Observer Design for Torque Balancing on a DI Engine

Torque balancing for diesel engines is important to eliminate generated vibrations and to correct injected quantity disparities between cylinders. The vibration phenomenon is important at low engine speed and at idling. To estimate torque production from each cylinders, the instantaneous engine speed from the crankshaft is used. Currently, an engine speed measurement every 45° crank angle is sufficient to estimate torque balance and to correct it in an adaptive manner by controlling the mass injected into each cylinder. The contribution of this article is to propose a new approach of estimation of the indicated torque of a DI engine based on a nonstationary linear model of the system. On this model, we design a linear observer to estimate the indicated torque produced by each cylinder. In order to test it, this model has been implemented on a HiL platform and tested on simulation and with experimental data . INTRODUCTION Torque balancing for diesel engines is a major feature of modern engine controllers for two main reasons: • Diesel injection systems introduce a bias in injected masses between cylinders (relative errors can be up to 20%). Torque production is a monotonic function of the fuel mass injected into each cylinder. • This torque variation is thus a periodic time function and generates a vibration mode in the engine. This phenomenon is significant at low engine speed and at idling conditions. For diagnostic purposes, the correct combustion must be monitored during engine operation. In case of misfiring, unburned gases are generated and the engine does not meet the legal limitation for HC emissions. We tried to estimate the torque produced by combustion while we only measuring the instantaneous angle speed on the crankshaft. Currently, an engine speed measurement every 45° of crankshaft rotation is sufficient to estimate torque balance and to correct it in an adaptive manner by controlling the mass injected into each cylinder. This problem has been studied before, but the different approaches where frequential approaches or founded on the derived measures [7]. The main advantage of our approach is to use a state-space model and control techniques to solve this problem. We describe the various torques (combustion, load, friction, ...) arising in the dynamics. This allows us to observe the instantaneous indicated torque. The objective of our work is to build an accurate observer of torque balance in transient mode (according to torque and engine speed). In Section 2, we describe the experimental setup. We explain the engine dynamics in Section 3 and the approximation we made to obtain a linear equation in Section 4. We then introduce the notion of residue in Section 5. In Section 6 , we describe our observer design and gives details of the results obtained. EXPERIMENTAL SETUP FOR CONTROL The synthesis of the state-model based observercontroller was first validated on a 4 cylinder DI engine model. This reference model relies on the Chmela combustion formula (heat production is proportional to the amount of injected fuel and to the burning velocity)[1]. This model includes combustion and a transformation into indicated torque and effective torque. The transmission is modeled as in [1]. A more realistic model with nonlinearities and imperfections of the flywheel will be integrated in future work. The observer is fed with instantaneous engine speed measurements coming from the reference model and signals from the test bench. Figure 1 : GLOBAL SCHEME The complete simulation was implemented in real time with the xPCTarget Hardware in the Loop platform and will finally be implemented on the motor bench through a fast prototyping system. The synopsis of the complete simulation is described in Figure 1. We implemented the simulation model (reference model + observer + controller) on a real time simulator based on xPCTarget [2]. Real time is not achieved due to the complexity of the reference model. With a 1 GHz Pentium based computer, 1 second of engine real time is simulated in 30 seconds. Nevertheless, this allows extensive simulation and parameter sensivity studies: pole placement calibration with a robustness study with noise on engine speed measurements, change of load... This HiL platform was transformed to a fast prototyping system by adding specific input/output boards. The same code can be implemented in the control system and on the test bench. ENGINE DYNAMICS The crankshaft velocity is the only measured quantity and we want to reconstruct the combustion torque. Following [3] we express the dynamics. With the kinetic energy theorem, the torque balance on the crankshaft is expressed as ) ( ) ( ) ( ) ) ( 2 1 ( 2 α α α α α α fric load comb T T T J d d − − = • Let fric load comb mass T T T T − − = denote the mass torque, the combustion torque is also referred to as indicated torque. We consider that the load torque load T is a low frequency signal (we assumed that the variation of the load torque between two TDC is small, we made a linear interpolation to have the value between two TDC) and that friction torque is a quadratic in dt dα [4]. We can split the mass torque into two terms