Advanced Nonlinear Control Systems for SI Engine Speed: Idle Speed and Cruise Control, Lecture notes of Applied Mechanics

Download Advanced Nonlinear Control Systems for SI Engine Speed: Idle Speed and Cruise Control and more Lecture notes Applied Mechanics in PDF only on Docsity! TMI - 2 : I O Advanced Nonlinear Engine Speed Control Systems Thomas Vesterholm and Elbert Hendricks Institute of Automatic Control Systems, IACS The Technical University of Denmark DK-2800 Lyngby, Denmark e-mail tv@sl.dth.dk Abstract Several subsidiary control problems have tumed out to be important for improving driveability and fuel consumption in modem spark ignition (SI) engine cars. Among these are idle speed control and cruise control. In this paper the idle speed and cruise control problems will be treated as one: accurately tracking of a desired engine speed in the presence of model uncertainties and severe load disturbances. This is accomplished by using advanced nonlinear control techniques such as inputloutput-linearization and sliding mode control. These techniques take advantage of a nonlinear model of the engine dynamics, a Mean Value Engine Model (MVEM), reported in earlier publications. 1. Introduction The dynamics of the mean value of the most important states of an SI engine can be written in the form [l] where n is the engine crank shaft speed, p, is the intake manifold pressure and the f<s and 8;s are nonlinear functions in the states n and p, [l]. The control input U is in this case cos(@, where 01 is the throttle position in degrees. The main problem when dealing with the control of nonlinear dynamical systems is to achieve a representation which at the same time is reasonably simple and accurate. A well known method to achieve this is by linearizing the system around an operating point of interest. This type of linearization has, however, a limited region of validity. Thus, in order to solve the general speed reference tracking control problem it would require the use of several linearized submodels to cover the entire operating range of the engine. In this way the controller would be designed based on different submodels leading to an operating point dependent feedback law. Recently some alternative linearization techniques have been presented in the literature [2],[3]. These linearization techniques, known as input/output- linearization (YO-L), have in general a larger range of validity. Using YO-L it is possible to achieve a linear representation of the model (1) which is valid over the entire operating range of the engine. 2. Controller Design In an earlier paper different control designs based on either of the linearization techniques mentioned above have been tested in the idle speed region [4]. From this paper it has become clear that for a specific operating point both linearization methods leads to satisfactory results. The main advantage of using the YO-L techniques is that only one design need be carried out to cover the entire operating range of the engine i.e. both the idle speed and cruise control regions. In order to achieve robustness with respect to parameter uncertainties and disturbances the use of sliding mode control has been adopted. Considering the crank shaft speed as the output of the model (1) the I/O-L design can be easily carried out. The derivative of the output with respect to time is simply the first state equation. This state equation is directly affectcd by the input, U, i.e. the relative degree of the system is 1 [2]. Introducing the virtual input v v = f,(n. P-) + g,(n, p-)u (2) In this new input the system (1) has now been partly linearized. The remaining part of the system is rendered unobservable by the linearization. It can be verified that this part of the system is stable for the operating range of interest and will thus be neglected in the remaining design. The system model (1) has been derived assuming that the engine runs with a stoichiometric aidfuel (AF) ratio. This is accomplished using A/F-ratio controllers reported earlier [4],[5],[61. Using sliding mode control (SMC) design it is now d = m Dossible to achieve a controller with nlinntifiahle