Systems & Control Letters 56 (2007) 25 – 33 www.elsevier.com/locate/sysconle Improving transient performance in tracking control for linear multivariable discrete-time systems with input saturation Yingjie He a , Ben M. Chen a , ∗ , Chao Wu b a Department of Electrical and Computer Engineering, National University of Singapore, Singapore 117576, Singapore b Institute for Systems Research, University of Maryland, College Park, MD 20742, USA Received 24 January 2005; received in revised form 15 July 2006; accepted 17 July 2006 Available online 23 August 2006 Abstract In this paper, we present a composite nonlinear feedback (CNF) control technique for linear discrete-time multivariable systems with actuator saturation. The CNF control law serves to improve the transient performance of the closed-loop system by adding an additional nonlinear feedback. The linear feedback can be designed to yield a quick response at the initial stage, then the nonlinear feedback is introduced to smooth out overshoots when the system output approaches the target reference. As such, the resulting closed-loop system typically has very fast transient response and small overshoots. The goal of this work is to complete the theory for general discrete-time systems. The technique is applied to a magnetic-tape-drive servo system design and yields a huge improvement in settling time compared to that of a purely linear controller. © 2006 Elsevier B.V. All rights reserved. Keywords: Nonlinear control; Transient response; Discrete-time systems; Actuator saturation; Tracking control 1. Introduction and problem formulation The problem of reference signal tracking has been a mature subject in the literature. Several excellent textbooks have cov- ered this topic in details (see, for example, [1,7]). Not only the steady state tracking performance but also the transient track- ing performance are required in most of the tracking control applications, such as motion control and process control. For the closed-loop transient performance, settling time and over- shoot are concerned during the control design procedure. How- ever, it is well known that, in general, quick response results in a large overshoot. Thus, most of the design schemes make a trade-off between these two transient performance indices. In order to improve the transient tracking performance, Lin et al. [14] proposed a so-called composite nonlinear feedback (CNF) control technique in their pioneer work for a class of second order linear systems. The CNF control is a scheme consisting of a linear feedback law and a nonlinear feedback law without any switching element. The linear feedback part is designed ∗ Corresponding author. Tel.: +65 6516 2289; fax: +65 6779 1103. E-mail address: bmchen@nus.edu.sg (B.M. Chen). 0167-6911/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.sysconle.2006.07.006 to yield a closed-loop system with a small damping ratio for a quick response, while at the same time not exceeding the actuator limits for desired command input levels. The nonlin- ear feedback law is used to increase the damping ratio of the closed-loop system as the system output approaches the tar- get reference to reduce the overshoot caused by the linear part. From the structure of the CNF control law, it is clear that the CNF controller reduces to a linear controller when the gains in the nonlinear feedback law vanish. Therefore, the additional nonlinear feedback make it possible to change the feedback gains to improve the transient performance. It is worth noting that when dealing with set-point tracking, the so-called reference management approach was proposed in the framework of model predictive control [2] and uncertain linear systems [3]. An improved error governor and a reference governor based on the concept of maximal output admissible sets were adopted to track reference signals inside some con- straint set for the output in Gilbert et al. [8] and Gilbert and Tan [9], respectively. In Graettinger and Krogh [10], the au- thors considered the computation of reference signal constraints for guaranteed tracking performance in supervisory control en- vironment. These ideas were also adopted in Blanchini and Miani [4].