Minimum-time predictive control of a servo engine with deadzone Martin Herceg, Michal Kvasnica à , Miroslav Fikar Institute of Information Engineering, Automation and Mathematics, Slovak University of Technology, 81237 Bratislava, Slovakia article info Article history: Received 21 November 2008 Accepted 23 June 2009 Available online 23 July 2009 Keywords: Piecewise affine model Deadzone Explicit predictive control Minimum-time control Tracking abstract This paper presents a hybrid approach to cope with deadzone types of nonlinearities, which are often present in many mechanical systems. If the effect of the deadzone is not directly considered in the control design, it may cause unwanted performance loss and may lead to chattering around the deadzone limits. It will be shown that the deadzone can be naturally modeled using piecewise affine (PWA) models, and that such models are suitable for design of control policies which take the deadzone behavior into account. In this paper, the controller design scheme is based on the so-called minimum- time principle. It is shown that such design task can be formulated as a model predictive control (MPC) problem, where the solution takes a form of a look-up table. It will be presented that such table can be evaluated in real-time, hence allowing to apply the concept of MPC to devices with very fast sampling rates. Experimental results show that the MPC controller based on a PWA description of the deadzone nonlinearity meets the desired goals. & 2009 Elsevier Ltd. All rights reserved. 1. Introduction Static nonlinearities are characteristic features in many mechanical devices, especially those containing gear transmis- sions, pressure gauges, friction parts, etc. (Merzouki, Davila, Fridman, & Cadiou, 2007). Generally these properties are neglected in the control design and are often treated afterwards as an implementation issue (Zabiri & Samyudia, 2006). If the controller is synthesized in this way, the control actions actually applied to a plant may differ from the calculated ones and this ideal assumption may lead to seriously degraded performance or even instability (Chow & Clarke, 1993; Tsang & Clarke, 1988). It is therefore not surprising that Bialkowski (1992) reports 30% of all control loops in Canadian paper mills were oscillating because of valve problems. A deadzone effect is one of the inherent characteristics of actuators. This effect might be indiscernible if the actuator is a brand new product, but it clearly becomes apparent as the actuator operates for longer time. The problem gained further attention and many publications appeared with proposed solu- tions. For instance, Yang and Clarke (1999) suggests a self- validation principle suitable for a broad class of static nonlinea- rities. Especially, the initial research around the deadzone was propagated by Recker, Kokotovi´ c, Rhode, and Winkelman (1991) and continued by Tao and Kokotovi´ c (1994, 1995). The solution in these cases relies on the so-called adaptive inverse control approach. Similar ideas were employed in other control approaches, involving artificial neural network (Knohl & Unbehauen, 2000), fuzzy logic (Campos & Lewis, 1998; Shahraz & Boozarjomehry, 2009) or model predictive control (MPC) (Chow & Clarke, 1993; Zabiri & Samyudia, 2006). Further approaches transform the deadzone directly to a process model and the control policy is based upon the modified model. Examples from Wang, Su, and Hong (2004) and Ibrir, Xie, and Su (2006) show the resulting model is nonlinear and uncertain. Robust and adaptive techniques are used to cope with these uncertain descriptions while closed-loop stability is guaranteed a priori. Hybrid models appeared in a collection by Milani and Coelho (2001) and Milani (2005) where it is shown how the deadzone can be naturally captured by the piecewise affine (PWA) model. Recently, the PWA description was efficiently deployed to model a backlash non- linearity in the MPC approach by Lagerberg and Egardt (2005) and Rostalski, Besselman, Bari´ c, Belzen, and Morari (2007). The aim of these two collections is to construct the optimal control problem which has a special structure of mixed-integer quadratic program (MIQP) and obtain parametric solutions. The MPC policy is then implemented in a real-time and experimental results are very promising. The motivation of this paper is to extend results of Lagerberg and Egardt (2005) and Rostalski et al. (2007) to the deadzone-type of nonlinearity and to present a tracking control policy which is real-time implementable. Specifically, a real servo engine device is investigated, which represents a mechanism for operating valves in pipes. It will show how to derive a suitable PWA model of the plant with deadzone and provide experimental results which confirm that the PWA model describes the real behavior of the plant with a high precision. As the servo engine operates under hardware constraints, the concept of MPC is adopted. It was ARTICLE IN PRESS Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/conengprac Control Engineering Practice 0967-0661/$ - see front matter & 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.conengprac.2009.06.009 à Corresponding author. Tel.: +421 252 495 269; fax: +421252 496 469. E-mail address: michal.kvasnica@stuba.sk (M. Kvasnica). Control Engineering Practice 17 (2009) 1349–1357