An enhanced bandwidth disturbance observer based control- S-filter approach

2021 Turkish Journal of Electrical Engineering and Computer Sciences  
A continuous time enhanced bandwidth Disturbance Observer Based Control (DOBC) scheme is proposed 3 in this paper. The classical Q -filter is implemented in feedback form and a signum function is inserted into the loop. 4 The loop with this modification becomes capable of detecting small magnitude matched disturbances and we present 5 an in depth discussion of the stability and performance issues comparatively. The proposed approach is called S-filter 6 approach and the results outperform the
more » ... assical approach under certain conditions. The contribution of the current 7 paper is to advance the subject area to nonlinear filters for DOBC loops with guaranteed stability and performance. A 8 specific case containing a signum function is elaborated throughout the paper and the obtained energy of the disturbance 9 prediction error is shown to be smaller than the Q -filter based counterpart. 10 Between 1989-2020, the number of outcomes with the keyword disturbance observer indexed by Web of 17 Science increased approximately like 0.22(n − 1989) 2.3 , where n is the corresponding year. This observation is a 18 clear indicator of how interesting the disturbance observers have been so far. Vast majority of the reported work 19 contributed to the application side of DOs and some advanced the subject area by contributing to the theory. 20 Current paper gives a new analysis and remodeling approach for the classical DO structure and proposes 21 a modification that makes the obtained DO nonlinear yet sensitive to small magnitude disturbance signals 22 entering through the control channel. 23 The notion of disturbance observer was introduced by the pioneering work of Prof. Kouhei Ohnishi, 24 in 1983, [1]. Since then numerous strides have been made and, among them, the works by Sarıyıldız and his 25 co-authors contributed mainly to the structure, stability, robustness, bandwidth and the issues focusing around 26 the functionality/limitations of disturbance observers rather than the applications, [2-7]. Cases concerning 27 minimum phase plant, plant with time delay, plant with right half plane zero and unstable plant are studied 28 and a set of bandwidth constraints are derived using Bode and Poisson integral formulas, [2]. Reaction torque 29 * Correspondence: onderefe@gmail.com This work is licensed under a Creative Commons Attribution 4.0 International License. observer is introduced to remedy the noisy velocity measurements in motion control system, [3], and this 1 necessitates the re-analysis of stability and performance issues keeping the bandwidth of the DO at the center. 2 The work in [3] is further elaborated in [4], where a Lyapunov approach is developed for robot manipulators. 3 The bandwidth constraints for the DO structure employing a first order lowpass filter is studied in [5], where 4 the stability of the Kharitonov polynomials are scrutinized using Mikhailov criterion with the goal of relating 5 robustness and bandwidth under parametric uncertainties. This is also considered in [6] with higher order 6 lowpass filters with a performance versus trade-off discussion. The issues of time delay is considered in [7]. In 7 [8], it is emphasized that the performance of DO gets better as the bandwidth of the lowpass filter gets larger 8 yet this is a significant issue the provoke the undesired effects of noise on the closed loop performance. In all 9 of the works in [2-6, 8], the used lowpass filter is a continuous and linear one, a typical choice is a first order 10 transfer function. In [9], the problem of bandwidth selection is formulated as an optimization problem and a 11 MATLAB toolbox is introduced that minimizes the energy of the error over a set of bandwidth values. 12 The concept of DOBC has successfully been applied to mechanical systems, [10-13] and comprehensive 13 surveys about the DOs can be found in [14-16]. In [17], an almost necessary and sufficient condition for robust 14 stability of the closed loop is studied for a Q -filter that has sufficiently large time constant. The design of the 15 Q -filter is performed via solving an optimization problem in [18], where the filter order is larger than one and a 16 gradient search is performed for the iterative tuning purpose. In [19], 35 years of DOBC experience is reviewed 17 and a useful list of relevant research outcomes is given. 18 Nonlinear versions of DO structures are reported in [20-22]. In [20], the DOBC approach is restructured 19 with the notion of variable structure systems employing discontinuous functions, an natural consequence of 20 which was emphasized as the sensitivity to noise. In [21], nonlinear DO is developed for nonlinear plant and 21 the time derivative of the disturbance signal is assumed to be bounded as in the current paper. In [22], dead 22 30 [30] assumes a saturation function, where a finite gain around zero is a necessity, whereas, the current paper 31 considers a signum function leading to a totally different theorem and proof. Further, the conclusions of the 32 current paper are different from those of [30] in that the required bound for the 1-norm expressions are different. 33 This work should therefore be viewed as a complementary work of [30] that guides the practicing engineers. 34 This paper is organized as follows: The second section presents an expansion of the Q-filter and derives 35 the governing equations according to variables defined within this new scheme. Third section introduces the 36 proposed modification and gives a discussion on stability and performance issues, as well as conditions related 37 to stability an performance. The fourth section gives a comparative exemplar case where the energy content 38 of the error signal is emphasized. The simulations compare the Q -filter approach and the proposed approach. 39 The fifth section lists explicitly the contributions of the S-filter based DOBC and the concluding remarks are 40 given at the end of the paper. 41
doi:10.3906/elk-2009-13 fatcat:rtx3hwrcznfgbmavg2wv3zgao4