A discrete-time sliding mode formulation for automotive cold-start emission control

Automotive powertrain control strategies are implemented on digital systems with finite sampling rates. If an infinite sampling rate is assumed during design, the resulting control law can exhibit degraded performance and instability when digitally implemented. In this work, a discrete-time sliding mode formulation is developed to overcome this hardware limitation. A Lyapunov function is used to verify stability. The formulation is used to develop control laws for the cold-start emission control problem. The performance of the discrete controller is simulated with the system model and compared to its continuous-time counterpart for various sampling rates. As the sampling time is increased beyond 20 milliseconds, the continuous-time version causes significant chattering and fails to meet the control targets. The discrete-time controller yields superior performance, as it demonstrates robustness to chatter and meets the desired targets even at sampling rates which cause instability in the continuous-time controller.