Control System in Automotive— Basics
In the automobiles the whole control system is designed as one single unit. The control algorithms are highly specialized and complex in contrast with typical PID loops in many conventional industrial PLC controllers.
There are a lot of nonlinear controls combining feedback and feed-forward algorithms. The engine RPM control algorithm is not one simple, elegant formula. For example idle speed control is often an algorithm of its own.
A lot of feed-forward control is deployed. For example just before the AC compressor is requested to start, a demand for larger torque reserve is made and the spark advance is gradually retarded. Then just as the AC compressor clutch is engaged, a request for fast torque increase is made and the spark advance jumps forward to provide it. Feedback control alone can’t react this fast. Similar approach (Read complex) with gear shifts.
PID / state space with some nonlinear coefficients/gain scheduling will compensate for some of the dynamics. We will need different coefficients for different operating conditions (due to various load conditions in the entire drive cycle) . At one point a native nonlinear controller such as neural network supervisor or model predictive control starts to become more revelant.
Estimators and Observers
For the balance of torques we would need estimation of: indicated torque (from combustion), friction torque (from engine coolant temperature and RPM), pumping losses torque (from RPM, throttle position, valve timing, turbo), Mechanical brake torque. The difference of those torques will drive your car.
Tables (if you can’t understand it — calibrate it :D)
Automotive industry is known for large numbers of lookup tables that are “calibrated” i.e. tuned to match the specific operating conditions in specific vehicle hardware.