INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL Int.J. RobustNonlinear Control 2010; 20:515–530 Published online 21 April 2009 in Wiley InterScience (www.interscience.wiley.com). DOI:10.1002/rnc.1445 A hybrid feedback for a benchmark problem of idle speed cont A. Balluchi 1 , C. D’Apice 2 , M. Gaeta 2 , B. Piccoli 3, ∗, † , A. L. Sangiovanni Vincentelli 4,5 and K. Zadarnowska 6 1 DANA ITALIA S.p.A., Off-Highway Products Group, Zona Industriale Lifano, 38062 Arco (TN ), Italy 2 DIIMA, University of Salerno, Via Ponte don Melillo, 84088 Fisciano (SA), Italy 3 I.A.C.-C.N.R., Viale del Policlinico 137, 00161 Roma, Italy 4 PARADES, Via di S.Pantaleo, 66, 00186 Roma, Italy 5 Department of Electrical Engineering and Computer Sciences, University of California at Berkeley, Berkeley, CA 94720, U.S.A. 6 Institute of Computer Engineering, Control and Robotics, Wroclaw University of Technology, ul. Janiszewskiego 11/17, 50-372 Wroclaw, Poland SUMMARY The ever increasing demands on passengers’ comfort, safety, emissions and fuel consumption imposed by ca and regulations call for advanced techniques and the use of cycle-accurate models in automotive control. In this paper, we focus on such approach to the idle speed control. It is natural to resort to hybrid methodologies, because of the rich combination of time and event-based behaviors exhibited by a controlled engine. A hybrid benchmark proble and addressed first by analyzing the equilibria of the system and then testing a simple hybrid feedback strat Copyright q 2009 John Wiley & Sons, Ltd. Received 26 September 2007; Revised 14 October 2008; Accepted 12 January 2009 KEY WORDS : hybrid control; automotive; idle speed control 1. INTRODUCTION The increasing demands of performances in the auto- motive industry, in terms of safety and time-to-market, callforthe use ofadvanced control algorithms with guaranteed properties. Traditionally, practices are based on extensive experimentation and tuning. ∗ Correspondence to: B. Piccoli,I.A.C.-C.N.R., Viale delPoli- clinico 137, 00161 Roma, Italy. † E-mail:b.piccoli@iac.cnr.it Contract/grant sponsor:Network of ExcellenceHYCON; contract/grant number: E.C.IST-511368 The use of moreaccuratemodelsandcontrol algorithms with guaranteed properties reduces grea the need for extensive experimentation and points to potential problems early in the design cycle. Hybrid system techniques promise to be a good approach fo this needed improvement [1, 2]. An accurate model of four-stroke automotive engines has a ‘natural’ hybri representation because pistonshavefourmodesof operation corresponding to the strokethey arein, while powertrain and air dynamicsare continuous- time processes. The timing of the transitions between two phasesof the enginecycleis determined by the continuous motion ofthe crankshaft, which,in turn,depends on the torque produced by each piston Successful approaches to design of control algorithm Copyright q 2009 John Wiley & Sons, Ltd.