1. http://chess.eecs.berkeley.edu/ November 21, 2005 Center for Hybrid and Embedded Software Systems Engine Hybrid Model A mean value model of the engine forms the basis of our hybrid model. Hybridness was introduced in the mean value subsystems that offered higher modeling accuracy by being in a hybrid form. The strokes of the engine define a different set of dynamics inside each cylinder and affect the production of torque, pollutants and heat. The stroke of the engine also determines the amount of exhaust gas and hydrocarbons produced at a given time. The variation of these variables from stroke to stroke is considered here as the main element of hybridness. The hybrid model consists of the following subsystems: intake manifold, intake port, thermal behaviour of the engine, torque production and catalyst. Controller Performance The controllers designed were applied to the engine and the catalyst models and the performances were simulated at idle condition. The hybrid controller, in which the gains on the two lower level controllers can be changed in real-time was simulated. The figure below shows the performance of the hybrid controller. Even though the catalyst light-off is not fast, the cumulative tailpipe HC emissions are lower than in the case of the mean value controller. Reachability Analysis As engineering systems have become more complex, methods for verifying the correct behavior of such systems have been developed. Model checking, in particular, is an important issue in this regard. It is a verification method in which the state space of the design is explored in order to determine whether the system can enter into an unsafe or incorrect state. Many model checking algorithms attempt to compute a reachable set. Automotive Engine Hybrid Modeling and Control of Hydrocarbon Emissions Pannag Sanketi Carlos Zavala Karl Hedrick Engine Hybrid Controller Mean value controllers were also de base to develop the hybrid control of engine exhaust gas temperature Texh and AFR. In the context of coldstart emissions control, Texh is important to get the catalyst warmed up faster, whereas keeping the AFR lean reduces the raw emissions. The figure below indicates the hybrid nature of the controller. The oscillations in the HC ppm graph correspond to the switching of the hybrid controller between its two modes. By doing so, it exploits the trade-off between the raw emissions and the catalyst light-off. Hence, the hybrid controller performs better than the mean value controller. Catalyst light-off is one of the essential factors in coldstart control. With an aim to find out the time required to achieve the light-off of the catalyst starting from a particular initial condition, we analyzed the reachability of the catalyst subsystem. The backwards reachable set at any instant t gave the range of Tcat in which the system should start so as to reach the light-off temperature within time t. The results obtained for an AFR of 14.8 and a maximum input of 400 C are shown on the right. The y -axis represents the level set as a function of catalyst temperature which is represented on the x -axis. The figure shows how the level set grows with time. In order to analyze the stability of the controller designed, the forward reachable set of the closed-loop system was calculated. The intention was to show that the states remain bounded under the closed-loop control. Initially, the forward reachable set for the whole system comprising of 5 states was attempted. However, the reach set calculation was very slow, even on a coarse grid. Hence, a subset of 3 states was analyzed. The simplifications made were considering the engine operating at idle. The figure on the left shows the forward reach set at t = 50 s of the closed loop system starting from a set which is the set of all possible initial conditions. It was observed that the reach set remains bounded as expected. Conclusions Mean value model based exhaust gas temperature and air-fuel ratio controllers were used to synthesize a dynamic surface controller where the effects of the catalyst were included in the feedback loop for real-time control. In this way, catalyst temperature control combined with raw hydrocarbon (HC) emissions control was achieved. As an approach to optimizing the trade-off between minimizing the raw HC emissions and decreasing the catalyst lightoff time, a hybrid controller was derived. The simulations show a decrease in the production of cumulative HC. Hence, the application of the hybrid automata for improvement in coldstart control is demonstrated. The backwards reach set was found not to intersect with the set of possible initial conditions of the system, thus concluding the safety of the controller with respect to the specified unsafe set. The use of reachability tools was found to be useful for our case. Two high level dynamic surface controllers for catalyst temperature and raw HCs were developed using Texh and the AFR as synthetic inputs respectively. There is a trade-off between the two. The two dynamic surface controllers were designed without incorporating the coupling between them, i.e. each controller tries to achieve its own objective. Hence, a mean value controller which consists of these two controllers running in parallel with static gains may not exploit the trade-off By designing a switching controller consisting of two modes where one of the two controllers is preferred in each mode, the coupling between them is made use of and either of the two objectives is not highly penalized. In one mode, fast catalyst light-off is favoured and in another reducing the raw HC emissions is favoured. Automotive engine models vary in their complexity depending on the intended application. Pre-prototype performance prediction models can be very complex in order to make accurate predictions. Controller design models need to be as simple as possible since model-based controllers must operate in real time. We develop hybrid models for engine control that incorporate time and events in their formulation. The resulting hybrid controllers have the capability of switching between two alternative control modes. The first mode is designed to reduce the raw HC (hydrocarbon) emissions while the second mode tries to increase the temperature of the catalytic converter as rapidly as possible during the initial transient or ”cold start” period. Reachability, as a tool for system analysis, is used to verify the properties of the closed loop system. Engine Hybrid Model Engine Hybrid Controller Engine Hybrid Controller Performance Emissions under Hybrid Controller