters provide obtaining more precise models of dynamic systems. This is verified by comparison between models based on new filters and models based on classical filters. Practical realization of these filters with adjusting parameters of bilinear transformation and transfer function is performed. An application in modeling continuous-time systems as a complex industrial process is given, and it is shown that in that way we obtain more quality models than by using the classical filters.

scholarly journals NEW CLASS OF DIGITAL MALMQUIST-TYPE ORTHOGONAL FILTERS BASED ON THE GENERALIZED INNER PRODUCT; APPLICATION TO THE MODELING DPCM SYSTEM

2019 ◽  
Vol 17 (3) ◽  
pp. 385
Author(s):  
Nikola Danković ◽  
Dragan Antić ◽  
Saša Nikolić ◽  
Marko Milojković ◽  
Staniša Perić
Keyword(s):  
Differential Pulse ◽  
Inner Product ◽  
Pulse Code Modulation ◽  
Bilinear Transformation ◽  
New Class ◽  
Differential Pulse Code Modulation ◽  
Code Modulation ◽  
And Control ◽  
Orthogonal Filters

A new class of cascade digital orthogonal filters of the Malmquist type based on bilinear transformation for mapping poles to zeroes and vice versa is presented in this paper. In a way, it is a generalization of the majority of the classical orthogonal filters and some newly designed filters as well. These filters are orthogonal with respect to the generalized inner product which is actually a generalization of the classical inner product. Outputs of these filters are obtained by using polynomials orthogonal with respect to the new inner product. The main quality of these filters is that they are parametric adaptive. The filter with six sections is practically realized in the Laboratory for Modeling, Simulation and Control Systems. Performances of the designed filter are proved on modeling and identification of the system for differential pulse code modulation. Real response and response from the proposed filter are compared with regard to the chosen criteria function. Also, a comparative analysis of the proposed filter with some existing filters is performed.

scholarly journals Lyapunov Functions for State Observers of Dynamic Systems Using Hamilton–Jacobi Inequalities

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 202 ◽  
Author(s):  
Angelo Alessandri
Keyword(s):  
Nonlinear Systems ◽  
Dynamic Systems ◽  
Continuous Time ◽  
Lyapunov Functions ◽  
Estimation Error ◽  
State Observers ◽  
Continuous Time Systems ◽  
Estimation Problems ◽  
The Stability ◽  
Time Systems

Lyapunov functions enable analyzing the stability of dynamic systems described by ordinary differential equations without finding the solution of such equations. For nonlinear systems, devising a Lyapunov function is not an easy task to solve in general. In this paper, we present an approach to the construction of Lyapunov funtions to prove stability in estimation problems. To this end, we motivate the adoption of input-to-state stability (ISS) to deal with the estimation error involved by state observers in performing state estimation for nonlinear continuous-time systems. Such stability properties are ensured by means of ISS Lyapunov functions that satisfy Hamilton–Jacobi inequalities. Based on this general framework, we focus on observers for polynomial nonlinear systems and the sum-of-squares paradigm to find such Lyapunov functions.

scholarly journals Reaching Law Based Sliding Mode Control of Sampled Time Systems

Energies ◽  
2021 ◽  
Vol 14 (7) ◽  
pp. 1882
Author(s):  
Piotr Leśniewski ◽  
Andrzej Bartoszewicz
Keyword(s):  
Sliding Mode Control ◽  
Discrete Time ◽  
Sliding Mode ◽  
Rate Of Change ◽  
Reaching Law ◽  
Mode Control ◽  
Sliding Motion ◽  
Control Precision ◽  
Continuous Time Systems ◽  
Time Systems

In this paper, discrete time reaching law-based sliding mode control of continuous time systems is considered. In sliding mode control methods, usually the assumption of bounded absolute values of disturbances is used. However in many cases, the rate of change of the disturbance is also bounded. In the presented approach, this knowledge is used to improve the control precision and reduce the undesirable chattering. Another advantage of the proposed method is that the disturbance does not have to satisfy the matching conditions. In the paper two new reaching laws are analyzed, one of them ensures the switching quasi-sliding motion and the other the non-switching motion. For both of them, the robustness is assessed by calculating the quasi-sliding mode band width, as well as the greatest possible state error values. Specifically, the state errors are not considered only at the sampling instants, as is usual for discrete time systems, but the bounds on the continuous values “between” the sampling instants are also derived. Then, the proposed approaches are compared and analyzed with respect to energy expenditure of the control signal.

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