Estimation of Exhaust Manifold Pressure in Turbocharged Gasoline Engines with Variable Valve Timing

Feedforward A/F control in turbocharged gasoline engines with variable valve timing requires knowledge of exhaust manifold pressure, Pe. Physical conditions in the manifold make measurement costly, compelling manufacturers to implement some form of on-line estimation. Processor limitations and the calibration process, however, put constraints on estimator complexity. This paper assesses the feasibility of estimating Pe with an algorithm that is computationally efficient and relatively simple to calibrate. A traditional reduced order linear observer is found to perform well but has too many calibration parameters for practical implementation. Using the performance of the observer as a benchmark, static estimation is explored by parameterizing the equilibrium values of Pe with both the inputs and the outputs of the system. This nonlinear static estimate, combined with simple lead compensation, yields a practical observer implementation. INTRODUCTION Modern automotive emission control systems for gasoline engines rely heavily on feedforward air-fuel ratio (A/F) control to meet strict emissions regulations. For turbocharged applications, it has been shown [1] that knowledge of exhaust manifold pressure (Pe) is helpful in meeting the stringent accuracy requirements of the feedforward controller. When variable valve timing is added, the significance of Pe rises dramatically, since considerable valve overlap may occur over a large portion of the operating envelope. Measuring Pe can be quite problematic, however, due to the harsh environment in the manifold. System cost and durability considerations drive a strong desire by automakers for an estimate of Pe based on commonly measured signals. Most turbocharged gasoline applications employ turbines equipped with wastegates that open to divert flow around the turbine to control boost. Both the turbine and an open wastegate can be considered flow restrictions in the exhaust path of the engine. This interpretation of the physical system implies that the pressure in the exhaust manifold varies with mass flow rate and the effective size of the restrictions. The total effective restriction varies greatly with wastegate opening. For a given command from the powertrain control module (PCM), the wastegate position may vary from its minimum to maximum deflection depending on the operating condition. This position is not typically measured. Therefore the size of the flow restriction in the exhaust path is not accurately known, making estimation of exhaust manifold pressure quite difficult. This is in contrast to modern diesel applications which employ variable geometry turbines where vane position is readily available. In addition, cost and durability concerns also discourage measurement of temperature or other useful properties downstream of the engine. Thus, Pe must be inferred from measurements of signals significantly distant and often related through dynamic elements. Nonetheless, cost and time to market pressures dictate a simple and efficient estimation algorithm. Online computing resources are limited in automotive-quality processors, while growing hardware complexity and regulatory requirements continue to increase the number of computations and memory requirements of the software. Not coincidentally, calibration effort is also increasing, with each additional task lengthening development time and increasing cost. As such, strategies are highly scrutinized prior to implementation and those with added states or complex calibration procedures must demonstrate a clear and significant advantage to gain acceptance. Here we use model-based analysis to determine the feasibility of estimating Pe with a simple, efficient algorithm that can be easily calibrated. First we consider a traditional reduced order linear observer. Although nonlinearities in the system lead to a large number of calibration parameters, this approach establishes feasibility of a solution and provides a benchmark for comparison. Static estimation is then explored. Analysis of a linearized, steady state model of the system leads to a static linear estimate of exhaust manifold pressure based on conditions in the intake. This estimator provides excellent accuracy when applied to the nonlinear model in steady state. Transient performance, however, is shown to be poor due to the slow dynamics connecting the intake and exhaust. Simple lead compensation of the nonlinear static estimate produces a practical implementation with excellent steady state accuracy and improved transient performance. SYSTEM DESCRIPTION The system under consideration is an I-3 turbocharged engine equipped with variable intake cam timing, a conventional pneumatically operated wastegate to control boost and an intercooler to increase charge density and reduce tendency for engine knock. A schematic of the system is shown in Figure 1. The model used for concept development is described in [2]. This model includes most of the major components of the desired system, with a notable exception being the pneumatically actuated wastegate. The effects of wastegate are incorporated in the model through a virtual actuator, wastegate flow rate, by assuming flow through the valve is a known input. This enables investigation of the estimation problem, for this and future applications, without the limitations imposed by current actuator technology. A four state representation of the modeled system is given by ẋ = f (x,u) x = [Pi,Ptip,Pe,Ntc] T (1) u = [ETC,VCT,Wwg,N] T y = [Pi,Ptip] T where Pi is intake manifold pressure, Ptip is throttle inlet pressure, Pe is exhaust manifold pressure, Ntc is turbocharger shaft speed, ETC is throttle angle, VCT is variable cam timing, Wwg is flow rate through the wastegate and N is engine speed. Since engine speed is measured, this model representation uses N as an input; and since temperature changes slowly compared to the remaining states, manifold temperature dynamics are ignored. This simplified representation of the turbocharged system facilitates formal analysis of the estimation problem. Turbine Compressor Intercooler Wastegate Actuator Throttle Figure 1. SYSTEM SCHEMATIC. OBSERVER DEVELOPMENT The system (1) has four states, two of which are measured, Pi and Ptip. Therefore, a reduced order linear observer is explored for estimation of Pe. Consider a linear representation of (1) given by δẋ = Aδx+Bδu (2) δy = Cδx where δ indicates deviation from the equilibrium point about which the system was linearized. In order to compare the relative influence of system parameters, (2) represents a system scaled relative to this equilibrium point such that deviation is defined in terms of fractional change.1 Following the development described in [3], the linear system is partitioned by grouping measured and unmeasured states as follows x1 = [Pi,Ptip] T x2 = [Pe,Ntc] T , such that