Robust Control of the Air to Fuel Ratio in Spark Ignition Engines with Delayed Measurements from a UEGO Sensor

Abstract

A precise control of the normalized air to fuel ratio in spark ignition engines is an essential task. To achieve this goal, in this work we take into consideration the time delay measurement presented by the universal exhaust gas oxygen sensor along with uncertainties in the volumetric efficiency. For that purpose, observers are designed by means of a super-twisting sliding mode estimation scheme. Also two control schemes based on a general nonlinear model and a similar nonlinear affine representation for the dynamics of the normalized air to fuel ratio were designed in this work by using the super-twisting sliding mode methodology. Such dynamics depends on the control input, that is, the injected fuel mass flow, its time derivative, and its reciprocal. The two latter terms are estimated by means of a robust sliding mode differentiator. The observers and controllers are designed based on an isothermal mean value engine model. Numeric and hardware in the loop simulations were carried out with such model, where parameters were taken from a real engine. The obtained results show a good output tracking and rejection of disturbances when the engine is closed loop with proposed control methods.

Low cost DSP‐based educational embedded platform for real‐time simulation and fast implementation of complex systems in Simulink

“…The following are the equations implemented in both platforms in real‐time, as well as the control law for the hardware‐in‐the‐loop implementation. For more information related to the equations and the control strategy . The mathematical model utilized during the experimentation belongs to the mean value engine model of British Leyland internal combustion engine with spark ignition, which is sub diveded in three fundamental equations:…”

Reciprocal convex approach to output‐feedback control of uncertain LPV systems with fast‐varying input delay

“…Parameter dependence of the block matrices in the LMIs (14) and (26) for the induced  2 -norm or in (23) and (32) for the  2 −  ∞ norm results in an infinite-dimensional problem since the scheduling parameter belongs to a continuous real vector space. In order to address this challenge, first, it is proposed to use a gridding technique of the parameter space 6 and check the obtained results on a finer grid to ensure that the scheduled design matrices satisfy the design objectives within the whole parameter space.…”

“…The parameter space is assumed to be the same for the delayed scheduling parameter as well. Despite the dimension of the design LMIs (26) or (32), such a gridding increment is not imposing a large computational burden. In fact, the careful choice of the grid can significantly lead to an efficient and rather fast numerical solution.…”

“…≤ 0.03. The LMIs (26) and (32) are solved using the YALMIP package with MOSEK solver 39 with constants are set as 1 , 2 = 10 −3 . Since our objective is to track the commanded AFR reference as well as to regulate the variation of the amount of oxygen stored in TWC, the tuning parameters are chosen to make a compromise between these two objectives.…”

A Novel Sliding Mode Control Scheme for a PMSG-Based Variable Speed Wind Energy Conversion System

“…This approach is useful when the control variable depends on itself and/or its time derivative as already shown in [23,24]. Now, we define the tracking error for the pitch angle as ζ 2 = β − β re f , and, with the help of Equation (4), the corresponding dynamics for ζ 2 are as follows:…”