Linear systems with unstructured multiplicative uncertainty: Modeling and robust stability analysis

This article deals with continuous-time Linear Time-Invariant (LTI) Single-Input Single-Output (SISO) systems affected by unstructured multiplicative uncertainty. More specifically, its aim is to present an approach to the construction of uncertain models based on the appropriate selection of a nominal system and a weight function and to apply the fundamentals of robust stability investigation for considered sort of systems. The initial theoretical parts are followed by three extensive illustrative examples in which the first order time-delay, second order and third order plants with parametric uncertainty are modeled as systems with unstructured multiplicative uncertainty and subsequently, the robust stability of selected feedback loops containing constructed models and chosen controllers is analyzed and obtained results are discussed. © 2017 Matušu et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.CZ.1.05/2.1.00/19.0376, ERDF, European Regional Development FundEuropean Regional Development Fund under the project CEBIA-Tech Instrumentation [CZ.1.05/2.1.00/19.0376]; Ministry of Education, Youth and Sports of the Czech Republic within the National Sustainability Programme project [LO1303, MSMT-7778/2014

Analogue Implementation of a Fractional-Order PI^{\lambda} Controller for DC Motor Speed Control

In this paper, an approach to design a fractional-order integral operator s(lambda) where -1 < lambda <0, using an analogue technique, is presented. The integrator with a constant phase angle -80.1 degree (i.e. order lambda = -0.89), bandwidth greater than 3 decades, and maximum relative phase error 1.38% is designed by cascade connection of first-order bilinear transfer segments and first-order low-pass filter. The performance of suggested realization is demonstrated in a fractional-order proportional-integral (FOPI lambda) controller described with proportional constant 1.37 and integration constant 2.28. The design specification corresponds to a speed control system of an armature controlled DC motor, which is often used in mechatronic and other fields of control theory. The behavior of both proposed analogue circuits employing two-stage Op-Amps is confirmed by SPICE simulations using TSMC 0.18 mu m level-7 LA) EN SCN018 CMOS process parameters with +/- 0.9 V supply voltages

Note on describing function analysis of fractional order nonlinear control systems

This paper presents extensions of some results, obtained for the analysis of classical nonlinear control systems, to the nonlinear fractional order systems. It is shown that the results related to limit cycle prediction using describing function method can be applied to the fractional order plants. The frequency and the amplitude of the limit cycle are used for auto-tuning of the PID controller for nonlinear control systems with fractional order transfer functions. Fractional order control system with parametric uncertainty is also considered for the nonlinear case. On the other hand, a New method is provided for stability margin computation for fractional order nonlinear control system with parametric uncertainty structure using the Nyquist envelopes of the fractional order uncertain plant and the describing function that represents the nonlinearity of the system. Maximum perturbation bounds of the parameters of the fractional order plant are computed. Numerical examples are included to illustrate the methods presented

Proportional Integral Accelerator Controller Design and Theoretical Investigation of Disturbance Rejection Performance

In this study, Proportional Integral Accelerator (PIA) controller parameters are obtained using Random Search (RS) optimization algorithm by compromising between Reference to Disturbance Rate (RDR) criteria and control error. Thus, robustness performance of PIA controller against the input disturbance is investigated. First, the robustness of the system controlled by the PIA against input disturbance is theoretically demonstrated. Then, the performance analysis of the PIA control system whose parameters obtained by RS optimization is examined with application examples in Matlab/Simulink environment