Stability of softly switched multiregional dynamic output controllers with a static antiwindup filter: A discrete-time case

Abstract

This paper addresses the problem of model-based global stability analysis of discrete-time Takagi-Sugeno multiregional dynamic output controllers with static antiwindup filters. The presented analyses are reduced to the problem of a feasibility study of the Linear Matrix Inequalities (LMIs), derived based on Lyapunov stability theory. Two sets of LMIs are considered candidate derived from the classical common quadratic Lyapunov function, which may in some cases be too conservative, and a fuzzy Lyapunov function candidate, which has been proven to significantly reduce the conservatism level, although at the cost of increasing the number of LMIs. Two numerical examples illustrate the main result.

P1-TS fuzzy scheduling control system design using local pole placement and interval analysis

“…Assuming the desired intervals of stable poles (11) for the nominal operating points (9), and deriving the controller's parameters from (14), the P1-TS system is used to interpolate the model and controller parameters at a given operating point w i ∈ [w i ] to determine according Algorithm 1 the number of nominal points α i,j (j = 2, ..., n i ) lying between α i,1 = w − i and α i,ni+1 = w + i . Incrementing i from 1 to r, the interval [w − i , w + i ] of currently considered input variable is divided into the n l number of subintervals to obtain l = 1, 2, ..., n l + 1 sample points.…”

“…Starting to increment l from 1 to n l + 1, the current number of intervals [α i,j , α i,j+1 ], specified for w i variable, is incremented n i = n i + 1, and each sample point w i,l is temporally considered as the upper bound of the interval [α i,ni−1 , α i,ni ]. The desired intervals of closed-loop system characteristic polynomial coefficients (13) are calculated for nominal operating points (9) associating with the considered sample point α i,ni = w i,l , and the parameters of controller are derived from (14). The condition (15) is tested for the most hazardous operating points {w i } (16) and (17) corresponding to the all possible combinations of the intervals [α i,j , α i,j+1 ] midpoints determined for previously and currently considered inputs and the upper and lower bounds of intervals specified for input variables w i (i = c + 1, c + 2, ..., r, where c is the number of currently considered input) which have been not considered yet:…”

“…The survey of scheduled control synthesis is presented in [1,2], however, the effectiveness of a gain scheduling control system is still the subject of attention in the recent works [3][4][5][6]. The numerous research works demonstrate the usefulness of a fuzzy scheduled based control in different applications [7][8][9], developed especially based on the Takagi-Sugeno (TS) model [10]. Also, numerous authors adopted the interval mathematics [11,12] for robust control systems synthesis [13][14][15].…”

Evolutionary optimization of interval mathematics-based design of a TSK fuzzy controller for anti-sway crane control

“…Numerous authors, frequently inspired by Kharitonov's theorem (Kharitonov, 1978), studied the problem of robust controller design in the presence of system parameter variations (Dahleh et al, 1993;Chapellat et al, 1994;Mallan et al, 1997). Some practical techniques of designing robust control schemes are based on iterative methods (McNichols and Fadali, 2003), modal controllers synthesis (Bańka et al, 2013), methods derived based on Lyapunov stability theory (Zubowicz and Brdyś, 2013), as well as soft computing techniques, e.g., Genetic Algorithms (GAs) (Hsu et al, 2007) and artificial neural networks (Lee et al, 2002) applied to tune linear controller parameters in terms of acceptable ranges for phase and gain margins. In this paper, EA-based synthesis of a robust TSK (Takagi and Sugeno, 1985;Sugeno and Kang, 1988) fuzzy controller which places the coefficients of a closed-loop characteristic polynomial within desired intervals is proposed and addressed to the problem of an anti-sway crane control.…”