A new reduction-based LQ control for dynamic systems with a slowly time-varying delay

Abstract

Time delays in the feedback control often deteriorate the control performance or even cause the instability of a dynamic system. This paper presents a control strategy for the dynamic system with a constant or a slowly timevarying input delay based on a transformation, which simplifies the time-delay system into a delay-free one. Firstly, the relation is discussed for two existing reduction-based linear quadratic controls. One is continuous and the other is discrete. By extending the relation, a new reduction-based control is then developed with a numerical algorithm presented for practical control implementation. The controller suggested by the proposed method has such a promising property that it can be used for the cases of different values of an input time delay without redesign of controller. This property provides the potential for stabilizing the dynamic system with a time-varying input delay. Consequently, the application of the proposed method to the dynamic system with a slowly time-varying delay is discussed. Finally, numerical simulations are given to show the efficacy and the applicability of the method.

Experimental Study ofH∞Control of Flexible Plate with Time Delay

“…The proposed method in [13,14] is applicable for both small time delay and large time delay problems, which is experimentally verified by working on different flexible structures [15,16]. Hu et al [17,18] then modified the method in [14] and proposed a treating method for slowly time-varying delay systems. There also have been many studies on the time-delay robust control of structures.…”

Suboptimal variable structure control of uncertain nonlinear slowly varying systems

“…One of the major categories of the time-varying systems is systems with slowly varying parameters (called slowly varying systems) (Khalil, 2002). The slowly varying systems have various applications such as air vehicles cranes, underwater vehicles, satellites and so on (Binazadeh & Shafiei, 2013a;Feintuch, 2012;Liu, Haraguchi, & Hu, 2009;Shafiei & Yazdanpanah, 2010). Using the control algorithms of time-invariant systems to control the slowly varying systems may cause instability and bad performance (Feintuch, 2012).…”

“…The controller design for linear slowly varying systems has been presented in many articles (Amato, Celentano, & Garofalo, 1993;Desoer, 1969;Feintuch, 2012; CONTACT T. Binazadeh binazadeh@sutech.ac.ir Fung, Chen, & Grimble, 1984;Ilchmann, Owens, & Prätzel-Wolters, 1987;Liu et al, 2009;Rosenbrock, 1963;Zhang, 1993). However, very few articles have been studied the problem of control design for the nonlinear slowly varying systems (Binazadeh & Shafiei, 2013b, 2014Shafiei & Yazdanpanah, 2010).…”

Explicit expression-based practical model predictive control implementation for large-scale structures with multi-input delays

“…In particular, the system state equation with multiple time delays is discretized and transformed into a standard discrete form without any explicit time delay by a particular augmenting for state variables (Chen and Cai, 2009a, 2009b). Subsequently, Hu and coworkers modified the discrete method (Chen and Cai, 2009a, 2009b), proposed a new treating method for time delay, and then applied it to the dynamic system with a time-varying time delay (Liu et al., 2009). Despite the augmented state vector method being successfully applied for controller design with an input delay problem, there is still a huge space for improvement.…”