Approximate optimal control of the air path of a diesel engine

Abstract

The problem of regulating the fresh mass air flow M AF and the absolute pressure in the intake manifold M AP in the air path of a Diesel engine to set-point reference values is considered here. To begin with, a NARX model of the air path of a Diesel engine is obtained in terms of two (coupled) difference equations from input/output measurements of the actual system. A continuous-time state-space representation of this model is then determined and used to design a control law that solves the regulation problem, achieving at the same time a criterion of optimality. To conclude the paper, the performances of the proposed control law are tested in simulation.

Constrained optimal control of multi-dynamometer internal combustion engine test benches

“…Determine a control law u such that the cost functional (10) is minimized along the trajectories of the resulting closedloop system. Note that in the following the approach presented in [9] is used to calculation an approximation of the solution of the optimal control problem. The computation of a so called algebraic P solution is enough to obtain the dynamic control lawξ…”

“…[4]- [6]) have been proposed to approximate the solution of the HJB partial differential equation in a neighborhood of the origin with a desired degree of accuracy as the determination of the explicit solution is hard or even impossible in practical cases. An approach to approximate the solution of the HJB partial differential equation by means of a dynamic extension to the state is presented in [7] and successfully applied to a test bench for internal combustion engines in [8] and the air path of a turbocharged Diesel engine in [9].…”

Direct C/GMRES Control of The Air Path of a Diesel Engine

“…Since the C/GMRES model has been developed in a continuous domain framework in the preceding section, here we shall illustrate the main sufficient steps to transform the in/output recursive polynomial NARX problem into the stateinput continuous-time description following Sassano et al (2012). This includes some steps must be performed.…”

“…The simple nature of these models is also well suited as a basis for nonlinear optimal control design. An example of this combination has been shown in Sassano et al (2012), in which such a model has been used for the design of an optimal control based on a relaxed Hamilton Jacobi Bellman (HJB) equation, which has been proven to work both in simulation and practice. However, this optimal control method does not allow easy consideration of constraints and/or bounds, and at the end of the day it is not completely clear which cost function is optimized.…”

“…This paper combines the C/GMRES method with the polynomial modelling approach of Hirsch and del Re (2010a) and shows its viability for a reference automotive application which is shortly presented in the next section. Then the key elements of the C/GMRES method are summarized, the adaptation of the nonlinear discrete time model produced by the procedure of Hirsch and del Re (2010a) to the continuous time setup of C/GMRES according to Sassano et al (2012) explained and experimental results shown, in which the performance of the examined method is compared to the behavior of the production engine control unit (ECU). This comparison confirms that the approach is a viable alternative to heuristic design, and it can be performed in a fully systematic way, starting from the data acquisition and ending at the final measurements.…”