Vehicle control synthesis using phase portraits of planar dynamics

Phase portraits provide control system designers strong graphical insight into nonlinear system dynamics. These plots readily display vehicle stability properties and map equilibrium point locations and movement to changing parameters and system inputs. This paper extends the usage of phase portraits in vehicle dynamics to control synthesis by illustrating the relationship between the boundaries of stable vehicle operation and the state derivative isoclines in the yaw rate-sideslip phase plane. Closed-loop phase portraits demonstrate the potential for augmenting a vehicle's open-loop dynamics through steering and braking. The paper concludes by applying phase portrait analysis to an envelope control algorithm for yaw stability and a sliding surface controller for stabilising a saddle point equilibrium in drifting.