1. Hybrid Controller Reachability Reachability analysis can be useful to determine how the continuous state of a system evolves. Ideally, this process can be used in combination with the guards of the hybrid states, in such a way that even with discrete transitions it would be possible to describe the trajectories. In this particular case, two engine subsystems were analyzed to explore reachability: the catalyst and the engine fuel injection system. In both cases, the approach consisted of defining a safe set and letting the levelset algorithm extend the safe set in time. May 11, 2005 Automotive Engine Hybrid Modeling Pannag Sanketi,Tomoyuki Kaga, Carlos Zavala, Karl Hedrick http://chess.eecs.berkeley.edu Abstract Automotive Engine models can be broadly classified into three types: mean value, event based and finite-element based models. Their differences lie mainly in the degree of details in the system description. With the objective of acquiring a deeper understanding of the influence of the events taking place in the engine during the initial seconds of operation, a hybrid model was developed. The results of the simulation of the hybrid plant operating together with a mean value controller are presented. A hybrid controller, directed towards solving the conflicting objectives of reducing the HC (hydrocarbon) emissions and lighting off the catalysts as fast as possible, is also developed. The simulation results of the controller operation are also presented. Reachability as a tool for stability analysis is explored using a simplified version of the engine model with the aid of the LevelSet Toolbox developed by Ian Mitchell. The advantages and disadvantages of a hybrid model are discussed. Hybrid Models for Automotive Engines Introduction A common practice in control system design is to model an automotive engine using mean value models. They offer a simplified description for the processes taking place in the engine. These models are acceptable for the purposes of control synthesis, in fact, it it is desirable to base control design on easily expressable plants. However, when detailed description is required for short transients (such as during the first seconds of the warming-up period), event based models could be useful. In particular, hybrid models are suitable to the intrinsic event- based operation of an automotive engine.The main elements of an automotive engine are shown below. Throttle angle T exh sensor UEGO sensor HC Analyzer Catalyst model Engine out HC estimation Exhaust temperature estimation Tailpipe HC estimation Engine Model Amount of Fuel Spark Timing The discrete modes of the hybrid model are shown next. The events on which the behavior is based are the four engine strokes. The modeling tool used is Ptolemy. Hybrid Engine Model The open loop torque response of the hybrid model is shown next. {More raw emissions but faster catalyst light-off} {Less raw emissions but slower catalyst light-off} HC Emissions Control Catalyst Temperature Control The simulation results of the controller are presented in the following plot. Catalyst Reachability Analysis Objective: Find the inputs to the catalyst that can make the catalyst temperature higher than 350C Target set More info: Input: T exh (max = 800 C) AFR assumed const Hamiltonian Affine in Input 2 dummy dimensions created AFR Engine Reachability Analysis Objective: Starting in a set with AFR=14.7. what are the states that will allow to stay in the set? Target Set : Problem: complex nonlinear dynamics, so simplified model was desirable. Fuel dynamics, afr and pressure effects were neglected. AFR Reachability Observations As expected, the AFR can be maintained in the safe set even even with large changes of the air flow, but not with large variations in fuel injection. The safe set does not change significantly in the selected speed range. As the dimensions of the grid array are increased, the simulation becomes unstable. Conclusions The use of the hybrid model paradigm allows to accounts events and their influences in the behavior of the system. The advantage versus the mean value models is that it can provide a more detailed system description. Its application in the study of the cold-start engine control problem seems to be a natural approach. One of its disadvantages is that validation remains difficult to perform, mainly due to the requirements of extra sensing capabilities. Hybrid controllers offer a possibility of dealing with conflicting objectives and parameter changes. Analysis tools are still being developed. Reachability analysis also offers the possibility of studying the evolution of a system. It could serve as a tool for stability analysis. Development of a hybrid model of plant and controller was presented in this poster. Reachability of subsystems was also introduced and briefly discussed. This work was supported by Toyota, Chess and Conacyt. The authors would like to thank the assistance of Dr. Jonathan Sprinkle and Professor Shankar Sastry, in the department of Electrical Engineering, at the University of California, Berkeley. Controlling the engine during the first two minutes of operation requires not only lighting off the catalyst as fast as possible so that the maximal conversion efficiency is guaranteed, but also keeping the afr (air to fuel ratio) as lean as possible, to avoid the generation of large amounts of HC’s. These two conflicting objectives can be addressed by the use of a hybrid controller. Reach Set grows in the expected direction Target set can be reached within 2.8 s starting. Note: –not be possible to produce so high Texh constantly –AFR assumed constant in the analysis Catalyst Reachability Observations