IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 18, NO. 6, NOVEMBER 2010 1325 Synthesis and Experimental Validation of the Novel LQ-NEMCSI Adaptive Strategy on an Electronic Throttle Valve Mario di Bernardo, Senior Member, IEEE, Alessandro di Gaeta, Umberto Montanaro, and Stefania Santini Abstract—This paper is concerned with the design of a novel adaptive controller, namely the linear quadratic new extended minimal control synthesis with integral action (LQ-NEMCSI). We present for the first time the analytical proof of asymptotic stability of the controller and experimental evidence of the algo- rithm effectiveness for controlling an electronic throttle body: an element of any drive-by-wire system in automotive engineering, affected by many nonlinear perturbations. Index Terms—Adaptive control, automotive control, mecha- tronic, nonlinear control, piecewise smooth systems. I. INTRODUCTION I N MANY application areas a control action is aimed at guaranteeing optimality with respect to a certain cost function subject to some constraints. Optimal control schemes are usually characterized by fixed control gains: a classical approach is that of the well-known linear quadratic regulators (LQR)[1]. It has been shown that, typically, LQ schemes lack the flexibility and the structural stability of other more sophis- ticated control approaches as, for instance, exemplified by the two significant cases discussed in [2] and [3]. One way of achieving greater control flexibility is to use adap- tive control schemes, where the control gains are appropriately varied according to the system behavior. To address this issue, a novel family of controllers was presented in [4], where the LQ action is provided via an adaptive control strategy. Here, we present a novel LQ-adaptive algorithm, namely the linear quadratic new extended minimal control synthesis with integral action (LQ-NEMCSI), which relies on minimal knowl- edge of the plant. A simpler version of the algorithm can be found in [4]. The proposed strategy is based on the standard MCS algorithm [5] augmented with integral and robust control actions, where the reference model is a nominal linear model controlled by a classical LQ optimal strategy. In so doing, the Manuscript received January 23, 2009; revised June 24, 2009. Manuscript received in final form November 20, 2009. First published January 12, 2010; current version published October 22, 2010. Recommended by Associate Editor A. Giua. M. di Bernardo, U. Montanaro, and S. Santini are with the Department of Systems and Computer Engineering, University of Naples Federico II, Naples 80125, Italy (e-mail: mario.dibernardo@unina.it; umberto.monta- naro@unina.it; stsantin@unina.it). A. di Gaeta is with the Istituto Motori, National Research Council, Naples 80125, Italy (e-mail: a.digaeta@im.cnr.it). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TCST.2009.2037610 controller has the benefits of the adaptive strategy, while also matching the performance of the well known LQ regulator. We found this novel approach particularly feasible to the con- trol of an electronic throttle body (ETB). The ETB is a mecha- tronic device dedicated to the regulation of the air mass flow rate. In this system a shaped body duct regulates the relation- ship between the angular position of the throttle valve and the incoming air flow into the manifold. The desired plate position is imposed by a microcomputer in a drive-by-wire configuration (see, for example, [6] and [7]). From the control perspective, the ETB is a highly nonlinear and uncertain plant, since the transmission friction and the return spring limp-home nonlinearity significantly affect the system performance (see Section V for further details). Another control requirement is the simplicity of the strategy that has to be implemented on a typical low-cost automotive micro- controller. For these reasons, we select the ETB control as a significant and appropriate test problem to design and vali- date, both numerically and experimentally, the LQ-NEMCSI algorithm. In the literature, many control schemes have been proposed to solve the ETB control problem. Typically, they are aimed at achieving a small tracking error with a rapid valve time opening without overshoot. To solve the problem, often classical controllers, for example those based on a proportional–inte- gral–derivative (PID) structure [8]–[10], are used, but they are equipped with some feed-forward action to compensate the nonlinearities acting on the ETB. Existing compensators can be divided in those which are model-based (see, for example, [11], [12], and [13]) and those which are not (see [9]). Further control techniques are based on constrained optimal control [14] and hybrid approaches [13], [15]–[19], but again they are based on a good knowledge of the plant dynamics. With respect to the previous approaches, the adaptive law pro- posed in this paper relies on minimal knowledge of the plant and can be implemented easily without requiring time consuming experiments for the precise characterization of the system non- linear dynamics. Moreover, the robustness to unmodeled dy- namics and parameter uncertainties is provided by the adaptive gains of the LQ-NEMCSI strategy. Here, we present for the first time experimental evidence showing clearly that the novel scheme can guarantee excellent tracking performance and transient behavior. All experiments are performed by using a reliable experimental setup based on a dSPACE control station. 1063-6536/$26.00 © 2010 IEEE