On the design of electronic automotive engine controls using linear quadratic control theory

This paper describes the application of linear quadratic (LQ) optimal control theory to the design of electronic automotive engine controls. The resulting structure of the control is different from conventional controls in that the accelerator pedal is connected to the microcomputer control rather than directly to the fuel metering device. This strategy is analogous to the "fly by wire" aircraft concept. Simulation results indicate that this approach has better engine torque and speed responses to driver commands. This suggests the possibility of improved vehicular driveability. A LQ tracking controller was designed using constant coefficient state variable models (17 states) obtained by linearizing about nominal operating points. Time delays were modelled by first order Pade approximations. Carburetor throttle blade position, spark advance, exhaust gas recirculation, and fuel flow were defined as controls and output variables include speed, torque, manifold vacuum, fuel and air flows, and exhaust emissions (carbon monoxide, hydrocarbons, and oxides of nitrogen). It is assumed that both engine torque and exhaust emissions are similarly affected by actuator, intake, and combustion dynamics thereby allowing the experimental models to be derived from torque response data. Parameter values for the models are derived from measured static data and perturbation frequency response tests about the nominal operating conditions. Simulations show that the optimal design has superior driver command step response performance. Whereas the conventionally controlled lean calibrated engine has a torque sag (suggestive of poor driveability) the optimal design yields a smooth torque increase with no torque undershoot. This is explained physically by the fact that the LQ controller slows down the air control loop (throttle) to match the slower fuel control loop dynamics thereby avoiding the lean air-fuel ratio transients which are the main cause of the torque sag. In addition, the spark is advanced rapidly to achieve the initial torque increase.